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Learning by Problem-Posing and Agent-Assessment

Tsukasa HirashimaHiroshima University

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Learning by Problem-Posing and Agent-Assessment

Feedback and guidance are strongly requiredInteractive and Intelligent Learning Environment

Feedback and guidance are strongly requiredInteractive and Intelligent Learning Environment

Learning method

Automatic Assessment of Posed Problems

•Students are required to make problems that the students are usually required to solve.•Promising method to promote deeper comprehension for problems

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•Several sentence cards are provided•Problems are composed by selecting and ordering sentence cards

•Simplification problem posing•Computer Readability•Keeping Essential Activity

Problem Posing as Sentence IntegrationProblem Posing as Sentence Integration

Learning by Problem-Posing and Agent-Assessment

How to pose problemsArithmetical Word Problems

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Contents

Categorization of Learning by Problem-Posing• Solution Based Problem Posing

Interactive Learning Environment for Problem-Posing• How to pose problems

• Sentence Integration

• Explanation of Monsakun

Experimental Evaluation by Two Months Use

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Categorization of Problem-Posing

Solution-Based Problem-Posing Problem-Based Problem-Posing Episode-Based Problem-Posing

Problem = “Given Information” + “Required Information”

Method to derive R-Info from G-Info is Solution Method.

A set of given information is Episode.

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How to pose problems

(1) Natural Language(2) Sentence templates

• Sentence template has several blanks• Fill in the blanks by prepared concepts• Make a problem with the sentences

(3) Problem template• Problem template has several blanks• Fill the blanks by prepared concepts

(4) Sentence cards• Sentence cards are provided• Make a problem by selecting and

combining them• Problem-posing with sentence integration

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Process Model of Problem-Solving of Arithmetical Word

ProblemTom had five pencils.Ken gave three pencils to Tom.How many pencils does Tom have?

NaturalLanguage

sentence

sentence

sentence

sentence

sentence

○＋△= ? ?=□

Integration

…

Transformation Plan Execution

A process model of problem-solving of arithmetical word problem

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Problem-Posing by Sentence-Integration with Sentence Cards

NaturalLanguage

sentence

sentence

sentence

sentence

sentence

○＋△= ? ?=□

Integration

…

Transformation Plan Execution

Most important process in the problem solving is “Integration”.

(1) Provide with a set of sentence cards. Each card has one sentence.(2) Select necessary sentence cards and arrange them in proper order.

Integration process is remained, but transformation process is simplified

Problem-posing activity becomes simple, but keep the essential process

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Learning Environment for Solution-Based Problem

Posing as Sentence-Integration

•Simple arithmetical word problems•Solved by one addition or subtraction

•Solution-based problem posing•To make problems that can be solved by specified solution method

•Problem-posing as sentence integration

•Problem posing by Combination of sentence cards

•Simple arithmetical word problems•Solved by one addition or subtraction

•Solution-based problem posing•To make problems that can be solved by specified solution method

•Problem-posing as sentence integration

•Problem posing by Combination of sentence cards

Learning environment for leaning by problem-posing: MONSAKUNLearning environment for leaning by problem-posing: MONSAKUN

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Return

Pose a problem that can be solved by " 5 - 3 ".

Quit Change task

Put a card in this blank

Put a card in this blank

Put a card in this blank

Eject

Eject

Eject

Tom has five pencils.

Ken received three pencils from Tom.

How many pencils does Tom have?

How many pencils does Ken have?

Ken gave three pencils to Tom.

Tom received three pencils from Ken.

Check the problem!

Put a card in the same shape blank

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Return

Pose a problem that can be solved by " 5 - 3 ".

Quit Change task

Put a card in this blank

Put a card in this blank

Eject

Eject

Eject

Tom has five pencils.

How many pencils does Tom have?

Ken gave three pencils to Tom.

Check the problem!

Put a card in the same shape blank

Ken received three pencils from Tom.

Ken received three pencils from Tom.

How many pencils does Ken have?

Tom received three pencils from Ken.

Wrong!!

Let’s think about the second sentence.Does this problem solve by 5-3?Try again.

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Demonstration

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Experimental Uses in Elementary School

•Two classes in the third grade: 44 students（ two class times）•Three classes in the second grade: 91 students (two class times)•Six classes in the second grade: 132 students (two class times) •Three classes in the second grade: 99 students

（ two class times and two months use in free time）•Two classes in the second grade: 46 students (two class times) •Three classes in the second grade: 76 students (two class times)•Three classes in the first grade: 104 students (one class time)•Four classes in the second grade: 143 students (two class times)•Two classes in the fourth grade: 39 students [eight class time]

•Two classes in the third grade: 44 students（ two class times）•Three classes in the second grade: 91 students (two class times)•Six classes in the second grade: 132 students (two class times) •Three classes in the second grade: 99 students

（ two class times and two months use in free time）•Two classes in the second grade: 46 students (two class times) •Three classes in the second grade: 76 students (two class times)•Three classes in the first grade: 104 students (one class time)•Four classes in the second grade: 143 students (two class times)•Two classes in the fourth grade: 39 students [eight class time]

774 students774 students

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Long Term Use

•Subjects:•99 elementary students•3 classes in the second grade

•Period:•2 months (46 school days)

•Situation•Two systems in a class (6 systems in the school)•Out-of-class time•Free use

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Experimental Evaluations

● Whether students use the system on their own will

(1)Problem Posing Logs(2)Questionnaires

● Effect of long-term use(1) Extraneous Problem Test

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Results of the use

•Total Posed Problems: 8,386 problems

•30.4 problems were posed in a day

•A student posed 84 problems in average.

•A student used the system 8.5 days in average.

Total days were 46 daysThere were only 6 systems for 99 students.

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Results of Questionnaires

Answer

Question Yes No

No

idea

Do you think MONSAKUN make arithmetic enjoyable? 84 1 6

Do you think MONSAKUN is a game? 52 21 18

Do you think MONSAKUN is useful for arithmetic learning? 82 3 6

Do you like to use MONSAKUN more often? 80 2 9

Do you think you could make problems easier than before? 75 3 13

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Extraneous Problem Test

There are two apples.There are three oranges.There are seven bananas.How many apples and oranges are there in total?

•Extraneous problem includes extraneous sentence that is not necessary to solve the problem.

•It is required to judge the relevant sentences and extraneous sentence.

•It is useful to assess the ability to integrate sentences.

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Extraneous Problem Test

Pre-test score

High-score(>8.32)

Low-score(=<8.32)

Number of posed problems

High-posed(> 77)

32 20

Low-posed(=< 77)

12 21

Average score of pre-test = 8.32Median of the number of posed problems = 77

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Extraneous Problem Test

Condition Pre-test Post-test

High-score/High-posed (n =32) 11.06 (SD=1.16) 10.96 (1.28)

High-score/Low-posed (n =20) 10.65 (1.18) 10.50 (2.25)

Low-score/High-posed (n =12) 4.41 (2.78) 7.25 (2.52)

Low-score/Low-posed (n =21) 4.14 (3.04) 4.71 (3.81)

• Full marks are 12.• In the comparison between pre-test and post-test, there is significant difference only at low-score/high-posed group .

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Results of experimental use

(1) Some of students posed problems with the system eagerly even in free use situation.(2) Students and teachers accepted the problem-posing as useful learning activity.(3) This problem-posing was useful to improve problem-solving performance for lower score students who posed problems eagerly.

Our approach to realize “learning by problem-posing” is promising.

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Related Future works

Related and future works• Solution-based and sentence-integration

• Lower grade students: first grade students• Comparing with other learning

• Other type of problem-posing• Problem-Based Problem Posing: Problem-Transformation• Story-Based Problem Posing

• Other domains• Mechanical problems• Multi-digit problems• Equation problems

• Model of problem-posing• As a promotion method for metacognition