setsuya kurahashi: teaching simulation on collaborative learning, ability groups and mixed-ability...

Teaching Simulation on Collaborative Learning, Ability Groups and Mixed-ability Groups Setsuya KURAHASHI* and Keisuke KUNIYOSHI Graduate School of Systems Management (GSSM) University of Tsukuba, Tokyo

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Agenda • Motivation and Aims • Related Work of Learning theory

•  Item Response Theory •  Graphical Test Theory •  Complex Doubly Structured Network

•  Learning Model with Complex Doubly Structured Network • Experiment 1 : Effect of teaching strategies • Experiment 2 : Effect of collaborative learning • Experiment 3 : Effect of seating arrangement • Experiment 4 : Effect of ability classes • Discussion and Summary •  Future work

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Development of Human Resources

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Development of Human Resources

Cultural Capital Education

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Motivation and Aims •  What kind of influence could teaching

strategies have on learning effects? •  Modeling of a learning process of each student and

teaching strategies.

•  What kind of influence could the seating arrangement of learners have on collaborative learning effects?

•  Modeling of learner’s interaction in a classroom.

•  What kind of influence could ability groups and mixed-ability groups have on collaborative learning effects? •  Scenario analysis of learning environments.

•  The aims of the model is to analyse the actual conditions of understanding of learners regarding instructions given in classrooms.

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Test theory

This study

Item Response Theory (IRT)

Related Work of Learning Theory

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Graphical Test Theory Bayesian Network

Learning structuration study

•  Learning Material Structure Analysis

•  Course Outline Determination

•  Item Relational Structure (IRS)

Social network

study

Complex Doubly Structural Network

Doubly Structural Learning Model

Probabilistic reasoning method

The approach of this study

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The understanding status, knowledge structure, and collaborative effect of each learner are simulated on an agent-based model integrated by using a complex doubly structural network.

Test theory for exam questions (IRT) Learning material structure model (Bayesian net)

Collaborative learning approach

In-class learning process regarding a teaching strategy is one of unexplored fields.

Quantitative method of collaborative learning has not been developed yet.

■This study

Experiment 1: Effect of teaching strategies in a classroom Experiment 2: Effect of collaborative learning Experiment 3: Effect of seating arrangements Experiment 4: Effect of ability classes

Probability of Understanding Item Response Theory : IRT

•  IRT •  Standard Test Theory •  n Parameters Logistic Model •  Xn : exam question n

Estimation of Item Parameters(2PL)

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2PL Model

Item Response Theory (IRT) has been proposed to evaluate examina9on ques9ons.

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Graphical Test Theory: Bayesian Network

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■Estimation of a learning material structure

fx3 = P(X1)× P(X1,X3)P(X3)

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fx2 = P(X1)×P(X3)×P(X4)× P(X2,X1,X3,X4)P(X1,X3,X4)

= 0.74

fx4 = P(X1)×P(X3)

×P(X4,X1,X3)P(X1,X3)

= 0.83

fx5 = P(X2)×P(X3)×P(X4)

×P(X5,X2,X3,X4)P(X2,X3,X4)

= 0.61

Dependency relationship

Learning item

Conditionally probability of dependency

Complex Doubly Structural Network

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Internal Network (knowledge)

Social Network (society)

Internal Network

This model can express networks in microscopic and macroscopic ways as an integrated model.

Doubly Structural Learning Model

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Understanding probability

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Internal Network

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Level of achievement

Knowledge structure

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Internal (Knowledge) Network �Teaching strategy

Knowledge

Collaborative learning

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■Criteria 1)  Attainment degree : the proportion of correct answer 2)  Average teaching time : the time until the attainment degree has reached 1

Simulation Method

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■Internal network From arithmetic exam answer data of 300 learners, estimating (1) understanding probability(IRT), (2) material structured model(Bayesian Network)

■Simulation This simulation is to estimate what material should be taught, in what order and how many times, until all learners in the classroom could give the correct answer.

■Social network From seating allocation and correct answer data in a class, modeling a social network in a classroom.

■In-class learning model ・30 learners in a classroom ・5 teaching materials: X1, X2, X3, X4, X5

Estimated Ability and Understanding Probability

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　 Correct or Incorrect

Ability Probability

X1 X2 X3 X4 X5 X1 X2 X3 X4 X5

1 1 1 1 1 1 0.8457 1 0.93 0.96 0.95 0.68

2 1 1 1 1 0 0.1658 0.99 0.77 0.89 0.87 0.39

3 1 1 1 0 1 0.2427 0.99 0.8 0.9 0.88 0.43

4 1 1 1 0 0 -0.297 0.97 0.57 0.79 0.76 0.22

5 1 1 0 1 1 0.2 0.99 0.78 0.89 0.87 0.41

6 1 1 0 1 0 -0.332 0.97 0.56 0.78 0.75 0.21

7 1 1 0 0 1 -0.268 0.98 0.59 0.8 0.77 0.23

8 1 1 0 0 0 -0.731 0.91 0.37 0.64 0.63 0.12

9 1 0 1 1 1 0.0953 0.99 0.74 0.88 0.85 0.37

10 1 0 1 1 0 -0.419 0.96 0.52 0.75 0.73 0.19

… … … … … … … … … … … …

29 0 0 0 1 1 -1.102 0.78 0.22 0.49 0.49 0.07

30 0 0 0 1 0 -1.475 0.55 0.12 0.35 0.35 0.04

31 0 0 0 0 1 -1.427 0.58 0.13 0.36 0.37 0.04

32 0 0 0 0 0 -1.817 0.31 0.06 0.23 0.24 0.02

Item parameters: ability, difficulty, discrimination (IRT) Understanding probability (IRT, Bayesian network)

Simulation procedures

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For each knowledge Xn { For each learner { If a learner's Xn == 0 { if a collaborative relationship == true on the social network and a student on the relationship already understand the knowledge { P(Xn) <- 1 } else { Select subsequent knowledge connected Xn on the internal network. The probability is calculated as multiplication of the probability of all precedent knowledge connected and the conditional probability. } Based on the probability calculated, the value is conversed into two values 1 and 0. } }

A=er evalua9ng understanding status of all students for every material, a teacher decides the most effec9ve material to teach next.

Transition of the understanding status

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ODD protocol

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Overview 1.Purpose What kind of influence could teaching strategies have on learning effects? What kind of influence could ability groups and mixed-ability groups have on collaborative learning effects? 2.Entities, State valuables and Scales Teacher: teaching strategy, understanding status of students Students: understanding status, 3.Process overview and scheduling Applying teaching strategies for some class patterns in which students are seated, and then by comparing the average time of teaching sessions and the attainment degrees.

ODD protocol

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Design concepts

4.Design concepts ・Basic Principles: Item Response Theory for understanding probability model Bayesian Network for the course material structure model Social Network and the complex doubly structured network model ・Emergence: Collaborative learning ・Adaptation: A teacher decides order of a teaching material depending on understanding status of students. ・Objectives: Understanding status of students, teaching time ・Learning: No ・Prediction: A teacher predicts the most effective order of a teaching material. ・Sensing: Understanding status ・Interaction: Collaborative learning between students ・Stochasticity: Seating arrangements, ・Collectives: In-class social network between students and a teacher ・Observation: Understanding status, teaching times

ODD protocol

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Details 5.Initialization Teacher: 1, Student: 30, Material: 5 Teaching strategy: 4 types Learning style: lecture, left-and-right, group Seating arrangement: random, concentrated, dispersed Ability class: mixed-ability, high ability, medium ability, low ability 6.Input Data Arithmetic examination results of 300 students from an online learning system 7.Submodels Item response theory Graphical Test theory Course material structure model Complex doubly network theory

EXPERIMENT 1: EFFECT OF TEACHING STRATEGIES

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TS No. Method

TS 1 Teaching along with estimation by the complex doubly structured network method

TS 2 Teaching by selecting items to teach in a random manner

TS 3 Teaching an item where many learners gave wrong answers

TS 4 Teaching by moving to next item when all learners understood an item by order of the highest correct answer rate

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What kind of influence teaching strategies could have on learning effects.

■Teaching strategy

Comparison between teaching strategies

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The transition of attainment degree

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TS 2 TS 1

TS 3 TS 4

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Results of Experiment 1: Teaching Strategies

TS 1 has the highest attainment degree, TS 4 is the second best which adopts the teaching order of the highest correct answer rate.

No. Method Lecture style (Non-collaborative)

TS 1 Teaching along with estimation by the complex doubly structured network method

22.5

TS 2 Teaching by selecting items to teach in a random manner

41.4

TS 3 Teaching an item where many learners gave wrong answers

32.3

TS 4 Teaching by moving to next item when all learners understood an item by order of the highest correct answer rate

23.4

■Simulation result （The average teaching time）

EXPERIMENT 2: EFFECT OF COLLABORATIVE LEARNING

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Collaborative Learning Model

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Group collaborative learning

Left-and-right collaborative learning

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High academic capability

Lecture style learning (non-collaboration)

What kind of influence collaborative learning could have on learning effects.

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Results of Experiment 2: Collaborative learning

1)  Collaborative learning effect is higher than non-collaborative one. 2)  Group collaborative learning is higher than left-and-right collaborative

learning.

No. Method Collaboration type

Lecture Left-and-right Group

TS 1

Teaching along with estimation by the complex doubly structured network method

22.5 8.2 6.0

TS 2

Teaching by selecting items to teach in a random manner

41.4 17.7 13.6

TS 3

Teaching an item where many learners gave wrong answers

32.3 11.8 8.3

TS 4

Teaching by moving to next item when all learners understood an item by order of the highest correct answer rate

23.4 9.3 6.0

■Simulation result （The average teaching time）

EXPERIMENT 3: EFFECT OF SEATING ARRANGEMENTS IN COLLABORATIVE LEARNING

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Comparison between seating arrangements

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What kind of influence the seating arrangement could have on learning effects.

Concentrated arrangement

Dispersed arrangement

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Effect of seating arrangements in “left-and-right” collaborative learning

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Concentrated arrangement Dispersed arrangement

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Average teaching time: Left-and-right collaboration

High academic capability

Effect of seating arrangements in “group” collaborative learning

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Concentrated arrangement Dispersed arrangement

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Average teaching time Group collaboration

Results of Experiment 3: Seating arrangement

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Seating arrangement

Collaborative learning type

Random Concentrated Dispersed

Left-and-right 8.2 9.5 7.7

Group 6.0 8.4 5.6

Average teaching time

1)  While the teaching time increases in the concentrated arrangement. it decreases in the dispersed arrangement.

2)  Learning effects vary by making changes in the seating arrangement and the dispersed arrangement could enhance teaching effects.

EXPERIMENT 4: EVALUATION OF EFFECTS ON ABILITY CLASSES

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Evaluation of the effects on ability classes

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High ability class Low ability class Medium ability class

High Medium Low

17.0 20.0 23.7

Average teaching time of ability classes

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Lecture style What kind of influence ability classes could have on learning effects.


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High Medium Low

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Average teaching time of ability classes


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Average teaching time Group collaboration

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6.0 6.9 7.0

Results of Experiment 4: Ability class

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Learning type Mixed-ability classes

Ability classes

Lecture (non-collaborative)

67.5 60.7


23.1 25.5


16.8 19.9

Total number of average teaching time for mixed-ability and ability classes

In the lecture model, teaching time for the ability classes is less than the mixed ability classes. In the left-and- right, group collaborative learning model, teaching time for the ability classes is more than the mixed ability classes. The results indicate that ability classes have adverse effects on learners in collaborative learning.

Results of Experiment 4: Ability class

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Mixed-ability class

Ability class

Learning style High Medium Low

Lecture 22.5 17.0 20.0 23.7

Left-and-right 8.2 7.8 8.4 9.3

Group 6.0 6.0 6.9 7.0

Average teaching time for mixed-ability and ability groups

The ability classes for students of high academic capability are effective more than or equal to mixed-ability classes, while not effective for students of medium and low academic capability in collaborative learning.

Discussion and Summary •  We designed the integrated simulation model for in-class learning

processes considering academic capability, leaning material structure and collaborative relationship by interfacing internal and social network.

•  1st experiment: Effect of a teaching strategy

•  Different teaching strategies cause different effects of learning. •  The proposed teaching strategy has the highest attainment degree,

•  2nd experiment: Effect of a collaborative learning •  Collaborative learning has a positive effect more than the lecture style.

•  3rd experiment: Effect of a seating arrangement •  A dispersed seating arrangement is more effectively than a concentrated seating

arrangement.

•  4th experiment: Effect of ability classes •  Mixed-ability classes are more effective than ability classes in the collaborative

learning, while ability classes are effective in the lecture style.

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Discussion and Summary

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How influence could teaching strategies have on learning effects?

(1) When different teaching strategies, seating arrangements, and collaborative learning are used, learning effects vary, (2) group style collaborative learning on dispersed seating arrangements using the doubly structural learning model has high learning effects, and the second best is the method in order of the highest answer rate, and (3)an ability group has negative effect on collaborative learning because they reduce diversity in a class, so homogeneity between learners has the risk to make collaborative effect fall into decline, (4) whereas, if teaching is done one time for one knowledge item, some learners could fall behind in the learning progress. Reviews should be conducted repeatedly to facilitate the anchoring of the knowledge in a class.

Future work • We were not concerned about negative effects from

unskilful students or misunderstanding, so we’ll add the negative effects in the model.

• Some classes adopt more dynamic collaborative learning where high ability students are allowed to walk around and teach or discuss with others in a class. This dynamic situation should be designed in our model.

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setsuya kurahashi: teaching simulation on collaborative learning, ability groups and mixed-ability...

Science

learning process

learning material structurefx3

learners xn

study6test theory

ability groupsand

estimated ability

teaching simulation

integrated model