Summary:
No one doubts the notion that the quality of teachers’ mathematical knowledge is one of the most defining factors pertaining to what goes on inside the classroom and what the students will ultimately learn. “No one can teach what they do not know” (Fennema, & Franke, 1992, p. 147).
Subject matter knowledge in itself, however, is not enough. A teacher’s educational actions comprise a complicated interactive process and are not simply a matter of narrowly following a plan. During the teaching process three basic factors need to be balanced: teacher’s understanding of what s/he is teaching, teacher’s ability to identify what the students already know and how the latter can productively build on pre-existing knowledge (Thompson, & Saldanha, 2003).
An effort is made in this thesis to understand, to a certain extent, the subject matter knowledge and pedagogical content knowledge of educators when it comes to multiplication comparisons. Such situations were described in problems given to educators who where asked to fill in a questionnaire. The results showed that educators do not have a deep understanding of the subject of multiplication comparisons and as a consequence present limitations when it comes to teaching them. At times, they reach correct conclusions based on numerical reasoning. However, no quantitative reasoning seems to lie behind this process. Their knowledge seems to be superficial and mechanical.
