Mathematical fluency is important for academic and mathematical success. Fluency training programs have typically focused on fostering retrieval, which leads to math performance that does not reliably transfer to non-trained problems. More recent studies have focused on training number understanding and representational precision, but few have…

This paper seeks to describe the importance of using the context of a candy shop and how focusing on discourse can deepen place value understanding in the base ten number system. Using the language of pieces (ones), rolls (tens), and boxes (hundreds) helps situate place value in a familiar context for K-2 students. Best practice in mathematics…

These studies tested two questions about the developmental origins of children's sensitivity to iconicity with regard to number gestures: (1) whether children initially learn number gestures with sensitivity to the one-to-one correspondence between fingers and quantities or whether they learn them as unanalyzed symbols; and (2) whether sensitivity…

In Brazil we have identified a predilection of the authors of Mathematical History books for the discussion of the fundamentals of Differential and Integral Calculus. On the other hand, when we consider the teaching of Mathematics in the school context, it is essential to know the teaching of the historical and dynamic evolution of the concepts,…

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…

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…

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…

In that current study, pattern conversion ability of 25 pre-service mathematics teachers (producing figural patterns following number patterns) was investigated. During the study participants were asked to generate figural patterns based on those number patterns. The results of the study indicate that many participants could generate different…

The aim of the study is to examine whether classroom teachers' Pedagogical Content Knowledge (PCK) on numbers develops in the period from their university education to their active teaching profession. Cross-sectional comparative study method was used in this research in order to examine what kind of development classroom teachers? pedagogical…

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…