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A COMBINED MATHEMATICS LABORATORY AND CLASSROOM ENVIRONMENT MARC GOULET, MICHAEL PENKAVA, AND ALEX SMITH

3. Project Summary The Department of Mathematics at the University of Wisconsin-Eau Claire seeks to equip a new classroom with laptop computers connected to a university wide server. Students currently have difficulty integrating experiences in classroom and computer laboratory environments. Our laboratory classroom addresses this problem by blending these environments. The laptop computers address software and networking needs but have a low profile, which helps to maintain a more balanced classroom atmosphere. The objectives of the project are to use the laboratory classroom to implement curricular changes in the department’s major and minor programs, in specific courses which are taken by pre-service teachers of mathematics at UWEC and in a newly developed Interdisciplinary Computational Science Program. The principal investigators will achieve the objectives of the project by continuing to adapt the Calculus, Concepts, Computers and Cooperative Learning project. The main DUE themes emphasized in this project are integration of technology in education and teacher preparation. A major outcome of the project is to create an environment conducive to the blending of technology into the teaching and learning of mathematics. Another outcome is that pre-service teachers will obtain greater exposure to technology in a setting that exemplifies ways that software and collaboration can be used to teach mathematics.

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4. Project Description a. Goals and Objectives. The Department of Mathematics at the University of WisconsinEau Claire seeks to equip a laboratory classroom consisting of collaborative work spaces with fully networked and secure laptop computers. An equipped room will provide an environment where the use of the computer can be more naturally woven with other classroom practices such as the use of collaborative groups, discussions and lectures. The Department is committed to using this laboratory classroom to implement curricular changes in: • Our major and minor departmental programs; • Specific courses which are taken by pre-service teachers of mathematics at UWEC; • A newly developed Interdisciplinary Computational Science Program at UWEC. In 1995, the principal investigators attended a two-week workshop at Purdue University on the Calculus, Concepts, Computers, and Cooperative Learning Calculus project (C 4 L) begun by Ed Dubinsky [6], currently at Georgia State University. They then began adapting this project to UWEC. At that time, some sections of our four-credit calculus courses continued to be taught by four hours of lecture, while others began meeting two hours per week in a computer laboratory and for two hours in a more traditional classroom environment. Various assessments of this approach at UWEC [3, 4, 9] indicated that • students in the lab sections performed as well as students in traditional sections in exit interviews conducted by members of the science faculty. • in general students had a very positive attitude about cooperative learning. • students perceived that they were not learning calculus as well as students in traditional sections. • students had trouble seeing connections between laboratory work and the mathematical concepts of the course. As a consequence of these assessments and a desire for a common experience for our students, we recently (1999-0) began teaching all sections of our four-credit calculus courses by lecturing for three hours per week and meeting two hours per week in a computer laboratory.

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We have begun a preliminary assessment of this new approach, and find that students are performing very well on traditional exams and still appreciate the cooperative learning component. First semester calculus students still report that they have trouble seeing connections between their laboratory and classroom experiences while second semester calculus students are more likely to report that the laboratory activities helped them to understand mathematical concepts. A major aim of this project is to investigate the effect on student learning and attitudes of integrating our current classroom and laboratory components, beginning with the calculus courses. Another goal is to develop strategies to incorporate laboratory components into some upper division classes. We have both curricular and instrumentation goals in mind. The primary instrumentation goal of this project is to equip a dedicated laboratory classroom for the Department of Mathematics with 21 networked and secure laptop computers. The computers will be connected to existing university file servers, so that outside of class time students will be able to access the files which they create in the laboratory classroom from twenty existing general access computer laboratories located around campus, networked dormitory rooms and faculty offices. The funding of the project would result in the equipping of a classroom which has recently been wired for networking, and also, in consultation with an architect, has been designed and furnished in such a way as to encourage collaborative work among students. An important objective of the laboratory classroom is to provide an environment where technology can be more seamlessly woven into our classroom instruction. Currently UWEC supports a wealth of software which is available to students in the general access laboratories, such as Maple, Geometer’s Sketchpad, SPSS, internet access and TEX. Making this software available in our laboratory classroom as well as giving students access to their archived work requires that we use networked computers. Laptop computers fit well with our architectural limitations and our primary instrumentation goal to create a technologically flexible, versatile and collaborative classroom environment. 2

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The primary curricular goal of the project is to strengthen our mathematics program by focusing the use of the equipped laboratory classroom on core calculus courses as well as selected upper division courses. Our main strategy is to continue the refinement of our adaptation of the C4 L project to the UWEC environment. Some evidence of the effectiveness of the laboratory classroom environment that we are proposing can be seen in the results of an NSF-ILI funded project undertaken by Grinnell College in 1994 [22]. The project sought to “weave variable length mini-labs into the fabric of lectures and discussions in a blended laboratory/classroom, instead of fixed length labs in a separate laboratory room.” In a final report to the NSF, they write that this effort “increased the impact both of the lecture and the lab experience.” They also reported that the format “enabled students to integrate experiential and discursive learning” and that conducting the entire session in one room was quite effective. Our equipment request is similar to that of another NSF-ILI funded project [5], undertaken by the University of Southern Mississippi. In this project, a traditional classroom was converted to a computer laboratory classroom by equipping it with laptop computers. The final NSF report stated that “the Computer Classroom Lab has greatly aided many of our courses which have computer activities associated with them” and that “the ease of combining lectures and instruction with lab work in the same classroom is a primary benefit of this lab.” The Southern Mississippi faculty went on to state, specifically related to their use of laptop computers, that “the room is able to function in three different ways and is providing the department with the instructional and computer power it needs.” Prosser and Trigwell in [18] observe “that the adoption of a conceptual change and student focused approach to teaching is associated with perceptions that the teacher has control over what is taught and how it is taught.” Integrating the laboratory and classroom experiences gives the instructor better control of the learning environment, and this could help us to achieve the goal of helping students to see the connections between laboratory experiences and mathematical concepts. 3

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By using the laboratory classroom, we expect to enable students to easily move between • listening to a lecture; • engaging in class discussion; • working collaboratively; • using available software to investigate concepts or solve problems; • accessing their archived work.

b. Detailed Project Plan. The experiences of the principal investigators in adapting the C4 L project in the calculus sequence at UWEC provide much of the impetus for this project. In this adaptation we have developed a wealth of Maple-based materials which engage students in active, collaborative learning. We now implement this approach in our four credit calculus classes by holding lectures and discussions in a classroom three days a week, and by engaging the students in active learning experiences one day a week for two hours in a general access computer laboratory. An active learning component emphasizing collaboration, technical writing and the use of technology also occurs in some of our upper division courses as well as in our new math course for the interdisciplinary computational science minor. More than fifty percent of our majors and minors are pre-service teachers, so this project will have a direct impact on their content preparation, particularly in calculus, geometry, linear algebra, probability, and our new course on technology in mathematics education. What we have in place: As a result of our efforts in adapting the C4 L project to the UWEC environment we have assembled the following resources. • a 430 × 230 classroom and, through institutional support, we have equipped it with a teaching computer and station, a video display projector, white boards, and tables for 42 students. There are seven round tables in all, each seating six students providing for a collaborative environment. The room has also been wired in preparation for networking 21 computers, through the support of the university’s office of Information and Technology Management. The PI’s have been involved in all aspects of the design process for this room, including consultations with the architects. 4

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• twenty networked general access laboratories, as well as networked dormitory rooms and faculty offices, from which students can access their archived files, and use university software, such as Maple, to work on their computer related assignments outside of class time. • over 200 Maple based calculus laboratory activities, written while adapting the C 4 L project. In these laboratory activities we ask our students to write technical explanations. The university also maintains a site license for the Maple software. Additional materials emphasizing active learning, technology and writing have been developed by the PI’s for differential equations (Maple), geometry (Geometer’s Sketchpad), number theory (Excel, Maple), differential geometry (Maple), and probability and statistics (Excel, Maple, Minitab). • a scheduling format for teaching our four credit calculus courses which consists of three hours of lecture and two hours of laboratory. This format is for all calculus sections, and therefore provides a common technology background for the students as they progress through the program. • recent assessments providing a baseline for student attitudes and content knowledge. What we need: This grant seeks funds from the NSF to (i) equip a laboratory classroom with networked laptop computers, to (ii) obtain expert advice through consultation with the external evaluators on assessment of student learning gains and attitudes, and (iii) release time for the principal investigators to carry out the project. Plan: Our assessments [3, 4, 9] and observations of these courses as well as student feedback indicate that our adaptation of the C4 L project has been generally successful. Our current resources require that the majority of active learning experiences which might benefit from the use of a computer take place in a general access computer laboratory. With this project, we would like to address the principal shortcoming of this approach as evidenced by our assessments, namely that the laboratory experiences can seem unnatural and disconnected from classroom lectures and discussions. Currently, our calculus students work in small groups in a general access laboratory on activities written by us. Most beginning students when placed in an environment where the computer is dominant, will focus too much of their attention on the computer rather than on other aspects of the problem such as developing a conceptual understanding. The instructor can play an important role in focusing the students’ attention on these other aspects. But 5

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a general access laboratory is not the right environment for doing this. The environment of a general access laboratory is such that discussion and lecture is inhibited by the difficulty in making eye contact, the lack of adequate sight lines to common blackboard space and by the dominating presence of the desktop computers and monitors. General access labs are not designed with any particular pedagogical motives in mind−they are good quality networked labs where students can read their email or work individually outside of class on their academic assignments. What we would like to do is create a laboratory classroom where the instructor may move easily among the students, lines of sight are unobstructed, and different modes of instruction can be used. Frustration felt by students, particularly by women [9], related to the difficulty in connecting laboratory experiences to the conceptual classroom discussions, often manifested by the proverbial complaint that all their difficulties are merely due to technicalities of computer syntax, is partly due to the unnatural division between classroom discussion/lecture and computer activities. As professional mathematicians and educators we see an interconnection between the classroom and laboratory experiences. A laboratory classroom would help the students understand this inter-relationship better. Another primary objective of our project is to implement in courses beyond the calculus the technical writing component of our calculus reform course. The writing is done by students in their weekly, Maple-based laboratory assignments. The development of a student’s ability to write technical mathematics requires that the student’s drafts go through a cycle of revisions [16, 10]. The laboratory classroom environment would give faculty and students timely opportunity to access previous drafts for revision. Students need to further continue the development, begun in their calculus courses, of their ability to articulate and verbalize. Our students need to make a transition from viewing mathematics as a “plug into the right formula” activity to one where mathematics is seen as a science, so that they can think critically and abstractly about the mathematical objects they manipulate. Such thinking requires advanced verbal skills. We think that this transition does not take place in one 6

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course or in one semester, but typically requires all four years of the student’s undergraduate experience. In order to catalyze this transition, we want to require all of our majors to (a) write coherently using basic mathematical terms, (b) be able to phrase their ideas clearly enough so that they can critically read a textbook and (c) become reflective learners. In a study [1] by Anderson et al. of third-year mathematics students, the authors conclude that, “students had such a fragile understanding of the material that reconstructing forgotten knowledge seemed alien to many of those taking part; if the answer could not be (immediately) recalled, then one passed on to the next question.” The importance of student writing in encouraging reflection, coupled with the time scale required for it to develop makes it advantageous for instructors to have classroom access to archived student work. The fully networked laboratory classroom would provide this for us. For instance, early students typically write a poorly articulated initial laboratory report, but during an ensuing classroom discussion gain insights and make connections which enable them to better explain their work. At this point, it can be of value to provide an opportunity for the student to immediately revise their work, and a laboratory classroom would provide for this. Another example of classroom use of archived student work which spans a longer time frame, could take place in an upper division advanced calculus course. For instance, a student’s investigation of the Implicit Function Theorem for several variables would benefit from referring to archived work done on implicit differentiation in first semester calculus. Servicing Pre-Service Teachers: The laboratory classroom is also envisioned as enhancing the preparation of pre-service teachers of mathematics. UWEC began as a normal school, and the training of pre-service teachers is an important part of its mission. Many majors and minors within the Department of Mathematics are pre-service teachers. Currently our largest emphasis within the major is the secondary teaching emphasis (70 students) and we also have a large number of elementary education majors selecting mathematics as their minor course of study (50 students). We also offer the Master of Science in Teaching and Master of Arts in Teaching degrees. 7

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The Mathematics Department has a close working relationship with the Department of Curriculum and Instruction, and has specifically integrated technology into several courses taken by pre-service teachers. The MAA specifically recommends [13] for pre-service teachers that, “All institutions involved in educating mathematics teachers should provide specialized classroom and laboratory facilities equipped with state-of-the-art demonstration materials, calculators, and computers, at least comparable to those used in the best elementary and secondary schools, so that prospective teachers, like graduates from other professional programs, can be properly prepared for their careers.” A laboratory classroom would provide a technological environment which would enable mathematics instructors of pre-service teachers to integrate content with good pedagogy. In particular, the Mathematics Department at UWEC will begin (in Spring 2001) teaching on a yearly basis a new course titled Teaching Mathematics Effectively with Technology. We anticipate that this course will become required of all secondary education mathematics students, and it would directly benefit from the technologically flexible environment that the laboratory classroom would provide. Computational Science: During the 1998-99 academic year an interdisciplinary Computational Science Minor was initiated at UWEC. The principal investigators have been very involved in the development of the minor, working closely with faculty from biology, computer science, chemistry, geography, geology, mathematics and physics. These faculty have recently created two co-requisite courses specifically for students electing the Computational Science Minor. Both of these, a mathematics course titled Survey of Numerical Methods and an interdisciplinary course titled Computational Science I, would be taught in the laboratory classroom. Timetable: Our timetable for carrying out the project anticipates that we can purchase the computers late in the Fall 2000 semester. Between semesters, our office of Information and Technology Management has agreed to install and network the computers in the classroom.

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During the Spring 2001 semester and during Summer 2001, the PI’s will redesign calculus course formats and laboratory materials to blend the Maple activities into a lecture environment. These materials have been tailored for a two-hour lab experience, and have gone through extensive revisions since the beginning of our C4 L adaptation in 1995. We need to adapt these materials for use in the blended environment of the laboratory classroom beginning in Fall 2001. With the release time, we will be able to prepare these materials and pilot their use in some of the calculus sections. During this semester, our new course Teaching Mathematics Effectively with Technology is scheduled to be taught in the laboratory classroom and Marc Goulet will teach the computational science mathematics course, Survey of Numerical Methods in the laboratory classroom. In Summer 2001, the PI’s will consult with the external evaluators Arnie Ostebee and Ed Dubinsky to develop assessment instruments for assessing student learning gains and attitude changes, beginning in Fall 2001. The project will involve teaching some of the calculus sections with three hours of lecture and two hours of laboratory, as is currently done, and for which we have collected baseline data through performance on final examinations and attitudinal surveys. This will comprise our control group. The other calculus sections will be taught in the laboratory classroom where students will meet for five hours and make use of materials adapted during Spring 2001 by the PIs for the blended laboratory classroom environment. This will be our experimental group. In Fall 2001, we will initiate the experiment and will continue the experiment in Spring 2002 and Fall 2002, making the entire duration of the project two years. We plan to have the two external evaluators come to UWEC during the 2001-2 academic year. During this semester the PIs will also teach Linear Algebra, Geometry and Probability in the laboratory classroom, incorporating collaborative learning, technology and technical writing into these courses. All three of these upper division courses are taken by our Mathematics Education majors. 9

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The above plan will result in concrete products in the form of written, integrated “minilabs”, which would be adaptations of our current calculus laboratory activities, as well as in selected upper division courses. Such products will be made available through our web sites. Data obtained from our comparison study of calculus students will inform us and other similar institutions of the effectiveness of a blended laboratory classroom environment. Equipment Request: The equipment request is for 25 laptop computers, each with active matrix video display, ethernet card, Windows NT, and locking devices. Our plan is to install these in our recently acquired 430 × 230 classroom, which has been wired for networking. For our larger classes students will be working collaboratively, so 21 computers will suffice. In choosing laptops over desktop computers, the main factors affecting our decision were space limitations and pedagogical considerations about the lower profile, but we also looked into issues such as reliability, durability, security, and viewability. According to conversations with a Dell representative, laptop computers, which used to have a reputation for not lasting very long and not being too reliable, have now reached a point where they meet or exceed the same standards as desktops. The active matrix display has better resolution than a standard PC monitor. Experience at our university has been that, with proper security laptop computers are no more likely to be stolen than desktop computers. The network equipment request is necessary to link the computers with the university network. Some reviewers of our previous submission suggested that we could accomplish our goals more cheaply with graphing calculators. But graphing calculators do not provide access to the wealth of software available on our campus, nor do they provide the capability to archive files for future classroom reference and revision. We are also requesting a networked HP laserjet printer. A printer would make the laboratory classroom self-contained. Implementation and Equipment Maintenance: Our office of Information and Technology Management is experienced in supporting networked computer laboratories, and in maintaining the performance of Dell computers. The room which will house the laboratory classroom 10

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(see appendices for a diagram and construction details) has been recently reconstructed. If the grant funds become available in the spring, we intend to install the computers for the fall 2001 semester. The university has a timetable for regular replacement of laboratory computers, so that if the project is successful, the laboratory classroom will be maintained as a department laboratory beyond the duration of the grant.

c. Experience and Capability of the Principal Investigators. This project has three principal investigators: Marc Goulet, Michael Penkava and Alex Smith. These investigators are all mathematics department faculty members at the University of Wisconsin-Eau Claire. Alex Smith has been at UWEC since 1990, Marc Goulet since 1993 and Michael Penkava since 1996. 1. Teaching Expertise: The University of Wisconsin-Eau Claire, a regional liberal arts university, recognizes and rewards excellence in teaching. All three investigators have been recognized as outstanding teachers, and their efforts in this regard are strongly weighted in promotion, tenure and salary considerations. All three investigators have taught MapleVbased calculus sections at UWEC. We write our own MapleV labs for these sections, and have our students work cooperatively in small groups on these labs. Students submit their MapleV worksheets to their instructor through the campus Student Global Server, and we often use this server to make substantial comments on student work by editing their MapleV labs directly on the server, whereby students then access their graded files. All three investigators routinely write their own laboratory activities for their upper division courses, making use of MapleV and other software. Marc Goulet has particular expertise doing this in statistics and probability courses, Michael Penkava in abstract and linear algebra as well as differential equations, and Alex Smith in geometry and number theory. 2. Curriculum Reform Expertise: The three investigators have all been active in various curricular reform efforts. The three investigators attended a one-week NSF-sponsored 11

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curriculum reform workshop at UW-Oshkosh in July 1998. At this workshop, the investigators worked together in designing the survey of numerical methods course for our new interdisciplinary computational science minor. Marc Goulet and Alex Smith were teaching fellows for the NSF-sponsored Women and Science Program in 1993-94. In this role they presented over twenty teaching workshops throughout the state on using writing, technology and cooperative learning in mathematics courses and have been members of numerous panel discussions. In addition, Marc Goulet has served as a consultant at the NSF-sponsored Women and Science Curriculum Reform Institute at UW-Oshkosh in the summers of 1997, 1998, 1999 and 2000. Marc Goulet and Alex Smith have been teaching the calculus sequence using cooperative learning and MapleV since 1995. In this role they have directed several independent study projects on constructivist methods in teaching calculus, and have presented over twenty workshops on these methods to college and pre-college instructors in Wisconsin. Together with Jeff Clay, an undergraduate majoring in Mathematics Education, and Andrew Balas of UWEC, Alex Smith and Marc Goulet have been involved in assessment projects of lab-based calculus courses at UWEC. Alex Smith, together with Andrew Balas and Jeff Clay presented a paper on this assessment project [3] at the International Conference on the Teaching of Undergraduate Mathematics at Samos, Greece in July 1998. Michael Penkava attended a 1997 ATLAST workshop on teaching linear algebra, and was a participant in the 1998 IAS Park City Mathematics Institute as part of the undergraduate faculty program, which again emphasized linear algebra reform. In addition to his own research, he has participated in the undergraduate/faculty research program at the university, and recieved a grant to work on a research project with an undergraduate student in the 1998-99 academic year. Since 1992, he has taught a number of sections of pre-algebra and college algebra using cooperative learning methods. Moreover, he has been a system administrator for a UNIX system, and was responsible for bringing Maple to the UWEC campus. 12

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d. Evaluation Plan. In an 1999 assessment of some of our calculus courses [9], it was observed that students–in particular women–would prefer a learning environment which would allow greater flexibility in the use of technology while solving problems. We recently surveyed our calculus courses where students attend lectures for three days a week and meet in a laboratory for two consecutive hours. This attitude survey was similar to one from the Fieldtested Learning Assessment Guide [15]. Students were asked to respond to the statement, “The laboratory assignments were effective in helping me to understand the mathematical concepts.” Where 1 represents Strongly Agree and 4 represents Strongly Disagree, 107 first semester calculus students had a median response of 2.8, while 58 second semester calculus students had a median response of 2.5. This contrasts with their response to the analogous assertion about the effectiveness of lectures, where their median responses were 2.3 and 1.8 respectively. This preliminary data shows that students do not see the labs as being as effective as the lectures. At the same time, faculty teaching the calculus courses perceived that the laboratory component had a positive effect on their test performance. In another study [3], exit interviews by science faculty in other departments compared calculus knowledge of students in traditional lecture sections with that of students who met twice a week in lecture and twice a week in a lab. This study was modeled after [25] and we found that faculty were not able to tell the difference between the two types of sections. We realize that perceptions are not good enough in quantifying student learning gains and we have recently created a baseline of student final examination performance for the 1999-00 academic year. We will use this data to obtain quantifiable information on student learning gains by comparing students’ performance in the laboratory classroom environment with those not meeting in this environment. Based on these prior assessments, we believe that the following criteria are the most important in evaluating the success of our project.

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• Students should improve their knowledge of the calculus as evidenced through demonstration of basic knowledge of facts and terms, concepts and theories, and ability to synthesize and integrate information and ideas. The common final exam will help us to determine success in this area. • Students should improve their communication skills, specifically as they relate to writing. We will assess this by weekly lab reports, and other instruments to be developed in consultation with the external evaluators Ed Dubinsky and Arnie Ostebee. • As a result of the laboratory classroom we expect students to better appreciate the value of learning mathematics using various tools such as software, cooperative learning and writing. The PIs have administered the attitude survey mentioned above, and other attitude inventories will be developed in consultation with the external evaluators. The timeline for the evaluation is as follows. Some baseline data has already been gathered and other baseline data will be established in the pilot project in Spring 2001. The primary assessment instruments will be developed in consultation with the two external evaluators in Summer 2001 and will be used in subsequent semesters to assess student outcomes. The data will be analyzed in Summer 2002. The principal investigators’ experiences in assessment [3, 9], Ed Dubinsky’s leadership in the C4 L and expertise in research in undergraduate mathematics education, specifically as it relates to cooperative learning and the use of technology, along with Arnold Ostebee’s familiarity with mathematics education reform and association with St. Olaf College, one of the ten undergraduate institutions reported on in [23], provide adequate expertise.

e. Dissemination of Results. A wealth of laboratory materials have already been written by the principal investigators, particularly in the calculus, but also in geometry and probability and statistics. One result of this project will be the adaptation of some of these materials and the construction of new materials appropriate for use in the new laboratory classroom environment. In order to make these new materials readily available for use by 14

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mathematics faculty at UWEC and at other institutions, we will make these materials available through our curricular web pages. We currently do this with the laboratory materials we have already developed. To reach a wider audience, we will link these materials to other sites frequented by the mathematics community such as the Math Forum at Swarthmore College. Two of the principal investigators have expertise in delivering workshops and seminars on pedagogy throughout the state of Wisconsin. These presentations occur through activities associated with the Women and Science Program, the Wisconsin Section of the Mathematical Association of America, other University of Wisconsin sister institutions, and the Wisconsin Mathematics Council. As a result of this project, the investigators will develop curricular innovations that will interest these groups. In particular, the investigators will report to these groups via workshops and seminars their efforts in integrating their earlier work on implementing pedagogies utilizing collaborative groups, student writing, technology, and active learning experiences into this new blended laboratory classroom environment. While the impact at these forums is primarily felt by Wisconsin SMET educators, there is significant national impact as well. Marc Goulet’s position as a consultant at the Women and Science Summer Curricular Reform Institute, which hosts faculty and administrators from across the nation interested in developing and implementing curricular reform with a special emphasis on issues related to science and gender, provides an opportunity for wider dissemination of our results. The principal investigators will also distribute our results to the national undergraduate mathematics education community by publishing work related to this project in publications such as the Journal for Research in Mathematics Education and Primus.

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5. References Cited References [1] J. Anderson, K. Austin, T. Barnard, and J. Jagger. Do third-year mathematics under-graduates know what they are supposed to know? International Journal of Mathematical Education in Science and Technology, 29:401–420, May 1998. [2] M. Asiala, A. Brown, D. Devries, D. Mathews, and K. Thomas. A framework for research and curriculum development in undergraduate development in undergraduate mathematics education. In J. Kaput, A. Schoenfeld, and E. Dubinsky, editors, Research in Collegiate Mathematics Education II, volume 2, pages 1–32. Washington DC: Conference Board on the Mathematics Sciences, 1996. [3] A. Balas, B. Bansenauer, J. Clay, M. Goulet, and A. Smith. Assessing calculus reform at uwec. In D. Hughes-Hallett and I. Vakalis, editors, Proceedings of the International Conference on the Teaching of Mathematics, Samos, Greece, pages 35–37. John Wiley & Sons, Inc, 1998. [4] A. Balas and J. Clay. Student perceptions of success in a reformed calculus class. Preprint, 1998. [5] D. Betounes and M. Redfern. Mathematical Computing Courses and an Inflatable Laboratory Grant DUE-9751156. NSF-DUE Instrumentation and Laboratory Improvement Award, 1997. [6] Ed Dubinsky. Calculus, Concepts and Computers DUE-9053432. NSF-DUE Course and Curriculum Development Award, 1990. [7] Ed Dubinsky, David Mathews, and Barbara E. Reynolds. Readings in Cooperative Learning for Undergraduate Mathematics. MAA Notes. Mathematical Association of America, 1997. [8] Bonnie Gold, Sandra Keith, and William Marion. Assessment Practices in Undergraduate Mathematics. MAA Notes. Mathematical Association of America, 1999. [9] M. Goulet and J. Clay. A comparison of student attitudes towards technology driven calculus activities versus technology flexible calculus activities. Preprint, 1999. [10] Donald E. Knuth, Tracy Larrabee, and Paul M. Roberts. Mathematical Writing. MAA Notes. Mathematical Association of America, 1989. [11] Steven Krantz. You don’t need a weathereman to know which way the wind blows. The American Mathematical Monthly, 106(10):915–918, 1999. [12] Carl Leinbach, Joan R. Hundhausen, Arnold M. Ostebee, Lester J. Senechal, and Donald B. Small. The Laboratory Approach to Teaching Calculus. MAA Notes. Mathematical Association of America, 1991. [13] J. Leitzel, editor. A Call For Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics. Mathematical Association of America, 1991. [14] James R. C. Leitzel and Alan C. Tucker. Assessing Calculus Reform Efforts. MAA Notes. Mathematical Association of America, 1994. [15] Eileen Lewis. Field-tested learning assessment guide. http://www.wcer.wisc.edu/nise/CL1/flag/, 2000. [16] John Meier and Thomas Rishel. Writing in the Teaching and Learning of Mathematics. MAA Notes. Mathematical Association of America, 1998. [17] C. Ney, J. Ross, and L. (editors). Mumford. Flickering Clusters: Insights in Science, Diversity, and Collaborative Communities. Madison: UW Press, 1997. [18] M. Prosser and K. Trigwell. Relations between perceptions of the teaching environment and approaches to teaching. British Journal of Educational Psychology, 67:25–35, 1997. 16

[19] A. Wayne Roberts. Calculus The Dynamics of Change. MAA Notes. Mathematical Association of America, 1995. [20] Alan Schoenfield. Student Assessment in Calculus: A Report of the NSF Working Group on Assessment in Calculus. MAA Notes. Mathematical Association of America, 1997. [21] J. Stewart. Calculus-Early Transcendentals. Brooks/Cole, third edition, 1995. [22] J.D. Stone. In-Class Experimental Learning in Four Fundamental Courses DUE-9451972. NSF-DUE Instrumentation and Laboratory Improvement Award, 1994. [23] A. Tucker, editor. Models that Work: Case Studies in Effective Undergraduate Mathematics Programs. Mathematical Association of America, 1995. [24] Thomas Tucker. Reform, tradition, and synthesis. The American Mathematical Monthly, 106(10):910–914, 1999. [25] J.C. Wright, S.B. Millar, S.A. Kosuik, D.L. Penberthy, P.H. Williams, and B.E. Wampold. A novel strategy for assessing the effects of curriculum reform on student competence. J. Chem. Educ., 75:986–992, 1998.

6. Biographical Sketches a. Dr. Marc Goulet. EDUCATION Ph.D. in Mathematics, Oregon State University, 1992 M.S. in Mathematics, Oregon State University, 1990 M.A. in Mathematics, Physics, University of Maine, 1986 B.A. in Mathematics and Philosophy, University of Maine, 1984 PROFESSIONAL APPOINTMENTS Associate Professor of Mathematics, University of Wisconsin-Eau Claire, 1999-present Assistant Professor of Mathematics, University of Wisconsin-Eau Claire, 1993-1999 Mathematical Program Director, Phillips Academy Math and Science for Minority Students Program, 1995-1997 Director of University of Wisconsin-Eau Claire First Year Seminar Program, 1998-1999 Visiting Researcher, University of G¨ottingen 1992 Assistant in Education, Technical University of Delft, The Netherlands, 1991-1992 PROFESSIONAL AND SCHOLARLY ACTIVITIES Marc Goulet has been teaching undergraduate mathematics for eight years. As an educator, he has been involved in curriculum reform efforts through the University of Wisconsin System’s Women and Science Program, serves on their board of directors, and he has been an invited consultant at its annual Curriculum Reform Institute during the summers of 1997, 1998, 1999 and 2000. He has particular expertise in working with under represented groups in mathematics through his work at Phillips Academy and through various Upward Bound and Educational Opportunities Programs. He has been teaching calculus using active learning techniques since 1995. He is on the Board of Directors for the Wisconsin Mathematics Council, and is the editor

of their journal, The Wisconsin Mathematics Teacher. He has received grants from UWEC to support pedagogical innovations and has given over twenty presentations and workshops throughout the state on teaching undergraduate mathematics. He has experience infusing technology such as Maple, Minitab, SPSS, and spreadsheets into his upper division courses, most notably into probability and statistics courses. PUBLICATIONS RELATED TO THIS PROJECT Teaching in the Wake of the Women and Science Program, in Flickering Clusters: Insights in Science, Diversity and Collaborative Communities. Ney, Cheryl, Ross, Jacqueline, and Mumford, Laura (editors). UW-Madison Press, 1997. The Math and Science for Minority Students Program, in Flickering Clusters: Insights in Science, Diversity and Collaborative Communities. Ney, Cheryl, Ross, Jacqueline, and Mumford, Laura (editors). UW-Madison Press, 1997. Assessing Calculus Reform (with A. Balas, B. Bansenauer, J. Clay, and A. Smith), Proceedings of the International Conference on the Teaching of Mathematics, Samos, Greece, pp.35-37, 1998. A Comparison of Student Attitudes Towards Technology Driven Calculus Activities versus Technology Flexible Calculus Activities (with J. Clay), preprint 1999. SELECTED OTHER PUBLICATIONS Practical Methods of Extreme Value Estimation Based on Measured Time Series for Ocean Systems (with R.M. Burton, and S. Yim), Ocean Eng., Vol 19, #3, pp.219-238, 1992. On 1-Dependent Processes and k-Block Factors (with R.M. Burton, and R.W.J. Meester), Annals of Probability, Vol 21, #4, pp.2157-2168, 1993. COLLABORATORS R.M. Burton (Oregon State University), J. Ganapathy (University of Wisconsin-Oshkosh), R.W.J. Meester (University of Utrecht), J. Szydlik (University of Wisconsin-Oshkosh) and S. Yim (Oregon State University).

b. Dr. Michael Robert Penkava. EDUCATION Ph.D. in Mathematics, University of California, Spring 1995 M.A in Mathematics, University of California, Spring 1991 B.A. in Liberal Arts, Raymond College, University of the Pacific, Spring 1975 PROFESSIONAL APPOINTMENTS 1996- Assistant Professor of Mathematics, University of Wisconsin, Eau Claire 1995-1996 Lecturer: University of California, Davis. 1995-1996 Instructor Cosumnes River College, Sacramento CA 1992-1995 Associate-In: University of California, Davis 1977-1995. Cartwright Holding Company. Night auditor for a small, popular San Francisco hotel. From 1985-1995 was the system administrator for a Unix system V, 3B2 computer. Designed a software package for the hotel for auditing and demographic purposes. PUBLICATIONS M. Penkava and P. Vanhaecke Deformations of Polynomial Poisson Algebras, Journal of Algebra 227, 365-393 (2000), math.QA/9804022 M. Mulase and M. Penkava Ribbon Graphs, Quadratic Differentials on Riemann Surfaces, and Algebraic Curves Defined over Q , Asian Journal of Mathematics, Vol 2, number 4, 875-920 (1998), math-ph/9811024 L. Lang and M. Penkava Infinity Algebras, Massey Products and Deformations, preprint (1996), math.QA/9808058 M. Penkava and A. Schwarz A∞ Algebras and the Cohomology of Moduli Spaces, in “Dynkin Seminar on Lie Groups” (1995), hep-th/9408064 M. Penkava and A. Schwarz On Some Algebraic Structures Arising in String Theory, in “Perspectives in Contemporary Mathematical Physics” (1994), hep-th/9212072 WORKSHOPS Aug 1997 ATLAST Linear Algebra Workshop, Madison, WI

Jul 1998 Park City IAS Summer Institute, Park City, UT PROFESSIONAL AND SCHOLARLY ACTIVITIES At Cosumnes River College, Dr. Penkava taught pre-algebra using cooperative learning techniques in a room with round tables and whiteboards, which inspired the design of our collaborative classroom. At UC Davis, he was an instructor in the emerging scholars program, an innovative approach to minority success in the calculus program, which has a consistent record of student excellence on the common final exam. Dr. Penkava has been involved with the C4 L project at UWEC since 1996, negotiated the Maple site license, has written Maple worksheets, as well as served as course coordinator for the experimental 3-2 Lecture-Lab version of the first semester calculus course. He has also taught the college algebra using cooperative methods, and has incorporated a writing component in the form of a written project into his upper division courses, as well as sponsored numerous talks by students in our math retreat. In 1998, he recieved a student/faculty research grant to work with Holly Hauschild, an undergraduate on a project titled “Rank Invariants of Polynomial Poisson Algebras Determined by Lie Algebras”. In relation to this work, the student gave oral presentations at several national, state and local meetings. In 1999, Dr. Penkava worked with Jill Malueg on an undergraduate research project in advanced topics in linear algebra, for a scholarship she received to pursue this research. She gave talks at the UWEC math retreat and a regional MAA meeting in relation to this work. COLLABORATORS Thesis Advisor: Dr Motohico Mulase, University of California, Davis Dr. Alice Fialowski, E¨otvos Lorand University, Budapest, Hungary Dr. Lynelle Weldon, Andrews University, Berrien Springs, MI Dr. Albert Schwarz, University of California, Davis Dr. Pol Vanhaecke, Universit’e De Poitiers, Cedex, France

c. Dr. Alexander John Smith. EDUCATION Ph.D. in Mathematics, University of California-Berkeley, 1987 B.A. in Mathematics, Oxford University, 1982 B.S. in Mathematics, Physics, New Mexico State University, 1980 PROFESSIONAL APPOINTMENTS Associate Professor of Mathematics, University of Wisconsin-Eau Claire, 1995-present Assistant Professor of Mathematics, University of Wisconsin-Eau Claire, 1990-1995 Mathematical Program Director, Wisconsin Center for Academically Talented Youth Summer Program, 1992-1996 Director, UWEC Mathematical Talent Development Program, 1995-1996 Instructor, UWEC Mathematical Talent Development Program, 1991-1996 G.C. Evans Instructor of Mathematics, Rice University, 1987-1990 Instructor, Department of Mathematics, University of California-Berkeley, 1986 PROFESSIONAL AND SCHOLARLY ACTIVITIES Alex Smith has been teaching undergraduate mathematics for thirteen years. As an educator, he has served as teaching fellow for the University of Wisconsin System’s Women and Science Program and he has been active in the gifted and talented education of precollege students. In his role as teaching fellow for the Women and Science Program, he has presented fifteen teaching workshops throughout the state on using technology and cooperative learning in lower division mathematics courses and he has been a member of numerous panel discussions. He has been teaching calculus using active learning techniques since 1995. In this role he has directed three independent study projects on constructivist methods in teaching calculus, and together with other faculty at UWEC, he has presented twelve workshops on these methods to college and precollege instructors in Wisconsin.

He has taught a number of upper division courses including Technology in Mathematics, Number Theory, Geometry for Education Majors, Complex Analysis, Real Analysis, Differential Equations, Advanced Calculus, Public-Key Cryptography, Turing Machines, Logic, Abstract Algebra, Linear Algebra, and Projective Geometry. He has had experience infusing technology such as graphing calculators, spreadsheets, Derive, Mathematica, MapleV and Geometer’s Sketchpad into most of these classes. The lower division courses he has taught include Calculus, Brief Calculus, College Algebra, and Math for Elementary Education Majors. He has had considerable experience using technology as a pedagogical tool in all of these lower division courses. PUBLICATIONS MOST RELEVANT TO WORK PROPOSED Assessing Calculus Reform (with B. Bansenauer, J. Clay and M. Goulet), Proceedings of the International Conference on the Teaching of Mathematics, Samos, Greece, pp.35-37, 1998. Using Spreadsheets to Develop Concepts in College Algebra (preprint 1998) Incorporating Spreadsheets into Number Theory (preprint 1998) The Influence of the Women and Science Program on the Teaching of College Mathematics, in Flickering Clusters: Insights in Science, Diversity and Collaborative Communities. Ney, Cheryl, Ross, Jacqueline, and Mumford, Laura (editors). UW-Madison Press, 1997. GRADUATE STUDENTS ADVISED Renee Thulsky, MAT 1992 Daniel Walker, MST 1997 COLLABORATORS Thesis Advisor: Dr. S. Kobayashi, U.C. Berkeley Dr. Sherrie Nicol, UW-Platteville Joshua Zucker, Enrichment Program for Gifted Youth, Stanford Continuing Studies Program Dr. Steven Semmes, Department of Mathematics, Rice University

A COMBINED MATHEMATICS LABORATORY AND CLASSROOM ENVIRONMENT

7. Budget

List Discount Quantity Price Price

Item Notebook Computers , Dell Latitude CPi Notebook 366 mHz Pentium II Processor 128 MB SDRAM Memory 24X max/10X min CD-ROM Drive Microsoft Windows 2000 13.3in TFT XGA Display 6.0 GB Hard Drive PS/2 Style Mouse C/Port2 Advanced Port Replicator Shipping and handling Kensington Microsaver Security System Networking Cisco Catalyst 3524-XL-EN 24 port 10/100 Ethernet Switch 1000Base-SX Gigabit uplink Multimode GBIC Gigabit uplink port on Cisco C3508G-XL-EN Printer HP Laserjet 4050 Evaluation/Assessment Travel and Honorarium for evaluators Faculty Time 1 20% Spring Release Time for PIs 2 Week Summer Salary for PIs Indirect Costs = .43× Faculty Salaries & Fringe Benefits

25

3602

2725

$68, 128.00

25 25

30 45

25

$750.00 $1, 125.00

1 2, 995

1, 797

$1, 797.00

2 1, 000

600

$1, 200.00

1

624

374

$374.00

1

1679

1, 582

$1, 582.00

2 2, 000

$4, 000.00

2 6, 800 3 3, 600

$13, 600.00 $10, 800.00 $10, 492.00

TOTAL BUDGET Non NSF Contribution NSF Request

1Note:

Total Cost

$113, 848.00 $56, 924.00 $56, 924.00

UWEC will cost share Faculty time and effort 1

MARC GOULET, MICHAEL PENKAVA, AND ALEX SMITH

The equipment portion of this budget and release time and summer salary for the principle investigators would also be expended in the first year. The travel and honorarium for the outside evaluators would probably be expended half in the first year, when the assessment tools are being designed, and half in the second year when the results of the assessment are evaluated. A detail description of the budget request follows. Computers and Printer The choice of a laptop over a desktop computer was made mainly for pedagogical reasons, but the small size of the available classroom was another factor. Because of this, our equipment considerations were restricted to notebook computers. In our choices, we relied on the experience of the university’s Information and Technology Management personnel. The Dell notebook computer is about a midrange priced machine, and possesses both the speed (366 mHz) and memory (128 MB) necessary to handle the software applications that we are using in our instruction. Our Computers and Networking staff is experienced in supporting Dell products. The choice of windows 2000 as the operating system is consistent with the plans for this to become the standard operating system on the campus. In a conversation with Andre Vlajk, the Dell education representative for our area, we were told that the video display on the notebook is easier to see than the standard desktop monitors. Because we intend to have two students working on a single laptop, we checked to see that the viewing angles were sufficient for this type of usage. The 6.0GB hard drive, 128 MB SDRAM memory, Windows 2000, and the CD ROM Drive, are all part of the standard package. We chose to include a PS/2 style mouse for $19 per machine, because it is easier for many users than the notebook style mouse, but does not add much to space requirements. The Kensington Microsaver Security System is compatible with Dell notebooks, and provides the means of locking the computers down. The HP laserjet printer will make the use of the laboratory classroom self contained, and is a product which our Computers and Networking staff is trained in supporting. 2

A COMBINED MATHEMATICS LABORATORY AND CLASSROOM ENVIRONMENT

Networking The Cisco Catalyst Ethernet Switch and the gigabit uplink and port are necessary to interface the computers to the university backbone. The cabling and wiring are already be in place in the floor of the room. Evaluation/Assessment The Travel and Honorarium fees for the external consultants will cover the consultation on the design of the evaluation instruments as well as two visits from Arnold Ostebee, and one by Ed Dubinsky. Arnold Ostebee, associate dean of Letters and Sciences at Saint Olaf College in Northfield Minnesota, is a leading expert in the Calculus Reform Effort. He will consult with us in developing an evaluation instrument. One of the reasons we chose him to consult on the project was the inclusion of Saint Olaf College in an MAA case study as an example of an effective undergraduate mathematics program [23]. The budget for him includes a $150 per day honorarium, and $700 per trip travel, lodging and per diem expenses. Ed Dubinsky, professor of mathematics at Georgia State University, is a leading expert in research in undergraduate mathematics education. He is an author of numerous articles and books on collaborative learning and the use of technology in learning mathematics. He was the principal investigator of the C4 L project which we are adapting. The budget for him also includes a $150 per day honorarium, and $1400 for one trip travel, lodging and per diem expenses. The release time for the principal investigators is equal to a 20% release for two of the PIs in the spring of 2001, in order to oversee the project, during which time a pilot version of the new calculus format will be run, as well as two other classes which will pilot the use of the new equipment. In the summer of 2001, the summer salary is equivalent to a two week salary plus fringe benefits for each of the three PIs.

3

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