1 Learning by Problem-Posing and Agent-Assessment Tsukasa Hirashima Hiroshima University

2 Learning by Problem-Posing and Agent-Assessment Feedback and guidance are strongly required Interactive and Intelligent Learning Environment Feedback and guidance are strongly required Interactive 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

3 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 Integration Learning by Problem-Posing and Agent-Assessment How to pose problems Arithmetical Word Problems

4 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

5 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.

6 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

7 Process Model of Problem-Solving of Arithmetical Word Problem Tom had five pencils. Ken gave three pencils to Tom. How many pencils does Tom have? Natural Language sentence ○ ＋△ = ? ?= □ Integration … Transformation PlanExecution A process model of problem-solving of arithmetical word problem

8 Problem-Posing by Sentence-Integration with Sentence Cards Natural Language sentence ○ ＋△ = ? ?= □ Integration … Transformation PlanExecution 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

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

10 Return Pose a problem that can be solved by " ". Quit Change task Put a card in this blank 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

11 Return Pose a problem that can be solved by " ". Quit Change task Put a card in this blank 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. 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.

12 Demonstration

13 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 students

14 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

15 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

16 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 days There were only 6 systems for 99 students.

17 Results of Questionnaires

18 Extraneous Problem Test 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.

19 Extraneous Problem Test Pre-test score High-score (>8.32) Low-score (=<8.32) Number of posed problems High-posed (> 77) 3220 Low-posed (=< 77) 1221 Average score of pre-test = 8.32 Median of the number of posed problems = 77

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

21 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.

22 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