This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians,…

Verification and validation are essential aspects of mathematics and beyond in STEM, but these constructs are not consistently defined in research nor in curricula documents. In this theoretical paper, we argue that verification and validation are largely characterized as binary judgments by teachers and researchers about what students do. We then…

Mathematics self-efficacy is considered an important variable in mathematics education because of its links to mathematics achievement. This paper reports on the development of the "Self-efficacy-effort in Mathematics Scale" (SEEMS), an instrument that has strong theoretical and psychometric properties. Based on a sample of n = 224…

Test developers are continually exploring the possibilities Computer Based Assessment (CBA) offers the Mathematics domain. This paper describes the trial of the Place Value Assessment Tool (PVAT) and its online equivalent, the PVAT-O. Both tests were administered using a counterbalanced research design to 253 Year 3-6 students across nine classes…

This is a common experience among education researchers: we notice a surprising instructional move enacted by a teacher. After deeper reflection, we ask, "How many other teachers in Singapore do this?" In this paper, we describe an instrument we designed that is part of the resource needed to answer such questions. [This paper is the…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…

This study reports on the development, validation, and reliability of a geometry disposition scale (GDS) to measure pre-service teachers' (PSTs') attitudes to geometry learning. PSTs from two Colleges of Education (CoEs) in Ghana volunteered to participate in the study (N = 153). A principal component analysis (PCA) extracted four factors: deep…

The instrument of mathematics enrolment choice motivation (MECM) is designed to measure factors that influence students' decisions to keep or drop mathematics in Year 11. Using survey responses from 289 Year 11 students, this paper presents the initial form of the instrument, examines its factor structure, internal consistency and discriminant…

This study employs Sfard's (2008) socio-cultural theory of Commognition to analyse student teachers' thinking and communicating practices. Specifically, we investigate the effectiveness of the student teachers' communication of a particular mathematical proof with reference of the four features of the commognitive framework (i.e., word use, visual…

Argumentation in mathematics teaching has potential to move students beyond tacit understanding of mathematical concepts and procedures towards articulation and justification of their ideas; a practice in which evidence is central. Design-based research was used to examine the nature of evidence used by a class of primary students through levels…

Students' attitudes toward mathematics and its learning have been subject to numerous studies in the past six decades. These studies treat such attitudes as both desirable learning outcomes and correlates of mathematics achievement. Many Likert-type attitude scales have been devised to measure significant constructs underlying mathematics-related…

Spatial visualisation is a subset of spatial ability and is exemplified in predicting whether or not a net will fold to form a target solid. The researchers examined video of interviews to explore the schemes of Year 5 students for determining the validity of nets for a cube and pyramid. Findings suggest the significance of imaged actions, shown…

After briefly analysing a classroom episode, we discuss aspects of the teacher's didactical knowledge, namely in its mathematical and instructional dimensions, as reflected in the answers of three prospective teachers to a written assignment based on the episode. We then raise some issues regarding initial teacher education, anchored in the notion…

As we move into the 21st century, educationalists are exploring the myriad of possibilities associated with Computer Based Assessment (CBA). At first glance this mode of assessment seems to provide many exciting opportunities in the mathematics domain, yet one must question the validity of CBA and whether our school systems, students and teachers…

Standardised testing has received a lot of political and public attention recently in Australia. This paper describes the sense-making of Year 3 students as they interpret items from the 2008 NAPLAN. Results show that student performance changed dramatically when the terminology of an item was modified and subsequently were not a true indication…