TY - JOUR

T1 - Experimental study of learning support through examples in mathematical problem posing

AU - Kojima, Kazuaki

AU - Miwa, Kazuhisa

AU - Matsui, Tatsunori

N1 - Funding Information:
This study was partially supported by the Grant-in-Aid for Young Scientists (B) 23700990 and 25870820 of the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Publisher Copyright:
© 2015, The Author(s).

PY - 2015/12/1

Y1 - 2015/12/1

N2 - When using mathematics to solve problems in everyday life, problem solvers must recognize and formulate problems by themselves because structured problems are not provided. Therefore, in general education, fostering learner problem posing is an important task. Because novice learners have difficulty in composing mathematical structures (solutions) in problem posing, learning support to improve the composition of solutions is required. Although learning by solving examples is adopted in general education, it may not be sufficiently effective in fostering learner problem posing because cognitive skills differ between problem solving and problem posing. This study discusses and experimentally investigates the effects of learning from examples on composing solutions when problem posing. We studied three learning activities: learning by solving an example, learning by reproducing an example, and learning by evaluating an example. In our experiment, undergraduates were asked to pose their own new, unique problems from a base problem initially presented after the students learned an example by solving, reproducing, or evaluating it. The example allowed the undergraduates to gain ideas for composing a novel solution. The results indicated that learning by reproducing the example was the most effective in fostering the composition of solutions.

AB - When using mathematics to solve problems in everyday life, problem solvers must recognize and formulate problems by themselves because structured problems are not provided. Therefore, in general education, fostering learner problem posing is an important task. Because novice learners have difficulty in composing mathematical structures (solutions) in problem posing, learning support to improve the composition of solutions is required. Although learning by solving examples is adopted in general education, it may not be sufficiently effective in fostering learner problem posing because cognitive skills differ between problem solving and problem posing. This study discusses and experimentally investigates the effects of learning from examples on composing solutions when problem posing. We studied three learning activities: learning by solving an example, learning by reproducing an example, and learning by evaluating an example. In our experiment, undergraduates were asked to pose their own new, unique problems from a base problem initially presented after the students learned an example by solving, reproducing, or evaluating it. The example allowed the undergraduates to gain ideas for composing a novel solution. The results indicated that learning by reproducing the example was the most effective in fostering the composition of solutions.

KW - Learning from examples

KW - Mathematical learning

KW - Problem posing

KW - Production task

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U2 - 10.1007/s41039-015-0001-5

DO - 10.1007/s41039-015-0001-5

M3 - Article

AN - SCOPUS:85007388191

SN - 1793-7078

VL - 10

JO - Research and Practice in Technology Enhanced Learning

JF - Research and Practice in Technology Enhanced Learning

IS - 1

M1 - 1

ER -