Background: South African teachers' mathematical knowledge for teaching and number sense are markedly low, evidenced in national and international research. There is a call for supporting teachers in developing their knowledge and confidence in teaching mathematics. Aim: The aim of this article is to share how pre-service teachers (PSTs) used the…

This qualitative, multiple case study provided comprehensive descriptions of the conceptual difficulties and learning experiences of in-service teachers as they improved their ability to effectively model fraction division with pictorial diagrams. Video data were collected on eight teachers as they individually progressed through a professional…

In this paper, we describe an idea for mathematics lectures that involves using digital tools for first-year university students. Materials in the Moodle course include live broadcasts, lecture recordings, Moodle tests, sample solutions and videos. The aim of the paper is to find out from students' feedback which digital tools help them understand…

This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video…

Representing and recording student thinking in public spaces during mathematics discussions is challenging work. In this article, the authors articulate why skillfully recording and representing during discussions matters. The authors share principles for recording student thinking in the moment and share an activity structure to use with…

Digital curricula can constrain teachers with ready-made instructional materials. The authors used Mathematics Teaching Practices (MTPs) to modify a digital curriculum to engage students in more thoughtful and meaningful lessons. In this article, the authors visit one of their third-grade classrooms, in which they used the prescriptive digital…

In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…

This article explores the role that gestures play in the development of mathematical understanding. Using Pirie Kieren's (1994) notion of image making and Lunney Borden's (2011) idea of verbing mathematics, we share two examples of how students respond to teacher requests to demonstrate what they know about arrays.

The fact that the mathematics course is abstract, that it is not possible to associate it with daily life, and that it is impossible to concretize abstract expressions causes a prejudice against the this course and leads to a decrease in the academic achievements of students. It is seen that throughout history, various studies have been carried…

This study used traditional and holographic video, along with eye-tracking technology, to examine how preservice teachers' physical act of looking is associated with how they attend to and assess students' fraction reasoning. Findings revealed that, although viewing of holograms may have influenced more focus on students' work area, there was…

Background: Within the ambit of the Fourth Industrial Revolution (4IR), the use of technology-based tools within teaching and learning is advancing rapidly at education institutions globally, including the teaching and learning of mathematics. Learners and teachers have challenges with teaching and learning fractions in mathematics. A learner's…

This paper aims to discuss the use of Brousseau's Theory of Didactical Situations in mathematics (TDS) for eighth-graders to explore the concept of triangle inequality in Euclidean geometry. Data sources included observation notes, video recordings of lessons, and students' written work. Data analysis was done through a deductive content analysis…

Given growing interest in K-12 data and data science education, new approaches are needed to help students develop robust understandings of and familiarity with data. The model of the "quantified self"--in which data about one's own activities are collected and made into objects of study--provides inspiration for one such approach. By…

The world in which students are learning is unique. Technology is progressing rapidly, and this is having a direct impact on teaching and learning. Teachers have the choice to embrace this or not. The instant access to information has the power to change pedagogies and students' experience of mathematics learning. Hence several questions arise: Do…

Time is an area of measurement that is difficult for children. This interview study addresses the question: What are children's solution approaches to position the hands of an analog clock? To explore this, we investigated problem solving when using a clock manipulative with mechanically linked hands. We compare overall success rates among…