This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

When Johann Bernoulli published his lectures on integrals in 1742, integral calculus had become very advanced since the time of their composition in 1692. Nevertheless, these lectures are of excellent clarity and simplicity even when the book deals with major problems of Mathematical Physics. Just to pique some interest, we offer a commented…

Psychological studies of early numerical development fill a void in mathematics education research. However, conflations between magnitude awareness and number, and over-attributions of researcher conceptions to children, have led to psychological models that are at odds with findings from mathematics educators on later numerical development. In…

We performed a meta-analysis of approximate number system (ANS) training studies to investigate the strength of the causal effects of practicing ANS related tasks on symbolic math performance. Across 33 effect sizes from 11 studies involving 754 participants, for which neither the treatment nor control group received symbolic training, we found a…

In this paper, dialogue among a group of adult women with basic adult education is examined. Women read books of mathematics in the context of a "dialogic mathematics gathering" (DMG). There is limited evidence in research on how adults develop their 'numerical understanding'. The objective of this study is to analyze how adults engage…

In this study, it was aimed to determine the errors and misunderstandings of 5th and 6th grade middle school students in fractions and operations with fractions. For this purpose, the case study model, which is a qualitative research design, was used in the research. In the study, maximum diversity sampling, which is a purposeful sampling method,…

Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.

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…

The internal representation of numbers generated during calculation has received little attention. Much of the mathematics learning literature focuses on symbolic retrieval of math facts; in contrast, we critically test the hypothesis that internally generated numbers are represented analogically, using an approximate number system. In an fMRI…

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…

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…

Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. The current study hypothesizes that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. In this study of 71 ninth…

We examined the role of executive attention, which encompasses the common aspects of executive function and executive working memory, in children's acquisition of two aspects of mathematical skill: (a) knowledge of the number system (e.g., place value) and of arithmetic procedures (e.g., multi-digit addition) and (b) arithmetic fluency (i.e.,…

A dedicated, non-symbolic, system yielding imprecise representations of large quantities (approximate number system, or ANS) has been shown to support arithmetic calculations of addition and subtraction. In the present study, 5-7-year-old children without formal schooling in multiplication and division were given a task requiring a scalar…

Student performance in mathematics has been linked to the mathematical knowledge of the teacher. Based on this finding, a 5-day professional development module was created to improve teachers' mathematical knowledge and their understanding of number sense. We found no difference prior to the professional development in mathematical content…