The focus of this study is the relationship between students' performance in mental calculation and the strategies they use when solving three-digit mental addition problems. The sample comprises 78 4th grade students (40 boys and 38 girls). Their mean age was 10 years and 4 months. The main novelties of the current research include (1)…

I found the need to explore the difficulties faced by Arabic-speaking English language learners studying mathematics as soon as I moved to the United Arab Emirates. Thus, I began a line of research that aimed to explain and understand these issues and find effective teaching strategies for the students. This case study describes the first research…

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

The aim of this study was to research the prospective mathematics teachers' ability to construct a mathematical model for a real life problem and to prove these models by generalizing them to use in similar situations. The study was conducted with 129 prospective teachers determined on a volunteering basis. The data were obtained with the help of…

Identifying and expressing relations between quantities is a key aspect of understanding and using functions. We are aiming to understand the development of functions understanding throughout school years in Israel. A survey instrument was developed with teachers and given to 20 high and average achieving students from each of years 7-11 and to 10…

This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two…

This paper draws from and contributes to two bodies of research: how particular elements of game design support learning; and how particular characteristics of feedback impact student engagement. This paper reports findings from two rounds of a design-based research project that focuses on better understanding how feedback is integrated into, and…

STEM major students often enter colleges with a need to strengthen their foundational mathematics, such as trigonometry. We designed an innovative undergraduate course that aims to strengthen students' trigonometry knowledge application through programming mobile apps. We explored how students applied trigonometry concepts in developing their…

This article examines a common proportional reasoning problem used in schools, often referred to as the Orange Juice task. The authors show how these six strategies described by Nikula (e.g., Unitizing, Norming, etc.) and one additional strategy can be used to either solve or make progress in the Orange Juice task. The article presents work from…

We evidence English teacher and student perspectives on the learning of pre-university mathematics 'A Level' courses through the pandemic period to July 2021. Data are drawn from a 2017-21 classroom-close study of enactment of such courses in 13 fairly representative centres, using an institutional ethnographic approach. The pandemic picture was…

Randomized evaluations of educational technology produce log data as a bi-product: highly granular data on student and teacher usage. These datasets could shed light on causal mechanisms, effect heterogeneity, or optimal use. However, there are methodological challenges: implementation is not randomized and is only defined for the treatment group,…

The goal of this paper was to investigate the role of formal constraints (e.g. definitions, theorems) in geometric reasoning. Four students participated in a task-based interview including 2D Euclidean geometric locus problems. Data were obtained from observations, interviews, and video recordings and analyzed by Toulmin's argumentation model. The…

Out-of-field teaching of mathematics is a reality in many secondary schools in the world. The incidence of out-of-field teaching generally occurs in low socio-economic communities and, in Australia, in schools located in rural and remote locations. The theory of boundary crossing enables positive perspectives of teaching out-of-field to be…

This study reflects on the importance of problem solving and the need to be aware of different methods and strategies to respond to the challenges posed by current mathematics education. The experience was carried out on the island of Tenerife and aimed to assess the training of primary education teachers in problem solving strategies. For this…

This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…