COOPERATIVE LEARNING STRATEGIES FOR ...

COOPERATIVE LEARNING STRATEGIES FOR TEACHING U N D E R G R A D U A T E T O N A L THEORY

by

JOY ELAINE O L L E N B. Mus., The University of British Columbia, 1991

A THESIS SUBMITTED IN PARTIAL FULFILLMENT O F T H E REQUIREMENTS FOR T H E D E G R E E O F MASTER OF ARTS in T H E F A C U L T Y OF G R A D U A T E STUDIES (School of Music, Music Theory)

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ABSTRACT The purpose of this thesis was to show that cooperative learning strategies are suitable teaching techniques for the instruction of undergraduate music theory. Literature in music theory pedagogy has concentrated primarily on content-based teaching issues and offers little information on the range of teaching techniques available for promoting student learning. Many instructors may be relying on traditional teaching methods with which they are familiar-lectures, lecture-demonstrations and teacher-led discussions-to instruct tonal theory classes and may not be aware of cooperative learning or its potential usefulness as another instructional strategy. The body of this thesis is divided into three main sections.

The opening section

demonstrates how traditional teaching methods alone fail to meet many learning needs of students and points to cooperative learning strategies as one alternative method that addresses these needs. In the next section, cooperative learning is further defined in order to differentiate it from traditional group work. The third and largest section contains ten sample lesson plans based on topics central to first- and second-year tonal harmony courses. Each lesson includes at least one cooperative learning technique and a discussion of why the particular technique was applied to the topic. Instructors of tonal harmony who are looking for additional teaching strategies that actively involve the learners should consider using cooperative learning. The sample lesson plans offered in this thesis illustrate how these techniques may be used either briefly in conjunction with more traditional methods or on their own in more extensive activities. Variety within cooperative learning strategies has also been demonstrated by providing techniques ranging from simple, user-friendly ideas for the inexperienced, to more complex and challenging activities requiring higher levels of experience and collaborative skills. A selected bibliography is included to assist readers in becoming familiar with some of the resources available to those who use cooperative groups for instruction.

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TABLE OF CONTENTS

Abstract

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Table of Contents

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Acknowledgements

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Dedication

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INTRODUCTION

1 Methodological Issues Issues Based on Learning Style Issues Based on Age Summary

2 4 6 9

Cooperative Learning

Learning Settings Problems Associated with Traditional Group Work The Five Basic Elements of Cooperative Learning Types of Cooperative Learning Groups Three Schools of Cooperative Learning Benefits of Cooperative Learning

12 13 14 19 20 23

Sample Lesson Plans

Introduction to Lesson Plan Format 25 Limitations 28 1. Introduction to the Uses of I and 30 2. Chromaticized 7-6 Suspensions Series 37 3. Using Seventh Chords in Sequences 44 4. Introduction to Simple Ternary Form 52 5. Review Session 59 6. Analysis of Excerpts for Uses of Seventh Chords 68 7. Analysis of Excerpts for Uses of Augmented Sixth Chords 76 8. 6/3 Chord Techniques 83 9. Harmonizing Modulating Melodies 94 6

10. Uses of VI

103

CONCLUSION

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Selected Bibliography

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Appendix 1

Kolb on Learning and Knowledge

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ACKNOWLEDGEMENTS I owe the first round of thanks to Dr. John Roeder, my thesis supervisor, who had the insight to recognize that my passion for teaching could be the foundation for a thesis topic rather than a barrier to its completion. He spent many hours patiently answering my 1001 questions and challenging me to convey my ideas in a way that would be meaningful to theory instructors. I count it a privilege to have worked with someone of such high calibre. I am indebted to a number of faculty members for allowing me to come into classes and experiment on their first- and second-year theory students: Dr. John Roeder, Dr. Richard Kurth, Dr. Bob Pritchard and James Schell. They were all very supportive of my attempts to incorporate cooperative learning techniques into the theory classroom and generously provided me with useful advice, timely encouragement, and constructive feedback on my lesson material. It was truly a pleasure to work with and learn from all of them. My appreciation extends to the hundred or so students with whom I spent many hours in the classroom. I only hope that they learned as much from working with me as I did from working with them! Their genuine responses to the cooperative techniques and activities are what provided much of the material for discussion at the end of each lesson plan. Many other individuals gave of their time and expertise at varying points along the way to help my progress. Dr. Inge Williams provided me with some inspiring ideas and helpful initial advice. Dr. Robert Walker was instrumental in steering me in the direction of some useful resources that I might have otherwise overlooked. I am thankful to Len Lythgoe for his positive comments on my lesson plan formats at a time when I needed some encouragement. Thanks to Lyle Courtney, a fellow facilitator at the Centre for Faculty Development, who bravely waded through a very rough first draft of my opening section and carefully pointed out ways to improve it. I was honoured that Dr. Jane Promnitz so graciously volunteered to read my final draft and to share from her extensive knowledge of cooperative learning techniques. Dr. William Benjamin's editorial contributions and comments have also been helpful. I would like to express my appreciation to numerous friends and family members who have supported me in my academic pursuits. This section would not be complete without acknowledging my husband and best friend, Charles. Throughout this past year, he never stopped believing in my ability to complete this thesis and at times, his enthusiasm for what I was doing outweighed my own! Despite my distracted state of mind, the many extra things done for me did not go unnoticed. Thanks, dear.

DEDICATION In memory of my father Roy William Allison, P. Eng. (1935-1994)

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INTRODUCTION

Instructors of undergraduate music theory face many challenges in their efforts to contribute to the training of tomorrow's musicians. The skills that students must gain are highly specialized and require years of experience to develop. Traditionally, tonal theory was taught privately, in a simple, one-on-one setting.

Today in many colleges and universities,

instructors are expected to teach a wide range of tonal harmony topics in four terms, to classes of ten, twenty, or more students who meet for only a few hours each week. While the instructors may be knowledgeable in areas related to the course content, very few are trained in the field of adult education or are equipped to meet the varied learning needs presented by a class of students. Existing literature in music theory pedagogy offers almost no exploration into the repertoire of available teaching techniques and its applicability to the field of tonal harmony. Some solutions to these problems can be found in a body of techniques called cooperative learning that has been used with great success across many other disciplines.

Its highly

structured use of groups in classroom settings has been shown to benefit students in ways that are relevant to the needs of music theory, and yet little documentation has been presented to indicate that cooperative learning is currently applied in this field. After demonstrating the need for cooperative learning techniques, this thesis will provide the reader with an explanation of cooperative learning, its strengths and potential suitability to the teaching of tonal harmony. Finally, a number of original applications of cooperative learning techniques to topics in tonal harmony will be presented in the form of ten lesson plans. Consider this metaphor : A newlywed couple arrived at their hotel in the early hours of the 1

morning after a long and tiring wedding day. Upon entering their honeymoon suite, they found the room furnished with only a sofa, television, small refrigerator, table, and some chairs. They soon discovered that the sofa converted into a bed, and so because of their exhaustion, they turned in for the night. The next morning, after sleeping fitfully on the lumpy 1 Cynthia Thomas, "Discipleship," Leadership: A Practical Journal for Church Leaders 15/1 (Winter 1994): 46.

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mattress with sagging springs, the groom gave the desk clerk a tongue-lashing about the inadequacy of the suite. Puzzled, the desk clerk asked, "Did you open the door in the room?" The groom returned to the suite and opened a door which he had thought was a closet. On the other side of the door was a beautiful bedroom with fruit baskets and chocolates laid out beside the king-sized bed! Instructors of undergraduate music theory may have more in common with the groom in this story than they care to admit. The demands of organizing course material, setting exams, and marking assignments can leave them with very little energy for exploring educational research and new or different teaching strategies. Instructors may limit themselves to using teaching techniques with which they are already familiar. Lectures, lecture-demonstrations, and teacher-led discussions may be the principal ways in which they were taught as students. Just as the groom did not test his assumption about the closet door, many instructors do not look to other sources, external to the discipline, for expanding their teaching methods. They may have presupposed that other techniques will not be appropriate for teaching music theory or that educational theories will not be relevant to their practical concerns. As a result, many instructors settle for a 'sofa-bed' teaching experience.

Student inattention, unequal

participation, low levels of motivation, and failure to take responsibility are only a few of the 'sagging springs' about which instructors complain. By failing to 'open the door', instructors are missing the opportunity to provide both themselves and their students with a more worthwhile and pleasurable experience. Successful teaching techniques should meet the needs of learners, but those needs depend on a number of factors.

Instructors should be aware of some issues surrounding

methodology, learning style, and age. A number of theories, models, and studies that treats these needs are directly relevant to teaching undergraduate music theory. They show that traditional methods are inadequate to meet the learning needs of students and are often inappropriately suited to the instructor's purposes. They also point to ways of optimizing the learning process. Methodological Issues This section presents samples from research pointing to the limitations of lectures, lecturedemonstrations, and teacher-led discussions. The reason for this section is not to condemn

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those who use these methods or argue that they should never be used, but to show that students require additional methods if they are to learn effectively . The traditional lecture method has three basic problems.2 Because the students are placed in a passive role, they will be unable to maintain a high level of concentration for the duration of the lecture. Several studies have shown that the average attention span for uninvolved listeners is about 15 minutes after which they may take notes on only 20-25 percent of the content presented.

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The second problem is that most listeners will recall only a small

percentage of what is said unless they are given an opportunity for rehearsal of information soon after its presentation. Finally, although as effective as discussion methods at helping 4

students learn facts, the lecture method has been shown in over 58 studies to be inferior to discussion for developing higher-level reasoning, problem-solving abilities, and positive attitudes toward the course. One way of avoiding exclusive lecturing is to combine it with some sort of demonstration. While this may help to keep the learners' attention from dropping as quickly, there are at least two potential challenges one must deal with when modelling how to do something to a group of learners. First, the level at which one demonstrates a skill or activity must be only slightly 5

more advanced than the level of the learners. Since students are at varying levels of ability, it may be difficult to find a satisfactory level which will be be appropriate for all their needs. Second, unless students practise what has been demonstrated and receive constructive feedback on their performance immediately after watching the demonstration, they will benefit only minimally. As another alternative to lecturing, an instructor may choose to lead a discussion with the

'Traditional lecture", i n this context means a presentation given by the instructor where the information to be learned is spoken or read to the class. The instructor may supplement the discourse with handouts, notes and/or visuals and may respond to student questions during or at the end of the lecture. Students are expected to follow the instructor's lecture by listening, taking notes, and/or reading any of the supplementary material. The qualifier "traditional" distinguishes this type of lecture from a modified lecture format introduced later in this work which incorporates Cooperative Learning techniques. 2

3 David W . Johnson, Roger T. Johnson, and Karl A . Smith, Active Learning: Cooperation i n the College Classroom (Edina: Interaction Book Company, 1991): 5:6. Ibid., 5:6-7; and Donald A . Bligh, "Methods of teaching," chap. 4 in Donald A . Bligh, David Jaques, and David Warren Piper, Methods and Techniques in Post-secondary Education. Educational Studies and Documents, no. 31 (Paris: Unesco, 1980). 4

5 Clark Bouton and Russell Y . Garth, eds., Learning in Groups. No. 14 of New Directions for Teaching and Learning, The Jossey-Bass Higher Education Series, (San Francisco: Jossey-Bass Inc., 1983): 78-80.

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students. Earlier in this section, discussions were mentioned as being superior to lectures in some important respects. Here again, a number of factors can stand in the way of maximizing students' learning. The structure of a whole-class discussion is one based on the sequential participation of speakers and so each student gets very little time to practise verbalizing his/her thoughts and to express an opinion. 6 Even if the instructor limited him/herself to speaking for ten minutes during a 50-minute class period, a class of twenty students would have an average per pupil active participation time of two minutes! The remainder of the time would be spent listening to others. Of course, most class discussions do not proceed with all students contributing equally. One study found that in classes of less than 40 students, four to five students accounted for 75 percent of all interactions. Finally, students may not be accustomed 7

to participating actively in class or may be difficult to engage in discussion. Another study of instructor-student interaction recorded that students only responded 50 percent of the time even when instructors were actively soliciting participation.

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If an instructor is relying on these traditional methods of instruction, student learning may be suffering due to some of the problems associated with the methods. One common element of all three methods is that students spend most of their time listening to the instructor. The next section will show that not all students benefit equally from the same learning settings.

Issues based on Learning Style Consider the following four students of undergraduate theory, and the differing approaches they take when asked to write a phrase in the four-part chorale style of J. S. Bach after a few introductory classes. Student A works on the assignment by combing through his class notes 9

and text to collect as many rules, observations or guidelines about writing in chorale style as possible, and then by attempting to organize them into some sort of model to guide him as he writes the phrase. Student B views the assignment as a puzzle to be solved, applying the rules and guidelines where they appear to be necessary as she works to complete the phrase in the

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Spencer Kagan. Cooperative Learning (San Juan Capistrano: Kagan Cooperative Learning, 1992): 4:5-

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Johnson, Johnson and Smith, Active Learning. 1:7-8

6. 8 Ibid. The four students are fictitious. They have been assigned a gender arbitrarily that in no way is meant to stereotype any of the approaches as being primarily 'male' or 'female'. 9

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given style. Instead of looking through class notes, student C sits down at the piano, relying on his sense of what a Bach chorale phrase sounds like, and improvises, adjusting the phrase until it 'sounds right'. Student D also refrains from any extensive viewing of rules and guidelines. She spends some time thinking about how chorale-writing was modelled by the instructor during class and plays through some chorales to get a sense of their style. After writing several versions of the phrase, she may end up submitting two or three of them, explaining that each one was representative of Bach's chorale style in a unique way. These four students' distinct approaches to learning illustrate the four general learning styles and basic types of knowledge proposed by David Kolb. 10 While learning is a complex process that involves numerous variables, Kolb's model of experiential learning is a valuable tool for communicating that students learn in different ways. Student A's approach centres on using inductive reasoning and creating theoretical models. Those individuals who prefer to learn in this way rely on assimilative knowledge. Student B's approach focuses more on applying the ideas for the practical purpose of completing the exercise. When individuals prefer to use hypothetical-deductive reasoning to solve specific problems, Kolb identifies this as convergent knowledge. Student C's approach is one involving trial and error to test ideas. Those who learn by placing themselves in situations where they must adapt to immediate circumstances prefer accommodative knowledge. Student D's approach relies on the generation of ideas from various perspectives. This is learning that uses divergent knowledge. Applied separately, some of these approaches to completing the fictitious assignment may raise a few theory instructors' eyebrows!

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However none of these approaches are 'wrong',

only incomplete. While identifiable learning achievements are reached through these elemental forms of knowledge, Kolb proposes that higher and more useful forms of knowledge can be attained when two or more are used in combination, as part of a cycle. Consider how much more musical the phrase of student B's phrase could have been if she had incorporated some student C's accommodative knowledge. The use of rules and guidelines alone to create a phrase of music is rarely sufficient. Of course, the combination of all four forms of knowledge produces the highest level of learning with the most adaptive potential. 10 David A . Kolb, Experiential Learning: Experience as The Source of Learning and Development (Englewood Cliffs: Prentice-Hall, Inc., 1984). More detail on Kolb's basis for four types of knowledge is given in Appendix 1. 11 It should be emphasized that the concept of learning style does not mean a person uses one particular approach exclusively. The isolation of the approaches is used here to facilitate their definition.

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Why is it important for instructors to know about learning styles? Since not all students will have the same learning style, one cannot expect that they will all benefit equally from any particular teaching method. If one typically relies on using the same few methods and approaches to the subject material, a portion of the class may be severely disadvantaged most of the time and remain unmotivated and frustrated. Instructors need to be aware that they are most likely to teach according to their own learning preferences, and make a conscious effort to use methods which will benefit other styles of learners on a regular basis. Finally, an instructor should consider teaching methods that incorporate sequences of learning activities to emphasize the cyclical element of Kolb's model. By designing lessons to promote all four forms of knowledge, the instructor can encourage students of all learning styles to broaden their abilities and heighten their levels of learning.

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Issues Based on Age Many undergraduate students fall between the ages of seventeen and twenty-two and are in transition from late adolescence to early adulthood. The range of intellectual and ethical diversity that an instructor faces within a class is broad. Between 1954 and 1963, William Perry and the staff of the Bureau of Study Counsel at Harvard documented the experience of undergraduates enrolled at Harvard and Radcliffe over their four years at college. After extensive interviews with over one hundred students, Perry and his associates proposed a scheme of the intellectual and ethical development which takes place during the college years. 13 The limited scope of the study leaves its broader applicability open to question. However, the findings do suggest some provocative explanations for students' attitudes towards their role as learners and their expectations of the instructor. Confronted with the pluralistic values and intellectual outlooks, cultural diversity, and the relativistic intellectual and social atmosphere on campus, most students in this study moved through nine identifiable stages of development. Perry called these "Positions" and grouped them into three general parts: The Modifying of Dualism (Positions 1-3), The Realizing of Relativism (Positions 4-6), and The Evolving of Commitments (Positions 7-9). 12 Marilla D . Svinicki and Nancy M . Dixon, "The Kolb Model Modified for Classroom Activities," College Teaching 35/4 (Fall 1987): 141-146. 13 William G. Perry, Jr., Forms of Intellectual and Ethical Development in the College Years: A Scheme (New York: Holt, Rinehart and Winston, Inc., 1970).

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College students in Positions 1, 2, and 3 move from seeing the world in polar terms of "we-right-good" versus "other-wrong-bad" to tentatively acknowledging that a plurality of viewpoints is occasionally unavoidable. They begin to accept that the instructor cannot always act as an authority to give them the "right answers" since not all the answers may have been found yet. In Positions 4, 5, and 6, a major turning point occurs. In struggling to deal with the scope of diverse human outlooks, students re-perceive all knowledge and values as being contextual and relativistic, and recognize the necessity of making some type of personal commitment in order to establish and maintain their identity. While a student in Position 4 might believe that no instructor has the right to evaluate any viewpoint, a student in Position 6 might feel that instructors should require students to take a side and then evaluate them on their ability to articulate it. Positions 7, 8, and 9 follow students as they make decisions in different areas of their lives, work on balancing the associated responsibilities and consider priorities. The diversity of outlooks covered by Perry's scheme may provide some explanation for how an instructor can be perceived so differently by various students in the class. Conversely, some differences between students which instructors attribute to personality type or ability level may in fact be developmental in nature. Because students will be at different Positions, the instructor needs to address students according to where they are in their development. At the same time, an instructor must not deal at a student's developmental level exclusively, but must introduce challenges which will encourage the student to grow. Perry's closing comments address the question of how an instructor can best support students as they move towards Commitment. The majority of students seemed to feel most supported when they sensed that they were part of a community. Perry states: "This was the realization that in the very risks, separateness and individuality of working out their Commitments, they were in the same boat not only with each other but with their instructors as well".

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Instructors wishing to stimulate students' growth may need to reflect upon the role they play in the class. Those instructors who restrict their role to being transmitters of content do not allow room for the degree of learner differences perpetuated by both learning style and intellectual and ethical development.!5 Domination of teacher-centred activities may reinforce students' dualistic attitudes. This role also fails to recognize an important characteristic of adult 14 ibid., 213. 15 See "Engineering Conception: Delivering Content" in Daniel D. Pratt, "Conceptions of Teaching," Adult Education Quarterly 42/4 (Summer 1992): 203-220.

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learners: their minds are not blank pages or empty vessels waiting to be filled. 16 Regardless of the topic, learners all begin with some level of knowledge in a field, referred to as "formative knowledge".1

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Unfortunately, their ideas and theories may be in varying stages of

articulateness and accuracy. Instructors must acknowledge the existence of formative knowledge and become facilitators who encourage students to test their existing beliefs and interpretations against new ideas. Students require an environment in which growth can exist. Malcolm Knowles, in his multidimensional theory of maturation, emphasizes how many traditional teaching environments actually inhibit, rather than nurture, individuals' movement towards maturity.

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At the same time, he indicates what factors contribute to its support. Maturity is not seen as a specific level of achievement, but as a continual process. Of the fifteen dimensions listed by Knowles, six are relevant to this context. 1. From dependence toward autonomy. As individuals mature, one of their primary quests is to achieve independence, or rather, self-directing interdependence.

Knowles defines

experiences that help one move away from dependence as educational, and those that make one more dependent as antieducational. Often the traditional teacher-student relationship is essentially one of student dependency. 2. From passivity toward activity. As children grow, they become increasingly active in exploring the world around them. While adults may not continue increasing their activity level quantitatively, maturing individuals will be those who are continually expanding their activities qualitatively. Knowles suggests that the roles a person is expected to play in educational settings-a passive recipient of knowledge or an active inquirer after knowledge-will impact the 16 Kolb, 28. 1 Jack Mezirow has formulated a theory of adult learning. Formative learning, which occurs during childhood through socialization and early schooling, plays a large role i n determining how an adult will understand the world and interpret experiences. As adults struggle to learn and deal with new situations, their ability to do so may be limited by unconsciously and uncritically assimilated habits of expectation which filter and distort perception and comprehension. Experiences which seem to support one's personal frame of reference will be accepted; those which do not are overlooked. In order to develop, adults must be prepared to reflect on uncritically accepted assumptions, recognize and check presuppositions and restructure their meaning perspectives when necessary. When this restructuring of distorted or otherwise invalid meaning perspectives occurs through reflective learning, formative childhood learning becomes transformative learning in adulthood. For more information, see Jack Mezirow, Transformative Dimensions of Adult Learning. The Jossey-Bass Higher and Adult Education Series (San Francisco: Jossey-Bass, Inc., 1991). 7

18 Malcolm Knowles, The Modern Practice of Adult Education: From Pedagogy to Andragogy. revised and updated (Chicago: Follett Publishing Company, 1980): 29-33.

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direction and speed of their movement towards maturity. 3. From few responsibilities toward many responsibilities. Frequently teachers underestimate the amount of responsibility that students can carry. As a result, growth in this dimension of the maturation process can be stunted as the teacher continues to make decisions that students are ready to make. 4.

From selfishness toward altruism. Children enter the world entirely concerned about

themselves and having their needs and wants met. A maturing person must learn to care about others.

When a student is placed in conditions where a spirit of rivalry and competition

prevails, their move away from selfishness will be slowed. 5. From focus on particulars toward focus on principles. One of the essentials in the process of inquiry is the ability to connect events and group objects in the formation of principles. Traditional pedagogy often denies inquiring minds the chance to discover principles by imposing existing ones on students. 6. From the need for certainty toward tolerance for ambiguity. This dimension is reflected in Perry's scheme. A maturing person needs to accept and learn to live with ambiguity. By introducing experiences in the classroom to students where they must confront uncertainty, students will be able to develop an increased sense of security with it and the self-confidence to tolerate it. If Perry is correct in suggesting that students' transition into adulthood is accompanied by movement through a sequence of positions, instructors can contribute to student growth by cultivating a more flexible role for themselves. This role must take into account students' present stage of development and also encourage them to become more self-directing.

Summary These theories, models and studies have been discussed to show that the needs of the learners in undergraduate theory classes cannot be met through traditional teaching strategies alone.

Studies have been cited that indicate three popular methods, by their very design,

contain barriers to learning. Regardless of the quality of any one method, the range of learning styles within a class calls for a variety of methods to be used, during each lesson and the term. Traditional strategies also limit the instructor from creating a nurturing environment for students' growth and development.

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Cooperative learning techniques encompass many of the qualities that have been shown to be lacking in traditional teaching methods. Many cooperative teaching strategies involve using altered versions of the lecture, lecture-demonstration, and discussion group that are intentionally designed to help students stay focused, retain the information, and increase their amounts of participation. The range of cooperative techniques offers an instructor countless creative possibilities from which to choose when approaching a topic. Student diversity is viewed as a strength to be utilized for the benefit of all. Within a well-designed cooperative lesson, students will be participating in a number of activities calling for different types of knowledge. Because most of the techniques require students to take an active role in their learning, the instructor becomes less prominent as the 'source of all knowledge' and takes on the roles of guide and facilitator. The extensive use of groups allows the instructor to interact with individual students and become aware of their learning needs. Students share their knowledge and are expected to help each other learn. In general, the use of cooperative learning techniques creates an environment where students are encouraged to become a community of learners. They would thus appear to be an important body of skills for an instructor of tonal theory to have. There have been only a few articles published applying cooperative learning to postsecondary music education; the most recent article-published after this thesis' inception-is devoted entirely to its use in music theory. 19 The authors organize and present a large body of valuable information on the subject in a small amount of space. They explain how to structure cooperation, outline four sample cooperative lessons, provide a strong rationale for introducing cooperative learning into theory classes, and cite a number of useful references. Until now, this article was the most comprehensive source available for theory instructors interested in using the techniques in their classes. What it lacks, however, is the necessary detail and quality lesson plans to assist first-time users. The four lessons do show a variety of applications, but their suitability for many theory classes is, in this writer's estimation, questionable. Unfortunately, many journal readers may dismiss the feasability of this teaching strategy before giving it a try.20 Lawrence M . Zbikowski and Charles K. Long, "Cooperative Learning In The Music Theory Classroom," Journal of Music Theory Pedagogy 8 (1994): 135-157. 20 This may be encouraged by the editor's ill-informed reference, categorizing the article as a pedagogical strategy for "that ever-present group of students who need remediation in music theory." Mary Wennerstrom, "From the Editor," in Ibid., 1. 1 9

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This thesis aims to provide the reader with a significantly more thorough application of cooperative learning to the teaching of tonal harmony. The lesson plans address topics that are central to the subject. An attempt has been made to show a number of cooperative strategies that are not only varied, but also easily achievable for the inexperienced user. Each lesson plan features discussions about related issues, and suggests different applications of the techniques to other topics. To ensure one's success in implementing cooperative lessons, it is crucial to be familiar with the principles on which cooperative learning is built. It is equally useful to know for what purposes cooperative learning techniques have been most successful and so the next section will present a summary of this data. An instructor with a firm grasp of this information will find it a useful tool for the creation of effective learning activities and for the treatment of problematic situations that may occur. Cooperative learning techniques do require the instructor to exercise many different teaching skills. The selected bibliography included provides, among other things, references to guide instructors in the acquisition of some of these.

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Cooperative learning is one of the most highly structured forms of collaborative learning. A detailed definition states: "Cooperative learning is the instructional use of small groups so that students work together to maximize their own and each other's learning".

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Most higher-

education instructors have neglected exploring the inclusion of structured student-student interaction within the classroom, and have focused instead on the interaction between the instructor and student, and between the student and subject material.

By examining

cooperative learning's placement within the broad context of learning settings, and then in a narrower context of group work, the following review will make its value as an additional teaching approach evident.

Learning Settings Using any given subject material, an instructor may create one of three possible classroom environments, or learning settings: competitive, individualistic and collaborative. Each of these respectively fosters one of three types of student-student interaction. When an instructor creates an environment where students must work against each other in order to achieve a goal that only one or a few can attain, the learning setting is competitive.

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One of the most

common ways of structuring a competitive learning setting at the college and university level is to grade exams and assignments on a curve or to use some form of norm-referenced grading criteria. As a result, student interaction is primarily oppositional since one's goals can be reached easier when others fail to succeed. Students are most likely to either work hard and concentrate on outcomes beneficial to themselves, but detrimental to others, or coast along, doing very little work because they do not feel they can succeed. Most students believe that of

1 David W . Johnson, Roger T. Johnson, and Edythe Johnson Holubec, Cooperation i n the Classroom (Edina: Interaction Book Company, 1991): 1:5. 2

David W . Johnson, Roger T. Johnson, and Karl A . Smith, Active Learning: College Classroom (Edina: Interaction Book Company, 1991) 1:27. 2 2

Cooperation i n the

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the three types of learning settings, college classes are mainly competitive environments.23 When an instructor creates an environment where students work alone to attain a goal unrelated to those of other students, the learning setting is individualistic.,24 Individual research projects and computer-assisted instruction programmes requiring students to meet preset criteria to progress through course content are both examples of individualistic learning settings. Student interaction in these settings is seen as unnecessary. The tendency is for students to focus primarily on their own achievements and ignore the efforts of others. When an instructor creates an environment where students must work together to achieve shared goals, the learning setting is collaborative.

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Examples of collaborative learning

settings range from highly structured forms like cooperative learning and problem-centered learning to less structured forms such as discussion groups, seminars, and learning communities. Student interaction is supportive as individuals share resources, offer help and encouragement, provide each other with feedback and influence each other's efforts to meet the group's goals. 26

Students' achievement is now positively linked with the achievement of

others.

Problems Associated with Traditional Group Work While all cooperative learning techniques involve group work, the reverse is not true. Placing students in groups and directing them to work on a learning task together does not mean that an instructor is implementing cooperative learning. Many instructors may assign some type of group project in hopes that students will join together in cooperation as they work to complete the assignment.

Unfortunately, the students may not possess the skills or the

inclination to work cooperatively and the final result may just be one or two students' work with everyone's name on it. Indeed, traditional learning groups are susceptible to many problems. The scenario just mentioned, where some group members do less than their share of the work and essentially

23 Ibid., 1:14. 24 Ibid., 1:27. 25 Ibid.; and Jean MacGregor, "Collaborative Learning: Umbrella Term for a Growing Array of Approaches." Learning Together: Collaborative Learning at BCIT 2 (Spring 1994): 1-2. Researchers of Social Interdependence use the term "promotive interaction". See Johnson, Johnson and Smith, 2:4-5. 2 6

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"hitch-hike" on the work of others, is called the "free-rider effect". 27

Because it is harder to

identify individual contributions as a group grows larger, people often decrease their level of productivity with an increase in group size. This tendency has been labelled "social loafing". 28 Group members with high ability, in an attempt to avoid being left with a heavy workload, may purposely participate less and expend less effort.29

On the other hand, these same members

may actively take over, or passively be given, leadership of the group. They may dominate group discussions and squelch other members' ideas, regardless of merit. Conversely, other group members can apply pressure on one or two group members to conform to the status quo simply by being the majority. Numerous dysfunctional divisions of labour may occur, from assigning the least popular task to a member of a racial minority to consistently expecting a female member to take notes.

30

Finally, a variety of deliberately destructive behaviours and

forms of conflict can arise.31 After attempts to incorporate traditional group work produce even some of the listed problems, it is not surprising that instructors are hesitant to continue using groups and are skeptical of, even hostile towards yet another form of group work. Students, too, are often reluctant to enter into yet another group experience when so many of their previous encounters with a group learning setting have left negative impressions. Cooperative learning is significantly different from traditional group work and while it is not a panacea, many of the problems typically associated with group work can be eliminated through the careful structuring of cooperative learning techniques.

The Five Basic Elements of Cooperative Learning What differentiates cooperative learning from other forms of collaborative learning is the

N. Kerr and S. Bruun, 'The Dispensability of Member Effort and Group Motivation Losses: Free-rider Effects," Journal of Personality and Social Psychology 44 (1983): 78-94. 2 7

28 B. Latane, K. Williams, and S. Harkins, "Many Hands Make Light the Work: The Causes and Consequences of Social Loafing," Journal of Personality and Social Psychology 37 (1979): 822-832. 29 Johnson, Johnson and Smith, 3:2. Elizabeth G. Cohen, "The Dilemma of Groupwork," chap. 3 in Designing Groupwork: Strategies for the Heterogeneous Classroom. 2nd ed. (New York: Teachers College Press, 1994): 24-38. 3

0

Further discussion of conflict can be found in David S. Jalajas and Robert I. Sutton, "Feuds in Student Groups: Coping with Winners, Martyrs, Saboteurs, Bullies and Deadbeats," The Organizational Behavior Teaching Review 9/4 (1984-1985): 94-102; and Richard G. Tiberius, Small Group Teaching: A TroubleShooting Guide. Monograph Series 22 (Toronto: OISE Press, 1990). 3 1

15

presence of five essential components. 32 When structured into group activities, these five elements can create the conditions for cooperative efforts to be more productive than competitive or individualistic efforts. Additionally, these elements obviate many of the problems traditionally associated with group work. There are numerous practical ways to incorporate each of the elements into group activities, so only a few will be mentioned. Positive Interdependence is likely the most important element of a successful cooperative learning experience.

Group members must perceive that they need each other in order to

complete a task. Many of the traditional group problems mentioned above, specifically the free-rider effect and dysfunctional divisions of labour, can be eliminated when students clearly understand that their own efforts are essential to group success and that each member has the potential to make a unique contribution to the group. There are two general categories of positive interdependence: outcome interdependence and means interdependence.

33

Outcome interdependence strategies create situations where students

share a common fate, strive for mutual benefit so that all group members can succeed, and value joint productivity. One type of outcome interdependence, goal interdependence, involves giving the groups a clear objective that each member must meet. All members are responsible to help each other meet that goal. Reward interdependence is structured so that each group member receives the same reward for completing a given task. One may choose to give a joint reward where all group members must reach some predetermined criteria. Groups whose members do not all meet the criteria do not receive a reward. outcome interdependence include

using

Other strategies for creating

intergroup competition

(outside enemy

interdependence), hypothetical situations {fantasy interdependence), and group names or mottos (identity interdependence). The second category, means interdependence, is concerned with the creation of strategies that require students to work together to accomplish the task. Using strategies from this category will highlight individuals' personal responsibility to contribute to the group. There are four main types of means interdependence. Resource interdependence is created by giving each group member only a part of the information or materials needed to complete the task. In

32 Johnson, Johnson and Smith, 3:1-16. 33 David W. Johnson and Roger T. Johnson, 'Positive Interdependence: Key to Effective Cooperation," chap. 8 in Rachel Hertz-Lazarowitz and Norman Miller, eds., Interaction in Cooperative Groups: The Theoretical Anatomy of Group Learning (Cambridge, NY: Cambridge University Press, 1992): 180-182.

16 order to be successful, group members must combine their resources. The second technique involves assigning roles to each group member which reflect some of the task's essential actions and responsibilities.

Role interdependence might entail a discussion group of four

being assigned such roles as encourager of participation, checker of understanding, elaborator of knowledge, and devil's advocate.

Placing some boundaries on a group's physical

surroundings, like putting students in a specific location, can create

environmental

interdependence. Finally, the fourth type of means interdependence, task interdependence, is structured by assigning students a division of labour such that one person must complete his/her task before the next one can begin. Researchers have posed many questions about various issues involving positive interdependence over the years. Evidence from a recent study seems to support findings from an earlier study indicating that group membership alone is not enough to produce higher achievement and productivity.34

Rather, it is the presence of clearly defined positive

interdependence in conjunction with group membership that accomplishes these results. While it would be close to impossible and quite unnecessary to incorporate all the cited types of positive interdependence into every group activity, it is highly recommended that one use three to five types whenever cooperative groups are desired. At least, one should select a strategy from each of the two categories. Students need a form of outcome interdependence to give them a reason why they should work together and at least one type of means interdependence to give them some guidance as to how they should accomplish the task as a group. Of course, the more types one uses, the stronger the interdependence between group members will be. The second element of cooperative learning is Face-to-Face Promotive Interaction. When positive interdependence is carefully structured and students perceive that they need each other to succeed, the ways in which they deal with fellow group members will be affected significantly.

Promotive interaction is the pattern of verbal and nonverbal interchange which

occurs when students encourage and aid each other's efforts to learn. The "face-to-face" component

makes reference to group members' physical working conditions.

In most

situations, group members should be seated in such a way that they can easily see each others' faces. Sitting in a circle or around a table will accomplish this in a room with movable seating.

34 ibid., 183.

17

However, in lecture halls with fixed seating, groups involving four to six members would need to be arranged so that half the group turns around to face the other half in the row behind, as opposed to group members all sitting in one row. These logistical considerations facilitate student efforts to assist each other in learning. Once students, have been assigned a task where they need to work together and are physically arranged in such a way as to facilitate this, one cannot assume that they will automatically work together efficiently and effectively. This is why Interpersonal and Small GrOup Skills must be taught. While many social skills are learned through family and community experiences,35 post-secondary students may still need guidance and training in cooperative behaviours because of the education system's predominantly competitive atmosphere. Effective groups are groups where individuals know and trust each other, communicate accurately and unambiguously, accept and support each other, and resolve conflicts constructively.36 When implementing cooperative learning techniques, an instructor needs to observe students' behaviour, identify social skills that are lacking, and actively encourage students to use them. Techniques for teaching interpersonal and small group skills are varied.3 One 7

method is to introduce the skills in the form of roles {role interdependence) for students to take on during the group task. Paraphrasing, for example, is important for establishing clear communication and an instructor may initially require that one group member focus on paraphrasing others' ideas. Eventually, the role of paraphraser should be rotated so that all members are required to practise the skill. If members do not participate equally, an instructor might introduce a group activity which involves one member acting as an observer and compiling data using some type of observation instrument.38 The fourth element of cooperative learning is Individual Accountability. Group members are held personally responsible to do their fair share of the work. In order to ensure individual accountability exists, instructors need to establish methods of identifying and assessing 35 Johnson, Johnson and Holubec, Cooperation in the Classroom. 5:2. 36 Johnson, Johnson and Smith, 3:9. 3 For further discussion about how to teach cooperative skills, see Johnson, Johnson, and Holubec, Cooperation in the Classroom. 5:15-23. 7

38 These instruments can range in complexity and purpose. A n excellent resource is: Anita Simon and E. G i l Boyer, Mirrors for Behaviour III: A n Anthology of Observation Instruments (Wyncote: Communications Materials Centre, 1974).

18

individuals' contributions and informing both the individual and the group of the results. By doing so, the instructor can help prevent both free-rider effects and social loafing. Group members need to be aware of the quality of other members' learning so that they can offer appropriate assistance and encouragement. After all, the main purpose for using cooperative groups is to strengthen individuals so that once they have learned something together, each will be able to demonstrate mastery alone.39 There are many ways to establish individual accountability; the following represent only a sampling. Groups should number no higher than six. The fewer the members, the higher the accountability. Students can be required to take individual tests or to teach what they have learned to someone else. Lastly, an instructor may randomly select a group member to report on the group's work. The final element essential to cooperative learning is Group Processing. In order for groups to develop and become more efficient, it is important that some attention be paid to the quality of the group session. Group processing is a time of reflection where members spend time considering what actions were helpful and unhelpful, and then make decisions about how and what they should continue or change. There are three levels at which processing may take place: individually, in small groups and as a whole class. At the end of a lesson using cooperative groups, an instructor should allow some time for students to reflect individually or together in their groups. Occasionally, an instructor may choose to use whole-class processing. After systematically observing the various groups working together during the class, the instructor shares the results of the observations with the students. Since group processing is a bit time-consuming and not directly connected to the subject matter being learned, it is the one element of cooperative learning that is often neglected. There are six important reasons why group processing should be regularly included with cooperative groupwork. It allows students to focus on maintaining good working relationships among members. Instructors can use this time to direct students' attention to assessment of how well they are incorporating various interpersonal and small group skills. It ensures that group members hear feedback from their peers about their participation. Students will spend some This statement may surprise many readers who have been misled to believe that Cooperative Learning advocates giving group grades. While there are many ways in which grades can be influenced by or reflect groupwork, these are not necessary to use, but optional. For more information, see David W . Johnson, Roger T. Johnson, and Edythe Johnson Holubec, "Assessment and Evaluation," chap. 7 i n Advanced Cooperative 3

9

Learning, rev. (Edina: Interaction Book Company, 1992).

19

time reflecting on how they learn, not just what they learn so that this information can be applied to new learning situations in the future. Group processing can be an opportunity to boost morale and self-esteem as students identify positive behaviours and celebrate group successes.

40

Last of all, research has indicated that students who learn information and more

complex skills in cooperative settings with group processing are more likely to achieve higher levels of learning and retention than students learning in cooperative settings without group processing or in individualistic settings.

41

Types of Cooperative Learning Groups Cooperative learning techniques are both numerous and versatile. They do, however, fall into three broad categories, according to the purpose, duration, size and membership of the groups. The three types are informal cooperative learning groups, formal cooperative learning groups and cooperative base groups. When an instructor wants to focus students' attention on what is to be learned, or to motivate students to learn, or to check that students are actively processing lecture material, or to provide closure to a class session, informal cooperative learning groups can be used.

42

These are temporary groups, usually consisting of two to four members, which can stay together for anywhere from one brief discussion to one class period. Most often, informal cooperative learning techniques require only three to six minutes of class time to perform, and are used to break up a long lecture into shorter ten- to fifteen-minute segments, coinciding with students' attention spans. Because this type of cooperative learning is so brief and focussed, little attention needs to be paid to the formation of groups. Most informal techniques are successfully carried out by having students work with the person or people sitting around them. Finally, this is the only type of cooperative learning group where group processing, one of the five basic elements, is de-emphasized because of the short duration of the activity. Formal cooperative learning groups are groups with fixed membership which may remain 4

0

These five points are from Johnson, Johnson, and Smith, 3:12.

Two studies that compare cooperative and individualistic learning settings and provide empirical evidence are: Stuart Yager, Roger T. Johnson, David W. Johnson and B i l l Snider, "The Impact of Group Processing on Achievement in Cooperative Learning Groups," The Journal of Social Psychology 126 (1986): 389-397; and David W . Johnson, Roger T. Johnson, M . Stanne, and A . Garibaldi, "The Impact of Leader and Member Group Processing on Achievement in Cooperative Groups," The Journal of Social Psychology 130 (1990): 507-516. 4 1

4

2

For a more detailed discussion, see: Johnson, Johnson and Smith, 5:10-29.

20

together for one class period up to several weeks, depending upon the need. 43 Instructors can use these groups to teach specific content or to complete a task or assignment. Student activity may center around learning new information or concepts, problem-solving, or creating some group product. This type of cooperative learning group requires a higher level of structure than the informal type. Instructors will need to pay more attention to how the various groups are formed. Many researchers and practitioners have investigated and experimented with different issues regarding group composition. 44 in general, groups with members of varying ability levels are best for all students so that all groups have an equal chance to succeed. Because of this, it is recommended that the instructor assign students to groups. Random selection techniques can also be used to accomplish some form of heterogeneity, especially for shorter formal activities. Cooperative base groups are the third type of cooperative learning group.45 These groups function to provide students with support and assistance in their academic progress. They are instructor-selected, and heterogeneous in composition. Usually an instructor will assign the students to four-, five- or six-member base groups within the second or third week of a course and students will remain together for the entire term or year. Base groups are most often used for academic support tasks, such as helping each other prepare for tests, and routine tasks, such as collecting assignments. They can also be used as a forum for discussing issues involving interpersonal and small group skills, and other personal matters. Once an instructor is comfortable using informal and formal groups on a regular basis, and is operating his/her courses in a collaborative setting, cooperative base groups are a natural and logical step towards a promoting more general cooperative atmosphere.

Three Schools of Cooperative Learning While the concepts of collaboration and group learning are certainly not new in education, cooperative learning, as explained here, was first introduced into elementary and secondary 43 Ibid., 4:1-15. 44 For summaries of research, see Ibid., 2:17, 4:6-7; and Bonnie K. Natasi and Douglas H. Clements, "Research on Cooperative Learning: Implications for Practice," School Psychology Review 20/1 (1991), 120123. An interesting article written by authors not admittedly associated with Cooperative Learning comes to similar conclusions about group selection: Susan Brown Feichtner and Elaine Actis Davis, 'Why Some Groups Fail: A Survey of Students' Experiences with Learning Groups," The Organizational Behavior Teaching Review 9/4 (1984-85): 58-71. 45 For a more detailed discussion, see Johnson, Johnson and Smith, 6:1-18.

21

teacher-training by Roger and David Johnson at the University of Minnesota in the mid 1960's.46 Other cooperative learning procedures were developed in the 1970's by David DeVries and Keith Edwards at John Hopkins University (Teams-Games-Tournaments [TGT]) and Shlomo and Yael Sharan in Israel (Group Investigation). In the late 1970's, Robert Slavin modified TGT to create Student-Team-Achievement-Divisions (STAD) and another procedure, the Jigsaw approach by Elliot Aronson, to create Jigsaw II. Concurrently, Spencer Kagan developed the concept of learning structures and the Coop-coop procedure and Elizabeth Cohen created procedures called Groupwork.47 A l l of these 'strains' or 'brands' of cooperative learning listed above-and the list is by no means exhaustive-are the products of differing theoretical perspectives on learning held by their developers. The methods may vary in many ways:

the types of activities used, the

degree of student interaction, the domain of student responsibilities, the reward structure, and the areas in which positive outcomes are centered.48 More significant for the purposes of this paper is how the different methods are taught or presented to instructors wishing to implement cooperative learning techniques in their own teaching. The following explanation is offered so that the reader may recognize and appreciate how the implementation of cooperative learning has been approached in this thesis. There are essentially three major schools of cooperative learning: the conceptual approach, the structural approach, and the curriculum specific packages. 49 None of the approaches is discrete. In fact, each contains elements of at least one other approach. It is probably more accurate to classify the different procedures along a continuum, with conceptual approaches at one end and curriculum specific packages at the other, and structural approaches falling in between, slightly closer to the latter. However, for ease of explanation, each will be discussed here separately. 46 A brief look at historical instances of cooperation in education can be found in Ibid., 1:16-17; and E. Gil Boyer, Jean L. Weiner and Maureen P. Diamond, "Why Groups?" The Organizational Behavior Teaching Review 9/4 (1984-85): 2-3. 47 David W. Johnson and Roger T. Johnson, "Cooperative Learning: Where We Have Been, Where We Are Going," December 1992, manuscript to appear in Cooperative Learning and College Teaching. 7-8. 48 Presenting a comparative survey of these cooperative procedures is well beyond the scope of this thesis. A brief comparative study is available in Natasi and Clements, 113-117. The following two books provide readers with more thorough explanations and directions for implementing most of the procedures listed: Spencer Kagan, Cooperative Learning (San Juan Capistrano: Kagan Cooperative Learning, 1992); and Robert E. Slavin, Cooperative Learning: Theory. Research and Practice (Toronto: Allyn and Bacon, 1990). 49 Kagan, "Three Schools of Cooperative Learning," chap. 5.

22

The Conceptual Approach to implementing cooperative learning techniques emphasizes familiarizing instructors with the principles gleaned from theories and relevant research on small group learning in cooperative settings. Instructors are given a general understanding of what is involved in structuring a cooperative learning situation so that they can apply the techniques to any age group, curriculum materials, skill level and setting, adapting as needed. Proponents argue that this approach to instructor-training is beneficial because instructors become "educational" or "instructional engineers", as opposed to technicians.50 The Structural Approach, developed by Spencer Kagan, involves using many distinct ways of organizing individuals' interactions in the classroom.

51

These organized interactive

sequences -called "structures"-are numerous and independent from subject material. Each structure has a name and a given order of steps which must be followed quite strictly, although variations are often given or can be developed. Because a structure is simply a description of a series of social interactions, both competitive and cooperative structures exist. Different structures will function to achieve different objectives and so the structural approach classifies structures into such categories as mastery, information sharing, and thinking skills. When a structure is used to convey particular subject material, the instructor has created an activity. Once familiar with a number of structures, an instructor is then encouraged to combine them according to their appropriateness for reaching the desired objectives, and create multistructural lessons. Two of the benfits advocates cite for the structural approach are that instructors can use a few structures many times and with a wide variety of subject material, and that each structure automatically contains all the essential ingredients for a successful cooperative learning experience. Curriculum Specific Packages are one or more structures combined with curriculum materials specifically designed for cooperative learning. 52 Some examples of the more wellknown ones are Robert Slavin's Team-assisted Individualization (TAI) in math and Cooperative Integrated Reading and Composition (CIRC), and Edward DeAVila's Finding Out/Descubrimiento, an instructional approach for teaching math and science concepts in

50 Elizabeth G. Cohen, Designing Groupwork: Strategies for the Heterogeneous Classroom. 2nd ed., with a foreword by John I. Goodlad (New York: Teachers College Press, 1994): 3-4; and Johnson and Johnson, Where We Have Been. 8. 51 Kagan, 5:1-9. 52 Ibid., 5:10.

23

Spanish/English dual language settings. Since every discipline has its own unique curriculum issues, curriculum specific packages are designed to deal with these, as well as provide a method of classroom organization. Most packages emphasize the types of skills unique to the field, and they are designed to accommodate students with varying skill levels.

53

Benefits of Cooperative Learning In the last century, over six hundred studies have been done comparing the relative effects of cooperative, competitive, and individualistic efforts on instructional outcomes. From these 54

studies, there emerge numerous ways in which cooperative learning efforts are beneficial. They may be summarized by three categories: relationships, and psychological adjustment.

55

effort to achieve, positive interpersonal

The research studies have included participants

of varied economic class, age, gender, and cultural backgrounds, and have been performed by different researchers, using a variety of research tasks in different subject areas. 56 Because of this, the research is considered to have a wide generalizability. ? 5

A number of benefits can be cited regarding the effort to achieve. College and adult studies comparing the success of competitive, individualistic and cooperative efforts have shown that cooperative learning promotes higher achievement and productivity than competitive or individual learning. They also showed that more higher-level reasoning, more frequent generation of ideas and solutions, and more transfer of learning from one situation to another are the result of cooperative learning. Another benefit is that students develop more positive attitudes towards the subject area and are motivated to pursue it further.

58

In the area of interpersonal relationships, many benefits exist. Student relationships develop where higher levels of interpersonal attraction exist regardless of differences in ability level, gender, race, or social class. Because of the positive relationships, the occurrence of 5 3

5

4

5 5

For more discussion on the advantages of curriculum specific packages, see Slavin, 79. Johnson, Johnson, and Smith, 2:2. Ibid., 2:11-27.

6 A complete listing of these studies is available i n David W . Johnson and Roger T. Johnson, Cooperation and Competition: Theory and Research (Edina: Interaction Book Company, 1989). 5

5 7

Johnson, Johnson, and Smith, 2:12.

This benefit is corroborated in some field-based research that used cooperative techniques in a first-year wind performance class and an instrumental music course in teacher education. Bernard W . Andrews, "Group investigation in music instruction: A pedagogical scenario," Canadian University Music Review 13 (1993): 93-103. 5 8

24

absenteeism diminishes.

59

Students in cooperative settings like the instructor better and

perceive the instructor as being more supportive. Studies have shown that the establishment of a group of friends and academic involvement in classes increases the odds of students remaining in college and graduating. There is also supporting evidence that peer relationships formed through cooperative learning experiences will promote healthy social development. Cooperative learning can contribute positively in the area of psychological health. Factors linked to cooperativeness, such as emotional maturity, well-adjusted social relations, strong personal identity and basic trust in and optimism about people, are essential requirements for building and cultivating relationships and participating effectively in society. Cooperative learning tends to heighten students' ability to look at situations from different perspectives, other than their own. Both Perry and Knowles stress the importance this plays in stimulating growth towards maturity. Finally, college and adult studies indicated that cooperative learning promotes higher levels of self-esteem than competitive, and to a lesser degree, individualistic settings. In seeking to apply cooperative learning to the teaching of tonal harmony, it is helpful to know the areas in which benefits have already been demonstrated. By understanding the strengths of cooperative learning, one can identify areas in music theory that call for these types of outcomes, and begin using appropriate cooperative techniques to stimulate the learners' development to that end. Topics in music theory suitable for cooperative learning techniques are those which are highly important, require mastery and retention, involve highly complex or conceptual tasks, employ problem-solving, call for quality of performance, benefit from creativity and divergent thinking, and demand higher level reasoning strategies and critical thinking.

60

Another recent study related to post-secondary music corroborated this benefit. Glenn Lewis Hosterman, "Cooperative learning and traditional lecture/demonstration in an undergraduate music appreciation course," (Ph. D. diss., Pennsylvania State University, 1992): iv. 5

9

6 ° Johnson, Johnson, and Smith, 2:13-14.

25

SAMPLE LESSON PLANS

Introduction to Lesson Plan Format The following ten lesson plans represent a sampling of how cooperative learning techniques may be applied to the teaching of some central topics in core undergraduate theory classes. They are presented in order of increasing complexity based on a number of criteria. The first five lesson plans use informal cooperative learning groups that range from one brief exercise, as part of a lecture, to a more extended activity. In general, most of the techniques illustrated in these lesson plans could be easily used alongside more traditional teaching methods since they can be introduced with little disruption to the continuity of a lesson. An instructor who has little or no previous experience with cooperative learning can expect to encounter few difficulties, even when trying these structures for the first time. Students are not required to have extensive collaborative skills in order to participate. The first four plans incorporate the structures into teaching situations where the instructor maintains primary control over the delivery of new information and the pace at which it is being transmitted. As one continues to read through the remaining five examples, the degree of complexity rises. All illustrate formal cooperative learning groups. Many of the techniques require students to take on more active roles than they would in traditional classrooms. This departure from the status quo results in different seating arrangements, noisier classes, and more studentdirected learning. The instructor retains less direct control over what and how students are learning and assumes some less traditional roles of facilitator, guide, and consultant. The lesson plans call for the instructor to exercise a different set of classroom management skills. It becomes more necessary for students to use more sophisticated interpersonal skills. The lesson plans are presented in a standardized format composed of eight distinct sections. All eight sections are listed below with a brief explanation of their content and purpose: Each plan opens with an Introduction. Its purpose is to provide the reader with continuity between the lesson plans by making some comparative remarks about the applications of the different cooperative structures. General information about the specific structure(s) being

26

applied in that lesson and a discussion about the learning outcomes for which the structure is designed may be included. Following the introduction is a reference list of basic information pertaining to the lesson: the text reference, level, instructional objectives, cooperative structure(s), type of cooperative learning groups used, and amount of time required for the lesson. Unless otherwise indicated, all text references will be to Edward Aldwell and Carl Schachter, Harmony and Voice Leading. 2nd ed., the text currently being used in the theory programme at the University of British Columbia. Some references will be for the corresponding Workbook for Harmony and Voice Leading, Vol. 2., by the same authors. Since the core theory programme consists of four terms of instruction divided between two years, the year and term number will be given to indicate to what level each lesson was taught. The Summary of Lesson Format section provides the reader with a general overview. The lesson is laid out as a series of steps with each being identified as an activity, group task, discussion, or lecture. Approximate time limits are given for each step. For lesson plans that involve students physically moving to and between groups, the time given for each step is only the actual time that students are working. Next, a Rationale explains why the cooperative structure is being used to teach the lesson content. This might include discussion about the nature of the subject, problems that it poses for instructors and learners, and how the cooperative structure presents a solution. Specific reasons may also be given for the structure's location in the lesson. References to educational theories introduced in the opening section will be made. The section entitled Pre-Instructional Decisions contains the following four fixed subsections:

group size, assignment to groups, materials, and room preparation. When a

lesson plan includes the use of roles, this additional subsection is listed. Depending upon the total number of students and if the lesson plan calls for a fixed number of groups, the group size may vary. Ideal sizes are indicated with the understanding that adjustments may be necessary. Instructors should, however, never use groups of more than six or seven members for these lessons. Most cooperative learning specialists advise against larger groups because individuals' interaction becomes limited and subgroups often result. For the lessons using informal cooperative learning groups, assignment to groups is usually student-selected. For formal groups, heterogeneity is necessary and the lesson plans demonstrate several

27 interchangeable, random-grouping methods to achieve this. Since random methods cannot guarantee heterogeneity, some plans where this is crucial call for the instructor to pre-assign students to groups. For any of the lessons suggesting random grouping, an instructor may instead choose to select the groups ahead of time.

Some factors to always take into

consideration when grouping for heterogeneity are: knowledge or ability level, gender, race, age, and English-speaking ability. Depending upon the task, one may wish to mix students according to field, major, primary instrument, voice type, part-writing ability, or collaborative skills. The Lesson section is a more detailed version of the earlier Summary of Lesson Format section. It provides the reader with exact instructions on how to carry out the cooperative activities in the classroom. Much of the material relating directly to music theory concepts has been omitted, since it is assumed that readers are knowledgeable and competent with the subject matter.

In many cases, scripting is used to convey a sample of how one might

communicate various components of the lesson to students. It is used frequently for stating the cooperative tasks. The method consistently modelled throughout the plans is one where students are informed of the general structural procedures first, and given the specific task only after having moved into their groups. This method is recommended because it avoids one of these two possible situations from occurring: students become so preoccupied with the task that they fail to pay attention to how it will be performed or, the confusion and shuffle created as students move into groups causes them to forget the details of their task. Each lesson is based on a specific instructional model that includes the following four components: bridge-in, instructional objective, pre-test, and post-test.

61

Most of the terms

are widely used throughout the ten lessons and so a brief definition of each is necessary. The bridge-in occurs at the beginning of each lesson and focuses the students' attention onto the subject material. Many techniques for bridging-in exist and those used in the lesson plans serve as guidelines only. The instructional objective is a formal statement indicating what the learners should be able to do by the end of the lesson.

62

In all lessons, the objectives are

communicated to the students near the beginning so that they know where to focus their

Instructional Skills Workshop: Handbook for Participants (Vancouver: The University of British Columbia Faculty Development Program, 1993): 5-17. For further instruction on writing instructional objectives, see Norman E. Gronlund, Stating Objectives for Classroom Instruction. 3rd ed. (New York: Macmillan Publishing Company, 1985). 6 1

6 2

28

efforts. A pre-test determines what the students already know about the lesson material so that the instructor may begin teaching the lesson at an appropriate level. It need not be in the form of a graded 'test'; asking students to respond to a few questions is often sufficient. In the same way, a post-test can be either an informal or formal means of checking to see if the instructional objectives have been met. Many times, the cooperative activites are used as pretests or post-tests within a lesson. On a larger scale, an entire lesson itself, comprised of group activites based on lecture material from the previous class, may be considered as a type of posttest. Following the lessons using formal cooperative learning groups, is the section entitled Analysis for Basic Elements. This section is included primarily as a reference tool should the reader wish to alter any existing plan. By using pre-existing cooperative structures and then listing the specific features that contribute to creating the necessary conditions for cooperative learning, I am attempting to combine some strengths of both the structural and conceptual approaches. The section identifies the ways in which three of the five basic elements-positive interdependence, individual accountability, and interpersonal and small group skills-are structured. Over the course of the ten lesson plans, a variety of examples will be given. Many of the ideas could be interchanged between lessons to fit different needs. The element, group processing, is not included because it is easily identifiable within the context of any lesson. Since face-to-face promotive interaction is largely the result of appropriate seating arrangements and the enforcement of interpersonal and small group skills, it also does not warrant separate mention in this section. The final section, Comments and Reflections, presents a discussion of the lesson in light of the experience gained from teaching it. Comments will be made about the benefits of the lesson, as well as any problems which arose. Practical issues, such as the suitability of time limits, will also be assessed. Suggestions for varying parts of the lesson, or of other topics to which the structure might be applied, are included where pertinent. Limitations In producing the material for this thesis, there are areas in which limitations exist. The purpose of this work is to demonstrate the applicability of cooperative learning techniques to undergraduate theory classes. However, since this is not a comparative study of classes taught

29

using cooperative learning techniques and classes taught using more traditional methods, no claims may be made, nor proof offered, that cooperative learning is more effective than traditional teaching methods to promote learning in this setting. While teaching these lessons to students, this writer was acting in the capacity of a guest or substitute instructor. As a result, the opportunity did not exist to explore grading issues, writing follow-up assignments, and the use of cooperative base groups. Because students were not being taught using cooperative techniques on a continual basis, they required more coaching on using basic cooperative skills at the beginning of each lesson than would have been necessary if they had had regular practise to develop in this area. Occasionally, the time available in the class period to teach the lesson would be reduced at the request of the regular instructor and so modifications to the original plan would have to be made. Scheduling issues did not always allow for each lesson to be taught to every section of students.

30

1. INTRODUCTION T O T H E USES O F I AND V« 6

Introduction

The cooperative structure introduced in this lesson plan is called "Think-Pair-Share". 63 it is a popular informal structure that can occur in a variety of places during a lesson. The structure is useful when an instructor wishes students to reflect on a problem or question for which a number of answers can be generated. This lesson plan illustrates how it can be used at the end of a lecture to promote synthesis of the information.

Text Reference: Chapter 7: "I , V , and VII ", the "I and V " section only 6

Level:

6

6

6

6

1st year, 1st term

Instructional Objectives:

By the end of this class, students will be able to: list four uses

of I and/or V chords; discuss at least two reasons why I and V chords are desirable 6

6

6

6

additions to their harmonic vocabulary; and analyze six given excerpts to identify which of the four uses each represents. Cooperative Structure: Think-Pair-Share

Type: Informal Cooperative Learning Groups Time Required: 50 minutes

Summary of Lesson Format

1. Instructor introduction to whole class (4 mins.): Introduce topic by playing a

phrase of a chorale melody written on the board and adding roman numerals to indicate tonic and dominant harmonies. 2. Pre-test activity - Personal Truth Statements (6 mins.): Give students no more

than two minutes to write a short anonymous statement, based on their existing knowledge about I and V , that they are certain is factual. Direct students to exchange statements and 6

6

select a sampling to be read aloud. State the instructional objectives. 63 Kagan, 11:2.

31

3.

Instructor mini-lecture to whole class (20 mins.): Present the four situations in which I and/or V chords are found, illustrating them by harmonizing the chorale melody. 6

6

4. "Think-Pair-Share" task (10 mins.): Students think about the question, "Why are these two chords useful additions to your harmonic vocabulary?" for one minute, discuss their answers in pairs for two minutes, and then are randomly selected by the instructor to share their answers with the class. 5.

Post-test activity (7-10

mins.): Students are given about five minutes to check their

ability to recognize I and V uses by taking a Self-Quiz. Instructor reviews the answers 6

6

with the students, clarifying where necessary.

Rationale

The purpose for including this lesson plan among the samples is to show how one can use a lecture format and still avoid many of its pitfalls. Students are typically most familiar with the lecture for acquiring new information, and, according to Perry's observations of students' developmental stages, the majority of first-year students will accept the instructor presenting the material in this way. The particular content of this lesson lends itself well to being taught in such a manner because it is primarily factual knowledge to be understood. The objectives do not require students to have mastered how to write I and V chords in four-part settings 6

because this will be part of the following day's lesson.

6

At the same time, even factual

knowledge must be applied to be retained, and so specific activities are selected to supplement the lecture. The Personal Truth Statements written by the students help the instructor to measure the level of knowledge students already have on the subject. Because the exercise ensures the anonymity of the writers, it is non-threatening for students. The activity engages all students and the instructor can feel free to call on any of the students to participate, since they will be reading statements which are not their own. While it is not structured cooperatively in this lesson plan, the same activity could be presented in a Think-Pair-Share structure in which students would be expected to discuss the validity of the statements in pairs and then share their views with the whole class. However, this variation would require additional time.

32

Several techniques help focus the mini-lecture and hold students' attention. The instructional objectives remain on the board so that students can refer to them during the presentation to check that they are taking note of the essential points. At approximately the twelve-minute mark in the lecture, when listeners' attention spans may begin to fall, a question is asked. The Think-Pair-Share activity has several functions. It provides a break from the instructor's monologue, giving students time for both reflection and discussion. As with the Personal Truth Statements, the activity is relatively non-threatening: the question has many acceptable answers, students have time to think about some responses, and students can check their ideas with another person before sharing them with the whole class. Although many answers to the question have been given through the mini-lecture, students must do some synthesis to formulate their answers since the question demands that they look at the material from a different angle. The activity is likely to appeal most to students who prefer learning from accommodative knowledge. For all the learners, it is an additional opportunity to reinforce some of the underlying principles of I and V usage. 6

6

The post-test activity is extremely important for both the instructor and the student because it provides an indication of how well the students have understood the material. The quiz is not graded since its purpose is simply to help students determine if they need further explanation. It requires students to apply their knowledge of the four uses of I and/or V to new musical 6

6

examples. Real musical excerpts, not contrived examples, are used for the Self-Quiz, to emphasize the relevancy of the lecture material to actual compositions. Pre-Instructional Decisions Group Size: Two Assignment to Groups: Because the cooperative learning activity is informal in type, students work with the person sitting next to them. This minimizes the disruption to the flow of the lesson, and since the activity is so focused and brief, off-task behaviour is rarely a problem. Materials: For each student: one 3x5" index card and the Self-Quiz. Students should have

33

their textbooks with them, but this is not absolutely necessary. The Self-Quiz is composed of the following excerpts, five of which are found in the textbook: Directions: "Identify which of the four types of I and/or V uses each of the following 6

6

excerpts contains." 1. J. S. Bach, Little Prelude, BWV 824, m. 1

Example 7-8a, page 99

2. G. Handel, Double IV from Harpsichord Suite No. 5, m. 1

Example 7-3a, page 96

3. L. Beethoven, Sonata Op. 10 No. 3, II, mm. 9-10

(not in text)

4. G. Telemann, Die durstige Natur, mm. 1-3 (downbeat)

Example 7-8c, page 99

5. G. Handel, G minor Oboe Concerto, IV mm. 1-3 (downbeat) Example 7-12, page 101 6. R. Schumann, Papillons, Op. 2, Finale mm. 9-12

Example 7-6, page 98

No roman numerals and figured-bass symbols should be included with the examples on the Self-Quiz. Room Preparation: The instructional objectives and the chorale melody from page 95 in text are printed on the chalkboard; chairs are roughly arranged in a semi-circle (there may be two or more rows of seats) with an index card set out for each student. The Lesson Bridge-in: Play the chorale melody written on the board. "If you were asked to harmonize this melody using the limited harmonic vocabulary that your text has introduced up to this point, you would have very few options and would probably arrive at this solution." Write roman numerals under the melody which correspond to the harmonies used in the text. "If you were to write the solution out in four-part harmony, it might look like Example 7-la on page 95 of your textbook." Play the phrase for the students. Comment that while there is nothing "wrong" about the harmonization, it sounds a bit stilted and unsophisticated (see text p. 95-96). "Today, we are going to expand your harmonic vocabulary of I, V, and V to include 7

the chords I and V . I will be showing some of the ways in which they can be used by 6

6

adding them to the basic harmonic outline of the chorale phrase."

34

Pre-test: "Taking the index card in front of you,

I would like you to write down a personal

truth statement about 1 and V chords. In other words, write anywhere from one to a few 6

6

sentences that you would swear to be absolutely correct about these chords! Do not put your name on the card. If all you can say about them with any certainty is that they are the first inversions of tonic and dominant harmonies, then that is perfectly acceptable. However, if you know more than that, this is your chance to amaze your fellow classmates with your knowledge! You have one minute and thirty seconds to write." After the time has elapsed, shuffle the cards using any random procedure. Call on several students to read the card they are holding. The instructor should comment only minimally on the statements at this time. One might close this activity by saying, "Well, let's see if today's lecture confirms your statements."

Instructional Objectives: Point out the instructional objectives on the board to students. Provide additional structure for students by stating that today's lesson is primarily going to answer two questions about I and V chords: where are they used? and why are 6

6

they used? The next class will be concerned with how one goes about using them and the logistics involved in part-writing techniques.

Mini-lecture: On the board, harmonize the melody to illustrate the following three situations in which one might find 1 and/or V chords: chordal skips, neighbours, and substitution. 6

6

Provide appropriate explanations with each usage.

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The fourth use, arpeggiation, cannot be included in the harmonization of the melody, and must be explained separately.

'Think-Pair-Share" task: Give students one minute to reflect on the following question: "Why are these two chords useful additions to your harmonic vocabulary? You may want

35 to consider the question from different perspectives such as a bass singer, listener, and composer." Students should jot down their ideas. Ask students to turn to the person sitting next to them and compare their answers for two minutes. They should work together to think of some additional reasons. Randomly call on a few pairs of students to share their answers with the class. The instructor may note their answers on the board. After the class has heard the answers from the selected students, the instructor may ask volunteers to share any responses not already mentioned. Post-test: Hand out Self-Quiz to students and explain that although it will not be graded, they should attempt to complete it without looking at their notes or textbook. Alert the students that some of the questions have more than one possible answer since there may be different levels of harmonic movement occurring in the excerpt, but it is sufficient to correctly identify one of the types. After about five minutes, check if students need a few more minutes. When most have completed it, quickly ask a different student to answer each question. Play each excerpt and provide any additional comments. Closure: If time remains, review the instructional objectives with the students, confirming that they have been met.

Comments and Reflections

If an instructor is attempting to introduce Cooperative Learning techniques into the classroom, incorporating an informal exercise, such as Think-Pair-Share, and other active learning techniques as breaks in the more familiar lecture is perhaps the easiest and least risky method. Provided the instructor keeps the mini-lecture within its time allotment, the other activities outlined here can be easily managed by the instructor to fit the available time. For example, since student responses to both the Personal Truth Statements and Think-Pair-Share activities tend to have common elements, the instructor can choose to hear as few or as many as time allows. This lesson was taught to two classes and in both cases, it was successful in a variety of respects. First, the pace allowed any questions from students to be answered without rushing. Students readily involved themselves in the pre-test activity and seemed to enjoy listening to

36 each other's statements. Very few of the statements showed extensive knowledge about the topic. When the one or two more advanced statements were read, many of the students gasped and seemed intimidated by their apparent complexity. At points during the lecture where the material matched these statements, they were made reference to again and students were now able to understand them. The quality of student responses to both the question during the lecture and the Think-Pair-Share question was extremely high, showing that they were following the flow of the lecture and understanding the material. Most students who were asked to answer a question on the Self-Quiz gave a correct response and when an excerpt had two levels of harmonic movement, many of the students were able to identify both even though this was a relatively new concept to them and this lecture had not dealt directly with it. At the end of both classes, over two thirds of the students indicated that they had answered at least five of the six questions correctly on the Self-Quiz.

37

2.

CHROMATICIZED 7-6 SUSPENSION SERIES

Introduction

The "Turn to Your Neighbour" cooperative structure applied here is another simple technique that can get students used to working together in class.

64

It is like the Think-Pair-

Share structure, without the Think task. A n instructor can ask students to turn to their neighbour periodically throughout a lecture and spend three to five minutes in discussion. Directions for discussion may be to summarize the important points just given by the instructor, to practise explaining the concept just taught, or to generate a question that remains unanswered about the topic. One may not always ask students to share their thoughts with the class, although doing so periodically can ensure students do not waste the time. In this lesson, the Turn to Your Neighbour activity serves as the post-test. It requires over five minutes because students are given a more complicated task than the ones just mentioned.

Text Reference: Chapter 31: "Chromatic Voice-Leading Techniques", section 2. Level: 2nd year, 2nd term Instructional Objectives:

Students will be able to write a chromaticized 7-6 suspension

series in three voices; and reduce a musical passage containing a series into its essential three voices, showing a distinction between chromatic and diatonic elements. Cooperative Structure: Turn to Your Neighbour Type: Informal Cooperative Learning Groups Time Required: 50 minutes

Summary of Lesson Format

1) Instructor introduction (5 mins.): Ask students an introductory question to focus their attention and state the instructional objectives. 2) Instructor

mini-lecture and demonstration (10 mins.):

Beginning with a

descending parallel 6/3 series, transform it into a chromaticized 7-6 suspension series.

6 4

Johnson, Johnson, and Holubec, Cooperation in the Classroom. 1:19.

38

3) Models and M i m i c s

65

activity

(10 mins.): Students are randomly selected to come

to the front and mimic the instructor's demonstration. 4) Instructor mini-lecture and demonstration (10 mins.):

Using one of the two

excerpts on p. 525 of the text, write a reduction of the suspension series. 5) Cooperative task - T u r n to Your Neighbour (14

mins.):

Give students the

remaining excerpt from the text to reduce, working together with their neighbour. After about seven minutes, randomly select a pair to write their reduction on the board.

Rationale

This lesson plan incorporates an informal cooperative learning strategy and an active learning technique into a lecture-demonstration lesson. In doing so, some of the weaknesses associated with lecture-demonstrations are addressed. First, the addition of these activities at various points during the class ensures that students become actively involved, as opposed to remaining passive. Because both of the activities involve students randomly, there is greater motivation for students to remain focused on the material. Second, the instructor's modelling of the two basic skills-writing and reducing a chromaticized 7-6 suspension series-are immediately followed by opportunities for student practise. The Models and Mimic activity requires students to do more than simply copy the procedure from the board. They must process the information and be prepared to present it should they be chosen. By having students mimic the presentation of creating a chromaticized suspension series, the whole class benefits by hearing it more than once, and the instructor receives some indication of students' understanding. If there are some problematic issues, the extra time spent on the procedure through the Models and Mimics activity may allow students who are more hesitant to ask questions to formulate their thoughts and ask for help. The Turn to Your Neighbour cooperative activity is beneficial to both students and instructor. Instead of struggling alone, students must talk over their reductions with each other. This reduces the number of students requiring extra help from the instructor and challenges those students who understand more than their neighbour to find a way to communicate that knowledge. The instructor is free to circulate, monitor students, and gain Jolie Mayer-Smith (Faculty of Education, University of British Columbia), " A Trial Method for Promoting Student Participation in Problem Solving", November 3, 1994. 6

5

39

some insight into their thought processes by observing their work and discussion. The reductions from the text are simple enough that they can only be done one way and so the answers may be checked quickly at the end of the exercise. The whole activity provides a lowrisk situation for students to explore their ability to perform a reduction, before having to do one for a graded assignment.

Pre-Instructional

Group Size:

Two

Assignment to Groups: Materials:

Decisions

Students work with the person sitting next to them.

For each student, one copy of the following handout entitled "Evolution of a

Chromaticized 7-6 Suspension Series" (See page 40). Room Arrangement:

The descending parallel 6/3 series given below should be written on

the chalkboard:

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41

The Lesson Bridge-in and Pretest: "Here's the scenario:

you are writing the final exam for this course

and you come across a question asking you to add upper voices to a descending chromatic bassline. How would you do i t? Take about a minute to experiment with a solution. You may think in C major and work with a chromatic bass that begins on C." After a minute ask for a show of hands to indicate those who may have a solution. Let students share any ideas and then introduce the topic for the lesson.

Instructional Objectives: "Today we

are going to explore the potential for adding

chromaticism to 7-6 suspension series. By doing so, you will discover one way to harmonize a descending chromatic bass line. Additionally, you will learn how to reduce a musical passage containing a chromaticized 7-6 suspension series in preparation for a similar question on your assignment."

Mini-lecture and Demonstration: Before beginning the demonstration, it is important to warn students that any of them may be asked to mimic the process you are about to do. Students should pay careful attention, ask questions when they are uncertain about anything, and request the pacing to be slowed down if they cannot keep up with the explanation. Begin by playing the parallel 6/3 series as it appears on the board. Add a chain of 7-6 suspensions in the highest voice and play the result. Next, add chromaticism to the suspension series, one voice at a time, beginning with the lowest voice and using filled-in note-heads to distinguish the chromatic notes from the diatonic ones. Play the result.

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Announce that it is time for the students to check their

42

understanding of the procedure just demonstrated. Erase the chromatic alterations and return to the point where the diatonic 7-6 suspension series was completed. Explain the 'rules' of the activity: The instructor randomly selects a student to come up to the board and begin to add chromaticism to the suspension series. It is important that the student repeats, as exactly as possible, the explanation and behaviour just modelled during the demonstration. The student may bring any notes up to the board for reference. At anytime, the student may pass the chalk to someone else and that person must continue. The maximum any one student is allowed to mimic is the addition of chromaticism to one voice, at which point the chalk is passed to another student. If, during the mimicking, a student gets stuck, the instructor may assist by asking a leading question in hopes that the student will be able to continue. Do not insist, however, that s/he stay up front struggling. If the entire class is unable to move past a problem area, the instructor may have to return to modelling that portion of the demonstration again. The mimic exercise may be repeated again if the students do not feel completely confident after the first attempt. Mini-lecture and demonstration (part 2): Give the students the prepared handout, outlining the same procedure just demonstrated. Specifically take some time to play and discuss the fifth and sixth systems to show some different rhythmic alignment. Depending on how much time is remaining in the class, demonstrate how to reduce a musical passage containing a chromaticized 7-6 suspension series either by working through Example 3 l-2a (Bach, Crucifixus from Mass in B Minor, B W V 232, mm. 1-5) or beginning to reduce Example 3l-2b (Haydn, Piano Sonata, Hob. XVI/52,1, mm. 10-14). Cooperative task - Turn to Your Neighbour: Instruct students to work together in pairs with their neighbour to do or complete a reduction. They should have one answer between the two of them with which they both agree. One pair will be randomly asked to share the answer on the board. During the task, circulate among the students to check that they are working together and understanding the process of reduction. After the reduction has been written on the board, answer any questions students may have regarding discrepancies between their answers and the one of the selected pair. Close by returning to the opening question of the lesson. Ask students if they now would be able to harmonize a descending chromatic bass line.

43 Comments and Reflections

In almost all respects, this lesson was highly successful. There was no difficulty in completing all planned lesson material and activities in the class period. Students were able to complete the reduction by working together and required minimal guidance from the instructor. The pair of students selected in both classes to write their reduction on the board gave accurate answers. From observing other student work as it was in progress, the lack of questions at the end of class appeared to stem from genuine understanding rather than from fear or apathy. After each of the classes were over, students' responses were positive. Although not originally developed as a cooperative exercise, the Models and Mimics activity could have been adapted and structured as an informal technique in this lesson. After modelling the demonstration, the instructor would have asked students to turn to a neighbour and mimic the procedure. The instructor could have structured the activity further by requiring the students to switch roles between explainer and listener when half the time had elapsed. Following the paired mimicking, the instructor would have continued with the Mimics activity as is. The added benefit to employing this variation would be that all students must mimic part of the demonstration, not just those who are randomly chosen to do so in front of the class. More time would have been required to do the activity cooperatively, however, and so it was not attempted in this lesson. Applied separately, both the Turn to Your Neighbour and cooperative version of Mimics and Models structures have endless potential. They may also be used together as the following applications demonstrate.

When introducing sequences, one might try to teach students by

using the Models and Mimics activity to demonstrate how to write a sequence, and then use the Turn to Your Neighbour structure to check students' abilities at reducing a sequential passage. When introducing secondary dominants, one might model adding a few different types to basic chord progression and then ask students to mimic the procedure to a partner while the instructor monitors the efforts. At the end of the lesson, the Turn to Your Neighbour or ThinkPair-Share structure could be used as students work on analyzing a passage that contains several secondary dominants.

44 3.

USING S E V E N T H CHORDS

IN

SEQUENCES

Introduction

Two cooperative structures are incorporated into this lecture-based lesson. The flexibility of the Think-Pair-Share structure is demonstrated as it is used here to pre-test students at the beginning of the lesson. At the end of the lesson, a new structure, "Numbered Heads Together", is introduced. The structure exists in several forms and this lesson provides a 66

variation on the form "Simultaneous Numbered Heads Together with Blackboard Responses"^ An instructor can use Numbered Heads Together at any point during a lecture to make sure all students have mastered basic facts or essential skills. Lesson Plan #6 explores the structure further, using formal cooperative learning groups.

Text Reference:

Chapter 24: "Remaining Uses of Seventh Chords", "Seventh Chords in

Sequence" section only. Level:

2nd year, 1st term

Instructional Objectives:

Students will be able to: list the three basic types of sequences

that can use seventh chords; list the two types of root motion that can accommodate seventh chords (in or out of sequences); and write at least one descending-fifth sequence incorporating seventh chords, using correct voice-leading. Cooperative Structures: Type:

Think-Pair-Share; Numbered Heads Together

Informal Cooperative Learning Groups

Time Required: 50 minutes

66 Kagan, 10:2-5. 67 Normally when one uses this form of the structure, students in each group are assigned a number from one to four (for groups of four). After the groups have all worked to solve the same problem, or answer the same question, the instructor randomly calls out one of the numbers. A l l the students assigned that number-one from each group-write their groups' response on the board. When used i n this lesson, student groups are each given a slightly different question to answer and a volunteer from each group writes the answer on the board. Instead of assigning students a number, a random selection technique involving students' names is used to determine who will offer some explanation for their group's answer.

45

Summary of Lesson Format 1. Pre-test activity:

Think-Pair-Share (15 mins.): Give students one minute to write

down four main types of sequence and then, two or three minutes to check their answers with the person sitting next to them and their textbook. Write an example of each of the four types of sequences as students share their answers.

Introduce the instructional

objectives. 2. Instructor mini-lecture to whole class (15 mins.):

Show students how seventh

chords may be used in all but the Ascending Fifth type of sequence. 3. Group activity:

Numbered Heads Together (10 mins.):

Students are divided

into six groups, with each group writing a different variation of a Descending Fifth sequence. Groups write their product on the board.

4.

Group reports to whole class and Closure (10 mins.): Play through all six variations written on board and ask one member from each group for brief explanations. Ask students to reread instructional objectives and ensure that they have been met.

Rationale

The material for this lesson is suited to be taught combining lecture and demonstration methods. Since the new information builds on material that the students should already know, the beginning of the lesson entails some review. Few new concepts are presented; students simply learn that seventh chords may be added to sequences.

It is more challenging for

students to learn the principle determining where the sevenths may or may not be used and how to add sevenths to sequences appropriately. The last item requires some demonstration from the instructor. There are a number of problems associated with teaching this topic using only traditional lecture and demonstration methods.

Since the opening material constitutes a review,

presenting the four sequences in a lecture format will not acknowledge any of the students' existing learning and will place students in the role of passive recipients. Students who are comfortable with the material may lose interest. If an instructor chooses to ask students to volunteer information during the review, those who have mastered the material or who are

46 quick responders will be answering and those who have not will still be passive recipients. There is the additional possibility that students will not be motivated to volunteer and the instructor may have to call on students, regardless of their preparedness to answer. Besides listing the four types of sequences, the lesson content contains two more lists: the three types of sequences that can use seventh chords, and the six variations of the descending fifth sequence. If these lists are delivered in a similar way by the instructor, it will be very easy for students to lose interest and go through the motions of copying notes without mentally processing their meaning. Since lecture-demonstrations are often well-rehearsed performances by adept instructors, the complexity of the concepts or skills can be misrepresented to the students. If there is no immediate opportunity for students to practise using the concepts or skills themselves, they may leave the class with a false sense of having grasped the material. Only when they begin to work on an assignment will they realize that they do not understand the material as well as they originally thought. Unfortunately, the first form of feedback on their learning from the instructor will come in the form of a graded assignment. The opening Think-Pair-Share activity helps solve some of these problems by actively engaging the learners. Because the students should all know the four basic types of sequences, they are held responsible to recall them for the Think-Pair-Share activity. The "Think" task stimulates students to turn their attention toward the subject matter and quickly test their recall abilities. Students who respond faster in a discussion setting cannot answer before others have a chance to formulate an answer. Pairing off and comparing answers focuses students' minds further and allows for most gaps in their memories to be filled. The instructor can maintain a degree of dialogue during the opening portion of the lecture by randomly asking students to share answers and relevant information. This can motivate students to remain alert and let the instructor know how well the students remembered the four sequences. The Numbered Heads Together cooperative structure is used at the end of the class time for two main reasons:

to provide an alternate method of presenting another list and to give

students a chance to practise using some of the concepts. Although the variations are new material, most students should be capable of using figured-bass symbols to alter the given chord progression. While the students are occupied with the group task, the instructor can observe their progress, and give personalized assistance and feedback. Higher-ability group members may also serve as tutors to lower-ability members so that all students understand and

47

can explain how they arrived at the answer by the end of the activity. The activity not only provides variety in teaching method, but requires a shift in the type of knowledge students are using. During most of the lecture, students are relying on assimilative knowledge as they take in the examples presented by the instructor and process the information by watching it being demonstrated on the board. When they begin the group task, the students must exercise convergent knowledge as they take the concepts and ideas presented in the lecture and experiment with applying them to a specific situation.

Working in groups requires

accommodative thinking as students receive ideas and feedback from peers and the instructor.

Pre-Instructional Decisions Group Size: The groups for the Numbered Heads Together structure may vary from two to four members, depending upon class size. It is more important to have six groups to present all variations than to have groups of equal size. Assignment to Groups: For the Think-Pair-Share structure, students turn to and work with the person sitting next to them. To randomly form the groups for Numbered Heads Together, ask students to number off from one to six. Students who have the same number form a group. Materials:

For each group, one 3x5" index card with the specific instructions for each

variation. Listed below are the instructions for each group: "Group 1 Change the given chord progression to one with interlocking seventh chords, keeping the same soprano line as the original. See text p. 381 #3 if you need further explanation. Group 2 Change the given chord progression to one alternating 5/3 and 6/5 position chords, keeping the same soprano line as the original. See text p. 383 #6 if you need to see an example. Group 3 Change the given chord progression to one alternating 4/2 and 6/5 position chords, keeping the same soprano as the original. Group 4 Change the given chord progression to one alternating between 4/3 and root position

48 seventh chords, keeping the soprano the same as the original. Group 5 Change the given chord progression to one alternating between 4/2 and 6/3 chords. You will have to change the soprano note of every second chord to eliminate the seventh. Group 6 Change the given chord progression to one alternating between 4/3 and 5/3 chords. You will have to change the soprano note of every second chord to eliminate the seventh." After these instructions, every group's index card should include the following questions: "In what voice(s) are the sevenths? How are they prepared and resolved? Why might a composer use this variation of the Descending Fifths sequence?" Room Preparation: Instructional objectives written on the chalkboard.

The Lesson Bridge-in: "Today we are going to be examining material presented in chapter 24 of your text.

In order to do this, you have to be able to recall some essential pieces of

information." Pre-test activity: "On your own, working from memory, take one minute to list the four main types of sequences." Once a minute has passed, direct students to compare their lists with the person sitting next to them. If they do not have all four or cannot remember how the sequences are constructed, they should look in their textbooks. This paired activity should only be allowed to last for two or three minutes. Ask students to volunteer one type of sequence at a time. As each type is given, write an example of it on the board. Students may be asked to explain how each type is constructed or the instructor may choose to give the explanation without student participation. After writing the sequences on the board, announce to students that it is possible to incorporate seventh chords into sequences. Instructional Objectives: Point to and read the instructional objectives for the class. Mini-lecture: Begin by attempting to add sevenths to the the ascending fifth sequence and play the result for students. Students should recognize that the seventh cannot resolve

49

properly. Introduce the two root motions that will allow the seventh to resolve correctly: root motion by ascending second or descending fifth.

Add seventh chords to each of the

remaining sequences, ending with the Descending Fifth sequence. When it comes time to add sevenths to the Descending Fifth sequence, announce that a well-known T V theme that uses the sequence with seventh chords is going to be played. Play the section of the theme from M * A * S * H containing the sequence and ask if anyone can name the piece. Write the following reduction of the theme on the board, with the figured-bass symbols:

|

l

dm: iv

7

7

I

1

\

Announce that the Descending Fifth sequence can be varied in many ways by changing the inversions of the chords. Students are going to use this chord progression of the M * A * S * H theme as a basis for their group activity and alter it to produce six common variations of the descending fifth sequence. G r o u p Activity: Assign students to groups and insist that group members are sitting kneeto-knee, eye-to-eye. Give the directions for their task: "Each group is going to receive an index card with instructions for creating one of the six variations. You must use the chord progression on the board as a basis for your own variation. In other words, your group's product must be in d minor and should look almost identical to the example on the board. Only make changes to the voices where it is absolutely necessary in order to create the altered position. Work together on this task and make sure that each person understands your answer. I will be randomly calling on one member to discuss your solution. Be sure to discuss the questions on your card." Hand out the cards and monitor the groups to make certain that they are doing the exercise correctly. Since there is only a short amount of time for the activity, be directive if

50 students are having problems. As groups begin to finish, ask each to select a member to write the group's answer on the board. They should include the figured bass symbols. Play each of the variations. The student from each group whose first name is closest to the letter "a" is asked to respond to any questions. Avoid becoming pedantic by spending a lot of time with each variation and asking each group the same question. Questions should be used to highlight one or two aspects of each variation that other groups may not have dealt with in doing their variation. For example, one might ask the student representing Group 1 to give the term for the variation (interlocking seventh chords). Other groups may be asked one or two of the questions from their card. Return to the instructional objectives and check that all students feel that these have been met.

Comments and Reflections

This lesson was taught to three different second-year classes and was their first exposure to cooperative learning techniques being used in music theory. As a result, their responses to the change were mixed and the ease at which they performed the cooperative activities was less than anticipated. In general, the Numbered Heads Together activity presented the greatest challenge for students. While the lesson was completed in fifty minutes in two of the three classes, timing allottments for the various lesson elements were not entirely followed. Most groups had difficulties with starting the Numbered Heads Together activity because they tried to make the task harder than it was by starting to write the variation from nothing, rather than using the given reduction. These groups needed to have the directions explained again with some direct supervision until they were able to continue on their own. A l l three classes required closer to ten minutes for the exercise. Mainly because of their unfamiliarity with cooperative strategies, other logistical details, such as moving into groups and writing answers on the board, took extra time. In order to finish within the given time, there was little questioning of individual students about their variation and minimal closure. The third class had more difficulty with both the lecture material and the group activity, and so the group reporting activity and closure were held the following class period. As expected,

51

the concept of root motion was quite new to most students and needed to be carefully explained with some additional illustrations. Several students in the third class, however, still asked for further explanation. Because it is such an important concept and because they seemed to have trouble understanding it, some extra time had to be spent during the lecture. To further ensure that students were confident with the point, two or three students were then asked to summarize the instructor's explanation in their own words. Although this extended the lecture to twenty minutes or so, both instructor and students could continue knowing that everyone felt confident with the principle. The discrepancies between the planned and actual timing described in this lesson are to be expected, especially when introducing cooperative activities to classes. Learning to work cooperatively is a skill that develops with practise in much the same way that learning to play an instrument does. At first, it will seem strange for students to participate in group activites during a 'lecture' and they will with some degree of awkwardness. Moving into groups will take longer than one may anticipate. Students may not take the time to make certain they are correctly following the directions. If students are not used to sharing answers on the board, they may be reluctant to do so initially, even though the answer represents their group and not just them personally. Over time and with persistence on the part of the instructor, students will begin to accept their increased involvement as normal and begin to develop the necessary skills until cooperative activities become integrated into their routine. In this lesson plan, the use of random assignment to groups for the Numbered Heads Together could have been substituted by simply having students divide into six groups with their neighbours. Since the structure was being used in an informal way and students were not adept at quickly moving into groups, random assignment was unnecessary and some time would have been saved.

52

4.

INTRODUCTION T O SIMPLE T E R N A R Y F O R M

Introduction

This lesson plan introduces a structure called "Concept Induction" as a means of stimulating the students to actively participate and contribute to the lecture.

68

The structure is

different from those previously used because students work in pairs to perform a series of tasks throughout the lesson. Concept Induction requires students to figure out, or induce, rules or principles from examples and offers some contrast to the deductive approach to teaching where the rules are presented first.

Text Reference:

Terminology is from Peter Spencer and Peter M . Temko, A Practical

Approach to the Study of Form in Music (Englewood Cliffs: Prentice-Hall, 1988). Level: 1st year, 2nd term Instructional Objectives: Students will be able to: identify some elements which play an important part in defining a form; and distinguish between three types of formal structures. Cooperative Structure: Concept Induction Type: Informal Cooperative Learning Groups Time Required: 50 minutes

Summary of Lesson Format 1.

Instructor

mini-lecture

to

whole class (12

mins.):

Introduce topic and

instructional objectives. Briefly present a short analysis of one piece in simple binary form and one in rounded binary form. 2.

Question for reflection and discussion (5 mins.): Students are asked to list some musical elements which the instructor used to determine the pieces' forms.

3. Inductive task #1 (10 mins.):

Instructor hands out a third piece telling students only

68 This lesson plan makes some modifications to the original structure as it is described i n Johnson, Johnson, and Smith. Active Learning. 5:23. Usually, the instructor places two or three items i n separate categories for students to examine giving little or no explanation. After the pairs have had a chance to discuss their ideas together, the instructor adds new items to each category and the pairs have an opportunity to refine their ideas. Once the instructor has finished adding examples, pairs must present a definition for each category and create new examples for each, or categorize some more given examples.

53

that it is not the same form as either of the other two pieces. Working in pairs, students have four minutes to use the list of elements from step 2 to determine in what ways this piece is different. Students are then randomly called upon by the instructor to share their observations with the class. 4. Inductive task #2 (10 mins.): Instructor gives students two more pieces to analyze. One is identified as being in rounded binary form and the other is the same form as the third piece with which the students have just been working. Students continue to work in pairs and determine why these two pieces are similar to the other two.

5.

Informal student presentations

(10 mins.):

Instructor randomly chooses students

to present their findings to the class. 6. Closure (3 mins.):

With input from students, the instructor generates a chart that

compares the main differences between rounded binary and simple ternary forms.

Rationale

The inductive approach encourages students to focus on the elements that determine form. Instead of being preoccupied with assigning the correct label to a given piece, students must present a case for why the piece exemplifies a certain form. The importance is placed on analysis and identification of structural elements, not on how quickly one can give the right title. By introducing ternary form in conjunction with a review of binary forms, students are able to practise their existing analytical skills and apply them to a new situation. They already possess the necessary knowledge to discover the differences between rounded binary and simple ternary on their own and the activities in this lesson simply allow this to happen. The lesson i s designed so that students remain alert and actively engaged with the material. At the beginning of the mini-lecture, the instructor tells the students to take note of particular information. The instructor then checks to see that they have, by asking a question at the end. The inductive tasks require students to practise using this information to come to some conclusions about ternary form. Working in pairs provides some variety and forces students to verbalize and possibly defend their analyses to each other. After discussing the answers with a partner, students will be more confident to share their conclusions with the class. Any errors

54

can be corrected by the instructor at this time. The five compositions, which are the basis for the students' conclusions about form, have been carefully selected. A l l five are very short and for the most part, quite sparsely textured. There is a sample of both a major and minor piece in rounded binary and ternary form. Examples of ternary form have the restatement of A section written out. To emphasize that formal contrast does not have to be achieved through melodic means, the last two examples-one each of rounded binary and ternary-have B sections that use transposed melodic material from their A sections.

Pre-Instructional Decisions Group Size: T w o Assignment to Groups: Students choose to work with a person sitting on either side of them. Materials:

Non-permanent pens for the overhead, overhead transparencies of the

instructional objectives, the five pieces and two additional transparencies prepared as overlays with all the analytical information pertaining to the two pieces presented in the opening mini-lecture. One set of cards with the names of all the students in the class can be used to randomly select students to present material. For each student, one copy of each of the five pieces. The pieces should be copied onto coloured paper so pieces that are the same form are on the same colour of paper. The five pieces selected for this lesson are: J. S. Bach, Sarabande from Suite in B - Simple Binary b

J. Kuhnau, Menuett in a - Rounded Binary L. Mozart, Menuet in D from the Notebook for Nannerl - Rounded Binary L. Beethoven, Bagatelle Op. 119, No. 9 - Simple Ternary R. Schumann, Trallerliedchen Op. 68, No. 3 - Simple Ternary Room Preparation: Overhead projector in place and copies of the Bach Sarabande and Kuhnau Menuett on students' tables.

55 The Lesson

Bridge-in:

"Today we are going to be examining five short pieces and analyzing their formal

structure. You will be spending quite a bit of the class working together in pairs." Instructional Objectives:

Place the instructional objectives on the overhead and allow

students to read them. Mini-lecture:

"I am going to quickly provide you with an analysis of the two pieces you

have in front of you. They are both forms which you have already studied in previous classes and so this should be a review. Make note of the reasons I give for labelling each piece as either simple binary or rounded binary form." Place the transparency of the Bach Sarabande on the projector and play it for the students. Add the analytical overlay on top of the score and highlight key points such as phrasing, cadences and tonal areas. Conclude the discussion of the Sarabande by summarizing the main reasons for it being in simple binary form: the piece is in two sections; the first section is open and modulates to V; the second section is longer, tonally less stable, and moves back to I; and the melodic material of section A is not literally restated in section B. Place the transparency of the Kuhnau Menuett on the projector and play it for the students. Challenge them to try to identify the cadence points and tonal areas as they listen. Add the analytical overlay on top of the score. Briefly talk through the phrasing and cadences. Mention the contrast between the melodic material of section A and B. Close by summarizing why this Menuett is an example of rounded binary form: the piece is in two sections; the first section, comprised of a symmetrical parallel period, ends on a half cadence; the second section, beginning in the relative major, includes a return of the material from the first section; this reprise alters the opening material to end on a perfect authentic cadence. Question for reflection and discussion:

"Reflect back on these two pieces. What

musical elements did I consider as I analyzed the form?" Give the students thirty or forty seconds to quietly recall as many as possible. Then, ask students to volunteer their answers as you write them on the board. The following elements are likely to be given: cadences, phrasing, periodic structure, tonal areas or goals, motivic and melodic material,

56

repetition or restatements of material, texture, etc. Inductive task #1: Place overhead transparency of the Beethoven Bagatelle on the projector and hand out copies of the score to students. "This piece is neither simple binary nor rounded binary form. I am going to give you four minutes to work as pairs with your neighbour to analyze the Bagatelle and determine how it differs from the other two. When the time is up, I will be randomly calling on you to share your observations. Remember to pay special attention to the musical elements we just listed on the board." Play it for the students. Shuffle the name cards and call on students whose card is pulled from the pile to answer questions. Do not ask one student to give the entire explanation. Ask students to identify what is different about the piece and try to discourage students from tediously listing off all the phrase endings, cadences, etc. As these analytical points are mentioned in the students' explanations, mark them on the transparency with an overhead pen. The important differences that should be identified are: the A section is closed; the B section is contrasting; and the A section is repeated identically at the end. If this is easily recognized by the students and there is some remaining time, one may wish to ask students to share their thoughts about such items as where the G# in measure 4 resolves, the type of cadence which occurs at measure 4 (and 5?), and what 'key' the contrasting B material is in. Students may also have trouble identifying the Neapolitan harmony in measure 3. It is most likely that at least one student in the class will introduce the term 'ternary' by this point in the lesson. If not, the term can be introduced here or after the next task. Inductive task #2:

Hand out the final two pieces to students and play both of them. Direct

students' attention to colour of paper onto which each piece has been copied and explain that the Mozart Menuet is the same form as the Kuhnau and the Schumann Trallerliedchen is the same as the Beethoven. Announce that students are to continue working in pairs for ten minutes and analyze both pieces. They should be prepared to explain why each matches the appropriate piece studied earlier. Informal student presentations: Using the name cards, randomly select a student to come to the front of the class and explain why the Mozart Menuet is considered rounded binary form. The student may use the overhead pen to highlight important points on the transparency. While some analytical details can be noted, the most important point the

57

student should make is that the A section is tonally open and that when it returns to close the B section, the second phrase has been transposed so that it ends in the tonic key. Students should also be able to recognize that although Mozart uses the same material in the B section, contrast is achieved through transposition. In the same manner, call upon another student to discuss the Schumann example. Here, the student needs to explain that it is the same form as the Beethoven because the A section is closed and returns virtually unchanged after a contrasting B section. Due to time constraints, students may need the instructor to point out the minor differences between the two A sections and introduce the possibility of varied repetition occurring in ternary form. From comparing the two examples of ternary form, students should be able to accept that the B section may not present new musical material, but that the concept of contrast may be displayed in other ways. Closure: As a brief summary of the main points of the lesson, quickly draw a chart on the board or an overhead transparency and ask for students to participate as you fill it in. Since it is assumed that students already are familiar with both types of binary forms, you may only choose to compare rounded binary and simple ternary. Sample Chart:

SECTIONS PRINCIPLE A SECTION

ROUNDED BINARY

SIMPLE T E R N A R Y

2

3

statement+contrast+ tonic restatement open: modulating or

statement+contrast+restatement closed: tonally independent

half cadence

Comments and Reflections

The quality of students' responses to the questions and two inductive tasks was excellent. Throughout the lesson, students were attentive and participated appropriately. The technique used to acquire student responses to Step 2's "Question for reflection and discussion" worked well. Students used the reflective time to look over the analyses and willingly volunteered all the relevant elements without the instructor having to add any. Even a quiet student who had

58 been observed declining to speak in other classes contributed an item. A l l students who were randomly chosen to give explanations based on their work in pairs were prepared to articulate their thoughts clearly and required little help or prompting from the instructor. There did not appear to be any difficulty in students meeting the instructional objectives. The only aspect of the lesson which unexpectedly took longer than planned was the minilecture. Approximately twenty-five minutes were spent on the material and as a result, the student presentations and closure activity had to be held the following class. There are two reasons why the timing was so drastically underestimated. Firstly, students copied down the information, and the pace needed to slow down to accommodate them. Secondly, partly because the material was intended as a review, and partly out of concern that students might be copying the analysis without thinking about it, this instructor could not resist from spontaneously asking for some student participation throughout the analyses. In retrospect, much of the analysis could have been included on the students' copies so that they could concentrate on the material and follow a quicker rate of presentation. The lesson plan was only taught to one section of first-year students and so there was no opportunity to try this alternative. While the structure was altered in this lesson to accommodate an instructor-led review of Simple and Rounded Binary forms, the original structure could be applied to several other topics in tonal harmony. A n instructor could use Concept Induction when first introducing Simple Binary and Rounded Binary forms. When teaching students to distinguish between different types of periodic structures, one could select examples to show concepts of parallel versus contrasting, or symmetrical versus assymmetrical. One might also try using the structure to introduce the four basic types of sequences.

59 5.

R E V I E W SESSION

Introduction "Think-Pair-Square", a variant of the Think-Pair-Share structure, is applied in this lesson.

69

A n instructor may choose this variation when less direct control over students'

comments and thinking is desired. Students have more opportunity to interact with peers than in the Think-Pair-Share version. Although the structure is a type of informal cooperative learning, the tasks for each of the steps are lengthier in this lesson than those normally given, and so the activity is extended to fill a large amount of the class period. In a briefer version, the structure may only require eight to ten minutes.

Text Reference:

Chapters 1: "Key, Scales, and Modes," 2: "Intervals," and 4: "Triads"

section only Level:

1st year, 1st term

Instructional Objectives: Students will be able to: explain concepts they understand to each other; locate written explanations about topics which they need to review; and give a correct answer to a question for which they previously had no answer. Cooperative Structure: Think-Pair-Square Type: "Extended" Informal Cooperative Learning Groups Time Required:

50 minutes

Summary of Lesson Format

1. Instructor explanation to whole class (7 mins.): Catch students'attention, give instructional objective, explain structure and overall guidelines for the class. Hand out an index card and "Topics" sheet to each student. 2. "Think" task (3 mins.): Students work individually to identify topics they do and do not understand. 3. "Pair" task (6 mins.): Students pair up with one another, try to help each other by 6

9

Kagan, 11:3.

60

offering an explanation for the topic which their partner does not understand, and agree on or create one item to carry to the next task. 4. "Square" task (12-15 mins.): Each pair shares its item with another pair, discusses issues, and agrees on or creates one further item to contribute to class discussion. 5. Whole-class Discussion (15 mins.):

Each of the "squares" contributes one item to

be discussed by instructor and other class members.

Rationale

A review session before an exam can raise questions for an instructor who wants it to be a valuable experience for as many students in the class as possible. How does one choose which topics should be discussed and which left out? If one is reteaching material that students' assignments showed to be misunderstood, how does one really know that they will be able to understand it correctly in time for the exam? What if a small percentage of the class needs a basic concept retaught? Is there any way to prevent high-ability students from being bored by hearing material repeated they have already mastered? A teacher-centred review may not provide answers to these questions which are favourable to all the students. This lesson format for exam review was chosen specifically to deal with the extreme levels of student knowledge which are exhibited in the beginning of first-year theory. Entering students may range from having a limited knowledge of rudimentary theory to having some mastery of basic chromatic harmony. Often, students with such disparate backgrounds are placed together in the same class, and are required to take the same harmony curriculum, beginning with rudimentary topics. The main advantage the Think-Pair-Square structure offers to this particular application is that it ensures that problems relevant to the students themselves get addressed.

It is the

students, not the instructor, who are responsible to generate the review material. Additionally, students who might be too shy or afraid to ask for clarification in front of the entire class are given an opportunity to do so in a smaller and therefore presumably less threatening group. In fact, the "Think" task requires all students to find at least one item with which they are not completely comfortable. The risk of appearing 'dumb' in front of a peer is reduced because students know that the person or persons with whom they will form groups during the "Pair"

61

and "Square" tasks will also be taking a similar risk in sharing their own item(s). Once students have shared their questions with each other, the emphasis is placed on partners or group members working together to find answers, rather than testing their ability to provide answers based on their own knowledge.

Because of the disparity in students' knowledge,

many questions on simpler issues can be answered sufficiently by more experienced peers, and eliminated before reaching the whole-class discussion time. Since oral rehearsal reinforces and solidifies one's knowledge, the peer coaching not only helps the questioner, but the respondent as well. A question that cannot be answered by four group members will probably interest other class members when it is addressed by the instructor. Finally, such a session, can provide valuable feedback on the instructor's teaching effectiveness.

Pre-Instructional

Decisions

Group Size: Two for "pair" tasks and four for "square" tasks. Groups in classes with an odd number of students, or with a population that is not a multiple of four, will require adjustments. For example, a group of three may perform the pair task, and groups of three or five may perform the square task. Assignment to Groups: Students are seated in a circle. To form pairs, ask each student to establish eye-contact with the person sitting directly opposite them and to move their chairs to a location together for the task. For the move from pairs to groups of four, the instructor should direct which pairs move together, mainly on the basis of physical proximity. By observing students' discussions and their topics of conversation, one may also choose to join together pairs which could answer each other's questions, although it may not be possible to find suitable matches for all. Materials:

For each student, one 3x5" index card and one handout. Students need to have

their textbooks and class notes with them. The handout contains the following information: Topics for Theory 100 Class Test #1: Sept. 30 •Sound

four characteristics: pitch, loudness, timbre, duration overtone series sympathetic vibrations sound production: source, transmitter (medium), receiver

62 Doppler effect •Registers

nomenclature (text p. 7)

•Scales

major, minor (natural, harmonic, melodic) parallel versus relative minor or major traditional scale degree names (text p. 6) authentic and plagal modes 1-8 patterns of tones and semitones in various modes

•Key Signatures

musica ficta transposition of the modes

•Clefs

treble, alto, tenor, bass

•Intervals

simple and compound quality: major, minor, perfect, augmented, diminished consonant versus dissonant, perfect versus imperfect, tritone inversion of simple intervals diatonic versus chromatic semitones

•Enharmonic Equivalence •Triads

quality: major, minor, diminished, augmented inversions of triads: root position, first and second inversions figured bass symbols soprano position: root, third, fifth structure: open, closed Roman numerals to indicate the root and quality of triads in a key

Room Preparation: Chairs should be placed in a circle. The instructions for all three tasks are written on the chalkboard and covered by a screen, or are on an overhead transparency. (Tasks are included in the lesson section).

The Lesson Bridge-in: The following sample illustrates one method an instructor might use to ease some tension about the exam and create an environment where students recognize the onus is on

63 them to use the time wisely: "You are going to be taking your first test in this course next class. Let's have a show of hands... how many of you have finished studying and are confident about your understanding of 100 percent of the material? (This is asked with exaggerated enthusiasm and when no hands are raised, display mock surprise.) Is it then safe for me to assume that there are still some items you are not clear about or just need to review? (Check for general nods of agreement.) This is going to be a review class, but instead of me choosing what the class reviews, you are going to generate and work with the topics that you feel the most uncertain about." Instructional Objectives: State the objectives informally to the class. Explain general structure and record key words and time limits on the board: "You will be working individually for three minutes, working with a partner for six minutes sharing what you do and do not understand, then working with another pair for about twelve minutes. A t the end of this time, each group of four will present the class with one question about the subject material that they would like to hear discussed and answered." Give guidelines for behaviour: "1. Tasks are strictly timed so discussions must stay focused. 2. Do not talk while I give instructions for each task, otherwise time will be wasted by my having to repeat directions. 3.

I should be able to ask any group member to paraphrase what his/her group is

discussing at anytime. It is your responsibility to ensure you understand what your group members are saying. 4.

Make sure that you use this class as an opportunity to practise verbalizing your

knowledge about the material. Even answering someone else's question that you consider simple, helps you to gain a better understanding of it and retain the information." Hand out index cards and "Topics" sheet. " T h i n k " task: Uncover the following written instructions on the board: "Scan the topics on the handout and then complete the following sentences on your index card: 1. One topic I do not understand and need explained is... 2. One topic I do understand and can explain well is..." " P a i r " task: Direct students to form pairs. Uncover the next set of instructions on the board:

64 "1. Compare your sentences with those of your partner. 2. Try to offer an explanation for the topic your partner does not understand. If you or your partner are still uncertain about anything, try to locate more information in your class notes or text. 3. Agree on one topic or question that you both would like clarified further. 4. If time remains, practise explaining to each other the topics that you understand well." "Square" task: Direct students to move into groups of four. Uncover the final set of instructions: "1. As a pair, present your selected topic or question to the other pair. 2. Each pair should attempt to offer an explanation to the other and share any notes or information which could further their understanding. 3. As a foursome, create a question which you still have about the material to present to the class. Select a group member to write that question on the chalkboard. 4. If time remains, take turns quizzing each other on any of the material to be tested." Whole-class discussion:

Read the questions one at a time, soliciting members from

groups other than the contributing group to answer them. Add any further clarifications to the explanations and correct any misunderstandings. If no one has the answer, provide it for the class. After every question is answered, check back with the contributors to ensure that they are satisfied.

Analysis for Basic Elements Positive Interdependence: 1) Goal Interdependence - The goal of both group tasks is for all members to be able to offer explanations on the topics and questions brought up for discussion. 2) Outside Enemy Interdependence - Students are working to help each other succeed on the upcoming exam. Although students should not be taught to fear an exam, they are drawn together by it in that they see it as a common hurdle to overcome. 3) Task Interdependence - Because of the strict sequential nature of the directions, the students must rely on each other to complete the tasks.

65

Individual Accountability: This is structured in four ways. The instructor moves around and observes each group at work. A t any time, the instructor may ask any student to paraphrase the group's discussion. Students are checking and discussing each other's explanations to questions. In the following class, students will all take an individual exam on the material.

Interpersonal and Small Group Skills: The two skills being highlighted in this lesson are: stopping discussion for instructions between group activities and paraphrasing. While the first is a basic skill, it is useful to establish it as a standard procedure when initiating cooperative learning strategies in the classroom.

Paraphrasing is introduced mainly by asking students to paraphrase their

discussions to the instructor. However, while monitoring the group work, the instructor should also ask students within groups to paraphrase each other.

Comments and Reflections As this lesson was the first cooperative one the first-year classes received, it was impossible to predict whether or not the students would be resistant to working in groups. Several strategies were included to prevent as much off-task behaviour as possible. Asking students to form pairs with people sitting across from them in the circle increased the likelihood that students would not be working with a friend. The handout helped to focus students' attention, as did the written instructions for each task. Time limits were enforced strictly, with students being given notice shortly before each task was about to end. The instructor circulated among the groups, observing their discussions. During the classes, the students worked diligently at the tasks and were not hesitant to share their knowledge and experience with each other. Often, when students working together discovered that they were all unclear or in disagreement, they requested the instructor to give them the answer, or to identify whose answer was right. While it would have been simpler to comply, much of the value of the format would have been lost if students were given quick, oral solutions from the instructor for their dilemmas. Instead, students requesting help were reminded to follow the task instructions by checking their textbooks for more explanation and comparing their class notes and assignments.

They were also directed to test each other's

66

explanations by doing a sample question where possible, and to elaborate on their explanations to their group members. When a group seemed to have exhausted their resources in dealing with a problem, they were encouraged to save the question for the whole-class discussion and move onto another topic. Once students were prompted to explore these other methods to find answers, they were able to help themselves successfully in many instances. While no formal method was used to poll students' opinions of the class, several voiced their reactions after class. Some students claimed to find the review format useful because they were able to focus on issues that were problematic for them, and because they were able to receive some personal attention and guidance from the instructor while working together. Others were not comfortable with the amount of responsibility they were given to find explanations and assess each other's answers. It did not appear that there was a correlation between the student's ability level and their appreciation for the class. Most students who had complaints did not think that the group activities should be abandoned completely, but that they be used in addition to a more traditional instructor-led review class. Looking back at some of the various theories about college-age students and learning style preferences may provide some explanations for students' reactions to this lesson plan. According to Perry's developmental scheme, students who are in the beginning stages of dualism may find that this review format conflicts with their view of how an instructor should be helping them learn. If the primary teaching methods have been those which promote student dependence upon the instructor for the information and allow students to passively absorb what is presented to them, then the students' expectations will only be reinforced, not challenged. To a certain extent, students' learning style preferences will influence their responses to this lesson format. Those who enjoy learning through discussions and interaction will be more likely to enjoy the group tasks. This lesson plan could be changed slightly to allow more whole-class discussion. If students were given the handout one or two classes in advance, informed about how the review class was to proceed, and assigned the "think" task as a preparatory assignment, the discussion time at the end of class could be extended for seven to ten minutes. Time can also be saved by randomly assigning students to a partner as they enter the class, and by reviewing the procedure only briefly before students begin. This variation may be even necessary with classes of more than twenty-four students where the number of questions to discuss is

67

significantly higher. If students tend to be chronically unprepared for classes, one may insist that students present their written sentences before entering the room. While this may sound extreme, it should ensure that all students are ready to begin the "pair" task immediately. The nature of this structure carries with it two dangers when applied to a review format. Because there is a lot of peer tutoring occuring, it is possible that a student may give another an incorrect explanation. The instructor can attempt to minimize this by monitoring the group discussions, but ultimately, the responsibility rests with the students to check the validity of each other's answers. Another danger is that students may have questions beyond the scope of the exam or may be concerned about details which are irrelevant. Presumably, an instructor does not want students to use a review class as an opportunity to play a guessing game about exam content. One of the ways to prevent students from missing the important subject content is to differentiate between the essential and non-essential points in a lesson.

70

Consistent use

of instructional objectives and clear outlines of exam content are two effective methods of communication.

Michael R. Rogers, Teaching Approaches in Music Theory: A n Overview of Pedagogical Philosophies (Carbondale: Southern Illinois University Press, 1984): 153. 7

0

68 6.

A N A L Y S I S OF E X C E R P T S FOR USES OF S E V E N T H C H O R D S

Introduction

This lesson plan is the first one using formal cooperative learning groups. The entire lesson is built around the Numbered Heads Together structure and uses it as a means of posttesting students' learning from a prior lecture. When the same structure was applied in lesson plan #3, the task involved writing a chord progression. Here, the structure is applied to analysis. Students share their answers more formally through presentations at the front of the class.

Text Reference: Chapter 24: "Remaining Uses of Seventh Chords" Level: 2nd year, 1st term Instructional Objective:

Students will be able to identify how seventh chords are being

used by analyzing given excerpts. Cooperative Structure: Numbered Heads Together Type: Formal Cooperative Learning Groups Time Required: 50 minutes

Summary of Lesson Format

1. Instructor explanation to whole class (10 mins.): Present a summary of types of seventh chord uses from Chapter 24. Introduce the group activity to students and discuss some of the rationale behind working in groups to learn. Divide the class into groups and explain the task. 2. Small group task - Numbered Heads Together (10 mins.): Students work in groups of three to analyze and determine how the seventh chord or chords are being used in an assigned excerpt. 3. Presentation of excerpts to whole class (25 mins.): One student from each group is randomly selected to present the group's analysis of its excerpt to the class. 4. Group Processing activity (5 mins.)

69 Rationale

Analysis of musical excerpts is a very important part of teaching theory. It is in these passages that one sees the transformation of abstract techniques into meaningful musical expression. Instructors may frequently call attention to an isolated excerpt or two during their lectures to illuminate an abstract concept. When doing so, an instructor may wonder whether students will benefit more from being asked about or told the salient features of the passage. While every situation calls for a different answer, the issue of dealing effectively with excerpts is compounded when an instructor intends to spend the majority of a class period on analysis. If the instructor presents the analyses as a monologue, even the most motivated students will be challenged to maintain high levels of attention simply because of the passive role to which they have been assigned. In an effort to involve the students more, an instructor may choose to conduct the analysis using a class discussion format. While this may keep students more alert because of the possibility of being asked a question or the opportunity to contribute, the nature of the sequential contributions relegates most students to being passive observers most of the time. The Numbered Heads Together structure is one possible solution for the problems just mentioned. This type of analysis class is designed to follow classes where students are equipped with the terminology and definitions necessary for them to recognize the devices on their own. In essence, this analysis class serves as a post-test for previous lectures. Students should be told to treat the activity as a test to see whether they can work together to apply their knowledge with minimal guidance from the instructor. The structure offers a chance for students to become actively involved with one excerpt and challenges them by placing responsibility for sharing their findings with the class. Having a variety of presenters for the excerpts creates continual change which may add interest to and maintain students' attention for the twenty-five minutes allotted to presentations. By using a public presentation of the results, misinformation and mistakes are exposed and can be corrected quickly. Students have the opportunity to not only learn from the insight of their peers, but from the mistakes as well. The comments and brief discussion about working together in groups are vital in establishing a positive classroom environment where students take the group activities seriously. A discussion such as the one modelled in this lesson plan offers a lead-in for

70 instructors to begin teaching various interpersonal and small group skills to their students. Over the length of a term, an instructor may focus on several skills in which students are weak and spend time addressing them. Two very common problems that occur in groups are members either withdrawing from or dominating the others. While cooperative strategies such as individual accountability and positive interdependence are meant to minimize these problems, they cannot eliminate them entirely. Many students may be reluctanct to accept group work in the classroom from past experiences with domination or withdrawal. Hence, these are two behaviours which should be addressed early in a class' initiation into cooperative learning. Students must realize that each of them plays a key part in determining the success of their group and that they must encourage positive interactions from others.

Pre-Instructional Decisions Group Size: Three is preferrable. Assignment to Groups:

Students are randomly assigned to groups by the instructor.

Three name-cards are drawn at a time and those students then form one group. Materials: Name cards of every student in the class, enough candy for all students, 3x5" index cards with questions pertaining to each excerpt, blank index cards for Group Processing activity, one copy of the Verdi excerpts for each student, overhead projector, non-permanent overhead pens, and overhead transparencies of all the musical excerpts being studied and the following list of seventh chord uses: Chapter 24 Topics •Sequences

pp. 381 385

•Transferred resolutions

pp. 385 387

•Delayed resolutions

p. 387

•Extended sevenths

p. 388

•Subtonic sevenths

pp. 388 389

•Apparent sevenths -triads with added sixth

p. 390

-4/2 and