The lecture format, while being the subject of much criticism, is still one of the most common formats of university mathematics teaching. This paper investigates lecturing as a means of modelling mathematical discourse, sometimes highlighted in the literature as one of its most important functions. The data analysed in the paper are taken from…

Background: Appraisals of control and value are proposed as proximal antecedents of achievement emotions, which, in turn, predict achievement. Relatively few studies have investigated how control and value may interact to determine achievement emotions, or subsequent achievement mediated by emotions. Aim: To examine whether control, value, and…

This study tested the mediating role of self-directed learning skills (SDL) between students' conceptions of mathematics and their achievement in mathematics using a structural equation model. Data were collected using the "Conceptions of Mathematics Questionnaire" and the "Self-Rating Scale of Self-Directed Learning", together…

When we look at the theoretical relationships between the three types of geometry, we find that the most primitive type is topology and that both Euclidean and projective geometry are derived from this earlier type. Therefore, Piaget described the first stage or level of understanding geometry as topological understanding. In this study, the…

Experimentally manipulating Approximate Number System (ANS) precision has been found to influence children's subsequent symbolic math performance. Here in three experiments (N = 160; 81 girls; 3-5 year old) we replicated this effect and examined its duration and developmental trajectory. We found that modulation of 5-year-olds' ANS precision…

Combinatorial proof is an important topic both for combinatorics education and proof education researchers, but relatively little has been studied about the teaching and learning of combinatorial proof. In this paper, we focus on one specific phenomenon that emerged during interviews with mathematicians and students who were experienced provers as…

In this meta-analysis of 40 studies with 55 independent samples and 7,988 participants, we examined the relation between mathematics vocabulary (MV) and mathematics performance, and we investigated the mechanism underlying this relation. Our findings suggest that MV was moderately related to mathematics performance. Higher-order mathematics tasks…

This study aims to investigate prospective teachers' beliefs toward the realism of mathematics word problems. The study employed both quantitative and qualitative analysis. A 36- item survey was distributed to 28 prospective mathematics teachers in one of the private universities in Indonesia. The survey was developed using the framework proposed…

Implementing innovations in mathematics education relies on scaling up professional development (PD) for mathematics teachers. Within the German Center of Mathematics Teacher Education (DZLM), the complexities involved in scaling-up processes are addressed with three implementation strategies: a material, a personnel, and a systemic strategy. For…

A practice-based engineering degree, in which students worked on real-world, team-based projects from day one and throughout their course, was designed to address the need for employability skills in a rapidly changing world. Teaching mathematics in this way required a very different approach to the lecture-exam based model prevalent in most…

This paper examines a didactic phenomenon, a perception that the elements of sets have a common property, e.g. that {1, 2, 3} and {a, b, c} are sets but {1, 2, 3, a, b, c} is not a set. The paper reports manifestations of this phenomenon in one country: across a range of school students in textbooks and in curricula and across pre-service and…

The multiplicative reasoning that students should develop in elementary school is a key area of research in contemporary mathematics education. Researchers employ various views including multiplication as arithmetic operation, multiplicative structures, and multiplicative relationships. They also propose various classifications of multiplicative…

In this paper, we share details of a South African early grades' number intervention informed by aspects of Davydov's writing on early number teaching and learning. A key part of Davydov's approach to early number teaching involves starting with attention to relationships between quantities rather than with counting. The Structuring Number…

One of the topics within the course of Essential Concepts in School Mathematics (ECSM) for prospective mathematics teachers concerns maximum and minimum problems. This type of problems requires mathematization, i.e., the activity of transforming a problem into a symbolic mathematics problem and of reorganizing within the mathematical system, in…

Combinatorial proof serves both as an important topic in combinatorics and as a type of proof with certain properties and constraints. We report on a teaching experiment in which undergraduate students (who were novice provers) engaged in combinatorial reasoning as they proved binomial identities. We highlight ways of understanding that were…