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.

KEYWORDS:

• Affect in mathematics
• curriculum reform
• instructional tasks
• mathematical achievements
• primary mathematics

Funding

Hong Kong Institute of Educational Research, Chinese University of Hong Kong (6900840); Hong Kong Research Grant Council (CERG-449807,CERG-462405).

Notes

1. Mainland China has had a nationally mandated school mathematics curriculum since 1949. The nationally mandated school mathematics curricula have been developed and approved by central government-appointed committees (X. Ma, 1996; Ministry of Education, 2001, 2011). Accordingly, the development and publishing of textbooks is closely regulated and monitored by the central government, the Ministry of Education. In mainland China, there are only a few officially designated publishers who are permitted to develop textbooks. Only with the approval of a central government-appointed committee can developed textbooks be published and made available to public schools.

2. The test form for calculation and for routine problem solving (all multiple-choice questions) used for preassessment was as Form A and the form used postassessment as Form B. There were six common items between the two forms for the calculation part and routine problem solving part, respectively. Therefore, a procedure for common items nonequivalent groups equating was used to develop a common metric for linking the two test forms for the calculation part and the routine problem-solving part, respectively (Zimowski, Muraki, Mislevy, & Bock, 1996). Twelve open-ended mathematics questions were divided into form A and form B for the two administrations of the assessment, each with six questions. In equating the two forms of the open-ended questions, it was assumed that two random groups were selected to take the test form A and form B, respectively. Hence, presmoothing and postsmoothing equipercentile equating methods were used to link the two test forms (Kolen & Brennan, 2004), so that the scores for form B were equated onto the score scale of form A.