Teachers play a crucial role in the mathematical learning outcomes of their students. The quality of teachers' mathematical knowledge has been of interest to key stakeholders and several lines of inquiry have been running in an effort to better understand the kinds of knowledge that mathematics teachers need to acquire and use to drive their…

This study presented sets of 15 multiplication facts to each of 4 third-grade participants. The items were presented by an iPod each session three times at three different time delays. When mastery was achieved on a set (80% correct across 3 consecutive sessions), the participant moved on to a new set. Generalization probes were administered…

As one research priority for mathematics education is "to research how mathematical meanings are structured by tools available," the present study examined mathematical representations more closely by investigating instructional modes of representation (Noss, Healy & Hoyles, 1997). The study compared two modes of instruction of place value with…

"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…

Decimals are among the difficult subjects for the students because of its abstract nature. Therefore, the aim of this study is to develop instructional materials for students based on one of the four-stage models of constructivist approach related to the unit of "decimals". With this aim, a worksheet, analogy map and conceptual change…

The purpose of this action research was to determine the level of improvement of middle school students who were low performers in a mathematics class (N = 8) and who received "explicit instruction" with "double dosing" compared to their peer group who received normal instruction (N = 49). Results showed that at-risk…

This article presents an activity that allows students to use mathematics and critical-thinking skills to emulate processes used by the ancient Egyptians to prepare the site for the Pyramids of Giza. To accomplish this, they use three different methods. First, they create a square using only simple technological tools that were available to the…

Story problems either bring students to a screeching halt or send them into a frenzied search for numbers and operations. They cause greater anxiety, still, in English language learners. These problems are often the nemesis of many a math teacher. This author grappled with this challenge in the context of teaching a series of lessons on integers…

Open-ended tasks focused on content specific features are regarded as an effective way to promote particular concept development and to elicit higher-order thinking. Such tasks may vary widely in their focus and approach and they can be formulated without unnecessary complexity. When mathematics tasks are designed in an open-ended fashion they can…

The purpose of this study was to assess the effects of schema-broadening instruction (SBI) on second graders' word-problem-solving skills and their ability to represent the structure of word problems using algebraic equations. Teachers (n = 18) were randomly assigned to conventional word-problem instruction or SBI word-problem instruction, which…

It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics…

In this study we attempt to propose a new model of proportional reasoning based both on bibliographical and research data. This is impelled with the help of three written tests involving analogical, proportional, and non-proportional situations that were administered to pupils from grade 7 to 9. The results suggest the existence of a…

Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way…

The National Council of Teachers of Mathematics (NCTM) Algebra Standard states that instructional programs at the middle grades should enable students to "represent and analyze mathematical situations and structures using algebraic symbols" (2000, p. 222). Guess and check is a powerful problem-solving strategy that can connect a conceptual…

In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular…