Browsing by Author "Naukushu, Shiwana Teeleni"

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    A critical theory enquiry in the development of number sense in Namibian first year pre-service secondary mathematics teachers
    (Stellenbosch : Stellenbosch University, 2016-03) Naukushu, Shiwana Teeleni; Ndlovu, Mdutshekelwa Cephas; Gierdien, Mohammad Faaiz; Stellenbosch University. Faculty of Education. Department of Curriculum Studies
    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.