Learning mathematical symbolization: conceptual challenges and instructional strategies in secondary schools

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’ instructional strategies and their impact on learner performance in Grade 9 mathematics: Findings from TIMSS 2015 in South Africa

Teachers use a variety of instructional strategies when they teach various mathematical topics and concepts. Some of these strategies have been found to positively affect the performance of learners while others do not. This study analysed the teacher questionnaire data from the Trends in International Mathematics and Science Studies (TIMSS) 2015 study in which the teachers indicated the instructional strategies that they used in the mathematics classrooms. The five instructional strategies that were determined from the groupings of the questions were teacher-teacher interaction, teacher-learner interaction, teacher explanation of the content, problem solving with direct teacher guidance and problem solving without direct teacher guidance. The results indicate that the two instructional strategies of problem solving with direct teacher guidance and teacher-teacher interaction were found to be significantly associated with learner performance across the four content domains of algebra, numbers, geometry and data and chance

Teacher classroom practices and Mathematics performance in South African schools: A reflection on TIMSS 2011

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.Keywords: hierarchical linear modeling; Mathematics performance; teacher classroom practice; TIMS

Learners’ Misconceptions and Errors when Solving Inequalities

This study explored Grade 12 learners’ misconceptions and errors when solving inequalities. A test on Inequalities was administered to a randomly selected sample of 50 Grade 12 learners in Sekhukhune District, South Africa. A rubric was used to guide the assessment and scoring of learners’ scripts. Ten (10) learners were purposively selected  based  their  test  responses for interviews to explain their errors, misconceptions and reasoning. Results indicated that learners’ errors are due to misunderstandings from prior learning and insufficient mathematical content knowledge. Misconceptions and errors recorded from learners’ work include: learners solved inequalities as equations, treated inequality signs as an equal sign, and multiplying both sides of inequalities involving fractions by a variable. Learners had challenges in  presenting solutions of  inequalities using graphical and number lines. The study recommends that teachers should make an effort to understand learners’ thought processes and use this understanding to anticipate learners’ misconceptions and errors and prescribe remediation corrective strategies

National priorities in Indigenous Knowledge Systems: implications for research and curriculum development

No Abstract.Indilinga: African Journal of Indigenous Knowledge Systems (IAJIKS) Vol. 4(1) 2005: 31-3

Conceitos Matemáticos de Anciãos da Comunidade Explorando a Conexão entre Contextos Etnomatemáticos e práticas de aula

Os membros da comunidade possuem uma riqueza de conhecimentos em atividades indígenas e artefatos. A análise das várias atividades e dos artefatos indígenas mostra uma variedade de conceitos e processos matemáticos. Mesmo que alguns membros da comunidade não tenham frequentado a educação formal ou não tenham estudado a um nível significativamente elevado, eles são capazes de utilizar os conceitos matemáticos relacionados com facilidade na medida em que se envolvem nas atividades. Este texto identifica alguns conceitos matemáticos que estão embutidos nas atividades indígenas e mostra como a maioria dos membros da comunidade utiliza esses conhecimentos matemáticos com facilidade. O texto conclui indicando como esse conhecimento pode ser utilizado para avançar a compreensão matemática em sala de aula