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…

"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…

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…

Children's knowledge of arithmetic principles is a key aspect of early mathematics knowledge. Knowledge of arithmetic principles predicts how children approach solving arithmetic problems and the likelihood of their success. Prior work has begun to address how children might learn arithmetic principles in a classroom setting. Understanding of…

Is there an optimal grading scheme? Do psychology instructors prefer one grading scheme over another? These questions were recently posted on the Society for the Teaching of Psychology Facebook page. After reading the responses, we realized that research in the domain of math cognition might help to shed light on an optimal grading scheme and put…

Rational number knowledge is critical for mathematical literacy and academic success. However, despite considerable research efforts, rational numbers present perennial difficulties for a large number of learners. These difficulties have led some to posit that rational numbers are not a natural fit for human cognition. In this chapter, we…

This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

Research Findings: The focus of the current study was on the frequency and type of number talk of 2.5- and 4-year-old Argentinean children and their mothers (N = 23 dyads) in shared counting-type picture book reading. The book included sets of animals in ascending order (from 1 to 9), with their corresponding numerals and the animals' written…

Being able to perform computational estimations efficiently is an important skill. Furthermore, computational estimation experiments are used to study general principles in strategy development. Rounding strategies are common in computational estimation. However, little is known about whether and when children use a mixed-rounding strategy (i.e.,…

Here, we assess whether quantity representations are influenced by the perceptual biases hypothesized to manifest in depressive individuals. In contrast to this clinical model, several prominent models of numerical cognition assume that quantity representations are abstract, and therefore are independent of the items that are being quantified. If…

This study was to determine how teacher candidates perceive zero. In this study, which used the case study method from qualitative research approaches, 264 teacher candidates constituted the participants. The participants consisted of 66 elementary mathematics, 58 special education, 82 primary school and 58 preschool teacher candidates. The…