Abstract
The ability to solve linear function problems is a key facet of mathematical competence. According to current models, competence comprises not only cognitive but also affective aspects such as self-efficacy. However, there is a lack of test instruments for assessing both facets of competence with linear functions using the same test items. Although research documents a moderate and positive relationship between cognitive and affective aspects of mathematical competence, it is yet unclear which individual competency profiles can be identified with a task-specific assessment in the domain of linear functions. We asked 120 8th- and 9th-graders (14–15 years old) to predict their performance on concrete linear function problems and then solve the same problems. There was a moderate positive correlation between performance and self-efficacy. For both variables, we found significant gender differences in favor of the boys, underscoring the need to consider affective-motivational competence dimensions to understand individual differences. A cluster analysis identified five groups of students with different profiles of self-efficacy and performance. Among those were groups of students who greatly overestimated or underestimated their own ability to solve linear function problems. Students with different competency profiles also differed in the accuracy with which they assessed their performance on individual problems. The results of this study advance previous research on the relationship between performance and self-efficacy in mathematics by adopting a content- and task-specific perspective. The results are relevant to classroom practice because students with different competency profiles should benefit from different types of instruction.
Translated title of the contribution | Performance and Self-Efficacy as two Dimensions of Competence: An Assessment of Individual Competency Profiles in the Domain of Linear Functions |
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Original language | German |
Pages (from-to) | 267-299 |
Number of pages | 33 |
Journal | Journal fur Mathematik-Didaktik |
Volume | 41 |
Issue number | 2 |
DOIs | |
State | Published - 1 Oct 2020 |
Externally published | Yes |