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The study reported on here focused on pre-service teachers noticing learner thinking in the context of written work. The results show how pre-service teachers engaged in noticing learner thinking and on which aspects of learner thinking they focused. These results and related discussion broaden our conceptualisation of teacher noticing learner thinking as involving both disciplinary and non-disciplinary-specific aspects and provides related pedagogical implications for those who educate teachers.

Mathematics clubs are becoming increasingly researched in South Africa, yet what might constitute a curriculum for such clubs has not been discussed. We present and analyse a curriculum design for clubs that we set up and worked with over three years. The goals of the clubs were to foster strong mathematical proficiency, identities and agency among learners through supporting their enjoyment of mathematics as a useful way to make sense of the world. We therefore developed a curriculum where learners could become and be 'mathematical', through drawing on both their everyday reasoning and the mathematics that they learned in school. Our analysis suggests an emergent, responsive curriculum, with tasks that can be categorised as: (1) becoming mathematical with everyday tasks, (2) becoming mathematical about mathematics, (3) being mathematical and making mathematics, and (4) mathematics. We argue that through such a curriculum, we can develop mathematical reasoning on the basis of learners' everyday reasoning in ways that support their mathematical proficiency, identities and agency.

This paper argues that the practice of teaching and learning is being re-defined as technology enables a re-imagining of what can be taught, and how it could be taught. In Namibia, demands on mathematics teachers to incorporate technology use into their teaching practice are often mismatched with the curriculum. This theoretical paper proposes meaningful mathematics teaching via technology, instead of a mere response to societal adoption of digital tools. The concept of meaningful teaching is viewed through a Vygotskian lens. Kilpatrick et al.'s five Strands of Mathematical Proficiency inform the interpretation of goals for teaching mathematics with technology. We discuss the gaps in current models for professional development for teaching with technology when we take the Namibian cultural historical context into consideration. Activity Theory is used to conceptualise a two-triangle embedded activity system of teachers and professional developers, and to reflect on nodal interactions. We conclude by proposing some principles for the design of professional development programmes that aim to support mathematics teachers in using technology in their teaching. The principles may be useful for professional development in other developing countries with uneven access to both technology and reformed mathematics curricula.

Teaching statistics meaningfully at school level requires that mathematics teachers conduct classroom discussions in ways that give statistical meaning to mathematical concepts and enable learners to develop integrated statistical thinking. Key to statistical discourse are narratives about variation within and between distributions of measurements and comparison of varying measurements to a central anchoring value. Teachers who understand the concepts and tools of statistics in an isolated and processual way cannot teach in such a connected way. Teachers' discourses about the mean tend to be particularly processual and lead to limited understanding of the statistical mean as measure of centre in order to compare variation within data sets. In this article I report on findings from an analysis of discussions about the statistical mean by a group of teachers. The findings suggest that discourses for instruction in statistics should explicitly differentiate between the everyday 'average' and the statistical mean, and explain the meaning of the arithmetic algorithm for the mean. I propose a narrative that logically explains the mean algorithm in order to establish the mean as an origin in a measurement of variation discourse.

The South African people have a history of resistance to domination, injustice and inequality. It is therefore surprising that there has been an increase in social inequality, since the start of political democracy in 1994. Recently, the five teachers' unions refused to administer the Annual National Assessments. This action indicates some resistance to domination. In this article, we will first explore the concept of professional teacher agency in the light of teaching, both as a profession and as a vocation constrained by prior experience and social context. Second, we will draw on the current assessment context to outline its problems and perspectives, and consider within this context the enabling and constraining conditions for teacher agency. Third, we will discuss how assessment as a tool for monitoring teacher performance may impede the conditions for quality education. Finally, we would like to propose that the delivery of a good quality education requires adopting a teacher education model which supports agency, and in which the design of diagnostic assessments is locally responsive.

Meaning in statistics is fundamentally related to contexts, which poses the challenge to teach statistics in contexts, taking everyday reasoning as the basis from which to develop statistical reasoning. I investigate how 13 teachers-as-learners in an introductory statistics course co-structure their situation models toward a shared real model that can be treated statistically. I use focal analysis and the constructs of situation models and real models to analyse video data of education students' everyday reasoning about the question "What is a reasonable price for a used car?" As they struggled to structure the context into important variables and relationships between variables, their focus turned from personal decision making to properties of the aggregate of used cars when they were confronted with the emerging complexity of the context. The results show that their everyday reasoning has useful seeds of statistical reasoning which can be re-marked on and developed by the lecturer during the rest of the course.

The political and social environments in which learners with disabilities live often cause more limitation on the individual abilities of these learners than the disability itself (Capri et al., 2018:2). Likewise, mathematical thinking for learners who are severely mentally disabled is often limited to concretisation or memorisation, which tends to undermine mathematical number sense. This study was undertaken against the background of a lack of methodological guidelines for the teaching of mathematics in the new adapted curriculum for learners who are severely intellectually disabled. Context-rich mathematics tasks for the development of mathematical thinking in learners who are severely intellectually disabled were used during the study. A qualitative research approach was followed in which empirical data were generated through three action research cycles. Data were collected through in-depth discussions, field notes, a literature review and learner work. Vygotsky’s (1978:6) sociocultural theory was used as a theoretical framework because it highlights the importance of social interactions and mediated learning. The Reality, Abstraction, Mathematics and Reflection (RAMR) framework of Cooper and Carter (2016:177) is used as a didactic framework for a practical approach to mathematics education in the study. According to the data from in-depth discussions with five educators, learners with intellectual disability are perceived to have limited number sense knowledge. These educators also indicated that their choice of learning tasks only included number facts, arithmetic fluency, memorisation, and teaching with concrete apparatus. Data from the in-depth discussions with two mathematics subject advisors working in special education pointed out educators’ limited didactical knowledge for teaching mathematics to learners who are severely intellectually disabled. Based on these data, a teaching intervention was designed and implemented for six months. The purpose was to investigate the effect on participation and learning of changing the researcher’s practice to focus on mathematical reasoning in context rich tasks. The lived experiences of the ten learners who were involved in the teaching intervention were included as a background to mathematics problems to design context-rich tasks. The guidelines from the research entail that real-life contexts in which mathematical problem types are embedded are conducive to learning experiences that are rich in discussion for learners who are severely intellectually disabled. Such an approach has the potential to make mathematics more meaningful to learners who are severely intellectually disabled, improve their mastery of contexts, and develop critical thinking. Findings from the action research process can be adapted to similar mathematics teaching practices. [ABSTRACT FROM AUTHOR]