Bob is an elementary school student. He is learning to calculate. He just learned about addition and multiplication but there are some things that he doesn’t understand. For example, how come 1+3 = 3 + 1? How can it be the same thought Bob? Every morning I have 1 piece of bread for breakfast while…

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Negative numbers, the irrationals, and imaginary numbers are not that easy to make sense of for many students. But this is something understandable. One only needs to check-out the histories of these numbers. The mathematicians themselves took a long time to accept and make sense of them. But fractions? How can something so natural, useful,…

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Like most numbers, geometric objects such as angles, are abstraction from properties of real objects and quantities. For example, the idea of “two-ness” can be abstracted from real objects such as two apples, two chairs, two goats, etc. It will not take along for a learner to figure out what the idea of two means….

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