Exploring grade 11 learners’ mathematical problem-solving skills using Polka’s model during the learning of Euclidean geometry
- Authors: Hlupeni, Ratham
- Date: 2024-04-05
- Subjects: Mathematics Study and teaching (Secondary) South Africa , Euclidean geometry , Problem solving , Pólya, George, 1887-1985 , Mathematics Problems, exercises, etc.
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/436465 , vital:73274
- Description: The skill of Problem-solving in Mathematics is very imperative. Poor performance by most South African learners in schools and international tests such as the Trends in International Mathematics and Science, calls for emphasis to be placed on problem-solving in the teaching and learning of Mathematics. Euclidean Geometry is perceived, especially by learners, to be one of the difficult components of Mathematics. Thus, the aim of this study was to explore and develop the mathematical problem-solving and geometric skills of Grade 11 learners in Euclidean Geometry. Polya’s model of problem-solving was employed in geometric skills development as a tool for intervention. The concepts Geometry and problem-solving formed the conceptual framework of the study, while the social cognitive theory constituted the theoretical framework. A case study was used as the main research method following a mixed method approach within an interpretivist paradigm. Purposive and convenience sampling methods were used in the selection of both the Mathematics class and the six learners whose work was further observed and analysed. Data about the geometric skills displayed by the learners was gathered using a moderated pre-intervention test; observations; document analysis; a moderated post-intervention test; and focus group interviews. Data was analysed quantitatively using descriptive statistics and qualitatively using thematic analysis. In the pre-intervention test, learners did not bring with them expected geometric skills to the classroom before they were introduced to grade11 Geometry content and when doing problem-solving during intervention, the four stages of model used were not necessarily following each other in a linear sequence with most of the learners not applying the fourth stage “look back”. In the post intervention test, the frequency of use and application of most geometric skills improved in comparison to the pre-intervention test; the frequency of correct and inappropriate application of the skills increased at the expense of incorrect application. Learners appreciated the four stages model and gave their views related to the challenged faced during the use of the four stages model and the challenges revealed include: practice related challenges, challenges specific to certain learners, concept related challenges, curriculum-related challenges, model application challenge, and context related challenges. The study concludes that the effective use of Polyas’ four stages model can yield great results in developing learners’ geometric and problem-solving skills. The study recommends that teachers give more attention to prior geometric knowledge, teaching of geometric theorems, teaching of geometric problem-solving, and the learning environment. , Thesis (MEd) -- Faculty of Education, Secondary and Post School Education, 2024
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- Date Issued: 2024-04-05
Teaching for conceptual understanding : an analysis of selected teachers' practice
- Authors: Kashima, Andreas Akwenye
- Date: 2015
- Subjects: Teacher effectiveness -- Namibia , Student-centered learning -- Namibia , Constructivism (Education) -- Namibia , Problem solving , Teachers -- In-service training -- Namibia
- Language: English
- Type: Thesis , Masters , MEd
- Identifier: vital:2037 , http://hdl.handle.net/10962/d1017348
- Description: The purpose of this study was to explore how teachers’ practice either supports or constrains learners’ conceptual understanding. The study is structured within an interpretive paradigm. The research takes the form of a case study and focused on the teaching practice of two purposefully selected teachers who had been identified as being effective/successful practitioners. The data was collected in two stages. In the first stage, qualitative data was collected by video recording six classroom lessons, three for each of the two participating teachers. In stage 2, participating teachers were individually interviewed. In these interviews the two participating teachers were asked to reflect on their classroom practice, through a process of stimulated recall, where their actions seemed to either support or constrain the development of learners’ conceptual understanding. The study identified a number of elements of the two teachers’ practice that related to the development of learners’ conceptual understanding in the classroom. These include building on learners’ prior knowledge, the use of concrete manipulatives, questioning that promotes critical thinking, and the use of multiple representations and connections. The study also identified elements of the two teachers’ practice that had the potential to constrain the development of learners’ conceptual understanding. These include the lack of opportunities for co-operative or peer-oriented learning, the absence of questioning that leads to discussion, and a scarcity of activities that build mathematical concepts through hands-on engagement. The study highlights the need for supporting teachers and helping them strengthen their practice with regard to those activities that support the development of conceptual understanding in their learners.
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- Date Issued: 2015