Fourth- Through Sixth-Grade Students' Representations of Area-of-Rectangle Problems: Influences of Relational Complexity and Cognitive Holding Power

Abstract

The relational complexity of variables in a problem and characteristics of the learning settings may affect students' representations of word problems. The settings that pressure students into using and developing 1st- or 2nd-order cognitive procedures are known to have 1st- or 2nd-order cognitive holding power. In the present study, the author explored 382 4th-6th-grade students' representation levels of area-of-rectangle problems, which belonged to 4 templates with different relational complexity and influences of cognitive holding power. Students' representation levels improved across grades and their representation levels of 4 templates had a clear hierarchical order. The higher the relational complexity and knowledge requirements of a problem, the greater the grade differences in representations of the problem. 1st- and 2nd-order cognitive holding power significantly predicted the representation levels of each template. Moreover, the predictive power increased from Template 1 to Template 4, but the predictive directions were opposite.

Keywords:

• cognitive holding power
• learning settings
• problem representation
• relational complexity