Designing Knowledge Scaffolds to Support Mathematical Problem Solving

We present a methodology for designing better learning environments. In Phase 1, 6th-grade students' (n = 223) prior knowledge was assessed using a difficulty factors assessment (DFA). The assessment revealed that scaffolds designed to elicit contextual, conceptual, or procedural knowledge each improved students' ability to add and subtract fractions. Analyses of errors and strategies along with cognitive modeling suggested potential mechanisms underlying these effects. In Phase 2, we designed an intervention based on scaffolding this prior knowledge and implemented the computer-based lessons in mathematics classes. In Phase 3, we used the DFA and supporting analyses to assess student learning from the intervention. The posttest results suggest that scaffolding conceptual, contextual, and procedural knowledge are promising tools for improving student learning.