A goal of this study was to examine elementary preservice teachers' (PSTs) ability to contextualize and decontextualize fraction subtraction by asking them to write word problems to represent fraction subtraction expressions and to choose prewritten word problems to support given fraction subtraction expressions. Three themes emerged from the…

The recommendation to study statistical variation has become prevalent in recent curriculum documents. At the same time, research on teachers' knowledge of variation is in its beginning stages. This study investigated prospective teachers' knowledge in regard to a specific measure of statistical variation that is new to many curriculum…

As students contribute to social and sociomathematical norms, they will often reorganize their own understandings. As such, the purpose of this article is to describe the ways in which prospective elementary teachers contributed to the norms that were established and "re"-established throughout an entire semester in an undergraduate…

While only about one-third of each year's doctoral graduates in mathematics are women, about two-thirds of the doctoral graduates in mathematics education are women. This article reports on the results of a qualitative investigation into the nature of the graduate school-related experiences of women in collegiate mathematics education…

This study examines the research on middle school students' understanding of variables and explores preservice elementary and middle school teachers' knowledge of variables. According to research studies, middle school students have limited understanding of variables. Many studies have examined the performance of middle school students…

In the field of mathematics education, understanding teachers' content knowledge (Grossman, 1995; Hill, Sleep, Lewis, & Ball, 2007; Munby, Russell, & Martin, 2001) and studying the relationship between content knowledge and instructional decisions (Fennema & Franke, 1992; Raymond, 1997) are both crucial. Teachers need a robust…

Researchers have documented difficulties that elementary school students have in understanding volume. Despite its importance in higher mathematics, we know little about college students' understanding of volume. This study investigated calculus students' understanding of volume. Clinical interview transcripts and written responses to…

This study identifies the kinds of problems teachers pose when they are asked to (a) generate problems from given information and (b) create new problems from ones given to them. To investigate teachers' problem posting, preservice and inservice teachers completed background questionnaires and four problem-posing instruments. Based on previous…

Most teacher education programs do not incorporate financial education preparations into courses required for early childhood, elementary education, and middle level candidates. The authors of this manuscript explore the reasons for this omission, particularly the mathematics education component, and clarify the issues surrounding this decision.…

Fractions are important in young students' understanding of rational numbers and proportional reasoning. The teacher is fundamental in developing student understanding and competency in working with fractions. The present study spanned five years and investigated prospective teachers' competency and confidence with fraction operations as they…

This paper gives results of a study on a Personal Response System (PRS). Three sections of college algebra are compared; one section used PRS and PowerPoint, one used PowerPoint, and one was considered a control. Students were given a pretest and posttest with a retired version of a mathematics ACT test, and all students gained an average of one…

In this paper, we present data from an exploratory study that aimed to investigate the ways in which, and the extent to which, undergraduates enrolled in a transition-to-proof course considered examples in their attempted proof constructions. We illustrate how some undergraduates can and do use examples for specific purposes while successfully…

This article investigates prospective elementary teachers' conceptions of the repeating decimal 0.999... Five students from a first-semester undergraduate course "Mathematics for Elementary School Teachers" were interviewed to ascertain their conceptions about the mathematical statement 0.999... = 1. All of the students indicated they do not…

This article reports on the logical reasoning efforts of five prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The interview participants evinced various levels of reliance on personal relevance, linguistic contextualization, and…

In this study, it was hypothesized that problem solving success is dependent upon two related but district types of mathematical knowledge, content indicators and connectedness indicators. Results did indeed display that the problem solving success of 188 undergraduate students was related to these two indicators. The correlations of content…