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Mathematics and Computer Science Education

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Browsing Mathematics and Computer Science Education by Subject "APOS theory."

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    Exploring learners’ understanding of mathematical concepts necessary in the learning of grade 11 algebraic functions: the case of three schools in uMgungundlovu District.
    (2019) Ndlovu, Nkosinathi Emmanuel.; Goba, Barbara Busisiwe.
    The purpose of this study was to explore learners’ understanding of mathematical concepts in the learning of grade 11 algebraic functions in uMgungundlovu district, KwaZulu-Natal. In order to gain insights into learners’ understanding of mathematical concepts in learning grade 11 algebraic functions, APOS theory was used as a theoretical lens to explore learners’ level of understanding of functions. This study describes the mathematical concepts that are important in the learning of grade 11 algebraic functions. The CAPS document was used to analyse the mathematical concepts for functions to be learnt in grade 11. The data was gathered through written tasks and interviews of grade 11 learners in three schools in one district in KwaZulu-Natal. The research approach used for this study was the mixed method. Sixty grade 11 learners (twenty in each school) were purposively selected; however, this sample selection was conveniently done since learners were able to participate in the study after school. This study employed the interpretive paradigm and nine learners (three from each school) were interviewed during data collection. Multiple methods were employed for data collection in this study. Qualitative data was organised using interview transcripts and quantitative data was organised using the APOS analytical framework. The findings of this study confirm that learners’ level of understanding of algebraic functions at an object level is extremely poor.
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    Exploring university students' mental constructions of the limit concept in relation to sequences and series.
    (2019) Chagwiza, Conilius Jaison.; Maharaj, Aneshkumar.; Brijlall, Deonarain.
    The present thesis refers to some first semester calculus 1 university students’ mental constructions of the limit concept in relation to sequences and series. A plethora of research on the limit concept is available and suggests that the concept is on record of being difficult for students to learn and comprehend. However, in Zimbabwe, there is inadequate research on mental constructions made by students of the limit concept in relation to sequences and series. This research aims at filling this gap in the literature. This study utilized the Action-Process-Object-Schema (APOS) theory in exploring conceptual appreciative displayed by students when dealing with limits of sequences and series. The study proposes the genetic decompositions on how students might construct the mental constructions in learning the sequences and series through the use of Activities-Classroom discussions –Exercises (ACE). Collection of data was done by the use of a methodology that used practical teaching. All the thirty students who took calculus 1 accepted to participate in this study and answered the limit test questions. The students’ written responses were analyzed using APOS theory. Ten students were selected for interviews through purposive sampling. Two declined to take part leaving eight to take part in the process. The APOS theory was used to analyze the interview results. The revision of preliminary genetic decomposition was done basing on the analyzed data. The instructional method employed, facilitated the appreciation of the limit concept in relation to sequences and series by the students. Nearly all students showed that they operated at the Action level, a good number showed that they operated at least at the Process level and more than half of the students showed that they operated at the Object level. Three out eight interviewed students indicated that the managed to operate at the Schema level on some of the test questions. However, there is need for the establishment of a conceptual basis that promotes and allows the construction of the limit concept schema in relation to sequences and series. Furthermore, interviewed students’ responses paralleled the chronological improvement of the limit concept as reported in literature. Historical analysis of the development of concepts needs to be reflected upon when preparing and designing instruction. This would help the lecturer to foresee the challenges that lay ahead and address students’ difficulties during the learning process. The implementation of APOS Theory is recommended for the learning of other mathematical aspects, which cause difficulties in students’ learning. Moreover, other constructivist learning methods can be fused together with the APOS Theory to obtain improved results on students’ performance in mathematics.