Practical Advice for Improving Your Child’s Maths - Part 7 - Little and Often
In the series so far we have built up a solid foundation for your child’s fully-independent maths work. Using what we have covered, processed by you and passed on to your child, they should be getting an idea of how to work and what topics to work on. They have a map and a way to navigate it. But we won’t be stopping there. We are trying to support them in the best way we can and give them every bit of structure they could need to nudge them in the right direction. I have a lot more to say. Although we have a foundation, we still need to build the house.
In this article we’ll discuss more general topics around working: how often, for how long and the best setting for it.
Frequency over Volume
We want your child to be doing maths (almost) every day. In my last post I discussed the importance of repetition, and it should be done over a period of days at frequent, regular intervals. Half an hour a day is far preferable to three and half hours once per week.
I often have to deal with the problem of students going backwards. They can learn a topic and successfully handle questions in one lesson, then the following week they can’t even remember what we did. Sometimes they seem to know less than the start of their last lesson. The reason for this is that they haven’t thought about maths for a week.
For a secondary school age student, thinking about something once a week simply isn’t going to cut it. School holidays can be even more damaging. I’ve known teachers hand out “one-a-day” booklets in school holidays: a collection of questions designed to be done one at a time, one per day and in my opinion an excellent idea. Students then completely negate the benefit by leaving it all until the last day of the holiday (when, ironically, they can’t remember enough maths to complete it).
Conversely, I sometimes happen to catch a student straight after a maths lesson that they have actually managed to engage with. The concept and framework is there, fresh in their mind. We can discuss it at some depth (with them having real input!) and hopefully add to it, clear up any misunderstandings and improve the student’s mastery. This only works if it is building on earlier, recent work.
Incubation is a concept in psychology in which time spent away from a task makes the task easier when you return to it. Studies have shown that the brain does a kind of “background” processing, learning and solving problems subconsciously. These conclusions will come as no surprise to anyone who has attempted to teach maths. Furthermore, it is interesting to observe that most studies measure incubation periods in minutes or hours, not days and weeks. This stands to reason, as too much time between tasks would simply result in students forgetting what they were working on at all.
So learning maths is sort of like building a snowman. If you pile a bit of snow on the ground and leave it there for a week, you’re not going to have much of a snowman when you come back to it. But if you add snow at regular, frequent intervals you reinforce the snow that is already there, protecting it and preventing it from melting, and you get to build higher.
I would also like to add that I am not completely detached from reality (I hope). I want this advice to be practical. In addition to my lecturing above, I know that rest is important. It enhances learning. Students need time away from work. So I heartily prescribe a day or two off a week, and longer in the holidays.
Maths should be done little and often. Even 10 minutes a day at home would make a difference.
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Side note: Don’t students do maths at school everyday anyway?
Remember, way back in Part 3 - Breaking Free I outlined the ideal of your child eventually having full control over their own maths. In my ideal world their maths lessons at school are their own time to do the maths that is right for them at that moment - the topic they are trying to master. I know this is unrealistic, which puts you and your child in a difficult spot. They probably will still be doing maths at school, and school maths will probably be unhelpful to them (too fast, too shallow, too short - all the things I outlined in Part 2). Nevertheless, this time spent at school will eat into their “maths bandwidth”. If they’ve done an hour at school they are unlikely to want to do half an hour when they get home.
I do have a solution for this, but it is radical. I’ll justify it first, then drop the bomb.
I have taught students from a huge range of schools: good, bad and middling. And from all of those schools, the vast majority of students have found their maths lessons to be white noise. They get nothing from it. That is supported by the stats given in Part 1, but my personal experience is even stronger. Most students finish Year 11 no better at maths, and often worse, than when they finished Year 6. Those five years of sitting through maths lessons has actively hurt them. And it is this evidence that gives me the confidence to offer the following advice:
Disregard your maths lessons at school. If you can’t get out of them completely (which you should desperately try to do), do the bare minimum needed to not get in trouble. Spend the lesson daydreaming. Relax. Don’t use any of your fuel there, save your maths bandwidth. The real maths happens when you get home.
As a parent, do anything you can to reduce the maths burden from school. Ask for little to no homework. Basically do all the stuff I suggested in Part 3. I’ll state it again: the real maths happens when you get home.
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The working environment
The area a student works in is important. It reflects how seriously they are taking the work. It can help or hinder their progress. A tidy desk is a tidy mind.
Students, wherever possible, should therefore have a desk. Ideally I’d like it to be their own, and a place dedicated to doing schoolwork. I have many students who attend their online tuition from a sofa, or a bed, or an easy chair. This does not set the right tone. Remember, this approach is all about lots of little nudges in the right direction. Having a good desk is a nudge.
Distractions are a serious problem for the young student of today. As Arthur Smith put it very well almost 20 years ago, “they” are terrified of a person just sitting quietly doing nothing. Everything in the world is designed to distract. Some students will have never experienced a period of true focus and concentration, through no fault of their own. As a parent or guardian, you can help once again.
Above, I encourage short periods of work - it shouldn’t be too hard to negotiate half an hour away from phone and laptop. That is really what we need: short periods of no distraction. Studies show adults can only concentrate for between 20 and 30 minutes at a time before their concentration drops off, so for young people it may be even less. I would encourage 20 minutes at a time without distraction. If the student wants to study for longer, take a 5 minute break with their phone, refresh the focus, and then lock it away again for another 20 minutes.
This won’t be easy at first, especially if the student is unused to being focussed. It might be a good idea to start with shorter periods, say 5 minutes, then gradually increase them, working up to 20 minutes. However short it needs to be, the main thing is no distractions while working.
The Good Book
I also strongly advocate for all maths work to be done in a single, neatly organised workbook. No laptops for notes. There might be evidence out there that some students benefit from working on a computer but in my experience they are primarily a distraction. As parent, guardian or overseer of this whole operation I think you might find the “neatly organised” part the hardest to enforce at the beginning. In general students keep terrible notes.
You could start by explaining to your child why keeping good notes is important. Simply put, a sign of a good student is one who can find out information they have forgotten by going back and looking in their own notes. Among my students this is fantastically rare, almost unheard of.
It would help if the student knew what good notes looked like. If instagram is their bag, show them this:
https://www.instagram.com/p/BijxYTTlV0G/
You could start by putting the date at the beginning of each day’s work. You could put a title of the topic you were working on. You could keep your writing on the lines of the page (or squares if you have a squared workbook). When working across multiple lines you could keep your work neatly in columns. I’ll emphasise this again: most students will find this unbelievably difficult. It might take years to achieve (which is fine - in the meantime the textbook reliably contains all the information the student needs). Just make sure they are trying! Remember, each piece of advice here is a nudge in the right direction.
We’re in the weeds now
This has been one of my longest posts, because we are really starting to nail down the little details. In our earlier posts we laid out the broad strokes and now we are discussing how the sausage gets made. I hope I have outlined not just what we are aiming for, but why and how to get there. Don't worry about achieving this all at once. Take each piece of advice individually and try to implement it. It will take time, maybe a lot of time, but each piece that fits into place is a step in the right direction.
More to follow