THE MEANING of “EQUALS” Charles Darr Take a Look at the Following Mathematics Problem
PROFESSIONAL DEVELOPMENT THE MEANING OF “EQUALS” Charles Darr Take a look at the following mathematics problem. has been explored by mathematics education researchers internationally (Falkner, Levi and Carpenter, 1999; Kieran, 1981, 1992; MacGregor Write the number in the square below that you think and Stacey, 1997; Saenz-Ludlow and Walgamuth, 1998; Stacey and best completes the equation. MacGregor, 1999; Wright, 1999). However, the fact that so many students appear to have this 4 + 5 = + 3 misconception highlights some important considerations that we, as mathematics educators, can learn from and begin to address. How difficult do you consider this equation to be? At what age do you In what follows I look at two of these considerations. I then go on to think a student should be able to complete it correctly? discuss some strategies we can employ in the classroom to help our I recently presented this problem to over 300 Year 7 and 8 students at students gain a richer sense of what the equals sign represents. a large intermediate school. More than half answered it incorrectly.1 Moreover, the vast majority of the students who wrote something other The meaning of “equals” than 6 were inclined to write the missing number as “9”. Firstly, it is worth considering what the equals sign means in a This result is not just an intermediate school phenomenon, however. mathematical sense, and why so many children seem to struggle to Smaller numbers of students in other Years were also tested. In Years 4, develop this understanding. 5 and 6, even larger percentages wrote incorrect responses, while at Years From a mathematical point of view, the equals sign is not a command 9 and 10, more than 20 percent of the students were still not writing a to do something.
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