TY - JOUR
T1 - Supporting mathematical problem posing with a system for learning generation processes through examples
AU - Kojima, Kazuaki
AU - Miwa, Kazuhisa
AU - Matsui, Tatsunori
PY - 2013
Y1 - 2013
N2 - Problem posing, by which learners create new problems by themselves, is an important activity in mathematics education. However, novice learners have difficulty in posing problems, particularly when formulating appropriate solution structures of problems. Although they are provided with example problems that can serve as hints for composing novel problems, they do not necessarily understand the key ideas used to generate the examples. To improve problem posing for novices, this study discusses an approach that supports learning from examples as a production task. We propose a method of learning from examples through imitation, where a learner reproduces problems identical to given examples. We implement a system that presents examples of problem posing and supports learners in understanding the examples by having the learners reproduce them. We conducted an experimental evaluation in which learners learned from an example that embeds useful ideas to alter solution structures in the system. The results demonstrated that the learners successfully adapted the example when posing their own problems if they learned the example by the reproduction method. Thus, learning from examples through reproduction appears to be effective in the domain of problem posing as a production task.
AB - Problem posing, by which learners create new problems by themselves, is an important activity in mathematics education. However, novice learners have difficulty in posing problems, particularly when formulating appropriate solution structures of problems. Although they are provided with example problems that can serve as hints for composing novel problems, they do not necessarily understand the key ideas used to generate the examples. To improve problem posing for novices, this study discusses an approach that supports learning from examples as a production task. We propose a method of learning from examples through imitation, where a learner reproduces problems identical to given examples. We implement a system that presents examples of problem posing and supports learners in understanding the examples by having the learners reproduce them. We conducted an experimental evaluation in which learners learned from an example that embeds useful ideas to alter solution structures in the system. The results demonstrated that the learners successfully adapted the example when posing their own problems if they learned the example by the reproduction method. Thus, learning from examples through reproduction appears to be effective in the domain of problem posing as a production task.
KW - Problem posing
KW - learning from examples
KW - learning through reproduction
KW - production task
UR - http://www.scopus.com/inward/record.url?scp=84887861212&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84887861212&partnerID=8YFLogxK
U2 - 10.3233/JAI-130035
DO - 10.3233/JAI-130035
M3 - Article
AN - SCOPUS:84887861212
VL - 22
SP - 161
EP - 190
JO - International Journal of Artificial Intelligence in Education
JF - International Journal of Artificial Intelligence in Education
SN - 1560-4292
IS - 4
ER -