Teaching Maths at Home

Introduction

“I hear and I forget. I see and I remember. I do and I understand.” Well that’s what Confucius wrote and who am I to disagree.

I have started with this quote and I will come back to it later when I get on to talking about teaching maths at home.

But first – who is this article for? In writing this I am thinking about those who home school for one reason or another and also for those who want to support a child in their learning. It is also for other subjects too such as physics and chemistry where there is a large problem solving element.

OK, so back to the topic. How do you go about teaching maths at home?

How We Learn

I started with the Confucian quote as it is central to any methodology in teaching. I am basing my advice here on over three decades of teaching and private tutoring. But, let me start from how I started out tutoring and what I did wrong.

I would go to a student’s house, spend an hour there going through elements of the course, explaining things, showing examples and letting the student do some examples while I watched. I reckon now that 90% of what I did was a waste of time. Over the years I evolved as a tutor and now feel that I have achieved Yoda status. I know what I am doing, I know that it works and I know why it works.

Think about going for tennis lessons. You would expect that you would have a racquet in your hand most of the time and to be doing tennis practice. You would be very disappointed if most of the time was spent watching an expert show you what to do. On top of that you wouldn’t learn anything apart from how awesome the instructor is at tennis.

We learn best by doing and not by watching or listening. Any program of study must have a large element of doing or the learning will not happen.

I can’t emphasise this enough. Don’t approach teaching maths at home from the point of view of actually teaching. Getting very teachy will result in three things – boring the student, confusing the student and very slow progress. You run the risk of losing them completely.

What Works Best for Teaching Maths at home?

The best approach, and what I use extremely effectively in tuition, is to deal with difficulties. Let the student teach themselves. For this you will need a good well-structured resource like the one we offer. The student works through the materials, doing exercises and assessments. Your role or the role of a tutor (such as our online tutors) is to help with blocks – to clear them out of the way.

For example, in a typical tuition with me, a student comes with their agenda – I don’t have one. They tell me what they need. They come with things that they are stuck on. I then help them to understand it. How do I do that? Well we are right back at Confucius again.

Procedure for Helping Students

The procedure I use relies on the doing aspect. It also relies on realising the basic law of maths learning – The METHOD is king. So, before we get into the steps of the procedure you need to focus on the fact that you are teaching a method and not solving a problem.

So, here are the steps of the procedure:

• The student indicates a problem they can’t do
• I ask them a question or two about theory if relevant – for example, I might say “This problem requires Pythagoras’ theorem. Can you write it down?”
• If they write it down then we move to the next step. If they can’t then I write it down for them and relate the elements of the formula or whatever to the problem
• I then ask them to have a go at the problem.

PAUSE

At this stage I will have been speaking to them for no more than a minute, more likely I will have been speaking for less than half a minute. I keep the direction as simple and direct as possible so that the student remains engaged with the problem and doesn’t drift off as a result of not being able to follow half of what I am saying.

CONTINUE

• The student quite often gets stuck. I will then give another short input lasting seconds to get them moved on.
• This is repeated until the student finishes the problem.
• I go over the steps of the problem – briefly.
• I ask them to copy out the steps of the method they have just done – the exact same problem.
• I then ask them to turn over the page and do the SAME problem again, looking back if they have to or asking me if they need to. (This clears up any bits of the method that they still don’t get).
• I might ask them to do this a couple of more times.
• Then we move on to problems of the same type so they can practice the method.
• Then I move them on to past paper questions of the same type if there are any.

There is a final and vital step that I will come to in a moment. However, let’s pause to evaluate the procedure. Throughout the process, my involvement is minimal, only giving help as it is required, saying no more than is necessary. The student is fully engaged at all points of the process and does all the work. They do all the writing for the problem solving. The process is centred on the method and mastering it. The whole process goes from being completely stuck to near mastery in a matter of minutes. I say near, as mastery only comes if the student retains the method. That is achieved when I ask them to do the exact same problems when they get home. Then to do the same problems the next day and then to keep practicing them every few days. I avoid doing too much explaining in one go. In effect the student is nudged in the right direction as and when they need to be.

The Final and Most Important Step

Gosh! Are you wondering what it is?

Are you wondering why this mysterious step is SO important?

Well, let me introduce it by saying that for all students learning is an emotional experience. Problem solving can lead to huge emotional waves within the student – frustration, anger, relief, pleasure, joy. I have seen a student, shaking with anxiety due to being stuck on a problem for a week, suddenly light up with joy and relief after a few moments of the procedure above. In fact, one student, arriving in a terrible state actually said, after five minutes, “This is quite easy isn’t it.” With a huge smile on her face.

Understanding the effect that being stuck and becoming unstuck has on a student’s emotional state and self-perception is vital. It is something you should always address in the final step.

• I ask the student to think about how impossible they thought the problem was. I ask them to think about what they thought about themselves – stupid, incapable… I then ask them to consider how quickly they have gone from not having a clue to being adept – to reflect on how they view themselves now and how they feel.

So that’s it. Stick to these steps and the student will feel better, work harder and be more confident.