Billy is a boy known for his good achievement in mathematics, so it is with no major worries that he starts his last semester of the twelfth grade in a French lycée. He is sitting in a sunny class this morning ready to work, paying attention to his teacher. After a few words of welcoming, the teacher quickly summarises some of the algebra taught the preceding years. He writes the expression [2x=3x] on the blackboard. Billy looks at that a bit puzzled... and says : "but that's not true. 2x is not equal to 3x!" The teacher looks at him, surprised, and responds that for x=0 this  equation is satisfied. He adds : "Hey, Billy, what happen with your maths this summer? This is just an equation of the first degree". Laughs in the classroom. Billy feels ashamed. What has happened?

If the expression written on the blackboard had been [2x+5=11], then Billy would not have made a remark. He recognised first a proposition in the writing of [2x=3x], and when we discussed it, he was clear about the fact that this expression is false for all value of x but 0. But he could hardly see it as an equation, although he had manipulated expressions like [5x+8=12x+3]; in other words, expressions with x in both sides has been manipulated as part of the solving process of a problem within which it appeared, but were not seen first as an equation out of such a context.

This short story, drew my attention to the role of pattern recognition as part of the activity of reading and interpreting algebraic expressions. This role is known is algebra, for example when looking for a primitive or factorizing. It is sometimes seen as a technical weakness in manipulating  algebraic expressions. The fact that Billy is technically a good students in mathematics, may suggest that this time the role of pattern recognition must be considered at a conceptual level.