Using Balacheff's (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an interactive linear algebra textbook. An analysis of student responses to two similar reading questions revealed additional strategies that students used to decide whether a vector was in the spanning set…

Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling…

Little is known about the cognitive effort associated with algebraic activity in the elementary and middle school grades. However, this investigation is significant for sensitizing teachers and researchers to the mental demands of algebra learning. In this paper, we focus on the relationship between algebraic thinking and domain-general cognitive…

The goal of this study is to show a novel way of using large-scale data (N = 6203) to identify pupils' strategies when solving missing value number equations. It is based on the assumption that wrong numerical results appearing more frequently than would be the case if they were consequences of random guessing can be expected to be underlain by a…

Social institutions function not only by reproducing specific practices but also by reproducing discourses endowing such practices with meaning. The latter in turn is related to the development of the identities or subjectivities of those who live and thrive within such institutions. Meaning and subjectivity are therefore significant sociological…

In this paper, we analyse a large, opportunistic dataset of responses (N = 219,826) to online, diagnostic multiple-choice mathematics questions, provided by 6-16-year-old UK school mathematics students (N = 7302). For each response, students were invited to indicate on a 5-point Likert-type scale how confident they were that their response was…

This paper presents findings from a case study on the impact of high stakes oral performance assessment on third year mathematics students' approaches to learning (Entwistle and Ramsden, Understanding student learning, 1983). We choose oral performance assessment as this mode of assessment differs substantially from written exams for its dialogic…

To assess the strength of conceptual understanding of number sense, a three-tier number sense test (TTNST) for fifth-grade students was developed and validated in this study. The three-tier test includes a content tier that assesses content knowledge of number sense, a reason tier that assesses a reason given for selecting a first-tier response,…

Assessment is a crucial factor in the implementation of curriculum reform. Little is known, however, on how curriculum changes can be reflected adequately in assessment, particularly if the reform concerns process skills. This issue was investigated for the case of assessing mathematical thinking in a mathematics curriculum reform for…

Most studies of children's attitudes to mathematics have dealt with children in second grade or later, and have suggested that attitudes deteriorate, and anxiety increases with age. The present study investigated attitudes to mathematics in 67 English and 49 Chinese children at the end of their first year of school. The participants were given…

Gender differences in achievement in mathematics, a traditionally male-stereotyped subject, have long been a concern for many educators around the world. Gender differences in mathematical achievement have decreased in recent decades, especially in Western countries, and become small or insignificant in large-scale tests, such as the Programme for…

The hypothesis that mathematically superfluous brackets can be useful when teaching the rules for the order of operations is challenged. The idea of the hypothesis is that with brackets it is possible to emphasize the order priority of one operation over another. An experiment was conducted where expressions with mixed operations were studied,…

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite…

In this paper we report the results of an experiment designed to test the hypothesis that when faced with a question involving the inverse direction of a reversible mathematical process, students solve a multiple-choice version by verifying the answers presented to them by the direct method, not by undertaking the actual inverse calculation.…