Predictive Validity of Entry Level Mathematical on Mathematical Knowledge of Pre-service Teachers for Teaching Basic School mathematics in Ghana

Introduction: Knowledge about teaching mathematics remains a contentious issue in the preparation of pre-service teachers in Ghana. This study explored relationships among entry-level mathematical knowledge (ELMK), mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) scores of pre-service teachers in colleges of education (CoEs) in Ghana. Methods: The cross-sectional survey design was adopted for this study. A total of 998 pre-service teachers from ten (10) public colleges of education were sampled via multi-stage sampling technique. Structured questionnaire and unstructured observation schedule were used for the survey. College mathematics test results were used as secondary data. The data were analysed using descriptive statistics (frequency count, percentage) and inferential statistics (Pearson’s correlation, paired-samples t-test and regression analysis) with the aid of Statistical Package for Social Sciences software version 22. Results: The majority of pre-service teachers in Ghanaian colleges of education had average but relatively weak grades in ELMCK. ELMCK did not significantly predict pre-service teachers’ MCK statistically (p ≥ 0.05) although a statistically significant positive correlation existed between the variables. Although a negative correlation existed between ELMCK and PMCK, ELMCK significantly predicted pre-service teachers’ PMCK statistically (p ≤ 0.05) but the effect size was statistically negligible. Conclusions: This study concluded that, CoEs in Ghana admit pre-service teachers with average but weak grades in ELMK. Therefore, Ghanaian CoEs should structure and introduce PMCK alongside MCK for pre-service teachers. Mathematics tutors in CoEs should organize remedial lessons for pre-service teachers to scale-up their MCK and PMCK that adequately equip them with MKT. Keywords: Entry-level mathematical knowledge (ELMK), mathematics content knowledge (MCK), mathematics pedagogical content knowledge (MPCK), mathematical knowledge for teaching (MKT), pre-service teachers.

Unpacking Mathematics Pedagogical Content Knowledge for Elementary Number Theory: The Case of Arithmetic Word Problems

“Number” is an important learning dimension in primary mathematics education. It covers a large proportion of mathematical topics in the primary mathematics curriculum, and teachers use most of their class time to teach fundamental number concepts and basic arithmetic operations. This paper focuses on the nature of mathematics pedagogical content knowledge (MPCK) concerning arithmetic word problems. The aim of this qualitative research was to investigate how well the future primary school teachers in Hong Kong had been prepared to teach mathematical application problems for third and sixth graders. Nineteen pre-service teachers who majored in both mathematics and primary education were interviewed using two sets of scenario-based questions. The results revealed that innovative approaches were suggested for teaching third graders while the strategies suggested for teaching sixth graders were mostly based on a profound understanding of mathematical content knowledge. Many participants demonstrated sound knowledge about the sixth grader’s mathematical misconception, but most of them were unable to precisely indicate the third grader’s error in presenting a complete solution for a typical mathematics word problem. A deep understanding of elementary number theory seems to be a precondition for developing pre-service teachers’ MPCK in teaching arithmetic word problems.