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This study investigated student mathematics teachers' ability to recognise and explain their understanding of school level functions. We challenged the assumption that studying advanced mathematics automatically develops an understanding of school mathematics that is sufficient to explain concepts and justify reasoning. This case study tested this assumption by exploring the depth of pre-service mathematics student teachers' understanding of school function concepts at the University of Zambia. The test items required calculation, as well as justification of the answers, and an explanation of the concepts. Of the 22 participants, all final year mathematics education students, 18 student teachers scored below the 50% pass mark. The average mark was 8 out of a possible 28 (27%). The majority of the participants found it difficult to explain and justify their reasoning. This study resulted in the development of a new school mathematics module for prospective mathematics teachers at the University of Zambia.

This study investigated the developmental influence of collaborative games in the Grade 6 mathematics classroom. Development in areas such as awareness of mathematics, confidence, competence, curiosity, love for mathematics, appreciation of mathematics, creativity, recognition of mathematics, understanding, and knowledge and skills was investigated. The following three data collection methods were used: intervention, observations, and interviews. For the intervention, a quasi-experimental design was used to assign two out of four classes to an experimental group, and the other two to a comparison group. Fifty-one Grade 6 learners participated in the intervention, which covered the following four mathematics topics: multiplication, nets of 3D-objects, symmetry, and division. Each topic included a pre-test and post-test, with learners being observed during the completion of the post-tests. For the posttests, the comparison group completed the textbook activities individually as they usually would. The experimental group completed the same activities, but in a gamebased worksheet format while collaborating in heterogeneous pairs. The results revealed that the experimental group increased 4.28% more from the pretests to the post-tests than the comparison group. This implies that there was a developmental difference, which can be ascribed to the implementation of collaborative game-based worksheets. The Game Object Model, which was the framework used in this study, provided essential information regarding designing educational games that are conducive to learners' mathematical development. The experimental group increased the most in multiplication and division, which required skills in routine procedures. Low-achieving learners benefited the most from collaborating in heterogeneous pairs in their achievement in mathematics. The experimental group showed a high level of collaboration as they helped each other frequently. A need for support was noted in the comparison group when they asked for assistance from the teacher or a group leader according to the classroom seating arrangements, even though they were instructed to complete the activity individually. Although collaborative games have positively influenced learners' development in mathematics, observations also show that the teacher plays an important role in learners' development in mathematics with regard to focus, motivation, and stirring up a love for mathematics in the learners.

Mathematical Literacy (ML) is a compulsory subject in South Africa for those learners who choose not to do mathematics to Grade 12 level. ML is designed to enable a learner to become a self-managing person by providing opportunities to analyse and solve real-life problems, through the mathematisation of contextual situations. The subject thus lends itself to modelling situations in which a mathematical problem involves a process of transferring between the mathematics and reality. This article reports on an explorative case study conducted with four ML teachers who were required to facilitate mathematisation in modelling situations in their classrooms. Schukajlow's three categories of mathematical problems were applied to identify the type of problems the ML teachers used. The strategies used by the teachers in facilitating the mathematisation process were analysised using a framework in which a real-life problem is explored, a model is formulated, analysed and the result of its application is interpreted and validated in terms of the context. This study focuses on the horizontal mathematisation that lies between context presentation and model formulation. Classroom observations were used to collect the data and a deductive analysis approach was implemented. The study revealed that some teachers find it difficult to go beyond intra-mathematical problems and that the modelling process in general, and the function and direction of mathematisation in particular, are not well understood. The resistance to the use of real-life contexts in the ML classroom was based on disinterest in the context itself or an inability to relate to the real-life situation. We make the recommendation that the process of mathematisation in a modelling situation must be taught systematically and deliberately in pre-service mathematics teacher training programmes.