Cinemathematics
One of the earliest inaccuracies to which students are exposed in mathematics texts is something I refer to as “cinemathematics.”
Specifically, in the primary grades (K–2), cinemathematics is the fallacy of understanding mathematical operations as verbs.
Look at the model below. Something like this appears in many primary mathematics textbooks to introduce the idea of subtraction. In this case, the model is meant to represent the expression 5 – 2:
Of course, even if we accept the validity of cross-out models, the expression represented by the model above is really 5 – 1 – 1.
However, what is important to remember—and students will learn this in their later elementary years--is that mathematical operations do NOT, in truth, represent actions. Mathematical expressions that employ one or more of the standard operations are descriptive statements—one can think of them as speaking about something that has already happened. The model below is a more accurate representation of 5 – 2:
Specifically, in the primary grades (K–2), cinemathematics is the fallacy of understanding mathematical operations as verbs.
Look at the model below. Something like this appears in many primary mathematics textbooks to introduce the idea of subtraction. In this case, the model is meant to represent the expression 5 – 2:
Of course, even if we accept the validity of cross-out models, the expression represented by the model above is really 5 – 1 – 1.
However, what is important to remember—and students will learn this in their later elementary years--is that mathematical operations do NOT, in truth, represent actions. Mathematical expressions that employ one or more of the standard operations are descriptive statements—one can think of them as speaking about something that has already happened. The model below is a more accurate representation of 5 – 2:
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