### Abstract

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.

Original language | English |
---|---|

Article number | 1 |

Journal | Research and Practice in Technology Enhanced Learning |

Volume | 10 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Dec 1 |

### Fingerprint

### Keywords

- Learning from examples
- Mathematical learning
- Problem posing
- Production task

### ASJC Scopus subject areas

- Education
- Social Psychology
- Media Technology
- Management of Technology and Innovation

### Cite this

**Experimental study of learning support through examples in mathematical problem posing.** / Kojima, Kazuaki; Miwa, Kazuhisa; Matsui, Tatsunori.

Research output: Contribution to journal › Article

*Research and Practice in Technology Enhanced Learning*, vol. 10, no. 1, 1. https://doi.org/10.1007/s41039-015-0001-5

}

TY - JOUR

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

AU - Kojima, Kazuaki

AU - Miwa, Kazuhisa

AU - Matsui, Tatsunori

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

UR - http://www.scopus.com/inward/record.url?scp=85007388191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007388191&partnerID=8YFLogxK

U2 - 10.1007/s41039-015-0001-5

DO - 10.1007/s41039-015-0001-5

M3 - Article

AN - SCOPUS:85007388191

VL - 10

JO - Research and Practice in Technology Enhanced Learning

JF - Research and Practice in Technology Enhanced Learning

SN - 1793-7078

IS - 1

M1 - 1

ER -