In classroom learning, students need mathematical cognitive flexibility to be able to solve mathematical problems with the various ideas they express. To solve the problems, they must be able to grasp the problem, see it from various points of view, and should not be rigid thinking with one solving method. In fact, the students still lack the…

This case study describes how our research team conducted the qualitative think-aloud approach (or cognitive pretesting) to obtaining cognitive validity evidence for a biology inference-making and reasoning measure for undergraduate students. The main goal of our work was to gather high-quality student think-aloud data of reasoning while they were…

Instruction promoting reasoning and proof should be a part of K-12 mathematics teaching. Preservice teachers (PSTs) need mathematics content instruction that helps them construct valid justifications for mathematical notions and develop positive perceptions of proof. This case study describes instruction with proof-related tasks and manipulatives…