First year students’ understanding of specific concepts in selected mathematics topics : the case of the university of Zambia.

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Date
2021
Authors
Mwape, John
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Publisher
The University of Zambia
Abstract
This study investigated the understanding which University of Zambia (UNZA) first year students of mathematics had of specific concepts in selected mathematics topics. Procedural and conceptual understanding underpinned the investigation. It was also the intention of the study to determine whether there exists any relationship between students‟ confidence levels and their procedural and conceptual understanding of particular concepts. Further investigations were done to determine if there is a relationship between students‟ confidence and their actual performance in procedural and conceptual mathematics problems. The study also sought to develop and design instruments for measuring understanding of concepts in mathematics. A quantitative approach was followed and specifically a case study design was employed. Three hundred and seventy eight (378) randomly sampled first year students of mathematics wrote a test which was based on binomial expansions, systems of equations, inequalities, set theory, binary operations, partial fractions, polynomials, functions, trigonometry, quadratics and complex numbers, as taught in first year at UNZA. Three of the five lectures of first year mathematics at UNZA were also asked to answer the questionnaire after studying the questions in the test for students in terms of how they rated procedural and conceptual understanding they might expect. They were also asked to give their opinion on how they rated procedural and conceptual levels of difficulty associated to the questions in the test. Internal consistency of input variables was measured using Cronbach alpha. The correlation matrix was used rather than the variance-covariance matrix because it conformed to the research design of the study. The scoring criteria for the test items was made to measure procedural and conceptual understanding before the test was administered. It was found that procedural internal consistency was 0.879 while conceptual internal consistency was 0.842 which suggested that the test as an instrument prepared for research was reliable because all its components after testing for internal consistency were in the required range of 0.65 to 0.95. The test data was analysed using standard indices while the data derived through questionnaires was analysed using multivariate techniques. The study revealed that procedural understanding was 9.78 while conceptual understanding was 22.6. These results shows that the smaller the result the more explained the result was. Standard indices indicated that, students at UNZA understands procedural concepts more as compared to conceptual ones. The results also showed that the procedural confidence of understanding possessed by students was 6.56 while conceptual confidence of understanding was 12.9. The results indicated that students were twice more confident to answer procedural concepts as compared v to conceptual. The overall conclusion from this study is that, there was a significant relationship between students‟ confidence levels and their procedural and conceptual understanding. On this premise, the findings further indicate that there exists a relationship between students‟ confidence and their actual performance in procedural and conceptual mathematical problems. Furthermore, the study revealed that there was a positive correlation between students‟ understanding of mathematics concepts and their ability to execute procedures. Based on the findings, UNZA lecturers of mathematics should focus on teaching methods which would enhance students‟ conceptual understanding of concepts in mathematics. Further recommendations are that, the current study may stimulate further research of understanding of mathematics concepts at universities in Zambia and beyond. Key words: Procedural understanding, Conceptual understanding, Confidence levels, Standard indices, Multi-variate techniques.
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Keywords
Mathematics. , Mathematics-Study and teaching. , Applications of mathematics--Study and teaching.
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