How to gain confidence in Maths
Firstly, let’s talk about how not to lose confidence in Maths. We lose confidence in Maths when we try to solve problems for which we don’t have the right foundations. Every step of Maths builds on a previous step. If we haven’t mastered the first step, it is hard to solve maths problems that belong in the second step and if we have not mastered the second step then we lose confidence when trying to solve problems that belong in the third step and so it continues.
Suppose we have identified which step we need to work on, building confidence requires three types of actions:
a) Asking Why? This gives us the confidence that we actually understand why a formula is written a certain way.
b) Practice: Practice helps build problem solving skills. It also helps us recognise patterns. If we see a few examples of how a particular kind of equation is solved, then we can solve equations that look similar to the ones we have seen.
Practice ! Practice ! Practice !
c) Memory: If we practice enough, then we will build a memory. But we can also memorise just by looking at a formula again and again.
Here is a simple example of how these 3 elements work, with multiplication: how do we learn that 2 x 3 is 6?
Step a) You can ask why? you can show yourself that 2x3=6 by taking one set of three things (three leaves, say) and another set of three things (another three, leaves) and counting the total of both sets to find the total number of things in both sets is 6.
Step b) Practice. If you do the above step a) enough times, you will remember that 2 x 3 is 6.
In fact, you can practice for 2x4, 2x5 and the rest of the table till it all becomes reflexive.
Step c) Practice is time consuming. Instead and alongside, you just memorise your multiplication tables.
You could, in theory, skip the memorisation part and just work on steps a) and b) but it will take you much longer to be ‘fluent’. You could omit step a) and work with mostly step b), practice, and step c) memory, but when you come across truly novel problems, you will be lost because you did not build a solid understanding of why.
The examples given above are simple but the same principles work for all areas and levels of mathematics, from trigonometry to differential equations.