Changes of meanings in multiplication across different contexts: The case of Amy and Beth

This article focuses on how two mathematics teachers (Amy and Beth – pseudonyms) cope with the changes of meanings in multiplication due to the changes of contexts. It highlights the qualitative similarities and differences between these two teachers in the sense-making process of multiplication. A potentially useful framework of supportive and problematic conceptions suggested by Chin (2013) and Chin (2014) is employed in this study. Interviews are performed with Amy and Beth in order to collect the necessary data. Findings reveal that both teachers try to make sense of multiplication by building on the conception of repeated addition across different number systems. When multiplication is operated with negative numbers then problematic aspects emerge within the conception of repeated addition. It is observed that both teachers didn’t build on the meaning of repeated addition in the multiplication of fractions.