Date of Award

2008

Degree Type

Thesis

Degree Name

Bachelor of Arts Honours

School

School of Psychology and Social Sciences

Faculty

Faculty of Computing, Health and Science

First Advisor

Dr Craig Speelman

Abstract

Research within the field of mathematical learning has often focused on the extent to which knowledge of particular mathematical skills can facilitate the learning of new and unpracticed mathematical skills. Additionally, it has examined the influence of context on learning and the amount of practice necessary for complex skill acquisition to result. This paper provides a review of the research examining mathematical learning, skill acquisition and transfer of skills in a mathematical context. Pertinent theories in the field of cognitive skill acquisition are examined for their ability to explain transfer of skill. The review focuses on factors that influence the acquisition and transfer of skills, including: the impact of task difficulty on learning; the influence of context on skill retention and transfer; and the effect that understanding the underlying concepts of simple tasks has on the learning of complex tasks. The research evidence suggests that transfer of mathematical skill can occur if given the correct conditions. Learning contexts should be sufficiently difficult to result in enhanced learning, and comprehension of underlying strategies necessary for skilled performance of a task will facilitate performance on simpler tasks. The paper concludes that transfer is dependent on the skill that is learned and the manner it is learned in, and further research is needed to investigate how mathematical learning and skill transfer can be enhanced. This study examined mathematical skill transfer facilitated by a mathematical computer game based on Speelman and Kirsner's (2005) Components Theory of Skill Acquisition and Transfer. Two alternative hypotheses were investigated: (1) By mastering mathematical tasks in the experimental computer game, performance would be enhanced on all mathematical problems (multiplication, addition and pictorial) presented in the post-test; and (2) task performance would only be enhanced for the mathematical problems practiced in the computer game. Eighty-four third-grade students from three primary schools in Perth, Western Australia participated in the study. Students engaged in a 5 min pre-test of multiplication, additional and pictorial problems, followed by 30 min of computer game-play of one of three .computer games (experimental mathematical game, comparison mathematical game, and game unrelated to mathematics). They then engaged in a 5 min post-test of multiplication, addition and pictorial problems. Score differences between pre- and post-tests were recorded. A significant difference was identified between the control group game and the comparison mathematical game only, indicating that results did not support either hypotheses. Overall, students in the control group performed more successfully than students in the other groups. This finding was contributed to the low power of the test statistic due to low participant numbers, flaws in the experimental computer game, as well as student motivation and enthusiasm. It was concluded that learning is at its best when students have experienced task mastery and are motivated to take on challenges, however, the study needs to be repeated with more participants and after levels in the experimental computer game are amended.

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