for the learning of mathematics

an international journal of mathematics education

Laurent Theis - Vol. 25 Num. 3 (2005)
 Learning the = sign: a significant cognitive obstacle (online only)


Many first-grade children regard the equals sign essentially as a command to perform a foregoing arithmetical operation rather than as an indicator of a relation. This erroneous conception chiefly generates two types of problems: 1) these children have difficulties to assess non conventional number sentences, and 2) they cannot complete number sentences that differ from the “ a + b = c ” pattern.

The main goal of our research was to explore how first-grade children develop their understanding of the equals sign. After having carried out with a whole class a pre-test that has revealed to us that all interviewed pupils interpreted the equals sign as an operator (a “do something” symbol), we have taught the equals sign to three first-grade children (one weak, one average, and one strong) within the framework of a six-week constructivist teaching experiment.

During the teaching experiment, the three chosen children made progress towards the understanding of the equals sign, but to learn to interpret this symbol as a relational sign was by no means an easy task. At the beginning, the participants were reluctant to modify their conception of what the equals sign means. Several times during the teaching experiment, the children were inclined to return to their initial conception of the symbol. This tendency also became apparent through the results of the final assessment, held a few days after the teaching experiment, and in which two out of the three selected children failed to do as well as at the end of the six-week sequence.