The 21st-century mathematics classrooms should equip learners with well-grounded knowledge and thinking skills pertaining to geometry. However, Euclidean geometry remains one of the challenging, if not the most difficult topic for many learners. As a result, the purpose of this article is to interpret Grade 12 learners’ learning difficulties in Euclidean geometry. We use Van Hiele’s geometric thinking model and Hoffer’s skills to argue an interpretation of learning difficulties in Euclidean geometry as a focal point towards creating effective teaching and learning of this important topic. This explanatory sequential mixed-methods approach involved 60 Grade 12 learners who wrote a geometry test and completed a questionnaire based on Van Hiele’s geometric thinking levels. In addition, semistructured interviews were conducted with a sample of 12 learners and four educators to investigate their views about geometry learning difficulties. The findings of the study revealed that learners had poor conceptualisation of properties of shapes, visualisation skills, circle theorems and geometry terminology, resulting in them experiencing learning difficulties. The recommendations are that, during instruction learners should be given the opportunity to manipulate real geometric objects to enhance their visualisation and visual thinking skills. In addition, we recommend that educators should teach level-specific geometry vocabulary to enable learners to understand concepts at different Van Hiele’s levels. Furthermore, we recommend that educators should use constructivist teaching approaches that encourage learners’ conceptual understanding instead of traditional methods that promote rote memorisation of geometric facts. Educators should develop learners’ broad knowledge of geometry to overcome geometry-related errors and misconceptions.

Over the past year, research on ethnomathematics has been on an upward trajectory. Literature provides evidence that ethnomathematics can improve learners’ understanding and achievement in mathematics. Equally important, South Africa’s mathematics curriculum offers opportunities for integrating ethnomathematics by promoting using various sociocultural contexts in teaching mathematics. Nevertheless, research highlights the inadequacy of existing ethnomathematics research, particularly in pre-service mathematics teacher education in South Africa. As a result, this chapter uses Culturally Responsive Pedagogy theory to foreground teacher educators’ and student teachers’ views about ethnomathematics in pre-service mathematics teacher education. Purposive sampling was used as the sampling procedure to select teacher educators and student teachers. Focus group discussions and semi-structured interviews were used for collecting data collection. Data were analysed through thematic analysis. Three main findings were revealed in the study: mathematics is viewed as a product of diverse cultural contributions; ethnomathematics is perceived as a pedagogy that can enhance learners’ access to mathematical understanding; and ethnomathematics provides opportunities for learners to explore mathematics in everyday contexts. It is concluded that pre-service mathematics education should effectively equip student teachers with pedagogical knowledge and skills to integrate ethnomathematics into their prospective classrooms.

Pythagoras is a scholarly research journal that provides a forum for the presentation and critical discussion of current research and developments in mathematics education at both national and international level.

This article uses parts of qualitative data from the first author’s study that focused on exploring Pirie and Kieren’s process of folding back, revisiting previously held understandings of a concept for its extended understanding in order to solve the problem of enhancing Grade 10 learners’ reasoning in geometry. In South Africa, secondary school leavers and pre-service teachers have difficulties in understanding geometric concepts and little is known about learners’ geometric reasoning. Using teaching experiment methodology, we particularly tracked Grade 10 learners’ geometric reasoning through folding back. We targeted two groups of learners from a class of 54 in which learners grouped themselves: the first group consisted of two members and the second group consisted of three members. The selection of learners was prompted by the manner in which the learners argued and questioned each other during four weeks of exploratory teaching. Data were collected through participant observations, where notes were taken and video recordings made in different sessions. We analysed the field notes and verbatim transcriptions of the video recordings using Polkinghorne’s narrative analysis and analysis of narratives. Both the teacher’s and the learners’ interventions prompted effective folding back resulting in critical sharing of ideas. We thus argue that learners’ effective folding back is a powerful tool to enhance their geometric reasoning.

This chapter explores the field of ethnomathematics and its growing significance in the context of South African education, particularly within the mathematics curriculum. As outlined in the Curriculum, Assessment, and Policy Statement (CAPS), the mathematics curriculum's founding principles and specific aims provide fertile ground for integrating ethnomathematics in mathematics classrooms. Criticisms in ethnomathematics, which indicate its growing presence, are briefly discussed. Drawing from South African literature, various examples illustrate how ethnomathematics can be employed in the teaching and learning of mathematics. These examples reveal that mathematics is deeply embedded in diverse cultural practices, such as the Morabaraba games and traditional architecture. By incorporating ethnomathematics, educators can foster a learning environment that recognises and celebrates learners' cultural identities, facilitates meaningful connections between cultural practices and mathematical concepts, and promotes more accessible, equitable, and inclusive educational experiences.

The purpose of this article is to explore student teachers’ reflections on the pedagogy of play (PoP) as a modeling approach in mathematics. PoP has generally been perceived as a model characterized by a playful classroom environment where learners take risks, make mistakes, and explore new ideas. When student teachers are equipped with PoP knowledge, they can create effective learning environments in mathematics classrooms based on learners’ everyday contexts. This aligns with modern educational trends that advocate for integrating the arts into science, technology, engineering, and mathematics education. The phenomenological research design was employed to describe, understand, interpret, and explain student teachers’ reflections. The participants were 10 mathematics education student teachers who participated in post-intervention focus group interviews, which were used as the main data collection instrument. The findings revealed that PoP can bring a new innovative perspective into the teaching and learning of fractions. It was also revealed that music and boomwhackers may create disruptions in the learning of mathematics.