Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means…

A study with prospective teachers without prior mathematical modeling experience sheds light on how their newly developed conceptual understanding of modeling manifested itself in their work on the final task of a modeling module within a pedagogy course in secondary mathematics curriculum and assessment. The main purpose of the module was to…

Cognitive development of any concept is related with affective development. The present study investigates students' beliefs about the use of different types of representation in understanding the concept of fractions and their self-efficacy beliefs about their ability to transfer information between different types of representation, in relation…

Explores how students interpret algebraic notation and what teachers can do to support appropriate interpretations. Presents two research-based strategies and concludes that in the face of reform and technological advances, finding a definition for symbol sense takes on added significance. Contains 22 references. (ASK)

Aims for students to use a combination of stochastic ideas to simulate a basketball tournament. Uses the TI-83 calculator in the activity to simulate the binomial distribution. (KHR)

Observes the application of probability theory to a game between two players. Shows how basic techniques such as tree diagrams can be used to demonstrate optimum strategies, how the art of bluffing can be quantified, and how this might be applied to a game of poker. (Author/ASK)

Investigates the effects of inquiry activities on a dynamic geometry environment designed to confront students with contradictions and uncertainties. Characterizes epistemological, didactic, and cognitive aspects of the activities. Analyzes the interplay among these three aspects, students' investigations, and their explanations. (Author/KHR)

Explores useful ways of teaching the volume of pyramids using cubic blocks and spreadsheets. Presents a lesson plan with teaching suggestions. (KHR)

Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…

Examines four areas of difficulty with graphing and modeling, identifies confusions and misconceptions, and shows how these areas interact in the presence of data-collection devices. (KHR)

This study examined the effects of level of instructional scaffolding on students' use of Geometer's Sketchpad and other software tools in a technology-integrated geometry curriculum. In order to revitalize education at the secondary level and in particular in the mathematics curriculum, educational reformers have advocated the incorporation of…