Benchmarking is an important strategy for comparing the size of fractions. In addition, knowing whether a given fraction is greater or less than a particular benchmark (e.g., one-half) can support students with accurately locating the fraction on a number line. This article offers a game-based activity that engages students in discussions around…

Background: This study aimed to identify the mathematical domains affected in adults with neurofibromatosis 1 (NF1) and the impact of the numerical difficulties on the patients' activities of daily living. Methods: We assessed 28 adult patients with NF1 and 28 healthy control participants. All participants completed the standardised battery of…

Understanding signed quantities and its arithmetic is one of the challenging topics of middle school mathematics. The "specialized content knowledge" (SCK) for teaching integers includes understanding of a variety of representations that may be used while teaching. In this study, we argue that meanings of integers and integer operations…

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

This work aims to evaluate the relationship between early numerical competence in kindergarteners and their numerical representations as measured by the number line task (NLT). Thirty-four 5-year-old children participated in the study. Children's early performance on symbolic and non-symbolic numerical tasks was considered to determine which was a…

Too many students are entering post-secondary education lacking foundational mathematics skills that are critical to performance on placement examinations. As a result, students are forced to take remedial courses that are often non-credit bearing and hinder their progress toward graduation. Research suggests that a lack of number sense may…

Despite the growing attention being paid to teaching mathematics for students with disabilities, the existing research tends to focus on mathematical skill acquisition, but not on skill maintenance. Maintenance of mathematical skills is especially important as mathematics has applications in daily life and is directly related to important life…

Recent findings have suggested that adults' and children's approximate number system (ANS) acuity may be malleable through training, but research on ANS acuity has largely been conducted with adults and children who are from middle- to high-income homes. We conducted 2 experiments to test the malleability of ANS acuity in preschool-aged children…

This article takes the position that teachers can use simple manipulative materials to model relatively complex situations and in doing so scaffold the development of students' number sense and early algebra skills. While students' early experiences are usually dominated by the cardinal aspect of number (i.e., counting the number of items in a…

In this paper we examine the application of Tzur's (2007) fine-grained assessment to the design of an assessment measure of a particular multiplicative scheme so that non-interview, good enough data can be obtained (on a large scale) to infer into elementary students' reasoning. We outline three design principles that surfaced through our recent…

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

Research shows that students, and sometimes teachers, have trouble with fractions, especially conceiving of fractions as numbers that extend the whole number system. This paper explores how fractions are addressed in undergraduate mathematics courses for prospective elementary teachers (PSTs). In particular, we explore how, and whether, the…

Little is known about whether and how parents can foster their children's spontaneous focus on number, an unprompted measure of attention to small numbers of objects that predicts later math achievement. In the current study, we asked 54 preschool-aged children and their parents to play together in a children's museum exhibit using either a…

It has been hypothesized that developmental dyscalculia (DD) is either due to a defect of the approximate number system (ANS) or to an impaired access between that system and symbolic numbers. Several studies have tested these two hypotheses in children with DD but none has dealt with adults who had experienced DD as children. This study aimed to…