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Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa
Knowing how to correctly count, is fundamental to the future mathematics success of young children. Earlier studies show that many South African primary school students underperform in mathematics even when evaluated with task below grade level. Reports suggest that this is a problem stemming from t...
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| Format: | Thesis |
| Language: | English |
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School of Education
2022
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| _version_ | 1867613211300200448 |
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| access_status_str | Open Access |
| author | Nwaoha-Peterside, Fortune |
| author2 | Davis, Zain |
| author_browse | Davis, Zain Nwaoha-Peterside, Fortune |
| author_facet | Davis, Zain Nwaoha-Peterside, Fortune |
| author_sort | Nwaoha-Peterside, Fortune |
| collection | Thesis |
| description | Knowing how to correctly count, is fundamental to the future mathematics success of young children. Earlier studies show that many South African primary school students underperform in mathematics even when evaluated with task below grade level. Reports suggest that this is a problem stemming from the poor pedagogic, and or content knowledge of classroom mathematics teachers. Shulman (1986; 1987) refers to this area of knowledge as Pedagogic Content Knowledge (PCK). In the field of mathematics teaching and learning, Ball, Thames and Phelps (2008) refer to it as Mathematics Knowledge for Teaching (MKfT). Teachers' mathematics PCK, comprises of three core knowledge domain: (i) Teacher's Knowledge of Content and Teaching (KCT); (ii) Teacher's Knowledge of Content and Student (KCS); and (iii) teacher's Knowledge of Content and Curriculum (KCC). Teachers' KCS was considered in this study as it concerns what teachers know about what learners know and how they learn. The general interest of this project was to study the construction of experience of mathematics (non-core domain knowledge) by genetic endowment on the basis of contextual data. More specifically, the particular interest of the study is on the construction of the experience of counting in the pedagogic situations of Grade 3 schooling. For that purpose, video records of mathematics teaching in two schools situated in working-class communities were analysed. The study adopted an Integrated Causal Model approach which drew on resources from different disciplines such as mathematics education, cognitive science, evolutionary psychology and mathematics. The study was partly framed by Bernstein's pedagogic device, particularly with respect to his notion of evaluation, as well as the inter-related constructs of PCK, MKfT and KCS. The theoretical resources used to describe computations were drawn largely from Davis (2001, 2010b, 2011a, 2012, 2013a, 2015, 2018) and related work on the use of morphisms as elaborated in Baker et al. (1971), Gallistel & King, (2010), Krause (1969) and Open University (1970). These resources were used to produce the analytic framework for the production of and analysis of data. The analysis describes the computational activities of teachers and learners during the recorded lessons, specifically the computational domains made available pedagogically. In so doing, I was able to provide more illumination on what is described as teacher's KCS for teaching counting at the Grade 3 level. From the generated data, the study finds that counting proper was restricted to the constitution and identification of very small ordered discrete aggregates which can be handled by human core domain object tracking system and approximate number system, and that an implicit reliance on numerical order derived from computations on aggregates was central to the teaching and learning of counting. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/36138 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:31.718Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | School of Education |
| publisherStr | School of Education |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/36138 Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa Nwaoha-Peterside, Fortune Davis, Zain Mathematics Education Knowing how to correctly count, is fundamental to the future mathematics success of young children. Earlier studies show that many South African primary school students underperform in mathematics even when evaluated with task below grade level. Reports suggest that this is a problem stemming from the poor pedagogic, and or content knowledge of classroom mathematics teachers. Shulman (1986; 1987) refers to this area of knowledge as Pedagogic Content Knowledge (PCK). In the field of mathematics teaching and learning, Ball, Thames and Phelps (2008) refer to it as Mathematics Knowledge for Teaching (MKfT). Teachers' mathematics PCK, comprises of three core knowledge domain: (i) Teacher's Knowledge of Content and Teaching (KCT); (ii) Teacher's Knowledge of Content and Student (KCS); and (iii) teacher's Knowledge of Content and Curriculum (KCC). Teachers' KCS was considered in this study as it concerns what teachers know about what learners know and how they learn. The general interest of this project was to study the construction of experience of mathematics (non-core domain knowledge) by genetic endowment on the basis of contextual data. More specifically, the particular interest of the study is on the construction of the experience of counting in the pedagogic situations of Grade 3 schooling. For that purpose, video records of mathematics teaching in two schools situated in working-class communities were analysed. The study adopted an Integrated Causal Model approach which drew on resources from different disciplines such as mathematics education, cognitive science, evolutionary psychology and mathematics. The study was partly framed by Bernstein's pedagogic device, particularly with respect to his notion of evaluation, as well as the inter-related constructs of PCK, MKfT and KCS. The theoretical resources used to describe computations were drawn largely from Davis (2001, 2010b, 2011a, 2012, 2013a, 2015, 2018) and related work on the use of morphisms as elaborated in Baker et al. (1971), Gallistel & King, (2010), Krause (1969) and Open University (1970). These resources were used to produce the analytic framework for the production of and analysis of data. The analysis describes the computational activities of teachers and learners during the recorded lessons, specifically the computational domains made available pedagogically. In so doing, I was able to provide more illumination on what is described as teacher's KCS for teaching counting at the Grade 3 level. From the generated data, the study finds that counting proper was restricted to the constitution and identification of very small ordered discrete aggregates which can be handled by human core domain object tracking system and approximate number system, and that an implicit reliance on numerical order derived from computations on aggregates was central to the teaching and learning of counting. 2022-03-16T06:49:32Z 2022-03-16T06:49:32Z 2021 2022-03-11T08:15:25Z Master Thesis Masters MEd http://hdl.handle.net/11427/36138 eng application/pdf School of Education Faculty of Humanities |
| spellingShingle | Mathematics Education Nwaoha-Peterside, Fortune Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa |
| thesis_degree_str | Master's |
| title | Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa |
| title_full | Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa |
| title_fullStr | Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa |
| title_full_unstemmed | Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa |
| title_short | Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa |
| title_sort | knowledge used for teaching counting a case study of the treatment of counting by two grade 3 teachers situated in schools serving working class communities in the western cape province of south africa |
| topic | Mathematics Education |
| url | http://hdl.handle.net/11427/36138 |
| work_keys_str_mv | AT nwaohapetersidefortune knowledgeusedforteachingcountingacasestudyofthetreatmentofcountingbytwograde3teacherssituatedinschoolsservingworkingclasscommunitiesinthewesterncapeprovinceofsouthafrica |