Teachers’ pedagogical content knowledge of probability: the case of teachers of mathematics in Chongwe district Lusaka province, Zambia
Sinzala, Muzamaya, Gift
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This was a qualitative multiple case study that investigated mathematics teachers‟ pedagogical content knowledge of probability in selected secondary schools of Chongwe District, Zambia. A sample of seventeen (17) senior secondary school mathematics teachers was purposefully selected for participation in the study. A subject matter knowledge diagnostic test (SMKDT) based on Probability was administered to the sample to assess their subject matter knowledge of Probability. Documents such as teachers‟ schemes of work, lesson plans, and learners‟ exercise books were also analyzed followed by lesson observations and semi-structured interviews on all the 17 teachers. The intention of the observations and interviews was to investigate teachers‟ ability to use pedagogical strategies and enabling prompts as they taught probability. Data obtained from the SMKDT was analyzed using elements of the subject matter knowledge category of the study‟s conceptual framework. The elements included teachers‟ ability to make clear conceptual connections, interpret, and justify their reasoning in probability. In respect of data collected from lesson observations and interview schedules, the pedagogical strategies and enabling prompts categories of the conceptual framework were employed for analysis of teachers‟ ability to select and use appropriate multiple pedagogical strategies. Based on the analysis of the findings given in the SMKDT, the study showed that the sampled teachers were able to reflect the subject matter knowledge of probability in their processes of making conceptual connections, solving, interpretations, explanations and justifications of major mathematical concepts in relation to probability. However, majority of the sampled teachers (9) could not build on and extend beyond their understanding of the subject matter, instead they exhibited their own informal understanding of the subject matter knowledge of probability, which was a clear indication of a lack of understanding of the subject matter of probability. Likewise, in their lesson presentation and follow-up interviews, ten teachers showed less ability to use multiple pedagogical strategies and enabling prompts with regarding to the unpacking of the subject matter knowledge of probability in a comprehensive way to the learners. This was characteristic of incapacity to facilitate learners‟ clear conceptual understanding of probability. In regard to this, only seven teachers were able to demonstrate their ability to employ multiple pedagogical strategies to engage learners and use multiple forms of mathematical imagery to simplify and explain on the subject matter as they taught concepts such as independence and mutually exclusive events. Therefore, the implication of these findings indicate that despite teachers having taught for ten years and above, their experience could not guarantee them the development of the conceptualized components of PCK necessary for teaching probability of this study‟s conceptual framework. It is, therefore, recommended that teachers be provided with opportunities during training for in-depth study of probability concepts so that they could comprehensively teach learners probability with understanding. Additionally, issues of teachers‟ capacity to use multiple pedagogical strategies should be considered by serving secondary school mathematics teachers in their various continuous professional development activities. KEYWORDS: Pedagogical Content Knowledge, Pedagogical Enabling Prompts, Probability, Pedagogical Teaching strategies, Subject Matter Knowledge, Socially Agreed Conventional Meanings of Terms, Socially Agreed Qualitative Terms, Zambia.
The University of Zambia
SubjectMathematics--Study and teaching (Elementary).
Statistics--Study and teaching.
Mathematics--Study and teaching (Secondary).
- Education