This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

Making patterning the basis of mathematics investigations for an entire year produced unexpected results for Bruce Ferrington. A Year 2 class used the spatial tasks from the Pattern and Structure Mathematics Awareness Program (PASMAP) with a specific emphasis on patterning, to develop their thinking mathematically skills. The result was students…

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical…

This article provides a classroom resource for identifying, assessing and promoting one aspect of reasoning--analysing--through the Assessing Mathematical Reasoning Rubric. Practical examples of student work and rubric levels are offered.

How do students cope with and make sense of polysemy in mathematics? Zazkis (1998) tackled these questions in the case of 'divisor' and 'quotient'. When requested to determine the quotient in the division of 12 by 5, some of her pre-service teachers operated in the domain of integers and argued for 2, while others adhered to rational numbers and…

The study evaluates the linear number board game "100 House." Taking into account Krajewski's (2003, 2013) development model of mathematical competencies, this game supports the development of mathematical competencies in 6-year-old children. The board game design is based on the American cognitive alignment framework approach and aims…

This study has aimed to determine 8th grade middle school students' skills and knowledge on irrational numbers. A total of ten 8th grade students from a public school in Polatli District of Ankara were participated. In the study, a basic qualitative research design was used, and data were collected by means of clinical interviews. Interview…

Pattern activities have a crucial role in supporting early academic and language skills related to cognitive development, as they play a key role in understanding mathematical ideas and relationships, and in understanding the order, logic and concepts of mathematics. From this point of view, the research was conducted to investigate the effect of…

We investigated how pre-service teachers (PSTs) interpret their calculations in proportional tasks. A written questionnaire was administrated to 199 PSTs and an inductive content analysis approach used for data analysis. We found that one item that asked PSTs to interpret the meaning of their results had unusually low success; open coding on the…

Spatial skills are consistently linked to mathematical reasoning, and are sensitive to intervention. One important spatial skill is spatial scaling. We evaluated whether (1) a playful scaling game might promote learning by providing feedback during play, and (2) spatial scaling is related to number-line estimation based on the mutual reliance on…

Spatial skills are consistently linked to mathematical reasoning, and are sensitive to intervention. One important spatial skill is spatial scaling. We evaluated whether (1) a playful scaling game might promote learning by providing feedback during play, and (2) spatial scaling is related to number-line estimation (NLE) based on the mutual…

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data collected in a…

During a time when students are accessing instruction virtually because of COVID-19, reflecting on the sixth of the Standards for Mathematical Practice (SMP 6) is a vital step for educators to take. Although the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010) identifies SMP 6 as Attend to precision, associated expertise…

Implementation of evidence-based practices (EBPs) is paramount to students' development of mathematics proficiency. This study investigated "practice-based evidence" (Green, 2008) of interventionists' actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data…

We report results from a mathematics content course intended to help future teachers form a coherent perspective on topics related to multiplication, including whole-number multiplication and division, fraction arithmetic, proportional relationships, and linear functions. We used one meaning of multiplication, based in measurement and expressed as…