School of Mathematics, Natural Sciences and Technology Education

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Browsing School of Mathematics, Natural Sciences and Technology Education by Subject "Algebra"

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    Enhancing the teaching and learning of algebraic expressions and equations through reasoning in Grade 9
    (University of the Free State, 2021) Lika, Mohau Armstrong; Tlali, M. F.
    𝑬𝒏𝒈𝒍𝒊𝒔𝒉 This study sought to enhance the teaching and learning of algebraic expressions and equations using reasoning in grade 9. It is a participatory action research study underpinned by bricolage paradigm and construction theory. The underpinnings guide and enable learners to use what is at their disposal to construct reasoning constructs. The constructs help learners to forge rich algebraic and mathematical conceptual connections and interrelations. In this manner, the constructs help the instruction (teaching and learning) to achieve deep conceptual understanding (DBE 2011:8) rather than limiting it to procedural orientation. The evidence presented in literature about international best practices shows that procedure-oriented instruction and procedure fluency are, and should be, nested in conceptual knowledge. This study initiated the instruction that ensures that the nesting does not manifest in nature only, but throughout the teaching and learning processes as well. The initiative draws from the South African curriculum policy, CAPS, which requires that learners should achieve a deep conceptual understanding of the subject matter (DBE 2011:8). The operationalisation of reasoning to conceptualise procedural instruction draws from the underutilisation of the reasoning skill, despite it being the curriculum policy imperative. Reasoning attaches sensible meaning (Yackel 2001:1) to algebraic content matter and provides direction and cushion for logical arguments aimed at attaining high order cognition. Pursuant to the study underpinnings, the reasoning-based instruction deploys learners’ own reasoning constructs to ensure participatory and contextual conceptualisation. In the process, learners develop critical thinking and high order cognitive skills. These are the skills that the learners are expected to attain from the meaningful learning (Pramesti & Retnawati 2019:3) of algebra and mathematics inspired in the reasoning-based instruction. The study has come up with the components of solution and strategies to address the research question and challenges underlying the research. The primary challenge that guides the study, namely the non-alignment between the instruction and requirements of the curriculum policy, manifests under procedure-oriented instruction; assessment; teachers’ competences and curriculum-time contestation. In addition, the abstraction and complexity of algebra amidst insufficient basic mathematics competency, escalate the supremacy of algebra in the teaching and learning of mathematics. The net resultant thereto is an inherent sifting nature of algebra. The data analysis and interpretation presented enough evidence that the reasoning-based instruction is couched in multi-layered components of solution and strategies that respond adequately to the research question. The instruction proved the potential to break through the integrated challenges underlying algebraic instruction. The process of conceptualisation is an encompassing component of the solution. It entails contextualising and concretising textual representations of algebra in a manner that the representations make meaningful sense to learners; so much that the learners can apply algebra purposefully in advanced mathematics and related learning. Contextualisation often involves refocusing, integration and re-organisation of content matter in a manner that meets the subject and learners’ needs. Concretisation includes the use of materials and examples within learners’ reach to explain algebraic concepts. The analysis of the conditions necessary for successful implementation and that of the risks and threats likely to impede the implementation reaffirmed the sustainability of the reasoning-based instruction. The indicators of success confirmed that the study has succeeded in the reform, transformation and enhancement of the teaching and learning of algebra as sought and anticipated. The study has further empowered co-researchers to use what is at their disposal to develop sustainable solutions. It can then be concluded that the research empowered the initiatives to overcome the ‘lock-ins’ to existing protocols and approaches, which have not been effective for the majority of teachers’ and learners’ populations in South Africa and the world. ___________________________________________________________________
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    Exploring common algebraic expression challenges in a Grade 10 mathematics classroom
    (University of the Free State, 2022) Musi, Sophie; Moleko, M. M.
    The purpose of the study was to explore the common algebraic expression challenges in a mathematics classroom and to suggest the best practices or solutions to address these challenges. The study was qualitative in nature, underpinned by a Critical Emancipatory Research (CER) research paradigm. An Action Research (AR) design was adopted as a research design. Data were collected from a team of two mathematics teachers with experience of more than ten years of teaching mathematics in the FET-phase, and 43 Grade 10 learners in one of the high schools in Motheo District. The lesson observations and focus group discussions were used as the primary data collection instruments. Data were generated through active engagement and discussion among the participants using the Free Attitude Interview technique (FAI). Data were analysed by using Braun and Clarke’s (2006) six stages of thematic analysis technique. The findings revealed the following common algebraic expressions challenges and teaching issues pertaining to Grade 10 mathematics; Gap between algebra and arithmetic, Inability to represent word expression in algebraic format, Teachers’ lack of pedagogical knowledge, Teachers’ inability to explain algebraic concepts in-depth, Learners’ inability to manipulate algebraic expressions and Improper use of mathematical vocabulary/expression to mention a few. The study revealed these challenges as sources of difficulty for learning and teaching algebraic expressions in Grade 10. The study thus advocates for the need for knowledge acquisition of these common challenges and awareness thereof, in order for teachers to successfully teach the algebraic expressions.