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

[摘要] ENGLISH ABSTRACT : This study, 'A Critical Theory enquiry in the development of number sense in Namibianfirst year pre-service secondary mathematics teachers, inquired into the effectivenessof a Critical Theory informed intervention on the number sense training of Pre-serviceSecondary Mathematics Teachers in Namibia.The study proposed and evaluated a number sense training CRENS model based onCritical Theory of pre-service secondary mathematics teachers at the University ofNamibia. A convenient sample of sixty (60) pre-service secondary mathematicsteachers was selected. The study utilised both qualitative and quantitative methodswith a pre-test-post-test control design to draw data from the participants. The studyutilised a five tier-number sense test, an in-depth focus group interview, documentanalysis as well as a questionnaire with both open ended and closed ended questionsto draw data from participants.Regarding the question about the level of number sense comprehension both thequalitative and quantitative findings revealed that the number sense of the preservicemathematics secondary teachers was below basic before the intervention. Regardingthe association of the independent variable number sense the dependent variableacademic performance of pre-service secondary mathematics teachers the quantitativeresults showed a moderate positive association. The study also found out that thechanges in academic performance could be attributed to number sense up to 23% andvice-versa.The Multiple Linear Regression analysis results revealed that the individual contributionof the number sense proficiency variable was statistically significant while that ofnumber sense reasoning was not. The number sense proficiency variables meaningand size of numbers, meaning and effect of operations and estimation, were found tohave statistically significant relationship with the academic performance of preservicesecondary mathematics teachers.The qualitative data presented in section 6.3 indicate that the majority of the studentsdescribed 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 relevantand did not really impact their academic performance.Regarding the impact of Critical Theory intervention the study found out that there werestatistically significant differences in the performance of the students before and afterthe intervention, particularly, in both the number sense reasoning and proficiencyvariables. For the number sense reasoning variables, meaning and size of numbers,counting and computational strategies and estimation the study found that the impact ofa Critical Theory intervention was statistically significant. For the variables of numbersense reasoning statistically significant differences were observed in the estimation andcounting and computational strategies only.Overall the study found out that the impact of Critical Theory was effective. The resultsof the Cohen's d effect size indicated a very large effect size in both number senseproficiency and reasoning. The qualitative data showed some improved responses tothe number sense items for both number sense reasoning and number senseproficiency.It is therefore recommended that the CRENS based intervention could be used toimprove the number sense of pre-service secondary mathematics teachers. It is alsorecommended that the number sense be incorporated on the training of pre-servicesecondary mathematics teachers. Both the primary and secondary school curriculashould consider integrating number sense components to help the learners tounderstand mathematics better.This study considered an important contribution that it made in an African context wherethe quality of both primary and secondary mathematics education constantly falls shortof international benchmark standards such as TIMSS and PISA. That is, incorporatingnumber sense training in the curricula for preservice teachers should not just be atprimary school only but also even at secondary school level.By developing the multiple linear regression analysis model presented in the analysis ofdata, it can also be argued that the study makes a methodological contribution to theresearch on number sense. This relationship can be used to give guidance on the relationship between number sense and academic performance which from the citedliterature did not appear to have been explored.By applying Critical Theory and therefore introducing the CRENS model which as aunique characteristic of this study, the study fills a gap doing away with a monotonousconceptual frame work of constructivism that seems to be existing in the development ofnumber sense. The nature of resources utilised in the study were suitable for the levelof the participants, as a result, these could always be utilised in offering guidance on thenumber sense training by the other teacher training institutions or the University ofNamibia in developing a practical number sense course as per recommendations of thisstudy.

[发布机构] Stellenbosch University