This comparative study examined discourse and opportunities for interaction in two mathematics education methods classes, one face-to-face and one synchronous, online. Due to the content taught in the course, this study also sought to determine prospective mathematics teachers' understanding of variability and the role of discourse in each…

Ensuring that students have a strong foundation in mathematics by the end of 7th grade is essential if they are to move successfully into an advanced math curriculum that begins with algebra. But student achievement at the end of 7th grade varies widely in California--and this has consequences. Some 7th graders are taking a full Algebra I course;…

The purposes of this study were to (1) investigate non-accelerated middle schools students' understanding of pre-algebraic concepts, in particular, addition and subtraction of integers and the notion of equality; (2) describe and analyze how non-accelerated middle school students interact with The Geometer's Sketchpad (GSP) applets depicting…

This paper describes a study on research-oriented chemistry teacher education, in which fifty-six advanced, secondary school chemistry student teachers working in teams of two interviewed twenty-eight experienced chemistry teachers. The interviews focussed on teachers' personal viewpoints of how to best teach the different levels of…

In early 2008 researchers from the University of Melbourne's "New Technologies for Teaching Mathematics" project created a lesson for the Year 10 students at their Victorian research schools. Two important goals of secondary school mathematics education are to build students' conceptual knowledge and to teach students to think…

Discover what the best math teachers know and do to provide motivational and challenging math instruction for middle and high school students. From setting up the classroom through planning learning experiences and assessing results, this is an idea guide for inexperienced teachers, new staff members, and math faculty who are mentoring other…

This article contains investigative activities to assist students in constructing formulas out of an understanding of the area of geometric shapes. Included with this article are a "Finding Areas on Square Dot Paper Activity Sheet" and a "Finding Areas on Triangle Dot Paper Activity Sheet." (Contains 1 table and 11 figures.)

This reprinted article from the November 1976 issue of "Arithmetic Teacher" describes a series of calculator games suitable for all levels from kindergarten through calculus.

Since communication is an important feature of classrooms in which students are engaged in doing challenging mathematics, one concern that might be raised for teachers who are creating discourse-rich learning environments is what students who remain silent during discussions might learn. In this article, the authors consider this issue by…

Polish students learn about Platonic solids in the final year of secondary grammar school, but in such a way that few perceive the beauty of this branch of mathematics. An average student associates polyhedra with calculating lengths and angles in a cube, cuboid or pyramid. But for the author, 3-D geometry is the branch of mathematics that shows…

This article discusses the design of tasks for teacher education. It focuses on tasks that are used in a university course for pre-service secondary school mathematics teachers. Special attention is given to tasks that use analogical thinking in their construction or implementation. These tasks are categorized by type of teacher education goal and…

We report on two case studies in which we investigated mathematics for teaching. We were interested in the mathematical knowledge teachers need to know, and know how to use, in order to teach mathematics well. The two case studies focused on the teaching of probability in Grade 8 and the teaching of functions in Grade 10. We discuss the…

I identify and discuss ways in which different types of connections are described in the South African mathematics National Curriculum Statement and its related documents, particularly at the Further Education and Training (FET) level. I argue that connections are central to the way the discipline of mathematics, its learning outcomes, and…

The relationship between mathematics homework and learning in middle-school students and the impact on achievement is the focus of this paper. A review of the literature reveals mixed results. Studies support both positive and a negative impacts of mathematics homework on student achievement or no impact at all. The purpose of this paper is two…

Many middle-school students struggle with decimals and fractions, even if they do not have a mathematical learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children…