Practical Advice for Improving your Child's Maths - Part 6 - Tackling a Topic

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20 Apr

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In my last post we discussed how to work through the course and in what order. Hopefully at this stage your child knows what topics they should be working on. But what do I mean “work on a topic”?

How to start work on a topic

The instruction to the student here is almost painfully simple. Find the right chapter in the textbook. Go to the start of that chapter. Start reading, then start writing.

If there is an example, make notes on that example in your workbook. It is too easy, if one just reads an example, to skim over it, miss the details and not let it sink in. Copying the example, or making notes on it, requires the student to pick up a pen and write. It forces engagement with the material. The student, if they’re doing it right, has to think about what parts are important, and therefore worth writing down.

If there is an exercise, do every question. Do every question on every exercise, in order. I am designing this advice so that it can be done with no help from a teacher, so we have to squeeze everything we can out of the textbook. The student simply cannot afford to be skipping questions. When each exercise is completed, the student should mark their answers themselves using the back of the book. (If your textbook doesn’t have answers in the back, throw it out and get one that does. My recommendation is back in Part 3 - Gear Up) Marking is not a job for the parent or guardian! The student must do it themselves. Remember we are cultivating independence.

If the student finds the questions easy - great, it shouldn’t take too long! If the student finds them hard - great, this is where they need to put the work in!

To be completely clear, repetition is essential. Students need to practice dozens if not hundreds of questions on each topic. One of the biggest mistakes I’ve made as a tutor is to throw a couple of questions at a student and if they are successful, mark that topic as done and move on. Being able to answer the questions correctly is not enough. Students need repetition to remember. We need them to be able to answer questions on each topic correctly when they come back to it in five weeks, five months and in some cases five years. Doing ten questions is not enough to ensure that. Repetition is essential.

(I will talk more later in the series about how to ensure students retain previously completed topics)

What if it is not working?

Students are going to find some topics harder than others. They are going to get stuck, guaranteed. Given that we are trying to create a framework in which a student can manage without external assistance (that is the ultimate goal) we have to plan for what happens when they get stuck.

The first port of call is to check that everything described in the previous section has been done properly and to a good standard. It may not have been, as we are just getting started and the student isn’t in the swing of things yet. That’s natural, but it must be corrected. If any stage of this approach is done half-heartedly, without commitment, things will start to fall apart for us. Make sure notes have been taken and every question has been done from the start. That might help.

Now we’ll look at what to do if the student has made a serious, sincere effort and is still getting questions wrong. Most textbooks only give one or, at most, two explanations of any given topic and it just might not be connecting with your child. This is a great opportunity to drive home the academic independence they have. It is up to them to find a way to understand (but of course, you are there as a careful monitor at first). We can seek a different explanation of the same topic elsewhere. They could try googling it - get them to phrase the question as best they can and see what pops up. They should check the first few links for explanation. It could help.

Students often text me for emergency homework help for things that could trivially be googled, if they knew how. When I was at school looking things up on the internet was seen as a copout, but today I’m delighted if students have googled something. It shows they took some initiative and did something independently

Next, the problem still unsolved, we turn to YouTube, which I recommend only under very careful advisement. YouTube is like atomic power. When it was first discovered its benefits seemed obvious and various, but as we explored it further a dark side emerged. YouTube has some amazing, free maths resources (links included at the end of this article) but I find it to be dangerous for students. I warned earlier about the importance of active learning and the dangers of passively skimming a textbook. The same is true of YouTube. When using YouTube the student must be actively engaged. They must have a pen in their hand and be taking notes. And above all, only use YouTube when you are looking for an answer to a specific question. Do not let your child gaze blankly at maths videos for an hour and call it an hour of work.

All of the above may not be enough, and we still have a secret weapon. We can tap deeper into the vast resources of the internet, which is filled with people desperate to share their (very useful) knowledge. If a student has tried everything above and been unable to eke out what they were looking for, they could always ask someone. There are 3 main websites for doing this: Reddit, Quora and StackExchange. Each of those offers the user the option to write their own question and wait for someone in the community to respond. Naturally, all the usual caution should be applied when dealing with internet people but those three websites all offer anonymity and are relatively problem-free.

Remember, in all of this we are trying to develop a student who can find solutions for themselves. That does not mean they know everything, but that they are sufficiently resourceful to find out anything that they might need to know.

Mastery - How do you know when you have finished?

Most textbooks, including my recommendation, have a mixed exercise at the end of each chapter. This should bring together all the knowledge, skills and methods that have been trained in that topic. We can say that a topic is complete when a student can score, say, 80% or more on the mixed exercise. Needless to say, this is a high bar.

It is unlikely and expected that students will not get this score first time. That’s fine. That’s the point. Having done the mixed exercise, the student will know which parts of the topic they need to go back and work on, and they can go and do that. Repeating a part of the topic is fine - go back read the examples and try the questions again. Heck, repeating the whole chapter is fine. As I emphasised above, repetition is key.

Why have I set the bar so high at 80%? It is roughly the score we need to say a student has “mastered” the topic. They know it to a standard that could be applied in an exam setting. They could apply it in a situation combined with other topics to solve more complex problems. To score 80% means they have repeated it enough to stand a chance of remembering it in three years’ time.

Your role as parent/guardian

As we pass off more responsibility to the student, your role is to make sure all of the above is getting done - and properly. As I have promised all along, none of my recommendations will require you learning or doing any maths but it does need your heavy involvement, at least initially. Getting all up in their business, as I like to put it. So - if there were examples in the book, you need to check they have been copied into notes to a reasonable standard. Are the notes readable? Well-organised and with good handwriting? Have all available questions on the topic been completed. At this stage I want you to be as intimate with the textbook as you can be without actually working through it yourself. You need to know the textbook to ensure the student is interacting with it properly.

I know none of this is ideal, and requires you to assume more responsibility in what is certainly an already busy life. Let me give you the following encouragement: first, it’s not for long (or shouldn’t be). If we play this right your child will be able to handle more and more of this themselves in a very short time. Before long we want them to be more-or-less independent.

Secondly, the potential payoff here is huge. If you can get your child to learn maths self-sufficiently then you have achieved what teachers all over the world wish they could do. You have set your child up for success in maths and beyond. To be an independent thinker and a worker who can take the initiative is a skill that is universally appreciated. It is worth the effort.

More to follow.

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As always, if you have specific questions please contact me directly at jake@jakeharristuition.com

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Resources:

Websites for explanation:

https://stpaulsmaths.com/gcse/revision/

https://naikermaths.com/gcse9-1-exam-practice-questions/

https://www.mathsgenie.co.uk/papers.html

YouTube explanations:

https://www.youtube.com/user/mrbartonmaths1

https://www.youtube.com/channel/UCHz48selLuSORKqET7aZ49Q