Mathematics, Science and Technology Education

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Browsing Mathematics, Science and Technology Education by Subject "Algebraic activities"

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    An exploration of final year, pre-service mathematics teachers’ learning experiences in solving non-routine financial mathematics problems at a South African University
    (University of Zululand, 2021) Talasi, Tatolo
    This study explored pre-service mathematics teachers (PSMTs) learning experiences in solving non-routine mathematical problems in financial mathematics. To this end, the theories that formed the foundation of this study were the realistic mathematics education, socio-constructivist theory of problem solving and mathematical proficiency. Participants were drawn from an initial teacher education programme in South Africa. They were in the final year of their four-year Bachelor of Education degree, specializing in Mathematics, Science and Technology Education for intermediate and senior phase teaching. A total of 11 pre-service mathematics teachers participated in the study. The study employed a qualitative approach and a case study design. A single case study with multiple units was deemed appropriate for this investigation. The data for this investigation were generated through questionnaires, documents, observations and interviews. Firstly, PSMTs responded to an open-ended questionnaire which had 27 items. Secondly, PSMTs solved four non-routine mathematical problems, based on financial mathematics, in groups, over four weeks. The problem-solving sessions were conducted concurrently in different venues. The D_group and the M_group were video recorded during each session, while the T_group was audio recorded. Thirdly, and finally, the researcher interviewed the available members of each group. Content analysis was used to interrogate the data from the various instruments. The results were presented in the form of tables and excerpts. The findings across the various instruments showed that the PSMTs used numerical strategy, pictorial strategy, verbal strategy, and algebraic strategy to solve mathematical problems in financial mathematics. None of the groups used graphical strategy. The PSMTs grappled with contextual, linguistic, representational and transformational activities of algebra in their search for solutions to non-routine mathematical problems in financial mathematics. However, all the groups seemed to lack a knowledge of the time value of money principle and had inadequate knowledge of mathematical language. Consequently, all the groups committed linguistic and contextual errors, more than mathematical errors. iv It is recommended that LTSMs’ authors, curriculum developers and mathematics education instructors and lecturers design and implement learning outcomes which extend beyond the mere acquisition of mathematical concepts and mathematical skills. The learning outcomes that foster the acquisition of mathematical language, particularly financial mathematics language, should be prioritize in the assessment activities of PSMTs. Concerted efforts should be made to explicitly educate and expose PSMTs to problem situations that require the use of graphical problem-solving strategies, which have seemed missing in this cohort of PSMTs. The teaching of financial mathematics should focus upon the use of the time value of money principle and compounding of interest. To maximize the learning experiences of pre-service mathematics teachers (PSMTs) in solving problems in financial mathematics, mathematics education lecturers may have to supplement the examples and practice problems given in PSMTs textbooks, and other LTSMs, to include non-routine mathematical problems, which focus upon the use of graphical problem-solving strategy that seemed to be highly underdeveloped in this cohort of PSMTs. It is further concluded that mathematics education lecturers should engage PSMTs with non-routine mathematical problems in financial mathematics with superfluous (and or missing) information and in higher cognitive demands to maximize PSMTs’ learning experiences in solving these problems which are rarely found in textbooks and other LTSMs.
University of Zululand