The purpose of these notes is to generalize and extend a challenging geometry problem from a mathematics competition. The notes also contain solution sketches pertaining to the problems discussed.

To address student misconceptions and promote student learning, use discussion questions as an alternative to reviewing assessments. This article describes how using discussion questions as an alternative to going over the test can address student misconceptions and can promote student learning.

In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

Purpose: The purpose of the study was to evaluate the implementation and impact of the IDEA Public Schools' Mathematics Curriculum Redesign (MCR) effort, funded by an Innovation and Research (EIR) grant. Methods: The study used a quasi-experimental matching design to examine the effect of MCR on student achievement outcomes. The study compared…

The concept of a tangent is important in understanding many topics in mathematics and science. Earlier studies on students' understanding of the concept of a tangent have reported that they have various misunderstandings and experience difficulties in transferring their knowledge about the tangent line from Euclidean geometry into calculus. In…

The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…

These conference proceedings include two invited lectures, four working group reports, five topic group reports, a list of participants, and a list of previous proceedings. The invited lectures were: "Teaching Mathematical Proof: Relevance and Complexity of a Social Approach" (Nicolas Balacheff) and "Geometry Is Alive and…

The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…