Diagnostic information is a centrepiece of educational decision making. Far-reaching decisions like placements within multi-tiered school systems may have a huge long-term impact on the achieved level of education. Therefore, such decisions should be substantiated or complemented by objective and prognostically valid information. To this end, we…

Providing standards-based instruction in core content areas for individuals with moderate and severe disabilities is a hot topic in the field of special education, and teachers struggle to find the best methods for providing high-quality standards-based instruction in core content areas that also has personal relevance for the students. This…

This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…

This article reports the findings from a comparative analysis that examined several mathematical content strands, reasoning processes, and emphasis on technology in prior K-8 state mathematics standards and the Common Core State Standards for Mathematics (CCSSM). Various methodological tools were utilized to compare and contrast CCSSM with prior…

These Proceedings are a written record of the research presented at the 35th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 2013) held in Chicago, Illinois, November 14-17, 2013. The theme of the conference is Broadening Perspectives on Mathematics Thinking and Learning.…

This document presents a review of evidence commissioned by the Education Endowment Foundation to inform the guidance document "Improving Mathematics in Key Stages Two and Three" (Education Endowment Foundation, 2017). The review draws on a substantial parallel study by the same research team, funded by the Nuffield Foundation, which…

Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

The fun thing about teaching measurement topics is allowing students to create three-dimensional objects from cardboard or paper and then to use them to calculate volume and surface area. The project described in this article is one that author Shafer has used for many years at the high school and college levels to reinforce the concepts of volume…

The refraction problem, well-known in calculus and physics, continues to reveal new insights. This paper presents a geometric solution in which the trammel of Archimedes plays the prominent role. When properly configured, the trammel generates an ellipse and its family of normal lines. One normal line in particular intersects the boundary…

Proportional reasoning pops up in math class in a variety of places, such as while making scaled drawings; finding equivalent fractions; converting units of measurement; comparing speeds, prices, and rates; and comparing lengths, areas, and volume. Students need to be exposed to a variety of representations to develop a sound understanding of this…

The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…

Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold…

Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

"I CAN Learn"[R] is a computer software system that provides math instruction through a series of interactive lessons. These lessons are delivered with a one-to-one student-to-computer ratio. Students determine the pace of each lesson and must demonstrate mastery of the lesson before progressing to the next one. Teachers provide…

In recent years, experts and organizations involved in mathematics education have emphasized the importance of collaboration between mathematicians and mathematics teacher educators as a means of improving the professional preparation of mathematics teachers. While several such collaborative endeavors have been documented in the extant literature,…