title: 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.
authors.affiliation: Beijing Normal University, Institute of Developmental Psychology, 100875, Beijing, China. xinziqiang@sohu.com
authors.forename: Ziqiang
authors.initials: Z
authors.lastname: Xin
mesh_terms: D000367:Age Factors; D002648:Child; D003071:Cognition; D003210:Concept Formation; D005260:Female; D006801:Humans; D008297:Male; D008433:Mathematics; D009949:Orientation; D011340:Problem Solving; D012858:Size Perception; D013334:Students / Q000523:psychology*