In this paper we consider important factors influencing different curricular approaches to the study of numerically and geometrically defined pattern-type problems in the middle school curriculum. Our analysis involves the consideration of recommendations from national standards documents and their influences on state framework documents…

In this paper we analyze the mathematical treatment of numerically and geometrically defined patterns in a variety of middle school curricula. We provide several examples that illustrate a need for rethinking how the study of patterns and generalizations are presented in middle grade mathematics curricula and discuss some natural implications to…

This study examines how students solve problems that involve the concept of absolute value. One hundred seventeen students participated in the first (written) part of the study, 24 students participated in the second part (interview). Particular attention was paid to the actual process of problem solving and to the students' ability to establish…

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…

Based on data from the Longitudinal Study of American Youth (LSAY), students were classified into high-, middle-, and low-ability students. The effects of early acceleration in mathematics on the most advanced mathematics coursework (precalculus and calculus) in high school were examined in each category. Results showed that although early…

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…

Quantitative literacy involves a set of skills necessary to reason about data. Such skills are imperative in our increasingly data-oriented world. Despite the importance of such skills, assessment of quantitative literacy has not been a focus in education and there is a lack of assessment tools that specifically address these skills. This study…

The present study was implemented as a prelude to a study on the generalization of the single variable function concept to multivariate calculus. In the present study we analyze students' mental processes and adjustments, as they are being exposed to single variable calculus with polar coordinates. The results show that there appears to be a…

In this qualitative study, we initiate a discussion as to why instructors should implement numerous assessments into their mathematics courses. We describe the purpose and structure of formative and summative assessments implemented in an undergraduate two-semester sequence of abstract algebra. The evaluations included homework, exams, projects,…

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…

Performance in consistent arithmetical word problems was assessed in 941 pupils aged eight (N = 415), ten (N = 274), and thirteen (N = 252) classified in four achievement groups by standardised achievement tests: low achievement in both mathematics and reading (MLRL), in mathematics only (ML-only), in reading only (RL-only), and normal achievement…

This study examined the beliefs of individuals providing the mathematics instruction to elementary students with ED in a self-contained setting as compared to general educators in the same school. The study also attempted to determine the factors that influence beliefs of the NCTM Standards. Through analyzing teachers' beliefs of the NCTM…

Using sociocultural learning theories and feminist post structural theories of gender, we explore how a diverse group of parents (n = 28) construct their preschool sons and daughters as capable/not capable of doing mathematics. Our study examines the interactions between parents and children while playing an age appropriate board game. Following…

The purpose of this study was to examine the proportional reasoning skills of Turkish middle school students. It was also aimed at revealing the differences in students' performances in terms of their gender, grade level, and problem types--missing value and numerical comparison. The study was conducted with two sixth and seventh grade classes…