Resumo Este artigo investiga os desafios conceituais dos alunos sul-africanos, do décimo segundo ano, com simbolização matemática e estratégias de ensino que os professores usam para mitigar a simbolização matemática. O estudo é motivado pela falha dos alunos em conectar representações entre ideias simbólicas e matemáticas para entender conceitos e procedimentos. O estudo é uma tentativa de obter insights sobre símbolos matemáticos como barreiras potenciais para a compreensão dos alunos acerca de conceitos e processos matemáticos. O estudo, realizado no distrito de Sekhukhune, da província de Limpopo, África do Sul, abrangeu 120 alunos da 12ᵃ série, selecionados aleatoriamente, e quinze professores de matemática, selecionados propositalmente. Os dados foram coletados por meio de questionários e entrevistas com grupos focais. Um projeto explicativo sequencial, de método misto, foi empregado. Uma análise de agrupamento de dados SPSS produziu três (3) agrupamentos, consistindo de 50 (41,6%), 47 (39,3%) e 23 (19,1%) alunos com desafios severos, leves e menores, relativos aos símbolos matemáticos. Dois temas emergiram das dificuldades dos alunos com símbolos matemáticos. Em primeiro lugar, os alunos não têm senso de símbolo para conceitos matemáticos e visão algébrica para a resolução de problemas. Em segundo lugar, os alunos desconsideram os usos conceituais e contextuais dos símbolos. O estudo, portanto, sugere que a negociação dos alunos, referente ao discurso entre o símbolo matemático e o conceito ou procedimento matemático, é crucial para o desenvolvimento do significado simbólico. Portanto, os professores precisam usar estratégias adequadas para envolver os alunos em processos que lhes permitam fazer significados de símbolos matemáticos. O estudo recomenda que os conceitos sejam compreendidos antes de simbolizados.

Abstract This paper investigates South African 12th Grade students’ conceptual challenges with mathematical symbolization and instructional strategies that teachers use to mitigate mathematical symbolization. The study is motivated by the students’ failure to connect representations between symbolic and mathematical ideas to understand concepts and procedures. The study attempts to gain insight into mathematical symbols as potential barriers to students’ understanding of mathematical concepts and processes. The study consists of 120 randomly selected 12th Grade students and 15 purposefully selected mathematics teachers from Sekhukhune district of Limpopo Province, South Africa. Data was collected through questionnaires and focus group interviews. A mixed-method sequential explanatory design was employed. An SPSS cluster analysis of data produced three (3) clusters consisting of 50 (41.6%), 47 (39.3%) and 23 (19.1%) students with severe, mild, and minor challenges with mathematical symbols. Two themes emerged from the students’ difficulties with mathematical symbols. Firstly, students lack symbol sense for mathematical concepts and algebraic insight for problem-solving. Secondly, students disregard conceptual and contextual uses of symbols. The study therefore suggests that students’ negotiation of discourse between the mathematical symbol and the mathematical concept or procedure is crucial developing symbolic meaning. Therefore, teachers need to use appropriate strategies to engage students in processes that allow them to make meanings of mathematical symbols. The study recommends that concepts should be understood before symbolised.

Teachers play an important role in the provision of quality education. The variety of classroom practices they use in interacting with learners play a critical role in the understanding of mathematical concepts and overall performance in Mathematics. Following the work done by Hattie (2009, 2012) in relation to classroom practices this study investigated the association between learner achievement and selected teacher classroom practices. The Mathematics teacher questionnaire, administered as part of the Trends in International Mathematics and Science Study (TIMSS) 2011, comprised questions pertaining to the classroom practices of Teacher Clarity, Classroom Discussion, Feedback, Formative Assessment, Problem Solving and Metacognitive Strategies, and Collaboration. The results showed a positive association between teachers' high endorsement of the selected classroom practices and learner performance. The study also investigated how collaboration between Mathematics teachers affected learner performance. The analysis shows that teachers observing each other's lessons affected the learners' performance positively, although most teachers were not keen on collaboration with their peers. This study showed that various teacher classroom practices affect learner performance in Mathematics significantly and that these practices should be identified and mechanisms put in place to support teachers in terms of these practices.

For many years, education in South Africa has been based mainly on western values. This has contributed to the fact that many learners from disadvantaged backgrounds cannot see the connection between the education they receive at school and their everyday experiences. This may well have contributed to the high failure rate amongst mathematics learners as well as the perceived difficulty of mathematics. It is believed that indigenous knowledge, in general, can be used to promote the teaching of mathematics in multicultural classes. We report on an enquiry into the use of the indigenous game of morabaraba in the mathematics class. Various mathematical concepts have been identified from the game. It was found that learners enjoy playing the game, and that it can be used in the mathematics classroom to promote the learning of mathematics. It was also found that the use of this game promotes spontaneous interaction amongst learners as they communicate their activities to fellow participants. The enjoyment of the game was found not to be restricted to a specific cultural group, which suggests that it can be used in a multicultural setting.