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),…

I explore the impact of ambiguous referral to the unit on understanding of decimal and fraction operations during episodes in two different mathematics courses for pre-service teachers (PSTs). In one classroom, the instructor introduces a rectangular area diagram to help the PSTs visualize decimal multiplication. A transcript from this classroom…

This is a case study of an undergraduate calculus student's nonstandard conceptions of the real number line. Interviews with the student reveal robust conceptions of the real number line that include infinitesimal and infinite quantities and distances. Similarities between these conceptions and those of G. W. Leibniz are discussed and illuminated…

Developmental dyscalculia (DD) is a pervasive difficulty affecting number processing and arithmetic. It is encountered in around 6% of school-aged children. While previous studies have mainly focused on general cognitive functions, the present paper aims to further investigate the hypothesis of a specific numerical deficit in dyscalculia. The…

It is commonly assumed that there is an interaction between the representations of number and space (e.g., [Dehaene et al., 1993] and [Walsh, 2003]), typically ascribed to a mental number line. The exact nature of this interaction has remained elusive, however. Here we propose that spatial aspects are not inherent to number representations, but…

The study examined whether a professional development program for seventh grade mathematics teachers improved the teachers' knowledge of rational number topics and the performance of their students on a rational number test. Before the first year of the program, schools within districts were randomly assigned to either a treatment group that…

While numbers, data and statistics have been part of the bureaucracy since the emergence of the nation state, the paper argues that the governance turn has seen the enhancement of the significance of numbers in policy. The policy as numbers phenomenon is exemplified through two Australian cases in education policy, linked to the national schooling…