Applying contemporary views of mathematical proficiency to the examination of the relationship of motivation and mathematics achievement.

Abstract

Prior research has documented that aspects of motivation are important for mathematics learning. This study examined the relationship between student motivation and proficiency in mathematics, using well-established motivation constructs and contemporary conceptions of mathematical competence. Students' mathematical proficiency was assessed across a range of topics and types of mathematical knowing. A sample of 479 Southern California pre-algebra students responded to a self-report survey of motivation in mathematics (i.e., values, emotions, efficacy, and personal achievement goal orientation) and completed a performance assessment that differentiated between procedural/conceptual understanding and adaptive reasoning for the topic of addition of unlike fractions. Students' work on the performance assessment was compared with their scores on a multiple-choice readiness test and a state achievement test; the relationship of motivation to all three assessments was then examined. The performance assessment results revealed that many students had difficulty with both procedural/conceptual understanding and adaptive reasoning, and that understanding is a necessary but not sufficient condition for reasoning. The analyses suggested that, in addition to students' perceptions of value (including cost) and efficacy, their focus on learning and understanding (i.e., mastery-goal endorsement) is an important correlate of adaptive reasoning. The results also showed that students who score high on measures of both interest and efficacy are not necessarily high-achieving; rather, their performance depends on the relative levels of other aspects of motivation, such as their perceptions of cost and their math achievement goals (i.e., personal goal orientation). The findings of this study indicate that using a more refined conception of mathematical competence together with measures of a differentiated set of motivational constructs can help in understanding the relationship between motivation and student learning in mathematics. This study thus provides a framework for research on motivation in mathematics education that can further the understanding of how aspects of motivation relate to mathematical proficiency and achievement.