The ability to think creatively and solve problems is regarded as crucial for economic and personal success. The traditional approach in classrooms is not conducive to mathematical creativity, and prospective teachers should be exposed to alternative problem solving activities through which mathematical knowledge, competencies and creativity can be developed. Research studies have pointed out the possibilities and successes of a modelling approach in which complex, open problems or model-eliciting problems are used to develop meaningful mathematical knowledge and prepare learners for everyday life, as well as for tertiary studies and their occupations. Model-eliciting activities (MEAs) do not only develop mathematical knowledge, but also creativity. Five hundred and one preservice Foundation Phase teachers completed different model-eliciting activities (MEAs) in a longitudinal project over a period of two years. The purpose was to develop and consolidate their own mathematical knowledge, and at the same time develop creativity and modelling competencies. The ultimate purpose of the project is to prepare preservice teachers to use mathematical modelling to develop creativity in young children aged six to nine. Through solving MEAs learners also build and consolidate their mathematical knowledge and improve their own problem-solving abilities. A framework with four criteria for the identification of creativity was successfully used to evaluate levels of creativity in the solutions offered to the MEAs. Preservice teachers’ final models displayed reasonably consistent levels of creativity regarding the four criteria. Their willingness to solve MEAs and create multiple, original and useful – therefore creative – solutions also increased over the period of their exposure to modelling tasks.

This study examined pre-service teachers' (PSTs) capacity to create mathematical modeling problems (MMPs) for grades 1-3. PSTs created MMPs for their choice of grade level and aligned the mathematical content of their MMPs with the relevant mathematics curriculum.PSTs were given criteria adapted from Galbraith's (2007) MMP design principles, to guide their work. These criteria were then used to evaluate the resulting MMPs, leading to findings and implications relevant to two areas -mathematics teacher education and the design and evaluation of MMPs for young children. Results highlight an inclination toward creating problems for higher grade levels as well as concerns regarding both the PSTs' proficiency with the curriculum content and their capacity to create MMPs for particular content areas. Findings contribute to an important international conversation about the need for further research and development of resources aimed at supporting the integration of mathematical modeling in early childhood mathematics education.

Professional noticing of learners' mathematics reasoning is a crucial ingredient of a mathematics teacher's set of teaching competencies. Research lessons in the lesson study process, with its focus on learner reasoning, provide a structured environment for the building of mathematical knowledge as well as for reflection and the development of teacher professional noticing and sense-making. This paper reports on the depth and growth in noticing of three pre-service teachers during research lessons in their third and fourth years, using the Van Es noticing framework. The study showed that two of these teachers' noticing shifted to higher levels over the two years, with greater focus on learners' mathematical reasoning and sense-making than on teacher actions and teaching. Prospective teachers need well-structured and focused opportunities, individually as well as in groups, to learn to notice and make sense of learner thinking and reasoning.

Number sense studies have indicated that the development of number sense should be the focus of primary school mathematics education. The literature review revealed that learner performance is linked to teacher subject knowledge and that teachers’ confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics. This study was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests and explored the number sense of 47 final-year primary school pre-service teachers (PSTs) in Namibia. The data in this mixed method research design were obtained from a number sense questionnaire, a written computations questionnaire, a mental calculations questionnaire and the McAnallen confidence in mathematics and mathematics teaching survey (MCMMTS). Six PSTs, randomly selected from the 47 participants, were interviewed to determine their use of number-sensible strategies. The overall results of this investigation revealed that the final year primary school PSTs demonstrated limited number sense and possessed very few of the indicators of number sense. Unexpectedly, the confidence survey showed that they were confident in their ability to do and to teach mathematics. This study exposed one reason for the low standards of performance of Namibian learners in mathematics and the lack of improvement over the last few decades. It indicates a need for teacher training institutions to identify the mathematics that teachers should know and the ways in which teacher understanding of subject content has to be transformed to enable them to develop the number sense of primary school learners.

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