Competence in mathematics is integral to a wide range of disciplines, professions and areas of life. This Eurydice report reveals crucial elements of the policies and practices that shape mathematics instruction in European education systems, focusing on reforms of mathematics curricula, teaching and assessment methods, as well as teacher…

Research investigating algebra students' abilities to generalize and justify suggests that they experience difficulty in creating and using appropriate generalizations and proofs. Although the field has documented students' errors, less is known about what students do understand to be general and convincing. This study examines the ways in which…

For various reasons there has been a recent trend in college and high school calculus courses to de-emphasize teaching the Partial Fraction Decomposition (PFD) as an integration technique. This is regrettable because the Partial Fraction Decomposition is considerably more than an integration technique. It is, in fact, a general purpose tool which…

In this note, we introduce and discuss convolutions of two series. The idea is simple and can be introduced to higher secondary school classes, and has the potential of providing a good background for the well known convolution of function.

General Certificate of Secondary Education (GCSE) mathematics assessment previously included a piece of coursework that required learners to develop a general equation to describe the relationship between two groups of numbers on a number grid. In this author's experience, it became clear that Year 10 students often struggled to form a link…

This article presents an instructional approach to constructing discovery-oriented activities. The cornerstone of the approach is a systematically asked question "If a mathematical statement under consideration is plausible, but wrong anyway, how can one fix it?" or, in brief, "If not, what yes?" The approach is illustrated with examples from…

The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate…

As state and school leaders across the country push to have more students take algebra in 8th grade, a new study argues that middle schoolers struggling the most in math are being enrolled in that course despite being woefully unprepared. "The Misplaced Math Student: Lost in Eighth Grade Algebra," scheduled for release by the Brookings Institution…

This paper examines the relation between bodily actions, artifact-mediated activities, and semiotic processes that students experience while producing and interpreting graphs of two-dimensional motion in the plane. We designed a technology-based setting that enabled students to engage in embodied semiotic activities and experience two modes of…

This article examines how conversations during design reviews in which 8th-grade mathematics students shared population models with visiting specialists expanded the disciplinary expertise of the classroom. "Re-contextualizing" is a conversational exchange that visiting specialists initiated to invite groups to consider their models in novel…

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15-16 years old). Four levels of the development of constructing and using mathematical models were…

The purpose of this article is to explore the research and developmental needs for curriculum-based measurement (CBM) at the secondary level (9th through 12th grades) for mathematics. Much has been accomplished empirically on the validity, reliability, and utility of CBM as an assessment measure in mathematics at the elementary level.…

The purpose of this study is to analyze the relationship between student behaviors and the growth of mathematical ideas (using the Pirie-Kieren model). This analysis was accomplished through a series of case studies, involving middle school students of varying ability levels, who were investigating a combinatorics problem in after-school…

This article explores the issues associated with developing ideas of informal inference and introduces the software package, TinkerPlots, as a tool to facilitate this development. The activities suggested in this article are intended for use with middle and secondary students (grades 6 to 10). The data and suggestions presented have arisen mainly…

This article focuses on the ways in which four eighth-grade girls, each with varying levels of algebraic understanding, share ideas, debate, and gradually move toward generalizations inherent in the "Painted Cube" problem. The intent of this article is to examine how students move to progressive formalization and to provide insights into the ways…