Measuring computational fluency, an aspect of procedural fluency, is complex. Many attempts to measure this construct have emphasised accuracy and efficiency at the expense of flexibility and appropriate strategy choice. Efforts to account for these latter constructs through assessing children's computational reasoning using structured interviews…

Recent work has demonstrated that how we process the relative order--ordinality--of numbers may be key to understanding how we represent numbers symbolically, and has proven to be a robust predictor of more sophisticated math skills in both children and adults. However, it remains unclear whether numerical ordinality is primarily a by-product of…

Many of us embrace the order and beauty in mathematics. The order of operations is an iconic mathematics topic that seems untouchable by time, reform, or mathematical discoveries. Yet, think for a moment about a commonly heard statement in teaching the order of operations: "You work from left to right." At another point in the…

This study examined cognitive precursors of hierarchical mathematical development. Six-year-old children (n = 258) were assessed on number skills, cognitive skills, and arithmetic 1 year prior to school entry. Skills in advanced arithmetic and advanced mathematics were assessed in Grades 3 and 6, respectively. Path analyses were computed and…

Advances in technology have seen a proliferation of touch-screen interfaces available to young children. These screens have changed the way in which young children engage with digital technology; with increased exposure and use, it raises debates about the suitability of integrating digital technology within early childhood settings. There are…

This narrative review provides an overview of the research literature on the effectiveness of mnemonics in mathematics instruction for students with learning disabilities in a K-12 classroom. Eleven studies were identified in refereed journal articles and doctoral dissertations from 1975 to December 2018 that met the inclusion criteria. Overall…

"Mathematical Lens" uses photographs as a springboard for mathematical inquiry and appears in every issue of "Mathematics Teacher." Recently while dismantling an old wooden post-and-rail fence, Roger Turton noticed something very interesting when he piled up the posts and rails together in the shape of a prism. The total number…

Problem-posing is well known as an effective activity to learn problem-solving methods. Although the activity is considered in contributing to the understanding of the problem's structure, it is not clear how learners could understand it through the activity. This study proposes a method to offer a visual representation for analyzing the…

In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

In this study 2nd grade primary school students' skills and success of subtraction especially with borrowing three digit numbers is investigated. Two different models of the subtraction are analyzed. One of them is used in Turkey (1) and the proposed method which is used in Austria (2). The present paper describes the success, both of the…

The paper discusses children' attitudes towards school and learning soon after entering primary school in Hungary. First and second grade primary school students (N = 33) were interviewed. The interviews explored the following questions: What are the teachers' and the children's roles in the classroom? What is learning? Where do children learn?…

Tablets can be used to facilitate systematic testing of academic skills. Yet, when using validated paper tests on tablet, comparability between the mediums must be established. Comparability between a tablet and a paper version of a basic math skills test (HRT: Heidelberger Rechen Test 1-4) was investigated. Five samples with second and third…

It is imperative to identify contextual factors contributing to the development of early math skills, considering their role in later academic achievement. To pursue this goal, the present study investigated the paths connecting parental beliefs and practices during the preschool years to children's numeric skills at the end of kindergarten…

There have been mixed results in studies investigating proportional reasoning in young children. The current study aimed to examine whether providing visual scaling cues and structuring the reasoning process can improve proportional reasoning in 5- to 6-year-old children. In a series of computerized tasks, children compared the sweetness of 2…

Wynn's (1992) seminal research reported that infants looked longer at stimuli representing "incorrect" versus "correct" solutions of basic addition and subtraction problems and concluded that infants have innate arithmetical abilities. Since then, infancy researchers have attempted to replicate this effect, yielding mixed…