Proceedings of the International Group for the Psychology of Mathematics Education · Volume 1
Xiaoshan Huang, Sofia Ikonen, Koen Veermans, Jake McMullen
University of Turku
⬇ Download PDFGuided by theories of knowledge integration and adaptive expertise, this paper describes the design of number line estimation tasks that target adaptive rational number knowledge. We propose three design principles: (1) eliciting learners’ current knowledge, (2) introducing linking ideas and increasing element interactivity, and (3) embedding multiple solution routes with on-the-spot decisions. The design aims to stimulate students to coordinate five knowledge components embedded in number line estimation tasks—magnitude mapping, relational reasoning, cross-notation conversion, within-notation transformation, and arithmetic operation—and the manipulation of number line features (including non-integer-unbounded number lines) and target formats as two central mechanisms to support knowledge integration.
Knowledge integrationAdaptive expertiseAdaptive rational number knowledgeGame-based learning