Process Oriented Guided Inquiry Learning for Soft ... - Semantic Scholar

Process Oriented Guided Inquiry Learning for Soft Computing Clifton Kussmaul 1 1

Muhlenberg College, 2400 Chew St, Allentown, PA 18104-5586 USA [email protected]

Abstract. This paper describes several process oriented guided inquiry learning (POGIL) activities focused on soft computing (genetic algorithms, neural networks, and fuzzy systems). The paper provides background on POGIL, illustrates several activities, summarizes student feedback, and discusses lessons learned and possible future directions. Keywords: active learning, fuzzy logic, genetic algorithms, inquiry learning, neural networks, POGIL

1

Introduction

To improve learning quality and retention, particularly in science, technology, engineering, and mathematics (STEM) disciples, educators have developed a wide variety of approaches to engage students, enhance learning, and emphasize attitudes and skills rather than only knowledge (often rote). These approaches are generally referred to as active learning, and approaches where students work together are referred to as collaborative learning. Process oriented guided inquiry learning (POGIL) is a particular approach to collaborative learning which combines a set of effective practices, and has been developed and validated over many years. This paper provides some general background on POGIL. It then describes activities focused on soft computing (genetic algorithms, neural networks, and fuzzy systems) that have been used successfully and are being revised and generalized. This paper is novel in that it describes: a) POGIL in computer science in general and soft computing in particular; b) POGIL outside the USA, and specifically in India; and c) POGIL activities using presentation slides rather than paper handouts.

2

Process Oriented Guided Inquiry Learning

POGIL has three distinguishing features [11]. First, teams of learners (typically 3-5) follow processes with specific roles, steps, and reports that help students develop process skills and encourage individual responsibility and meta-cognition. Second, teams work on scripted inquiry activities and investigations designed to help them construct their own knowledge, often by modeling the original processes of discovery

and research. POGIL activities and processes are designed to achieve specific learning objectives; typically an activity is designed to focus on 1-2 (disciplinary) concepts and 1-2 process skills. Third, the POGIL instructor serves as a facilitator, not a lecturer. Typically this means that the instructor circulates among the student teams, checks on progress, and helps teams to resolve problems. Periodically the instructor may ask teams to share answers or insights with the rest of the class. POGIL is based on learning science (e.g. [14]), and shares characteristics (e.g. teams, processes, inquiry) with other forms of active, discovery, and inquiry-based learning (e.g. [5]). POGIL is distinctive in the way it combines a set of characteristics that support each other and strengthen learning outcomes. POGIL activities are generally designed to follow a learning cycle with 3 phases [1, 11]. In exploration, students look for trends or patterns in data they have collected or that is provided, and generate and test hypotheses to help understand or explain the data. In concept invention, the trends, patterns, or hypotheses are used to define a new concept or term; importantly, students have constructed understanding before the concept is introduced. In application, the new concept is applied in other situations or contexts to help students generalize its meaning and applicability. Thus, the scripted activity provides information and asks questions to guide students through the learning cycle and help them develop process and learning skills. (For various reasons, some POGIL activities introduce a concept, and follow it with application and exploration.) Designing effective POGIL activities can be time-consuming, but supporting resource are available [7]. Generally, the author first identifies learning objectives and the focus of the activity. For examples, teams could analyze data, derive equations, or explore the behavior of a physical system. Next, the author creates a sequence of key questions that guide teams through the inquiry process. Finally, the author identifies and develops supporting information, such as prerequisites, glossary of terms, references, handouts, and subsequent assignments or projects. Activities involve three types of key questions. Directed questions have definite answers, are based on material available to students, and provide a foundation for later parts of the activity. Convergent questions may have multiple answers, and require teams to analyze and synthesize information to reach non-obvious conclusions. Divergent questions are open-ended, do not have right or wrong answers, and may lead teams and individual students in different directions. POGIL has been developed and validated over the last 15 years. Multiple studies have found that POGIL significantly improves student performance, particularly for average and below-average students. (e.g. [6], [9], [10]). POGIL has been used extensively in chemistry, and also in materials science and engineering [4], and computer science (CS) [3]. Although active learning and discovery learning are increasingly popular in CS (e.g. [2], [13]), POGIL is not yet well known in CS education.

3

Context & Examples

The author developed and used POGIL activities and other active learning activities for a course on soft computing, including genetic algorithms, neural networks, and fuzzy systems [12]. The course was taken by roughly 20 first term graduate students in computer science at the University of Kerala, Karyavattom, where the author was a Visiting Fulbright-Nehru Scholar. Although most POGIL classrooms give each team or student a set of paper handouts for each activity, in this course the activities were presented as a sequence of PowerPoint slides which were posted online after class for students to review. The initial motivation was to reduce paper use. It also provided the instructor with more flexibility to tweak activities by adding steps or providing more information, and to manage the class‟s pace since students couldn‟t race forward to finish an activity or look for clues. This could make the class less student-centered, but it could also be more familiar to students who are accustomed to lectures. The following subsections briefly describe slides and other parts of several activities from the course. These particular examples were selected because they illustrate some (though not all) aspects of POGIL, and require relatively little context or background. Slides presenting concepts were covered in a few minutes of lecture and questions. Slides with questions improve students‟ understanding and enables the instructor to help resolve any questions or confusion before moving on to new topics. Early questions are simpler, and later questions may be more challenging or require more reflection. After the topic is covered in class, students apply it in a programming assignment, usually working with a partner. Given time (for development, and in the classroom) these activities could be improved or extended in various ways, some of which are discussed below. For these activities to be more readily adopted for other courses, it would be useful to: define learning objectives, prerequisites, resources, and vocabulary; provide more complete background information; and package them in a standard format. This work is ongoing (and perhaps unending). 3.1

Genetic Algorithms

The slides in Figure 1 are from an activity that introduces schemata (patterns of solutions), some issues in schemata counting, and the first steps in deriving the schema theorem. Before starting the activity, the instructor ensures that students are organized into teams, and might spend a few minutes introducing the activity. Slide Schemata defines terms and provides some examples. The instructor could reinforce these ideas verbally, or have the teams study them. Slide Schemata Count: Questions begins with a directed question about counting solutions, and uses convergent questions to develop formulas. The instructor could ask teams to share their answers to see if there is agreement. Slide Schemata Selection: Questions (1) defines some more terms, and uses more convergent questions to lead students toward an equation showing how more fit solutions become more common over time. Slide Schemata

Schemata In analyzing & discussing GAs & solutions, we often want to describe solution patterns, called schemata. In each schema, some values are required, and others are not (represented by *) Examples AB**AB** 0010*0011 Schemata present counting problems… Schemata Counting: Questions Assume there are s symbols in the alphabet, and each solution has L symbols. 1. Count the solutions for each schema: 1*0* 1**0**0* AA**C 2. How many solutions are there for a schema with w wildcard values? 3. How many schemata match a given solution? 4. How many schemata are possible, total?

Schemata Selection: Questions (1) A(t) is the population at time t f(a) is the fitness of solution a A(t) m(a,t) is the count of a at t 1. What is the total fitness of A(t)? 2. What is the average fitness? 3. What is m(a,t+1), the count of solution a at (t+1)? 4. Does #3 make sense? How could it be used? Schemata Selection: Questions (2) is a schema pattern does not depend on t, but members do m(H,t) is the count of H at t 1. What is m(H,t+1)? Hint: sum over solution counts 2. Substitute into #1 your earlier expression for m(h,t+1). 3. Explain the equality: H 

 f (h )  m( H , t ) f ( H ) i

4. 5.

H Substitute #3 into #2. Does #4 make sense? How could it be used?

Fig. 1. Sample slides from activity on genetic algorithms.

Selection Questions (2) extends this to schemata, as the first of three major steps in defining the schema theorem. These might prompt a brief class discussion of how the equation could be used or improved. Together, the slides lead teams to explore schemata terminology and invent concepts which will be applied in later slides or subsequent assignments, thereby completing the learning cycle and lead students to deeper understanding. To improve this activity and make it more widely applicable, we might:  Use exploration tasks to motivate schemata rather than starting with a definition.  Motivate the terms defined in the slides.  Provide more intermediate steps, particularly for students who are less comfortable with mathematical derivations & proofs.

ANN Design: Questions (1) Consider a neuron with F=-1, T=+1 and a step activation function. 1. Try to choose weights to compute a. logical NOT (1 input) b. logical OR (2+ inputs) c. logical AND (2+ inputs) 2. Can one activation function serve all 3 functions?

1.

2.

3. 4.

1.

2. 3.

ANN Design: Questions (2) On an (x1,x2) graph, draw lines for y = x1w1 + x2w2 for w1 & w2, y = {-1,0,+1} How would f() affect the lines? Extend & compare with a 3+ input network.

ANN Design: Questions (3) Try to choose weights to compute XOR with a single node. What new issues arise? What general statements (pros & cons) can you make about one-layer networks? Try to choose weights to compute XOR with a multi-layer network. What general statements (pros & cons) can you make about multi-layer networks?

ANN Design: Questions (4) Consider a 3x3 binary image:

1. 2. 3.

Design a network where each pattern above has a unique output. How could you use less neurons? How could you allow noisy data (1-2 incorrect pixels)?

Fig. 2. Sample slides from activity on neural networks.

3.2

Neural Networks

The slides in Figure 2 are from an activity that explores the capabilities of single and multi layer neural networks. Previously, students investigated the form and behavior of a single neuron, and the role and possible shapes for activation functions. Before starting the activity, the instructor might briefly summarize some of these concepts, or give a brief quiz to see how well students understand them. Slide ANN Design Questions (1) asks convergent questions about choosing weights for neurons that perform specific functions, to help the teams better understand how neurons compute results. Depending on the class, the instructor might provide a handout showing truth tables for each operation, or a spreadsheet or software widget where students could enter weights and see the output for different inputs. Slide ANN Design: Questions (2) leads students to plot contours (for specific values of y) in order to see how a neuron combines its inputs, and some of the effects of activation functions. The instructor might provide blank graphs. Slide ANN Design: Questions (3) introduces the XOR operation, which cannot be computed with a single neuron but can be computed with a sequence of neurons. This might prompt a brief class discussion of single vs. multi-

Fuzzy Sets fuzzy set generalizes regular (crisp) set with degree or grade [0.0 … 1.0] • crisp set elements have degree 0 (non-member) or 1 (member) membership function m(x) maps each element x  Universe to its degree. (Universe is a crisp set) • finite/infin, discrete/continuous

Fuzzy Set Relations: Questions Given fuzzy set C = {bla, whi, yel, mag} with mR(C)= { bla/0, whi/1, yel/1, mag/1 } mG(C)= { bla/0, whi/1, yel/1, mag/0 } mB(C)= { bla/0, whi/1, yel/0, mag/1 } 1. Identify all subset relations among R, G, & B. 2. Identify support of R, G, & B.

Fuzzy Sets: Examples materials A = {wax, steel, diamond} hardness mH(A) = {w/.1, s/.7, d/1} ages A = {0…} (non-neg ints) oldness mO(x) = {0.0 for x ≤ 20 (x-20)/60 for 20 ≤ x ≤ 80 1.0 for 80 ≤ x}

Fuzzy Set Operations: Familiar Union & Intersection AB {x/max(mA(x),mB(x))|xU} AB {x/min(mA(x),mB(x))|xU} Complement A’ {x/(1-mA(x)) |xU}

Fuzzy Set Relations Equality A=B ≡ mA(x)=mB(x)∀xU Subset AB ≡ mA(x)mB(x)∀xU A=B ≡ AB and BA Member xA undefined for fuzzy but U is universe (crisp set) Support {x | mA(x) > 0, xU} Fuzzy Singleton set with |support| = 1

Fuzzy Set Operations: Questions 11

x1x1

AA 00

1. 2. 3.

x2x2

1

x3x3 x4x4

B

x1

x2 x3

x4

0

Given sets A & B, draw: A‟, B‟, A  B, A  B, A‟  B‟ How are 1c & 1e related? Are crisp and fuzzy definitions for {, , „} consistent?

Fig. 3. Sample slides from activity on fuzzy sets (first part).

layer networks. Slide ANN Design: Questions (4) asks students to design networks to identify simple patterns, and prompts them to begin considering issues of efficiency (number of neurons) and robustness when data is noisy or incomplete. Here again, the instructor might provide a handout or a software widget. Teams that progress quickly could spend more time exploring ways to reduce the number of neurons or allow noisy data. To improve this activity and make it more applicable, we might:  Use more exploratory examples in slides a) and d), perhaps including some with continuous rather than binary inputs, and examples with multiple outputs.  Use a series of questions to better motivate the graphs in slide b).

Fuzzy Set Properties: Familiar Commu. AB=BA AB=BA Assoc. (AB)C = A(BC) (AB)C = A(BC) Distrib. A(BC) = (AB)(AC) A(BC) = (AB)(AC) DeMorgan (AB)‟ = A‟B‟ (AB)‟ = A‟B‟ Involution (A‟)‟ = A Idempotent AA = A Identity A=A A= AU=U AU=A • • • •

Fuzzy Set Properties: Unfamiliar Concentration & Dilation CON(A) {x/mA(x)2 |xU} DIL(A) {x/mA(x)½ |xU} Normalization NORM(A) {x/mA(x)/Max |xU} CON decreases degree, DIL increases degree. Do these names make sense?

Fuzzy Set Operations: Questions (1) 1

A 0

x1 x2

1

x3 x4

x1

x2

B

x3

x4

0

1.

Given fuzzy sets A and B, each with 4 elements, draw: CON(A), DIL(B), A NORM(A), A=A NORM(B)

Fuzzy Set Operations: Questions (2) Given previous definitions • ages A = {0… } (nonnegative ints) • oldness mO(x) = {0.0 for x ≤ 20 (x-20)/60 for 20 ≤ x ≤ 80 1.0 for 80 ≤ x} 1. For x = 0..100, draw : mO(x), CON(mO(x)), DIL(mO(x))

Fig. 4. Sample slides from activity on fuzzy sets (third part).

3.3

Fuzzy Sets & Relations

The slides in Figures 3 and 4 are from an activity that introduces fuzzy sets and relations. This activity focuses more on application than on concept invention, in part because the students were already familiar and comfortable with these concepts in regular (crisp) sets. In a setting where students were less familiar with these concepts, the activity might start more gradually and review these concepts. In Figure 3, the first three slides provide context and define some terms and relations, and slide Fuzzy Set Relations: Questions prompts students to apply these ideas. The instructor could ask teams to share their answers to see if there is agreement. Slide Fuzzy Set Operations: Familiar lists operations that students have encountered previously, and slide Fuzzy Set Operations: Questions uses convergent questions to prompt teams to apply these operations to fuzzy sets displayed as graphs, and to consider relationships among the new concepts. This might lead to a brief classroom discussion. The instructor might provide handouts for drawing the results of the 5 operations, and post each team‟s answers so other teams can study them.

Similarly, in Figure 4, slide Fuzzy Set Properties: Familiar defines concepts and slide Fuzzy Set Properties: Unfamiliar prompts students to consider the definitions before applying them; some teams may notice some subtleties before applying the concepts in slide Fuzzy Set Operations: Questions (1) and slide Fuzzy Set Operations: Questions (2). Again, the instructor might provide handouts and post answers for review and discussion. To improve this activity and make it more widely applicable, we might:  Review (crisp) set relations, operations, and properties to assess understanding and resolve gaps or misconceptions.  Use questions to explore and invent concepts such as membership degree and membership function. For example, the activity could start by considering different ways to describe someone‟s age (e.g. “under 21”, “over 65”, “middle aged”, “young”, “old”).  Use examples to explore and invent ways to define membership functions for finite and infinite sets.  Use questions to explore and invent ways to extend set relations and operations to fuzzy sets and the concept of support.

4

Results

At the end of the course, students were given a written survey and asked to briefly describe things that worked well and things that worked less well. Two examples follow: Group discussions & exchanging ideas with other groups is a better one. This makes us think about it in a better way. As you come to each group to talk, we can clarify our doubts by discussing it with you. And you encourage us to think more about the topic. Assignments also help us a lot to understand the subject in detail. Exams like this is new to us. This exams also make us think more about the things that we prepared for exams. Your way of teaching is entirely different from other classes. It helps me to think more and understand more things. When you are giving an assignment to us it is very different from the assignments that we are already done, at first was a strange experience but now I can realize that this is one of the best ways to think for students. In the case of exams also I feel the same. The group activities that you gave us is very helpful to know more about how helpful when working in a team rather than single. Other responses were consistent, though not always as eloquent. In sum, the responses included several recurring themes:

 Excitement about having a visiting faculty member from the US.  Initial uncertainty about an unfamiliar teaching and learning style, followed by the realization that they were understanding concepts better and acquiring useful process skills.  Some difficulty understanding the instructor‟s (American) English. However, within a team students could (and did) converse in English, Hindi, and Malayalam, so that students who had difficulty understanding the instructor could seek clarification from other team members.

5

Conclusions

POGIL is based on learning science and has a proven track record in other disciplines. POGIL classrooms are very different from lecture-based classrooms, but POGIL shares characteristics with other forms of active, discovery, and inquiry-based learning, so that faculty familiar with such approaches should not have difficulty adapting to POGIL. There are a variety of materials to help faculty develop and improve POGIL materials (e.g. [7], [8], [11]). There are several benefits to using POGIL, particularly in computer science and software engineering. Particularly in settings where students have varied academic and linguistic backgrounds, POGIL encourages students to collaborate and learn from each other rather than focusing attention on a single instructor. Software development is primarily a problem-solving activity where most background information is readily available, and POGIL helps students to develop their problem-solving abilities. Teams are an important part of most IT organizations, and POGIL helps students to develop important team process skills. There are also some challenges to using POGIL. Developing and revising effective activities can be time-consuming. Students and faculty who are not used to POGIL or other active learning approaches may be reluctant to try it or have difficulty at first. This paper is novel in that it describes: a) POGIL in computer science in general and soft computing in particular; b) POGIL outside the USA, and specifically in India; and c) POGIL activities using presentation slides rather than paper handouts. The author continues to develop, use, and revise POGIL activities for other topics in computer science, including Java programming, project management, and data structures and algorithms. One future direction is to extend and adapt the soft computing activities described here for courses and faculty at other institutions. Another direction is to explore the potential of supporting infrastructure, such as personal computers, learning management systems, or classroom response systems. Finally, the author hopes develop an international community of faculty using and improving POGIL activities in computer science.

6

Acknowledgements

The author thanks the US-India Educational Foundation and the University of Kerala for a Fulbright-Nehru teaching award that provided the opportunities and other support for this work. The author also thanks Muhlenberg College and the US National Science Foundation for support to develop and refine POGIL activities for computer science courses. Finally, the author thanks the National POGIL Project (http://www.pogil.org) for ongoing encouragement and support.

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