Maths I Should Understand Better
As a maths teacher, I can comfortably do a GCSE maths paper getting close to full marks (odd mistake perhaps) without really trying. This probably comes as no surprise. However, there are some parts of the maths that I actually don’t fully understand or don’t know why they work. Here are some of the ones I’d like a better understanding of:1) When dividing fractions, why does flipping the second one over and multiplying instead work? I have a vague grasp of those being two ‘inverse’ type operations but is that all there is to it? Is there a nice visual representation of why that works? 2) Using a quadratic curve and plotting a linear graph to solve a second quadratic. I don’t fully get why finding the ‘difference’ between the two quadratics and plotting that line means that the intersection of the line with the original quadratic gives the solutions. 3) In Statistics, for the standard deviation (Chi-squared for that matter) why do we square the terms? I understand the need to remove the negative signs but wouldn’t modulus do it? 4) Do trapeziums have to have exactly one pair of parallel lines? Why shouldn’t a rectangle count? Why does this shape appear to have some ambiguity in its definition? Who would be the person/group of people to have a definitive answer? 5) Perhaps not GCSE as such but is there any reason why 0 can’t be even? Or positive?
Am I alone in wondering these things (and think it’s important to wonder)?
Are there parts of GCSE maths that you teach methods for but don’t really get yourself? Do share – you’re amongst friends here!