Bridge the gap between cognitive attributes and mathematics achievement: which cognitive attributes for mathematical modeling contribute to better learning in mathematics?

Mathematical modeling is a thinking process that applies various sets of cognitive attributes – one component of intellectual resources (i.e., cognitive resources). Students are able to develop cognitive attributes when they engage in mathematical modeling activities. Furthermore, using many of the cognitive attributes developed during the mathematical modeling process, students solve mathematics problems, for example, in assessments. Examining students’ mastery of these cognitive attributes, we can investigate relationships between students’ cognitive development through mathematical modeling practices in classrooms and their performance on mathematics assessments. The purpose of this research is to quantitatively and empirically investigate the relationships between students’ development of mathematics cognitive attributes and their achievement. For the current study, we selected the four cognitive attributes representing different stages of the mathematical modeling practices – select, analyze, compute, and represent. The generalized DINA (deterministic inputs, noisy “and” gate) is applied to generate students’ mastery profiles of the cognitive attributes from their responses to test items. Using students’ mastery profiles as datasets, three secondary analysis studies are conducted with linear regression analysis and multivariate approach to repeated measure ANOVA. The findings show that development of the four cognitive attributes in mathematical modeling is positively related to mathematics achievement. In addition, students, who developed select and compute throughout 4th to 8th grades, scored higher in mathematics assessment with large degrees of effects. The findings suggest important implications to teachers: Students need to have opportunities develop a wide range of cognitive attributes of mathematical modeling, which would result in higher achievement. Teachers need to have instructional emphases on different stages of mathematical modeling depending on grade levels: students’ representing a solution at elementary-school levels; and analyzing a problem situation and selecting strategies at middle-school levels. The study also suggests teachers shift an instructional emphasis from learning mathematics contents to high-order thinking like mathematical modeling to accomplish higher mathematics achievement.