Research distinguishes three types of arithmetic: exact arithmetic, computational estimation and approximate arithmetic. Little is, however, known about the interrelationship among these three arithmetic skills and the general cognitive and early numeracy skills that underlie these arithmetic skills. The current study investigates this…

Mathematical creativity is perceived as an increasingly important aspect of everyday life and, consequently, research has increased over the past decade. However, mathematical creativity has mainly been investigated in children and adolescents so far. Therefore, the first goal of the current study was to develop a mathematical creativity measure…

Building a technology-driven world appears to be the main motivational force behind students choosing to undertake engineering studies. The first year of engineering education plays a significant role in demonstrating sufficient mathematical and scientific rigor to satisfy these motivational factors. The common applied mechanics courses play a…

Given the prevalence of research in undergraduate mathematics education focused on student reasoning and the development of instructional innovations that leverage student reasoning, it is important to understand the ways undergraduate mathematics instructors make sense of these innovations. We characterize pedagogical reasoning about…

The French National Cohort of Children Study ("Etude Longitudinale Française depuis l'Enfance"--ELFE) tested the literacy and numeracy skills of 4- to 5-year-old typically developing children in the second year of "école maternelle." Tasks were administered by more than 4,000 teachers at schools across France. One of the…

We investigate how students make sense of irrational exponents. The data comprise 32 interviews with university students, which revolved around a task designed to examine students' sensemaking processes involved in predicting and subsequently interpreting the shape of the graph of f(x)=x[superscript square root of 2]. The task design and data…

Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of…

Professional noticing of children's mathematical thinking (Jacobs et al. in J Res Math Educ 41(2):169-202, 2010) is a construct that is used frequently to understand the ways in which teachers attend to, interpret, and respond to children's mathematical thinking. In this paper, we present our analysis of prospective elementary mathematics…

The standard of critical thinking in this study, namely: first, interpretation is on a problem can showing/ writing what they know and what is asked about the problem correctly; second, analysis is the activity of identifying the relationship between statements, questions and concepts in a problem through making mathematical models and accompanied…

Competence with fractions is important for learning more advanced mathematics. The present study examined the predictive value of sustained attention, verbal and visuospatial working memory, cognitive flexibility, fluid intelligence, multiplication and division abilities for fraction knowledge in fifth grade. Participants were 97 elementary school…

Our goal was to study the impact of coding on preschoolers' math abilities and to analyze their coding behaviors. Participants were six preschoolers, four years of age, from a play-based accredited program. We measured their Math abilities using TEAM and observed their coding behaviors with a structured instrument. Children used a robotic toy to…

The script relativity hypothesis proposes that the scripts we read and write affect our cognition. The current study tested this hypothesis by comparing Chinese and English cognitive-linguistic skills and three cognitive abilities, including verbal working memory capacity, nonverbal IQ, and arithmetic calculation, across groups of children with…

Storytelling is an important method for removing obstacles to learning mathematics and making lessons understandable. This research aims to analyze primary school teachers' stories written to teach students concepts of problem solving, fluency, reasoning, and understanding skills. The study is a qualitative case study and the participants were 25…

This study aims to address the teaching of integrals in multivariable calculus concerning the role taken by geometry, specifically, geometrical content dealing with boundaries in integrals that appear as curves and surfaces in R[superscript 2] and R[superscript 3]. Adopting the framework of the Anthropological Theory of the Didactic, we approached…

Letters and numbers are different domains, and their differentiation increases with schooling. It has nonetheless been argued that reading alphabetic and numerical materials partly involves the same processes, even in adults. Whether individuals with dyslexia have difficulty reading and writing numbers remains to be established. This study…