Pre-service mathematics teachers’ subject matter knowledge of measures of central tendency / Komathi Jairaman

Komathi, Jairaman (2018) Pre-service mathematics teachers’ subject matter knowledge of measures of central tendency / Komathi Jairaman. PhD thesis, University of Malaya.

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Abstract

The purpose of this study was to investigate pre-service mathematics teachers’ subject matter knowledge of measures of central tendency and their level of subject matter knowledge of measures of central tendency involved in the enhancement of statistical literacy. Data of this study was collected using clinical interview technique based on open-ended questions as instrument. The materials that were collected for the analysis consisted of the audio recordings of the clinical interviews, video recordings of the clinical interviews, subjects’ notes in the task sheets, and researcher’s notes during the interviews. A total of fifteen tasks covering four constructs of investigation namely; measures of central tendency with reference to context, measures of central tendency in handling bias, measures of central tendency in problem solving, and measures of central tendency in making inference were devised and used in this study. The subjects of this study consisted of six pre-service mathematics teachers enrolled in a 4-year Bachelor of Science with Education (B. Sc. Ed.) in a public university in Peninsular Malaysia. The selected subjects either majored or minored in mathematics and at the point of data collection, they were either in their third or final year of the program. The findings of this study were summarised into five main themes of the subject matter knowledge of measures of central tendency that emerged from the clinical interview namely; as averages, data representation, procedures, data summary, and data comparison. The findings related to mean as average, mode as average, median as average, and idea of average were categorised under the theme averages. Mode as data representation, best data representation measure, and robustness of measures were categorised under data representation. Idea of mode, idea of median, backward mean calculation, representative nature of the mean, and forward mean calculation were categorised under procedures. Identifying and summarising data using measures of central tendency and summarising equal or unequal sized numerical or graphical data using measures of central tendency were categorised under data summary. Finally, utilising the appropriate measure of central tendency to compare and draw conclusions about equal or unequal sized numerical or graphical data were summarised under data comparison. The pre-service mathematics teachers’ levels of the subject matter knowledge of measures of central tendency in terms of the identified themes were also constructed. Most of the pre-service mathematics teachers attained either high or medium levels. However, it was also found that there were pre-service mathematics teachers who attained low levels for the themes data representation and data comparison, Regarding the overall level of the subject matter knowledge based on the emerged themes calculated for each of the six pre-service mathematics teachers, only one out of the six pre-service mathematics teachers attained an overall high level meanwhile the remaining five attained a medium level. The findings of this study are hoped to contribute to the discussion on what might constitute the subject matter knowledge of measures of central tendency involved in the enhancement of statistical literacy.

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