A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…

In the spring of 2015, Illinois students will take new state assessments that, like the new Illinois Learning Standards, challenge them to think deeply, write often and defend their reasoning--all skills they will need in the world. The Partnership for the Assessment of Readiness for College and Career (PARCC) covers math and English Language Arts…

College students' epistemological belief in their academic performance of mathematics has been documented and is receiving increased attention. However, to what extent and in what ways problem solvers' beliefs about the nature of mathematical knowledge and thinking impact their performances and behavior is not clear and deserves further…

Recent theoretical developments in cognitive psychology imply both a need and a possibility for methodological development. In particular, the theory of problem solving proposed by Allen Newell and Herbert A. Simon (1972) provides the rationale for a new empirical method for the processing of think-aloud protocols--trace analysis. A detailed…

This report describes 12 studies dealing with the knowledge monitoring component of metacognition. It is assumed that knowledge monitoring is basic to other metacognitive activities, such as evaluating learning, selecting appropriate strategies, or planning, because distinguishing between what students know and do not know ought to be a…

This document contains the fifth volume of the proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 59 research reports by presenters with last names beginning between Sac and Zaz:…