The Correlation between Prospective Teachers' Knowledge of Algebraic Inverse Operations and Teaching Competency--Using the Square Root as an Example

This study is part of a larger study investigating the subject matter knowledge and pedagogical content knowledge of Hong Kong prospective mathematics teachers, the relationship between the knowledge of algebraic operation and its inverse, and their teaching competency. In this paper, we address the subject matter knowledge and pedagogical content knowledge of eight Hong Kong prospective teachers in teaching the mathematical concept of the square root of a number in junior secondary school. The results suggest that insufficient understanding of the concept of algebraic operation is a major obstacle for effective teaching of this topic by prospective teachers. The results corroborate the viewpoint that subject matter knowledge and pedagogical content knowledge are interrelated constructs and that rich subject matter knowledge leads to high-quality pedagogical content knowledge. We conclude it with a suggestion on how teachers can enrich their pedagogical content knowledge by looking at elementary mathematics from an advanced standpoint (EMFAS), when they possess a substantial subject knowledge.