A critical theory enquiry in the development of number sense in Namibian first year pre-service secondary mathematics teachers

Naukushu, Shiwana Teeleni (2016-03)

Thesis (PhD)--Stellenbosch University, 2016

Thesis

ENGLISH ABSTRACT : This study, “A Critical Theory enquiry in the development of number sense in Namibian first year pre-service secondary mathematics teachers,” inquired into the effectiveness of a Critical Theory informed intervention on the number sense training of Pre-service Secondary Mathematics Teachers in Namibia. The study proposed and evaluated a number sense training CRENS model based on Critical Theory of pre-service secondary mathematics teachers at the University of Namibia. A convenient sample of sixty (60) pre-service secondary mathematics teachers was selected. The study utilised both qualitative and quantitative methods with a pre-test-post-test control design to draw data from the participants. The study utilised a five tier-number sense test, an in-depth focus group interview, document analysis as well as a questionnaire with both open ended and closed ended questions to draw data from participants. Regarding the question about the level of number sense comprehension both the qualitative and quantitative findings revealed that the number sense of the preservice mathematics secondary teachers was below basic before the intervention. Regarding the association of the independent variable number sense the dependent variable academic performance of pre-service secondary mathematics teachers the quantitative results showed a moderate positive association. The study also found out that the changes in academic performance could be attributed to number sense up to 23% and vice-versa. The Multiple Linear Regression analysis results revealed that the individual contribution of the number sense proficiency variable was statistically significant while that of number sense reasoning was not. The number sense proficiency variables meaning and size of numbers, meaning and effect of operations and estimation, were found to have statistically significant relationship with the academic performance of preservice secondary mathematics teachers. The qualitative data presented in section 6.3 indicate that the majority of the students described their number sense experiences to be relevant to their academic performance in mathematics, with a few of the students who felt their number sense was not relevant and did not really impact their academic performance. Regarding the impact of Critical Theory intervention the study found out that there were statistically significant differences in the performance of the students before and after the intervention, particularly, in both the number sense reasoning and proficiency variables. For the number sense reasoning variables, meaning and size of numbers, counting and computational strategies and estimation the study found that the impact of a Critical Theory intervention was statistically significant. For the variables of number sense reasoning statistically significant differences were observed in the estimation and counting and computational strategies only. Overall the study found out that the impact of Critical Theory was effective. The results of the Cohen’s d effect size indicated a very large effect size in both number sense proficiency and reasoning. The qualitative data showed some improved responses to the number sense items for both number sense reasoning and number sense proficiency. It is therefore recommended that the CRENS based intervention could be used to improve the number sense of pre-service secondary mathematics teachers. It is also recommended that the number sense be incorporated on the training of pre-service secondary mathematics teachers. Both the primary and secondary school curricula should consider integrating number sense components to help the learners to understand mathematics better. This study considered an important contribution that it made in an African context where the quality of both primary and secondary mathematics education constantly falls short of international benchmark standards such as TIMSS and PISA. That is, incorporating number sense training in the curricula for preservice teachers should not just be at primary school only but also even at secondary school level. By developing the multiple linear regression analysis model presented in the analysis of data, it can also be argued that the study makes a methodological contribution to the research on number sense. This relationship can be used to give guidance on the relationship between number sense and academic performance which from the cited literature did not appear to have been explored. By applying Critical Theory and therefore introducing the CRENS model which as a unique characteristic of this study, the study fills a gap doing away with a monotonous conceptual frame work of constructivism that seems to be existing in the development of number sense. The nature of resources utilised in the study were suitable for the level of the participants, as a result, these could always be utilised in offering guidance on the number sense training by the other teacher training institutions or the University of Namibia in developing a practical number sense course as per recommendations of this study.

AFRIKAANSE OPSOMMING : Hierdie studie, A Critical Theory enquiry in the development of number sense in Namibian first year pre-service secondary mathematics teachers, het die doeltreffendheid van 'n Kritiese Teorie ingeligte ingryping op die getalbegrip opleiding van voordiens Sekondêre Wiskunde-onderwysers in Namibië ondersoek. Die studie het ʼn getalbegrip opleiding CRENS model, gegrond in die Kritiese Teorie, van voordiens sekondêre wiskunde-onderwysers by die Universiteit van Namibië voorgestel en geëvalueer. 'n Gerieflike monster van sestig (60) voor-diens sekondêre wiskunde-onderwysers is gekies. Die studie het beide kwalitatiewe en kwantitatiewe metodes, met 'n voor-toets-na-toets kontrole ontwerp gebruik om data van die deelnemers te bekom. Die studie het 'n vyf-vlak getalbegrip toets, 'n in-diepte fokusgroep-onderhoud, dokument-analise asook 'n vraelys met beide oop einde en geslote vrae benut om data van die deelnemers in te samel. Ten opsigte van die vraag oor die vlak van getalbegrip vaardighede, het beide die kwalitatiewe en kwantitatiewe bevindinge getoon dat die getalbegrip van die voordiens sekondêre wiskunde-onderwysers onder die basis vlak was, voor die intervensie. Ten opsigte van die verhouding van die onafhanklike veranderlike, getalbegrip, en die afhanklike veranderlike, akademiese prestasie, het die kwantitatiewe resultate 'n matige positiewe assosiasie getoon. Die studie het ook bevind dat die veranderinge in akademiese prestasie toegeskryf kan word aan getalbegrip tot 23% en andersom. Die meervoudige lineêre regressie analise resultate het getoon dat die individuele bydrae van die getalbegrip vaardigheid veranderlike statisties betekenisvol was, terwyl dié van getalbegrip redenering nie statisties betekenisvol was nie. Die getalbegrip vaardigheidsveranderlikes, betekenis en die grootte van getalle, betekenis en die effek van bewerkings en beraming, het statisties beduidende verbande met die akademiese prestasie van voordiens sekondêre wiskunde-onderwysers getoon. Die kwalitatiewe data in afdeling 6.3 aangebied, dui daarop dat die meerderheid van die studente hul getalbegrip ervaringe relevant tot hul akademiese prestasie in wiskunde beskryf het, terwyl 'n paar van die studente gevoel het dat hul getalbegrip nie relevant was nie en nie regtig 'n impak op hul akademiese prestasie gehad het nie. Aangaande die impak van die Kritiese Teorie intervensie het die studie bevind dat daar statisties beduidende verskille was in die prestasie van die studente voor en na die intervensie, veral in beide die getalbegrip redenering en vaardigheid veranderlikes. Vir die getalbegrip redenering veranderlikes, betekenis en grootte van getalle, tel en berekeningstrategieë en beraming, het die studie bevind dat die impak van 'n Kritiese Teorie intervensie nie statisties beduidend was nie. Vir die veranderlikes van getalbegrip redenering is statisties beduidende verskille slegs waargeneem in die beraming en tel en berekeningstrategieë. Die studie het bevind dat die impak van die kritiese teorie oor die algemeen doeltreffend was. Die resultate van die Cohen d effekgrootte het aangedui dat daar 'n baie groot effekgrootte in beide getalbegrip vaardigheid en redenering is. Die kwalitatiewe data het enkele verbeterde reaksies op die getalbegrip items vir beide getalbegrip redenering en getalbegrip vaardigheid getoon. Dit word dus aanbeveel dat die CRENS intervensie gebruik kan word om die getalbegrip van voordiens sekondêre wiskunde-onderwysers te verbeter. Dit word ook aanbeveel dat getalbegrip opgeneem word in voordiensopleiding van sekondêre wiskunde-onderwysers. Beide die primêre en sekondêre skool kurrikulums behoort te oorweeg om getalbegrip komponente te integreer om die leerders te help om wiskunde beter te verstaan. Hierdie studie is'n belangrike bydrae in 'n Afrika konteks waar die kwaliteit van beide primêre en sekondêre wiskunde-onderwys voortdurend kort val van internasionale standaarde soos TIMSS en PISA. Dit is om getalbegrip opleiding te inkorporeer in die kurrikulum vir indiensopleiding vir onderwysers nie net op laerskool nie, maar ook selfs op sekondêre skoolvlak. Deur die ontwikkeling van die meervoudige lineêre regressie-analise model in die ontleding van data, kan dit ook aangevoer word dat die studie'n metodologiese bydrae tot die navorsing oor getalbegrip maak. Hierdie verhouding kan gebruik word om leiding te gee oor die verhouding tussen getalbegrip en akademiese prestasie. Dit blyk asof die teorie nie genoeg ondersoek is nie. Deur die toepassing van die Critical Theory en dus die bekendstelling van die CRENS model wat 'n unieke kenmerk van hierdie studie is, kan die leemte wat te doen het met 'n eentonige konseptuele raamwerk van konstruktivisme wat blyk in die ontwikkeling van getalbegrip bestaan,gevul word. Die aard van die hulpbronne wat gebruik word in die studie was geskik vir die vlak van die deelnemers. As gevolg van die bekombaarheid van die hulpbronne in die aanbieding oor die getalbegrip studie opleiding deur enige onderwys opleidingsinstelling of die Universiteit van Namibië in die ontwikkeling van 'n praktiese getalbegrip kurses is daar n sterk aanbeveling van hierdie studie.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/98447
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