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. / Dissertation (MEd)--University of Pretoria, 2017. / Science, Mathematics and Technology Education / MEd / Unrestricted

The aim of this thesis is to investigate and analyze practices in multilingual mathematics classrooms in compulsory school in Sweden. By using ethnographic methods, mainly participant observation, data were collected in a number of multilingual mathematics classrooms in suburban areas of a major city. The data include field notes, interviews and informal conversations with students, teachers and school administrators. The analysis is based on a coordination of Foucault’s discourse theory and Skovsmose’s critical mathematics education. The socio-political viewpoint defines power as relational and as having an effect on school mathematics practices. Discourse, agency, foreground and identity are used as analytic tools. In five articles, the thesis investigates how the various discourses affect multilingual students’ agency, foreground and identity formation as engaged mathematics learners. The effects of students’ and teachers’ agency on discourse switching in multilingual mathematics classrooms are also investigated. The findings indicate that bilingual communication in the mathematics classroom enhances students’ identity formation as engaged mathematics learners. Language- and content-based instruction seems to do the same, though monolingual instruction may jeopardize students’ identities as bilinguals while the discourse may normalize Swedish and Swedishness exclusively. Focus on linguistic dimensions in mathematics build up a communicative reform-oriented school mathematics discourse. The competing and intersecting discourses available in the multilingual mathematics classroom affect students’ agency, foreground and identity formation as engaged mathematics learners. For example, a reform-oriented school mathematics discourse intersecting with a social-relational discourse affects students’ active agency allowing power relations to be negotiated. A principal conclusion is that the success or failure of multilingual students in multilingual mathematics classrooms cannot be explained in terms of language and cultural factors alone, but only in relation discourse, and to social and political conditions in society at large. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Accepted. Paper 4: Manuscript. Paper 5: Manuscript.

In 2006 the Gauteng Department of Basic Education (GDoBE) launched a pilot project to introduce Assessment for Learning (AfL). This initiative was prompted by learners’ poor performance; especially in subjects such as Mathematics and English. The AfL project was introduced in selected primary and secondary schools. Grade 5 teachers for all subjects and Grade 10 teachers for all subjects within selected primary and secondary schools formed part of the pilot project. These teachers were oriented and introduced to AfL, after which workshops to strengthen teachers’ understanding and skills of AfL were conducted. Lead educators (District Learning Area facilitators or Subject Advisors), were required to monitor and support participating schools and teachers in implementing AfL. Based on a literature and empirical study, the researcher explored the comprehension and implementation of AfL by selected primary school Mathematics teachers that participated in the AfL pilot project of the GDoBE. The empirical study was approached by means of a qualitative research design in the form of a multiple case study. Individual interviews, observations and focus group interviews were used to collect data from purposive selected teachers from three Gauteng Districts (Johannesburg West, Johannesburg North and Ekurhuleni South). Both Township and ex-Model C primary schools were included in the study and eventually a total of 11 Mathematics teachers from these schools participated in the study. The research results revealed that the sampled teachers’ comprehension of AfL can be rated as satisfactory since they realise its potential in terms of learning and learner development. Moreover, these teachers show an awareness of the relation between formative (AfL) and summative assessment (assessment of learning (AoL)). With regard to its implementation, it is clear that a lack of support from colleagues, School Management Teams (SMTs) and District officials impede on the successful implementation of AfL. Other factors hampering the implementation of AfL include time constraints, uncertainty about appropriate resources and the simultaneous implementation of the Curriculum and Assessment Policy Statements (CAPS) and the Gauteng Primary Literacy Mathematics Strategy (GPLMS). It is further noted that the elements of AfL, which includes the sharing of learning intentions, questioning, feedback and peer and self-assessment, are all mediocrely implemented. / MEd (Learning and Teaching), North-West University, Vaal Triangle Campus, 2014

In 2006 the Gauteng Department of Basic Education (GDoBE) launched a pilot project to introduce Assessment for Learning (AfL). This initiative was prompted by learners’ poor performance; especially in subjects such as Mathematics and English. The AfL project was introduced in selected primary and secondary schools. Grade 5 teachers for all subjects and Grade 10 teachers for all subjects within selected primary and secondary schools formed part of the pilot project. These teachers were oriented and introduced to AfL, after which workshops to strengthen teachers’ understanding and skills of AfL were conducted. Lead educators (District Learning Area facilitators or Subject Advisors), were required to monitor and support participating schools and teachers in implementing AfL. Based on a literature and empirical study, the researcher explored the comprehension and implementation of AfL by selected primary school Mathematics teachers that participated in the AfL pilot project of the GDoBE. The empirical study was approached by means of a qualitative research design in the form of a multiple case study. Individual interviews, observations and focus group interviews were used to collect data from purposive selected teachers from three Gauteng Districts (Johannesburg West, Johannesburg North and Ekurhuleni South). Both Township and ex-Model C primary schools were included in the study and eventually a total of 11 Mathematics teachers from these schools participated in the study. The research results revealed that the sampled teachers’ comprehension of AfL can be rated as satisfactory since they realise its potential in terms of learning and learner development. Moreover, these teachers show an awareness of the relation between formative (AfL) and summative assessment (assessment of learning (AoL)). With regard to its implementation, it is clear that a lack of support from colleagues, School Management Teams (SMTs) and District officials impede on the successful implementation of AfL. Other factors hampering the implementation of AfL include time constraints, uncertainty about appropriate resources and the simultaneous implementation of the Curriculum and Assessment Policy Statements (CAPS) and the Gauteng Primary Literacy Mathematics Strategy (GPLMS). It is further noted that the elements of AfL, which includes the sharing of learning intentions, questioning, feedback and peer and self-assessment, are all mediocrely implemented. / MEd (Learning and Teaching), North-West University, Vaal Triangle Campus, 2014

The purpose of this mixed methods study was to identify the types of technologies teachers use in mathematics classrooms and how those technologies were implemented. Furthermore, the purpose of this study was to explore teachers' perceptions of the impact technology has on student achievement. This study explores teachers' perceptions of the available support teachers have for integrating technology in mathematics classrooms. Last, this study explores teachers' perceptions of being prepared to integrate technology into mathematics classrooms. Surveys were conducted for a quantitative approach on teachers' perceptions of technology in teaching and learning. Semi-structured interviews were conducted, and data was analyzed through item-analysis and coding to identify emerging themes. For each topic of inquiry, themes emerged. The themes were discussed in detail, findings were discussed, and recommendations were provided for supporting teachers to integrate technology into mathematics classrooms.

This study takes a particular look at mathematics teacher education communities of practice (CoPs) in order to provide rich descriptions of the CoPs and make claims about its relation/in relation to teacher preparation and particularly the preparation of preservice teachers for teaching mathematics in multilingual classrooms. The three dimensions of communities of practice proposed by Wenger (mutual engagement, shared repertoire and joint enterprise) were used in conjunction with Mortimer and Scott’s notion of meaning making as a dialogic process as a theoretical lens to gain an entry into the nature of communities of practice in pre-service mathematics teacher education classrooms. Data was collected through pre-observation interviews of 12 teacher educators at four Universities in one Province in South Africa in Phase One of the study. A methodological approach based on Wenger’s CoP theory and Mortimer and Scott’s dialogic process was developed and used to analyse classroom observation videos of four of these teacher educators’ classroom communities of practice in two universities in Phase Two of the study. Using the privileged practices in the CoPs as points of departure and how these practices shaped and were shaped by other dynamics in the CoPs, the findings emerging from the study indicate that within the multiply layers of teacher education, there is an overarching emphasis given to the acquisition of mathematical content. Nevertheless, the communicative approaches and patterns of discourse used by the different teacher educators opened up different possibilities as far as preparing preservice teachers for teaching (in multilingual classrooms) is concerned. Wenger’s community of practice theory has found applications in different spheres of life and in different organisational and educational settings. Its use to understand and describe mathematics pre-service classrooms is, however, still largely unexplored. A theoretical contribution that this study makes lies in the extension of Wenger’s CoP theory to include dialogic processes. A methodological contribution lies in the development of an organisational language (based on Wenger’s three dimensions of CoP) to characterise pre-service teacher education classrooms.

This is a study of assessment in mathematics classrooms and assessment is here regarded as a concept with broad boundaries including e.g. diagnostic tests, portfolios, and acts in teacher-student communication. The study’s purpose is to analyse and understand assessment acts in discursive practices in mathematics classroom communication in terms of affordances for students’ active agency and learning. Five mathematics classrooms are visited and the main data consists of video-recordings and written classroom material. In the study, I examine assessment acts, focuses of assessment acts, and roles of semiotic resources (symbols, gestures, speech etc.). With these findings as a basis, four discourses of assessment in mathematics classrooms are construed. A main conclusion is how the construed discourses hold different affordances for students’ active agency and learning. One discourse, “Do it quick and do it right” has similarities to a traditional discourse of assessment described in previous research. In a second discourse, “Anything goes”, students’ performances that can be regarded as mathematically inappropriate are left unchallenged. In both these discourses the affordances for students’ active agency and learning of mathematics are considered low. In a third discourse, “Anything can be up for a discussion”, the focuses of assessment acts are mainly on mathematics processes and available semiotic resources are connected to these focuses. The fourth discourse, “Reasoning takes time”, takes it one step further with a lower pace and an emphasis on mathematics processes such as reasoning and problem-solving. In these two latter discourses the affordances for students’ active agency and learning of mathematics are high. I contend that there is positive power in an increased awareness of discourses like these. The four discourses of this study can be powerful in discussions about, understandings of, and positive changes in assessment practices in mathematics classrooms.

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