Math and language are inextricably connected. Math cannot be taught without naming certain concepts and finding ways to express mathematical ideas. With the increasing demands on teachers to meet the needs of diverse learners, the role of language development in the mathematics classroom must be at the forefront of instruction. Identifying and…

Although findings from cognitive science have suggested learning benefits of confronting errors (Metcalfe, 2017), they are not often capitalized on in many mathematics classrooms (Tulis, 2013). The current study assessed the effects of examples focused on either common mathematical misconceptions and errors or correct concepts and procedures on…

Mathematics textbooks sometimes present worked examples as being generated by particular fictitious students (i.e., "person-presentation"). However, there are indicators that person-presentation of worked examples may harm generalization of the presented strategies to new problems. In the context of comparing and discussing worked…

This study examined how colored educational tools improve children's numerosity ("number sense") and/or mathematics. We tested children 6-10 years (n = 3,236) who had been exposed to colored numbers from the educational tools "Numicon" (Oxford University Press, 2018) or "Numberjacks" (Ellis, 2006), which map colors to…

Historically, numeracy has tended to be forgotten and overlooked in adult education, especially compared to literacy. Yet evidence exists to show that numeracy should be made a priority, and that building the foundational numeracy skills of young people and adults is vital for their well-being in work and life in the 21st century. In the past…

In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n =…

In today's digital society, people encounter a lot of information on a daily basis. This information should be understood by citizens in order for them to be able to properly engage in political issues, something the population of a healthy democracy does. Much of such information involves mathematics and fully comprehending it requires so-called…

Conditions under which group work leads to learning have been studied in collaborative settings. Little is known, however, about whether and how the interplay between collaboration and cooperation impinges on group learning. In this paper, we study this interplay in the context of mathematical problem-solving. We focus on how training students to…

Background: Dot enumeration is the basic mathematics competency in young children and a significant indicator of later mathematics achievement. Aim: The present study focused on (1) how children's dot enumeration ability changed as they progressed from late kindergarten years (K3) to the second year of primary school in Hong Kong (P2), and (2) the…

Comparing probabilities is a useful skill in life. Binary choice tasks are popular means in research on probabilistic reasoning. Falk, Yudilevich-Assouline, and Elstein ("Educational Studies in Mathematics," 81(2), 207-233 2012) noted that many of these tasks contain design flaws. We designed and evaluated an extended and improved binary…

Proofs are attempts to conclusively demonstrate the validity of the claim for all cases indicated within its domain, which implies that proving should involve thoughtful consideration of the domain. This study analyzed the enactment of three general claim tasks, or tasks where the domain of the claim referred to an infinite number of cases, that…

Research over the past 20 years has suggested that our intuitive sense of number--the Approximate Number System (ANS)--is associated with individual differences in symbolic math performance. The mechanism supporting this relationship, however, remains unknown. Here, we test whether the ANS contributes to how well adult observers judge the…

The goal of this study was to characterise how third-grade primary school students understand the concept of polygon as well as relationships between polygons. Following a teaching experiment, students answered a questionnaire on the recognition of polygons and relationships between polygons, providing information about how a polygon was…

Geometrical measurement is one of the most difficult fields in primary school mathematics and regularly found to be an area of weaknesses. The factors affecting the low understanding is due to the lack of valid and reliable assessment instruments. Thus, this study aimed to develop and validate a Geometrical Measurement Skill Instrument (GMSI) to…

In 2010, Nolan and Temple Lang proposed "integration of computing concepts into statistics curricula at all levels." The unprecedented growth in data and emphasis on data science has provided an impetus to finally realizing full implementations of this in new statistics and data science programs and courses. We discuss a proposal for the…