This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…

This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five…

In June 2018 the Canadian Mathematics Education Study Group/Groupe Canadien d'étude en didactique des mathématiques (CMESG/GCEDM) held its 42nd meeting in the idyllic setting of Squamish, British Columbia. This meeting marked the first time CMESG/GCEDM had been in British Columbia since 2010 and the first time it had been held at Quest University.…

Though it is widely acknowledged that teachers' knowledge of mathematics is a cornerstone on which their instructional practices are based, little research exists documenting the impact of changes in teachers' mathematical content knowledge on their teaching practices. As proving is a central activity in the study of mathematics, a teacher's proof…

The purpose of this study was to study the relationship between beliefs and teaching styles of teachers of mathematics and their students' academic performance in high schools of Yucatan. For this purpose, a questionnaire was administered to 72 high school mathematics teachers and the student academic achievement score of 1241 were used. A…

Over the past four decades, gender differences in mathematics learning have continued to attract attention from both the research and broader communities, in Australia and internationally. In this article, the authors briefly summarise key and persistent findings. They argue that the findings warrant a further investigation of the performance in…

This article centers on studying the progress of algebraic syntax once students have surmounted initial obstacles found in the transition toward symbolic algebra. It specifically analyzes students' progress concerning the operation on the unknown, when the latter is represented by an expression that involves a 2nd unknown. In curricular terms,…

This paper reports a study of three beginning secondary mathematics teachers and how their reflective practice developed during a one-year university teacher education program and concurrent professional fieldwork experience or practicum. The participants were interviewed three times during the practicum and once more in their first year of…

Many students and adults feel that algebra is merely the shuffling of symbols. The three interrelated concepts of variable, expression, and equation are central to beginning algebra, and in recent years, helping students understand the idea of a variable has been emphasized. Although graphing calculators help students solve equations, it is also…

Building coherence in the development of mathematical ideas across the grades is key to improving students' mathematical learning in the United States. Knowing the mathematical experiences, understanding, skills, and habits of mind that students bring to a grade level and what the expectations are for the following grades can help teachers bridge…

The inquiry-based approach to learning has gained popularity in recent times. Those who promote this approach maintain that mathematical investigation should be used to engage students. The National Council of Teachers of Mathematics (NCTM) recommends that problem solving be the center of mathematics teaching in promoting student learning through…

This article reports on research at the crossroads of on the one hand the procedural-conceptual cut in algebra in the transition from secondary education to higher education, and on the other hand the potential of ICT. Three key topics come together: algebra didactics (symbol sense), theories on tool use (instrumental genesis) and assessment…

Using a nonroutine problem can be an effective way to encourage students to draw on prior knowledge, work together, and reach important conclusions about the mathematics they are learning. This article discusses a problem on the mathematical preparation of chocolate milk which was adapted from an old book of puzzles (Linn 1969) and has been used…

Story problems are a part of most mathematics curricula and are sometimes used as writing exercises in mathematics classrooms. Such writing exercises may include requiring students to rewrite story problems in their own words, using language that is familiar to them, or rewriting story problems using simpler number facts. The current emphasis on…

How do mathematics teachers introduce the concepts of slope, rate of change, and steepness in their classrooms? Do students understand these concepts as interchangeable or regard them as three different ideas? In this article, the authors report the results of a study of high school Advanced Placement (AP) Calculus students who displayed…