Young learners often consider mathematics as a field of knowledge that consists of numbers and rules that they are told to follow. In my teaching practice, I often have to remind elementary school students (and college students!) that mathematics is about learning to think logically and problem solve.
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In this series, I will share mathematics concepts that are considered as rules by kids and also explained by kids. By understanding their thinking, hopefully it helps us identify their misconceptions and recognize the importance of building concepts rather than presenting concepts as a rule to follow.
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Concept 1: Two negative numbers multiply to be positive
Explained by a Grade 1 student:
Two negative numbers multiply to be positive because there are two dash lines altogether from the negative signs. The two dash lines combine to a plus sign, which is made of two dash lines.
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Concept 2: When dividing fractions, change the operation to multiplication and take the reciprocal of the second fraction
Explained by a Grade 5 student:
This is because the flip of division is multiplication
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Concept 3: All the angles in a triangle add up to 180 degrees.
Explained by a Grade 6 student:
Because in an equilateral triangle, all angles are 60 degrees, so all three angles add up to 180 degrees. So all the other triangles would have 180 degrees.
Explained by a Grade 7 student:
Because two triangles make a parallelogram, which is a quadrilateral, and that has 360 degrees [as a sum of all four angles]. So a triangle would have half [the sum], 180 degrees.
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Written by Mandy Lam
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