Why Maths Doesn't Need To Be As Hard or Horrible As Your Teen Thinks
A look into high school's most hated subject and how to get through it…
For so many high school students, maths is a subject shrouded in mystery.
Teens take one look at a question and see an unknown language staring back at them.
Well, maths is another language, but just like a language, it has rules. Rules that can be learnt and followed.
Follow. The. Rules.
Maths is actually known as the purest science, because it is the least subjective. It is governed by rules that (at least at high school level) cannot be broken.
Just like a Rubik’s Cube, the solution is 100% possible, you just need to follow certain steps to get there.
You follow the rules of Maths, you get the marks.
This is the beauty of Maths, and why it can be a really satisfying subject once you ‘get it’. Once you know the rules and how to apply them, that’s really all there is to it.
The Three Types of Maths Questions
I think it’s helpful to categorise Maths by the general hardness of the questions:
Easy, medium, and hard.
At high school, all Maths questions, regardless of their ‘hardness level’, are underpinned by the same type of theory.
For instance, algebra (don’t worry you don’t need to remember algebra!).
A nice and ‘easy’ question might ask your teen to solve for x where 6 + x = 9.
A ‘medium’ question might be a word-question, so your teen has to figure out what information in the word question is relevant to solving the problem.
And a ‘hard’ question might involve a word question and require them to put together their own equation and solve it.
But every type of question is underpinned by the exact same rules of algebra.
What makes the questions harder is that it becomes harder to discern from the question what it’s asking you to do and what information is actually relevant to solving the problem.
Let’s take a closer look at some examples to better understand how your teen can learn how to master the ‘easy’ questions, and then build upon that knowledge to start conquering harder ones.
For the sake of explanation I am going to generalise quite a lot in this next section, but I hope that I will be able to show your teen what I mean by easy, medium and hard questions, to make Maths a lot less scary.
Easy Questions
An easy question will generally give you the relevant equation or formula and the relevant values.
For instance: “Expand and simplify (x + 3)(x + 2)”
These questions are ‘easy’ because you are basically spoon-fed all of the information you need.
Your teen just needs to know the rules, or the steps required, to in this case ‘expand and simply’ a quadratic. (For the teens reading this, you will probably have heard of the FOIL method to expand this quadratic.)
Once they know the rules they can solve a million quadratic equations, because the only thing that will change question to question is the numbers, not the rules.
Medium Questions
A medium question will often give you the relevant values and relevant equation or formula, but will ‘hide’ the relevant values/numbers you need. The relevant values are often hidden amongst the words in a word-question.
For instance: “If Sarah walks for 2 miles in a north-westerly direction, and then walks for 3 miles in south-westerly direction, how many miles does she need to walk to get back to her starting point, assuming she walks in a straight line?”
This question requires us to use Pythagoras’ Theorem. For those of you that need a refresher, when dealing with a right-angled triangle, a2 +b2 ALWAYS = c2; where ‘a’ and ‘b’ are the two shorter sides of the triangle, and ‘c’ is the hypotenuse.
This question is harder than the first example, because it requires you to know, on your own, that the formula to use is Pythagoras’ Theorem, and it requires you to enter the relevant values into the formula on your own.
So yes, this question is clearly one up on the hardness scale from the first example, BUT — it’s actually not that scary.
The underlying theory — Pythagoras’ Theorem — never changes. And you are still GIVEN the relevant values! They are right there in the question, in plain sight. They’re just contained in a sentence rather than spoon-fed to you.
The only thing your teen would have to recognise on their own in answering this question is that they are dealing with a right-angled triangle, and therefore Pythagoras is the formula they need to use. Sometimes a question like this will even be accompanied by a diagram representing Sarah’s path (i.e. a right-angled triangle).
So even though this medium question might look a lot more complicated than the ‘easy question’, your teen is actually still given all of the information they need, and they still need to apply the exact same rules as an easy question.
Now, A Hard Question
A really hard Maths question can be incredibly challenging, especially in your teen’s senior year at high school.
Often, you’re not explicitly given the relevant values or relevant equation or formula. Like a medium question, the values will be there, but they will probably be hidden in the form of a word-question, or veiled in some other way, and it’s up to you to figure out what to do with them.
And — it’s up to you to figure out what equations or formulae are required to solve the problem. I say equations and formulae — plural — because a hard question may very well require you to use multiple equations and/or formulae to get the solution.
Hard Maths questions might also throw in irrelevant information into the question (‘red herrings’), and it’s up to you to know what information is required to solve the problem and what is extraneous.
BUT — and AGAIN — a hard Maths question will still only be based on the rules that you’ve learnt in class.
The question is just dressed up to appear a lot more complicated, and it requires you to think on your own a lot more.
I’m not saying this means every student should be able to answer every hard Maths question. Exams are purposefully written so that not everyone should get 100%. That’s just the game we’re dealing with. And really hard Maths questions are designed so that only a small portion of students get the answer.
But I want your teen to better understand how Maths works in terms of all questions being underpinned by the same theory, and that way, hopefully, they will be less intimidated by the medium and hard questions.
How This Can Help Your Teen
The key takeaway from this article is that high school Maths is entirely rule / step-based, and so your teen’s job is to learn the rules for each type of question they are going to be tested on, and then practice each type until they find it easy.
Then, once your teen understands the building blocks of each type of question, they can start trying ‘medium’ questions, and then, if they’re up for it, giving some ‘hard’ questions a go.
Every question thrown at your teen in a Maths test or exam will be based on what they have learnt in class. They will never be expected to have gone away and buried their nose in a Maths book pitched at a higher year level than they are, and they will never be expected to have read a biography on Isaac Newton.
Your teen needs to learn the rules, apply and practice the rules, and the marks should come.
Thanks so much for reading.
Clare
