Educators aim to equip students with learning strategies they can apply when approaching new problems on their own. Teaching design-thinking strategies may support this goal. A first test would show that the strategies are good for learning and that students spontaneously transfer them beyond classroom instruction. To examine this, we introduce…

The use of a visual representation in learning about proportional relations was studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability…

In an effort to create a mathematics learning environment in which the social nature of the classroom facilitates conceptual conjecture and justification, a visual representation has been designed that students can manipulate to make demonstrative proofs in the domain of proportional representation. This study explores student use, incorporation,…