Improving cognitive and affective learning outcomes of students through mathematics instructional tasks of high cognitive demand

Abstract

This study investigated the relationship between three cognitive features of mathematical instruction tasks (high cognitive demand, multiple representations, and multiple solution methods) and student learning outcomes among 1,779 students from 30 Chinese fifth-grade classrooms using a new mathematics curriculum. Measures of mathematics learning outcomes at two data points over 16 months were analyzed. These included cognitive (calculation, routine problem solving, and complex problem solving) as well as affective outcomes (expressed interest in learning mathematics, classroom participation, views of mathematics, and views of learning mathematics). The student post-assessment was administered 13 months after the assessment of teaching quality on the three task variables. The results indicated that the frequency of mathematical tasks involving multiple representations positively predicted students' improvement in solving complex questions. The frequency of mathematical tasks of high cognitive demand did not predict any of the three cognitive learning outcomes. However, it did positively predict students' indicated interest in learning mathematics, indicated classroom participation, and a dynamic view of learning mathematics. The results highlight the significance of the cognitive demand of instructional tasks—connecting procedural and conceptual aspects of mathematics—in facilitating students' positive relationships with mathematics and mathematics classrooms. The findings provide much-needed normative data of a systematic description that links the three cognitive features of instructional tasks to the specific student learning outcomes in a cultural setting, which is a unique addition to the literature of pedagogy on mathematics instructional tasks.