THE 5 STEPS TO UNDERSTANDING MATHS, EVERY TIME – WITHOUT SPENDING A DOLLAR

Last week we had a student that told us something that we hear fairly often.

“I want to put in more effort, but I don’t really know where to start.”

To give some context to this, the student was struggling with senior high school Maths. This had been going on for some time and the content was steadily increasing in pace. Week after week, day after day no matter how much she looked at the problems, they wouldn’t ever just ‘click’

It was around this time that we started working with the student to help them get back on track with their maths. Now due to financial constraints, this family could only afford an hour of tutoring a week. This wouldn’t normally be a problem but given how behind the student felt – it would take more than an hour a week to help fix.

But, the saving grace was the student’s mental fortitude. While they often said out loud that they couldn’t understand the maths, the attention during lessons made it clear that they were still eager to try more.

So we eventually said to the student that an hour per week with us would likely not be enough, so let’s look at what you currently do in your own study time.

Like most students, the time varied based on how ‘motivated’ they were to study (usually meaning the assignment or test is due tomorrow). But pushing on we found the original quote for this article coming from the student.

“I want to put in more effort, but I don’t really know where to start.”

…So we showed them where to start

Below you will find the exact same 5 step blueprint to studying anything in maths. We’ll label what to do, where to find materials, what it should help fix.

That being said, let’s get started:

STAGE 1: INTRODUCING THE CONCEPT

What grade you can expect if you don’t complete this stage: D

START HERE IF YOU:
– Feel like the teacher is explaining things too quickly
– Nothing is making sense in what you’re learning
– You struggle with completing stage 2

Any Maths topic can be broken up into 2 categories:

FACTS AND CONCEPTS

To give an example, a fact might be that 2+2=4, while the concept would be ‘Addition”

Most cases of ‘I just don’t get any of this’ stem from not understanding the concept of what is being taught in class. Put simply, you’ll never do well in maths if you don’t understand ‘why’ you do certain steps in an equation.

“SO HOW DO I FIX IT?”

There are 2 resources that I often recommend to students at this stage. The first is ‘External video tutorials’ that explain and demonstrate the concept. The Second is the ‘Worked example in the textbook’.

For example if I was student trying to learn Pythagoras theorem and didn’t understand it at all, I would start with some Internet tutorials explaining it. In particular I would recommend.

Khan Academy

Worked Example

While the wording can sometimes confuse students, it helps to try and comprehend the worked examples first in conjunction with any external videos before attempting the further questions.

If you feel like you get the idea behind the concept you’re learning, move onto Stage 2.

STAGE 2: TESTING YOURSELF ON SIMPLE ‘UN-WORDED’ QUESTIONS

What grade you can expect if you complete this stage: C to B-

MOVE TO HERE IF YOU:
– Feel like you have a grasp of the concept
– Want to apply the concept in uncomplicated questions

At this stage you should be able to complete the simple questions listed in the textbook. To use the addition example again, you should now be able to answer 2+2=?

This stage is just to confirm you have understood how to apply the concept when all the information is given to you.

A common issue with student’s not above average in maths is staying in this stage for the whole time they are learning the content.

This stage is only a place to confirm that you understand the concept basically, after which you should move on to Stage 3

STAGE 3: TESTING YOURSELF ON SIMPLE ‘WORDED’ QUESTIONS

What grade you can expect if you complete this stage: B- to B+

MOVE TO HERE IF YOU:
– Find most of the un-worded questions easy

When people talk about understanding maths until letters were added, they really should mean this instead of algebra. Think of these questions as how you might see the same concept applied in the real world.

If Stage 2 was having perfect vision, Stage 3 is where the vision becomes blurry. The whole idea with practising here is almost like developing prescriptions to see clearly again.

All questions studied here should involve a small paragraph of information, with students getting used to peeling back the layers to find the relevant information.

The whole skill that is trying to be taught here is :

‘HOW CAN YOU FIND THE RELEVANT MATHS IN A REAL WORLD SCENARIO’

This is a different skill set to just working through the same fact-based questions from earlier. Worded questions see whether you actually understand the concept, and you haven’t just developed a good memory to the steps of the previous questions.

All Queensland Maths textbooks contain a separate section with questions like these.

At this stage, you should find it much easier to keep up with your teacher in class if you felt they were going too fast originally. Doing well here ensures that you will likely do quite well when it comes to the test.

STAGE 4: TESTING YOURSELF ON COMPLEX ‘WORDED’ QUESTIONS.

What grade you can expect if you complete this stage: A- to A

MOVE TO HERE IF YOU:
– Find most of the simple worded questions easy
– Want to have a very high confidence in your ability

If you as a student have said this, or as a parent have heard the line “We were never taught *that question* that was on the test” Then you haven’t moved on to Stage 4.

This Stage is seeing how far can you push your understanding of the concept you were taught. Not only are the questions more complex, but they can also be written in a way that a student would have to use that concept in a scenario they’ve never seen before.

Questions like these will involve multiple steps and likely incorporate a few different concepts into one question.

Examples of these are usually found at the end of chapter in the prescribed maths textbook.

STAGE 5: TEACH IT TO SOMEONE ELSE

What grade you can expect if you don’t complete this stage: A to A+

MOVE TO HERE IF YOU:
– Feel confident and looking to help someone else whilst also taking away the stress of the test

This is the highest level of understanding of a given maths topic. Not only must you know the content, but you have to take into account what the other person does or doesn’t know about it.

Any student’s we’ve had that are at this stage are not worried about the test very much at all since it’s clear they understand the vast majority of the concept and how to apply it.

It doesn’t matter who you teach it to, so long as they are willing to try and learn it from you.

AND THAT’S IT! A STEP BY STEP GUIDE FOR STUDYING MATH, WHEN YOU DON’T KNOW WHERE TO START

To clarify, this was put together for our student who didn’t know what or where to study to improve her maths ability. There are many different methods on how to study the content in these stages, but some students need help with what to do, when you know nothing.