This qualitative study examined the everyday mathematical experiences and understandings of three, 4-year-old, African-American children from working-class backgrounds. The study drew on Street, Baker, and Tomlin's (2005) broad, ideological model of mathematics as "social" and their analytic concepts of mathematical events (units of…

The data used for the qualitative analysis reported here were generated as part of a larger study to understand and characterize teacher practice related to engaging students in algorithmic thinking associated with the fraction operations of addition, subtraction, multiplication and division. This paper presents ways in which teachers used…

Various measures have been used to investigate number processing in children, including a number comparison or a number line estimation task. The present study aimed to examine whether and to which extent these different measures of number representation are related to performance on a curriculum-based standardized mathematics achievement test in…

Can prospective elementary teachers "unlearn" harmful algorithms used with fractions as they are invited to develop fraction number sense? This study examined the development of prospective elementary teachers' fraction number sense during an intermediate (grades 5-8) mathematics methods course. During this course, participants' were involved in a…

Background: Previous work has yielded knowledge of teachers' attributions for children's behaviour. Other studies have helped to develop understanding of teachers' efficacy beliefs. Little work has been undertaken to examine teachers' efficacy beliefs with regard to classroom behaviour. Aims: This study aimed to investigate the relationship…

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

This paper reports the findings of two related studies that examined the mathematical strengths and weaknesses of children with dyslexia. In study one, dyslexic children were compared to children without special educational needs on tests that assessed arithmetic fact recall, place value understanding and counting speed. Study two used the same…

Introduction: In the present-day didactic process of transition from natural numbers to integers, a certain kind of measure is involved which is neither easy nor appropriate to integrate into the familiar numerical systems. We refer to measures and comparisons for which we need a third numerical system--what we will call "relative…

Math Teachers' Circles have been spreading since their emergence in 2006. These professional development programs, aimed primarily at middle-level mathematics teachers (grades 5-9), focus on developing teachers' mathematical problem solving skills, in line with the Common Core State Standards-Standards of Mathematical Practice. Yet, to date,…

This study investigated the relationships between children's home literacy environments and their early hypotheses about printed words in the year prior to entering school. There were 147 children (70 girls and 77 boys: mean age 57 months, range = 47-66 months, standard deviation = 4.5 months) in the study. Results showed that the children had…

If the ability to reason proportionally seems to be a good indication of likely success in further mathematical pursuits (Lamon, 1999), how do children develop this ability, and how can teachers facilitate this? In this present study, six ratio/rates task-based assessment questions were trialled on ten students from Grades 5 to 9 in an attempt to…

Number lines are part of people's everyday life and are frequently used in primary mathematics as instructional aids, in texts, and for assessment purposes on mathematics tests. There are two types of number lines; (1) structured number lines, which are the focus of this paper; and (2) empty number lines. Structured number lines represent…

The aim of the study was to elucidate whether and how reliance on a second language impacts the learning of new information under very basic learning conditions. The paradigm used to investigate this issue required individuals to learn a series of associations between numerals and particular letter strings. Participants were two groups of…

We present an empirical study that investigated seventh-, ninth-, and eleventh-grade students' understanding of the infinity of numbers in an interval. The participants (n = 549) were asked how many (i.e., a finite or infinite number of numbers) and what type of numbers (i.e., decimals, fractions, or any type) lie between two rational numbers. The…

Little is known about the neuropsychological factors that contribute to individual differences in the asymmetric orientation along the mental number line. The present study documents healthy subjects' preference for small numbers over large numbers in a random number generation task. This preference, referred to as "small-number bias" (SNB),…