### Abstract

The present study focused on a method of instruction that combined goal setting and self-graphing in time trials (test condition) to build math fluency in multiplication. The effects of this method were compared to the effects of instruction using only time trials (control condition). The experimental designs used were (a) a control group comparison, in which the participants were 3^{rd}-graders from 2 classes, and (b) a changing criterion design, in which the participants were 4^{th}-graders in 1 class. The target math skill was knowing the multiplication tables; the dependent variable was the number of correct answers in a 2-minute time trial. Analysis of the results for both designs indicated greater effects of the intervention in the test condition than in the control condition. Specifically, in the control group comparison, the results of an analysis of covariance showed that the scores on the post-instruction test were significantly higher in the test group than in the control group. In the changing criterion design, a linear mixed modeling analysis of the difference between the test condition scores and the maximum scores of the students in the control condition showed that the students' results in the test condition were significantly higher than the maximum scores of the students in the control condition. Spearman's rank correlation was used to test the relationship between the social validity of each student's test score and that student's increase in math fluency, defined as the difference between the student's pre- and post-instruction scores on a test of the multiplication tables. A significant positive correlation was found only in the test condition between the increase in math fluency and scores for the statement, "I could feel that I had made progress.".

Original language | English |
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Pages (from-to) | 132-144 |

Number of pages | 13 |

Journal | Japanese Journal of Educational Psychology |

Volume | 65 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Education
- Developmental and Educational Psychology