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Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge
Tesis (M. Ed.) -- Universiteit van Stellenbosch, 1998.
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| Other Authors: | |
| Format: | Thesis |
| Language: | Afrikaans |
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Stellenbosch : Stellenbosch University
2012
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| _version_ | 1867614069398175744 |
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| access_status_str | Open Access |
| author | De Witt, Ebenhaezer |
| author2 | Human, P. G. |
| author_browse | De Witt, Ebenhaezer Human, P. G. |
| author_facet | Human, P. G. De Witt, Ebenhaezer |
| author_sort | De Witt, Ebenhaezer |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Tesis (M. Ed.) -- Universiteit van Stellenbosch, 1998. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/55919 |
| institution | Stellenbosch University (South Africa) |
| language | Afrikaans |
| last_indexed | 2026-06-10T12:46:10.315Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2012 |
| publishDateRange | 2012 |
| publishDateSort | 2012 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/55919 Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge De Witt, Ebenhaezer Human, P. G. Stellenbosch University. Faculty of Education. Dept. of Curriculum Studies. Mathematics -- Study and teaching (Secondary) Dissertations -- Education Tesis (M. Ed.) -- Universiteit van Stellenbosch, 1998. Curve-fitting essentially means the construction of a function rule (formula) that fits a given set of data. In the case of a set of data (corresponding values of the two variables) of a linear function, additional function values as well as a rule (formula) for the function can readily be found by identifying the change in function value per unit increase in the value of the independent variable (i.e. the gradient). This study comprises a teaching experiment with Std 6 and Std 7 pupils, with a view to assess the extent to which pupils can acquire aspects of the gradient concept by doing simple curve-fitting. In the teaching of mathematics, mathematical concepts and methods are traditionally presented and practised prior to the application of this knowledge to problem-solving. In accordance with the problem-centred approach, the opposite sequence was followed — pupils were confronted with curve-fitting problems prior to any instruction about the gradient concept, in the anticipation that they would construct aspects of the concept during their efforts to solve the problems. The teaching experiment comprised a pilot study with Std 6 pupils in 1995, and a final project with Std 6 and Std 7 pupils in 1996. In the pilot study, a sequence of 20 learning tasks requiring curve-fitting were given to pupils. Most of these tasks were about linear functions, but some non-linear cases were included in order to counter narrow concept formation. Observations during the pilot study indicated the tasks were too simple, and did not present sufficient intellectual challenges to stimulate a level of thinking which supported concept formation. In the final project only 6 tasks, presenting a substantially higher level of intellectual challenge, were used. The typical structure of these tasks is that pupils have to extend a given table of values of a function, i.e. generate additional function values, and find a rule (formula) which makes it easy to find additional function values. Most of the tasks related to realistic contexts. A specific pattern of work was strived for in the experimental lessons, namely that pupils first tackle each task individually, and then discuss their efforts in a small group at a later stage. It was deemed important that pupils accept responsibility for their own work, and be directed to reflect on their efforts and to learn from it. It was deemed of specific importance that pupils should realise that although the solution to a problem is the immediate purpose of their work in the classroom, the acquisition of new knowledge is the ultimate goal. It emerges clearly that pupils in most cases used a recursive strategy to find additional function values. However, most pupils responded constructively to suggestions by the teacher (the researcher) that function values can also be found by identifying a computational (algebraic) relationship between the values of the two variables. The extent to which the sequence of tasks contributed to the construction and internalisation of the concept gradient, was evaluated by means of three written tests of which one was applied immediately after completion of the six tasks, and the other two two weeks later, as well as by analysis of some video-recordings of pupils’ work and discussions during the instructional program. The results indicate that curve-fitting tasks may indeed be useful in promoting construction of the gradient concept. Masters 2012-08-27T11:37:17Z 2012-08-27T11:37:17Z 1998 Thesis http://hdl.handle.net/10019.1/55919 af Stellenbosch University 188 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Mathematics -- Study and teaching (Secondary) Dissertations -- Education De Witt, Ebenhaezer Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge |
| title | Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge |
| title_full | Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge |
| title_fullStr | Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge |
| title_full_unstemmed | Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge |
| title_short | Krommepassing as probleemtipe in 'n probleemgesentreerde benadering tot algebra : 'n onderrig-eksperiment met standerd ses en sewe leerlinge |
| title_sort | krommepassing as probleemtipe in n probleemgesentreerde benadering tot algebra n onderrig eksperiment met standerd ses en sewe leerlinge |
| topic | Mathematics -- Study and teaching (Secondary) Dissertations -- Education |
| url | http://hdl.handle.net/10019.1/55919 |
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