We discuss the importance of bringing teaching to the forefront of instructional design. We do so by describing the process of developing an instructional sequence for early number, using design research. The instructional sequence was developed with the specific aim of supporting teaching, conceived as a complex and demanding job, not reducible…

The Numeracy Kit for Kindergarten 5-Year-Olds (NyKK-5) is a tool to support kindergarten teachers' numeracy practices. Based on a pedagogy of enactment, the NyKK-5 was designed to simulate the types of in-class supports that have been identified as critical elements of effective mathematics professional development (PD). Two groups of teachers…

Conceptual replications are part and parcel of education science. Methodologically rigorous conceptual replication studies permit researchers to test and strengthen the generalizability of a study's initial findings. The current conceptual replication sought to replicate the efficacy of a small-group, first-grade mathematics intervention with 240…

The mathematical abilities of children with autism spectrum condition have been understudied. Magnitude representation is a fundamental numerical ability that emerges early in development and is linked to children's learning of formal mathematics. It remains unclear about whether children with autism spectrum condition differ from their peers…

Background: South African learners face the double disadvantage of living in low socioeconomic conditions with access to few resources and attending schools with challenging learning conditions. Mathematics performance reflects such conditions with extreme performance gaps between wealthier and poorer learners. The need for early intervention is…

Individual differences in children's number knowledge arise early and are associated with variation in parents' number talk. However, there exists little experimental evidence of a causal link between parent number talk and children's number knowledge. Parent number talk was manipulated by creating picture books which parents were asked to read…

Two experiments were designed to investigate the developmental trajectory of children's probability approximation abilities. In Experiment 1, results revealed 6- and 7-year-old children's (N = 48) probability judgments improve with age and become more accurate as the distance between two ratios increases. Experiment 2 replicated these findings…

Both humans and non-human animals exhibit sensitivity to the approximate number of items in a visual array, as indexed by their performance in numerosity discrimination tasks, and even neonates can detect changes in numerosity. These findings are often interpreted as evidence for an innate 'number sense'. However, recent simulation work has…

When a number sentence includes more than one operation, students are taught to follow the rules for the order of operations to get the correct result. In this context, brackets are used to determine the operations that should be calculated first. However, it seems that the written format of an arithmetical expression has an impact on the way…

While the use of numbers in governance has a long history, the kinds of numbers we now produce enable a range of new possibilities for monitoring, regulation and policy decision-making. Global policy actors are now calling for a steep increase in investment in education data. The growing trust in numbers has been critiqued by education policy…

Building students' understanding of cardinality is fundamental for working with numbers and operations. Without these early mathematical foundations in place, students will fall behind. Consequently, it is imperative to build on students' strengths to address their weaknesses with the notion of cardinality.

In this study, it was aimed to reveal the explanatory strategies that preservice teachers use in the process of explaining the concept of divisibility by zero. It was investigated how the concept of divisibility by zero, which can be used in expressing the case where the denominator is present in the definition of important concepts of the…

"Place value," which underlies the meanings of multidigits, encompasses the principle of position and base-10 rules. To understand 65, one needs to know that the digits 6 and 5 occupy different positions and thus represent ordered values of different magnitudes (i.e., the "principle of position") and that the value of each…

This study analysed how preschool teachers differently enacted the same mathematical activity for preschool children to discern numbers, and how this affected the children's learning opportunities during the activity. The analysis was based on variation theory and Chi's taxonomy of learning activities. Two Swedish preschool teachers' enactment of…

In this paper, we focus on two particularly problematic concepts in teaching mathematics: the complex unit i and angles. These concepts are naturally linked via De Moivre's theorem but are independently misused in numerous contexts. We present definitions, notations, and ways of speaking about these terms from mathematics education that are not…