The equal sign: Teachers’ knowledge and students’ misconceptions

This article reports on a study that investigated the extent to which 57 Grade 6 students at a particular school have misconceptions regarding equality, with the equal sign as focus. It also investigated this school’s three Grade 5 and 6 teachers’ mathematical knowledge for teaching regarding equality, again focusing on the equal sign. The research took the form of a case study in which a qualitative approach was used. Data collection methods included teacher questionnaires and a focus group interview with teachers. Students answered a set of questions after which six students were purposefully selected, based on their responses in the questionnaire, and interviewed. To gauge students’ level of understanding of the equal sign, the construction map for knowledge of the equal sign developed by Matthews et al. was used, while the Mathematical Knowledge for Teaching model proposed by Ball et al. was employed to interpret teachers’ knowledge. Results indicate that few students had a well-developed relational conception of the equal sign. The majority of students could not describe the meaning of the equal sign correctly. The same group of students that applied ‘closure’ was inclined to ‘use all the numbers in an equation’. Grade 5 and 6 teachers’ Mathematical Knowledge for Teaching of the equal sign indicated that in general they lacked the knowledge and skills to identify, prevent, reduce or correct students’ misconceptions about the equal sign