Thomas Kuhn (1962/2012) introduced the term "paradigm shift" to the scientific literature to describe how knowledge in science develops. The aims of this article are to identify paradigm shifts, or revolutions, that have occurred in mathematics, and to discuss their relevance to teaching mathematics in schools. The authors argue that…

Standardized tests have been selected as a key assessment factor in expanding the academic achievement of the national student population. However, these tests position immigrant students at the risk of academic failure, leading education experts to search for new strategies and teaching models. The "Handbook of Research on Assessment…

This study addressed the problem of why students with learning disabilities in mathematics too often fail to develop multiplicative and divisional concepts/operations. We conducted a constructivist teaching experiment with 12 students (nine 5th and three 4th graders). This report focuses on three students' conceptual progress, particularly on…

Describes generalization activity as an opportunity to learn about seventh graders' understanding of functions. Findings indicate that the modeling efforts of students allowed them to analyze their understanding of representations of quantities, relationships among quantities, and relationships among the representations of quantities in both…

This study reports the cognitive processing of a Year 8 female student (Kerri) during a test, and during her subsequent homework as she consolidated as part of abstracting; a topic of recent research interest. This case adds to the body of knowledge about how constructing and consolidating can occur simultaneously. The analysis captured the…

Research conducted by the National Research Center on Student Learning (NRCSL) is reviewed as it moves toward a new understanding of learning and instruction. Research by the NRCSL into the kind of learning demanded by modern life has been shaped by the understanding, based on earlier research, that knowledge is actively constructed in the mind of…

Noting that effective teaching models that emphasize critical thinking in mathematics and science are used less often in early childhood classrooms than in those for older students, this book provides early childhood educators with an explanation of teaching models that promote 3- to 8-year-olds critical thinking, problem solving, decision making,…