Anyone Can Be Good At GCSE Maths
Anyone Can Be Good At GCSE Maths – Introduction
Everyone in the world could be a maths person if they wanted to. The keyword though is “if they wanted to”. That said, everyone in the UK could benefit from having that mathematical background in reasoning just to help everyone make very good decisions.
And here we are distinguishing already between maths as people usually conceive of it, and decision making and analysis, which is actually what maths is. So, for example, being a maths person means that you can recite the formulas between the sines, cosines, tangents and to use logarithms and exponentials interchangeably.
Concentrate
That’s not necessarily what everyone should try to concentrate to understand. The main things to concentrate on to understand are the mathematical principles of reasoning. But let us go back to these sines, cosines and logarithms.
Well actually they do have value. What they are is that they are ways to show you how these basic building blocks of reasoning can be used to deduce surprising things or difficult things. In some sense they’re like the historical coverages of the triumphs of mathematics, so one cannot just talk abstractly about “yes let’s talk about mathematical logic”, it’s actually quite useful to have case studies or stories, which are these famous theorems.
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For Everyone
Now, these are accessible to everyone. One reason mathematics is difficult to understand is actually because of that network of prerequisites. You see, maths is one of these strange subjects for which the concepts are chained in sequences of dependencies. When you have long chains there are very few starting points—very few things are needed to be memorised.
People don’t need to memorise, for example, all these things in history such as “when was the war of 1812?” Well actually that is a maths fact because it contains a date—it was 1812—but I can’t tell you a lot of other facts, which are just purely memorised.
In mathematics you have very few that you memorise and the rest you deduce as you go through, and this chain of deductions is actually what’s critical. Now, let us contrast that with other subjects like say history. History doesn’t have this long chain, in fact if you fully understand the war of 1812 that’s great, and it is true that that will influence perhaps your understanding later of the women’s movement, but it won’t to be as absolutely prerequisite.
In the sense that if you think about the concepts, history has more concepts than mathematics; it’s just that they’re spread out broader and they don’t depend on each other as strongly. So, for example, if you miss a week you will miss the understanding of one unit, but that won’t stop you from understanding all of the rest of the components.
So that’s actually the difference between maths and other subjects. Maths has fewer concepts but they’re chained deeper. And because of the way that we usually learn when you have deep chains it’s very fragile because you lose any one link—meaning if you miss a few concepts along the chain you can actually be completely lost.
If, for example, you’re sick for a week, or if your mind is somewhere else for a week, you might make a hole in your prerequisites. And the way that education often works where it’s almost like riding a train from a beginning to an end, well it’s such that if you have a hole somewhere in your track the train is not going to pass that hole.
Now, the way to help to address this is to provide a way for everyone to learn at their own pace and in fact to fill in the holes whenever they are sensed. And if everyone was able to pick up every one of those prerequisites as necessary, filling in any gap they have, mathematics would change from being the hardest subject to the easiest subject.
Everyone is a maths person, and all that one has to do is to go through the chain and fill in all the gaps, and you will understand it better than all the other subjects actually.
That’s not necessarily what everyone should try to concentrate to understand. The main things to concentrate on to understand are the mathematical principles of reasoning. But let us go back to these sines, cosines and logarithms.
Well actually they do have value. What they are is that they are ways to show you how these basic building blocks of reasoning can be used to deduce surprising things or difficult things. In some sense they’re like the historical coverages of the triumphs of mathematics, so one cannot just talk abstractly about “yes let’s talk about mathematical logic”, it’s actually quite useful to have case studies or stories, which are these famous theorems.