In an age when reform is based on standards and instruction is based on research, this article gives practical advice for how mathematics teachers can analyze errors in student problems to create interventions that aid not only the individual's development, but the entire class's as well. By learning how to correct mathematics…

This article confronts the issue of why secondary and post-secondary students resist accepting the equality of 0.999... and 1, even after they have seen and understood logical arguments for the equality. In some sense, we might say that the equality holds by definition of 0.999..., but this definition depends upon accepting properties of the real…

Increased reading difficulty of mathematics assessment items has been shown to negatively affect student performance. The advent of high-stakes testing, which has serious ramifications for students' futures and teachers' careers, necessitates analysis of reading difficulty on state assessment items and student performance on those items. Using…

Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These…

There is a dearth of research on the mechanisms for preservice teachers' development of the pedagogical knowledge necessary for effective use of such technologies. We explored the emergent Technological Pedagogical and Content Knowledge (TPACK) (Niess 2005, 2006, 2007) of a group of secondary mathematics preservice teachers in a methods course as…

This article argues that, as teachers struggle to implement curriculum reform in mathematics, an explicit discussion of philosophy of mathematics is missing from the conversation. Building on the work of Ernest (1988, 1991, 1994, 1998, 1999, 2004), Lerman (1990, 1998, 1999), the National Council of Teachers of Mathematics (1989, 1991, 2000), Davis…

This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich concept images.…

The use of technology to create multiple representations of a concept has become one of the significant instructional environments that the National Council of Teachers of Mathematics (2000) suggests strongly for mathematics teachers to consider. One example of this type of environment is educational software with linked multiple representations.…

In this article, we argue that the debates about mathematics education that have arisen in the United States over the past decade are the result of a major shift in how we conceptualize mathematical knowledge and mathematics learning. First, we examine past efforts to change mathematics education and argue they are grounded in a common traditional…

Today's technology standards (International Society for Technology in Education, 2000) challenge teacher education programs across the nation to address the need to produce computer literate teachers who are confident in their ability to choose and incorporate instructional technology into their classroom teaching. The purpose of this paper is to…

The prediction of students' achievement in algebra in eighth and ninth grades has become a research interest for practical issues of placement. A group of simple, easily accessible variables was used to predict student performance in algebra after completion of eighth grade. The three variables of school type, grade level, and previous year…

Reactions to the publication of the National Council of Mathematics (NCTM) "Standards", in both 1989 and 2000, revealed the extent to which differing sets of values and beliefs had divided the mathematical community. This paper rejoins the debate surrounding the "Standards", exploring some of the opposing points of view while offering some…

This study investigates the effects of gender and year in program on the performance and mathematical self-efficacy beliefs of 145 pre-service mathematics teachers in Turkey. One of the main purposes of this study is to investigate how duration in a teacher education program influenced the performance and mathematical self-efficacy beliefs of…

This article discusses how a teacher can prepare the terrain for students to understand what it means to define a figure. Drawing on writings from mathematicians and mathematics educators on the role of definitions in mathematics, the authors argue that students develop a greater appreciation for the conciseness of a mathematical definition if…

Since the advent of the NCTM "Standards" (1989), mathematics educators have been faced with the challenge of assessing the impact of "Standards"-based (or "reform") curricula. Research on the impact of "Standards"-based curricula has predominantly focused on student achievement; here we consider an alternative: Students' epistemological…