Why is 2 + 2 not equal to 12?

This might seem like an obvious question and the instinctive urge is to disregard it entirely. Perhaps you would think "well that's silly, it's just not!"

Well, that's the intention of the question. It highlights the way in which students are taught and have been taught, particularly in mathematics, for over a century.

Instead, we can explore this question. If 2 + 2 = 12, then 2 + 1 = 11 and 2 + 0 = 10. That means 2 = 10, 1 = 9 and 0 = 8.

If we drew a number line from 0 to 8, it's clear to see they can't be equal. So that's that.

Or, what if we drew a number circle, instead. So 0 goes to 1, which goes to 2, ... , which goes to 7, which returns back to 0. We could form an infinite space of number circles to span the intire integer set of numbers, only this time we're not basing our knowledge on the hexidecimal number system.

This is actually a really important branch of mathematics, called modular arithmetic, having far-reaching applications in computer science, music and even law.

Who would have thought by exploring a seamingly 'stupid' question, we'd reach such an important result.

Mathematics isn't black and white, and there are rarely wrong or right answers. This is the way teachers should adopt their teaching style, to respect all questions and all answers, and use adventure to explore them to their full capacity.