Practical Advice for Improving Your Child’s Maths – Part 12 – Foundation vs Higher

In the article we will discuss the differences, pros and cons between Higher level and Foundation Level maths GCSE.

There are lots of things that can be confusing about GCSE Maths, and these are often most apparent when trying to acquire a textbook for your child. You will immediately run into the problem that most textbooks are written for a specific exam board. There are 5 exam boards in the UK, each of which write different exams based on the curriculum (essentially a single list of topics laid out by the government). Each maths department decides which exam board they will use, and in my experience this is not often clearly communicated to students. They sensibly think they are simply doing “GCSE Maths”.

Some exam boards are considered to be easier and the main difference is the style of questions, although there will be some variation in the content of each course. It is important to use the right textbook, and if you don’t know (which you probably won’t) just ask the maths teacher. Frankly, you won’t have much control over what exam board your child takes for maths and it doesn’t matter that much.

The next thing you’ll run into is that within each exam board, you will find a choice between a Higher and Foundation textbook. This does matter.

To elaborate on what I wrote above, each exam board actually produces TWO sets of maths exams in each exam season: one is Higher Tier and one is Foundation Tier. Students will sit one of the tiers, never both. Foundation Tier exams are graded 1-5, Higher Tier graded 4-9. Clearly, a student can only attain grades 6-9 by sitting the Higher Tier papers, but if they fall below a 4 they attain no grade at all!

In almost all cases, students are assigned a tier at some point in Year 9 or 10 based on what set they are in and recent assessment results. It is my experience that this process is one of the faultiest parts of the maths education system* and why I draw your attention to it here. Make sure your child is doing the tier that is right for them. Don’t let the the school decide for you through their automatic processes, and don’t let them tell you you don’t have a say. The decision of which tier your child should take is between you and your child, not the school.

Below I will try to outline the pros and cons of each tier, why it really matters and how to decide which is right for your child

Higher Ground

The obvious upside of taking the Higher paper is that it gives a student access to the top grades. Naturally, this comes with a cost. In this case the cost is having to learn more material and a dramatically harder exam. It really cannot be overstated how difficult the Higher paper is for many 16-year-old learners, and it is especially punishing to borderline (Grade 5/6) students who have just scraped onto the higher paper.

Let me present a situation I have seen many times. Around the beginning of Year 10 a student has performed well on their Foundation tier mock assessments, comfortably achieving a Grade 5. Their lessons are at a good pace, they are able to follow closely and attain mastery of many of the topics they cover. Then, a teacher or an algorithm or the academy trust fills in a box on a spreadsheet with “Predicted Grade: 6” and bumps them up to Higher Tier papers and moves them up a set. They find themselves starting from a different point to where they left off, because of course the higher sets cover material more quickly. This speed with which the lessons move is too fast for the student, and the material harder than they are used to. Soon they are lost in a depressing maze of incomprehensible whiteboards, confusing textbook diagrams and incomplete homework. Their teacher is critical of them and their parents notice the negative school reports. Their skills and, worse, interest in maths is destroyed. 18 months later they wander helplessly into the exam. “Predicted Grade: 6” is still sitting in that spreadsheet cell, but realistically they will be lucky to scrape a Grade 4, the passing mark.

Disregarding the short-term problems of a sudden change in class, the decision to change exam tier has proven disastrous for the student. Forgive the overly poetic style of the previous paragraph, but sincerely this is a case I’ve seen time and again and it really illustrates the dangers of moving a mid-range student up to the higher tier. The material is so hard that they lose interest, they lose their ability and their grade actually goes down. They end up learning less maths.

This is not to say the the Higher Tier is always a bad idea. For some students it presents a meaningful and enjoyable challenge, but those students must be in a position to tackle it. This means by Year 10 they must be comfortably achieving at least Grade 6 in mock assessments.

Strong Foundations

Clearly I’m a big fan of the Foundation Tier essentially for the same reasons I’m wary of Higher. The Foundation exams present a useful and achievable target for most students. The amount of content is lower, which gives students time to get a good handle on much of it. They can see and feel that they are making progress, which encourages them to keep trying. There is far lower risk of them getting lost in the fog. In my opinion it is better to learn some solid maths skills that you will remember AND get yourself a Grade 5, rather than gamble everything on a possible Grade 6 with a high chance of losing it all.

It would be disingenuous of me not to mention the possible downsides of taking the Foundation paper. Materially, the highest grade you can get is a 5 (considered a “strong pass”) and you are not able to access a 6 or above.

Less tangibly, choosing Foundation Tier means being kept in or moved to a lower set. Theoretically that should just mean a slower pace and more time to master the material, but in this series I have tried to be as practical and realistic as possible. The reality here is, at state school, a lower set at best means worse behaviour among the class. It may also mean a lower standard of behaviour management and teaching. I’ve also tried to explain how to make your child’s maths success as independent of the school as possible, but we have to be honest with ourselves that school maths will still have an impact. It is worth assessing the size of this risk and its affect at your child’s school.

Frankly, the quality of the teaching at the school could be a consideration in general. Do the teachers have the skill to teach the demanding skills required to tackle the Higher Paper questions? Can they keep the lower sets in check? In an ideal world these things would not be factored but, like I said, we need to be realistic.

Ego No Go

Don’t let pride be a factor in this decision. It’s another thing that I have seen too many times. There are many students who have built a lot of their identity and sense of self-worth around their academic performance – especially in the core subjects. This is understandable since both the education system and society at large gives so much positive feedback to academic achievement, at least superficially.

This leads the student to disregard the Foundation Tier out of hand – “Why would I limit my Grade to a 5 at best?” This can be calamitous if they fall into the Higher Tier traps I outlined above. Those students who dismiss the Foundation Tier due to ego will be the same who beat themselves up when they sit the Higher Tier paper and, having been confused about maths for 2 years, only get a Grade 3.

Don’t let pride be a factor in this decision. Make it practically

To summarise, only do the higher paper if a student can do so comfortably: already getting minimum of Grade 6 without too much effort. Broadly speaking, if in doubt it is better to take the Foundation Tier and get it mastered.

As always if you have any further questions don’t hesitate to contact me directly by email jake@jakeharristuition.com

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*I wanted to add a footnote about why placing students into Higher and Foundation Tiers seems to be done so badly. Interestingly Ofqual is aware of the problem, having written to headteachers in January of 2020 essentially reminding them not to screw this up. Astoundingly in 2018, almost 10% of Higher Tier students performed so badly they achieved no grade at all. Of course there could be multiple factors for this but misplacement of students by teachers is likely to be principle among them. But why does this happen?

My working theory is that there are 2 causes. The first, not described in the main article above because I think it is misleading and distracting, is that the grade boundary for a pass on Higher Tier maths is staggeringly low. Roughly, a student on the Higher Tier can get 4 out of every 5 questions wrong, achieve a grade 4 and pass. Surely anyone can get 1 out of 5 questions correct, right? I think this is the logic that motivates teachers to bump so many students up to the Higher Tier. The grade boundary to pass is so low, it tempts teachers in to putting students there as an easy track to a pass, disregarding the fact that it will damage actual learning and risk a Grade U.

Secondly, it seems teachers (primarily at state schools) don’t have enough perspective of the population as a whole to make an accurate judgement about where their student cohort falls within it. The motivation behind it is as follows: The proportion of students who take each tier is roughly 50/50 (leaning slightly toward foundation in recent years, possibly as awareness of this problem increases). So if I need to place my students into the two tiers, the top half should do Higher and the bottom should do Foundation. Makes sense.

EXCEPT that this assumes that the students at your school are a proportionate sample of the student population as a whole, which they almost certainly are not. For instance, there will be some very high-achieving schools where almost all candidates score Grade 6 or above, so it would be unfair and cruel to place half of them into the Foundation paper just because that’s what happens on average. The reverse is true for schools with very low attainments. Yet consistently I see schools where Set 1-3 Maths do the higher paper, Set 4-6 do Foundation: the naïve 50/50 split.

Practical Advice for Improving Your Child’s Maths – Part 11 – For The Record

This is a blog post about keeping good notes. If you’re not already bored by that sentence, there’s something wrong with you. However, I have good reason to write about this: keeping good records and notes is one of the most essential yet overlooked aspects of preparing for GCSE Maths. It could make the difference between a pass or a fail.

Keeping Track

I often ask my students when they are preparing for a Maths exam: “How do you revise? When it’s time to sit down and do some work, what is that you actually do?” Of course, in most cases the student has never done any revision so I just get some incoherent mumblings. From the minority of students who have done some work, they usually tell me they sit down and do some questions, either from a textbook or more typically from a past paper. Students tend to take a scattershot, brute-force approach to revision where they sit down and just do something. And, while I am grateful that they have done anything at all, with a small amount of effort they could streamline their revision and get more out of it as a result.

This is where the record-keeping comes in. In this series we have been all about the lowest hanging fruit, the least effort techniques that yield maximum results, and my advice here is no different. Why not get a piece of paper, write the date and write the topic that you have covered next to it. Then the next time you sit down, you can check your record and revise a different topic, to make sure you are covering enough ground. Even better, you could also record how hard you found the topic in case you need to go back and try it again.

(I myself am fanatical about data and record keeping, and in my final year at uni I recorded the amount of time I worked each day almost down to the minute. I still have those records from almost 10 years ago! Clearly that’s overdoing it a little bit but the option is always there)

Over time you build up a record of all the work you’ve done and all the topics you’ve covered. For one thing, it feels good to have physical evidence of all the effort you’ve put in. This can give you the strength to push on through to the end. Secondly, you can start to see patterns in the topics you have found easy and hard and the things you need to focus on more. It’s quite the tool!

(An alternative is to combine an approach like this to an existing revision schedule or calendar: after each day of the calendar you write the topics you’ve covered in maths. It serves the same purpose.)

All The Right Notes

In earlier parts of this series I have mentioned the importance of keeping good notes and I’ll expand on that here. Making your own notes is beneficial in two stages: in the process of making them, and then looking back later.

The process of copying important information out of a textbook into your own notes works on multiple levels. At the very simplest, low-hanging-fruit level, the student has been exposed to the content at least once. They’ve seen it, so when it comes up in an exam it won’t be completely alien nor a shock. Secondly, even the most ardent student will not want to copy every detail from the textbook and this forces some level of engagement: what are the most important details to write down? Now the student is not just seeing the content from the textbook, they are thinking about it.

Once this is done, the student has a set of notes, in their own handwriting. When they get puzzled later they can go back and look at what they themselves wrote to hopefully refresh that topic.

It’s a double whammy. Students get something out of making the notes, and then looking back at them later.

Common Mistakes

I cannot overstate the importance of keeping notes organised. Write the date and title at the beginning of each section (I have even known students keep a contents page to make information easier to track down). I see this go wrong all the time, mainly because young people seem to struggle with the idea of notes being in any sort of order: they simply pick a random page in a notebook and start writing. If you’re a parent overseeing this process your child will almost certainly get it wrong first time – which is fine! Just be patient, explain the right way to do it and why it’s important. If you start this early enough (ideally Year 9 or before) the student will have got the hang of it by the time it matters.

Another thing to watch out for is handwriting. Thankfully we have moved past the Victorian approach of a rap across the knuckles for not dotting your i’s, but some students have such poor handwriting they cannot read it themselves. If an examiner cannot read your handwriting, you risk losing marks even if your working is correct. If a student cannot read their own handwriting it naturally means they are unable to check their own working out or even complete multiple lines of related calculation.

If your child is in this situation (and many, many are) there are two things to do. The student may have a minor coordination disability like dyspraxia, in which case they can qualify for extra time in future exams. This comes in very handy, so it is definitely worth a quick trip to the doctor to see if a diagnosis is possible. A lot of the time this will not be the case, and the student simply does have bad handwriting. I’m not a handwriting expert and you should seek advice for improvement elsewhere, but in my experience it stems broadly from a lack of due care and attention. If the student just slowed down a bit and put some focus on their writing it will probably improve a lot automatically.

This Instagram account I linked in a previous post has a ton of great examples of how beautiful notes can look: https://www.instagram.com/studyable/

To summarise, get organised and stay organised. Keep your notes in good order and during revision make a record of the work you’ve done. Turn your scattershot revision in a sniper rifle. Work smarter, not harder.

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

A-Level Maths Resource – Edexcel Past Paper Topic Lists By Question

At the link below find a list of topics covered in each question of all available Edexcel Pure A-level Papers for the current spec. Links to the actual papers provided also. Let me know if you have any problems.

Click here for the list!

Practical Advice for Improving Your Child’s Maths – Part 10 – The Summer Slide

Ask any secondary school teacher in any subject and they will tell you about the negative effect summer holidays have on student progress. Students return to school and, not only have they not progressed, they have in fact gone backwards. The academic research on this is a little less definitive than the anecdotal evidence but still points solidly to a significant loss of knowledge and ability over the Summer period.

It’s clear this a problem we need to solve. While we once again leave the educators and policy-makers to tackle the problem on a national level, we must determine how as parents and tutors we can help our students now.

Sun, Sea and Square Roots

There is some very low hanging fruit here. The obvious advice is: make sure your child does some maths in the summer holidays. Don’t do nothing. As I’ve emphasised in earlier blog posts it doesn’t even take a lot. “Little and often” is a good mantra. One question a day – heck, one question a week! – would make a positive difference.

Some teachers provide help with this by offering a “one-a-day” worksheet for students to tackle over summer with a particular focus on the topics they have done through the year and that they need for the next. This is a fantastic idea and I love to see it. It seems to be increasingly common so if this resource is available to your child make sure they take proper advantage of it. That means actually doing one question a day and keeping up with it as much as possible.

If you have no such teacher and no such worksheet (as many students do not) – no problem! You can still do one question a day. Just crack out the old textbook and do a question out of it. Ideally you would select a topic that you have done in the last school year so it’s optimally relevant, but in theory any section of your GCSE textbook should be useful.

Students will get stuck on some questions, and this is where the real treasure is buried! I would suggest looking back over Part 6 – Tackling a Topic for the details on what to do when stuck, but essentially you should:

1) Check an example in your notes or the textbook

2) Try Googling the problem

3) See if there is an explanation on YouTube

I’ll say it again: the most successful students are the ones who seek out answers to the questions they can’t do themselves.

Of course it’s not realistic to expect a student to keep up with a one-question-a-day program like this flawlessly. Things come up and distractions occur. Our jobs as parents, carers and tutors is to gently help the student back on track and avoid complete, permanent derailment.

You want me to do what???

To some, what I am suggesting is utterly horrifying and – without exaggeration – bordering on abusive. How dare I suggest we place a greater burden on our already beleaguered students? To which I reply: I am simply laying out the reality. This is what is needed to be successful in maths. For many students this level of work is necessary simply to scrape a pass. And make no mistake, your children are competing against peers who most certainly are doing this and getting ahead. Over the summer, across the country, there are students (many privately educated but plenty of them not) who are taking their education into their own hands and doing the type of work I am describing. Students who your child will be competing with for university places and jobs in a few years’ time.

For those of you who don’t find my proposition too appalling, I would suggest just trying it out. It’s not as bad as it sounds and takes less than 15 minutes per day. The results are well worth it.

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

Practical Advice for Improving Your Child’s Maths – Part 9 – Praise the Primary

While writing this blog I have tried to be clear that I lay little of the blame for the poor maths performance of the student population at the door of teachers. The quality of teaching is of course up for further debate beyond the scope of this work, but it’s transparently obvious to any observer that it is the bloated system that is mainly at fault.

I do, however, want to single out primary school maths teaching for particular praise. It is my anecdotal experience that students come out of primary school with:

i) A strong grasp of the important mathematical concepts (arithmetic, including negative numbers and fractions, basic algebra, statistics)

ii) remarkably uniform performance across the population, especially compared to the massive range of outcomes at GCSE level

It seems to me that primary schools are doing a very good job at teeing up the maths careers of their students, only to have the secondary school maths system pitch it into the bunker. My sense of this has grown alongside my teaching experience, but until now has been only anecdotal. So I went to look at the data.

Getting Down with the Data

A set of information exists called “The National Tables” that tracks various aspects of students’ GCSE performance each year. I used the data for students completing GCSEs in 2019 to avoid any Covid-19 affects. The information I sought was surprisingly accessible as the spreadsheet provides a student’s GCSE results relative to their Year 6 SATs.

So let us consider the 2019 GCSE cohort, who completed their Year 6 SATs in 2014. At the time, SATs were graded in 5 levels from Level 1 as the lowest and Level 5 as the highest. 502,912 students are recorded as attending a state-funded mainstream school, and of those 492,264 scored a Grade 3 or above. That’s a whopping 97% of students scoring those top 3 out of 5 grades. Interestingly the majority of those were achieving a Level 4.

This rough calculation goes to provide some evidence for my claim that students come out of primary school doing pretty well at maths. We could of course argue about how the boundaries of the levels are determined and whether a “Level 4” actually means a student is performing well, but based on my experience and taking the actions of the grading bodies in good faith, I am convinced.

Let us now look at how those same students performed 5 years later. At this time the 1-9 grading system had been introduced for GCSE students, with 1 being the lowest grade and 9 being the highest. It is difficult to convey this information without derision, but there are 2 ways to pass a GCSE. Grade 4 is a standard pass, and Grade 5 is a “strong pass” that maps to a high C or low B in the old grading system.

So how did our 2019 cohort turn out? Of the 226,362 students achieving a Level 4 in their SATS (the second highest grade!!), an incredible 36% went on to fail their GCSE maths. Remember, to fail requires Grade 3 or below. If we dare to ask how many of the Level 4 SATs students achieved Grade 4 or below (a disappointment considering their high achievement five years prior), the number increases to a staggering 69%. That means: of students achieving the second-highest grade at twelve-years-old, 69% could not, to use the government’s own words, reach a “strong pass” five years later.

Bigger is not Better

So what is going on? Are primary schools over-performing or secondary schools under-performing? Actually, I think the main factor is that there is so much less to learn at primary school. Students work within a limited framework that gives them time to process and master the topics. Comparatively, secondary school maths teachers are positively starved for time, dashing from one topic to the next in a desperate attempt to get through all the material.

Well then, is it not natural that primary school students should do better at maths, given the level of the content is lower and there is less to learn? This is a fair question, however we must not forget that we control the level and content at GCSE level. Therefore, we can’t just shrug and say “that’s just the way it is”; it’s the way we made it!

As it stands, we have a maths GCSE system where the sheer volume of work overwhelms students. Rather than learning a small selection of important topics to a high standard, they half-learn an encyclopaedia’s worth of knowledge to a very low standard. As the stats I presented above show, many students go backwards.

Your Primary Concern

As a parent reading this, I am advising you to take your child’s primary maths teaching seriously. It might well be the best maths teaching they ever get, and it will stick with them for the rest of their lives (much more than anything they learn at secondary school). If your child is already in secondary school, it’s not too late, for there is a lesson here. For students struggling in maths the Primary vs Secondary comparison is a case study in how students learn best. Focus on a small set of the most important GCSE topics and learn them to a high standard. For everyone, we should do what we can to facilitate changes in maths education such that the drop off from Year 6 to Year 11 is not so great, and our children can get around to learning some maths.

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

Practical Advice for Improving Your Child’s Maths – Part 8 – The Tutor Problem

A tutor is not going to help. At least not at first.

…a strange thing for me to say in a blog post on my website for tuition services. However, in all I do, including this blog series and my tuition work, I try to be as open and honest as possible. The goal of this series is to improve your child’s maths and it is simply not necessary to get a tutor, and in some cases can be counterproductive.

If a parent or guardian is fortunate enough to have the spare money available, and their child is struggling in maths, it is common and quite natural to seek out the help of a private tutor. If you have read many of the earlier articles in this series, I talk at length about the goal being to cultivate academic independence. Hiring a tutor may transfer the dependence of the student away from their school teacher, but it doesn’t make them independent. It simply gives them someone else they expect to poke, prod, guide, carry and cajole them to some imagined future success.

In my experience, the most common state of a tutor-student relationship is as follows: The tutor might be good or bad, well-intentioned or money-grabbing, but they have at the very least done enough to convince a parent to pay them weekly. They turn up to the lesson and present some information to the student, maybe the pair work through some questions together. The student might listen or might not. What happens in the lesson is irrelevant because the student will leave the lesson and for the next week will either:

i) Not think about the subject

ii) Do a few minutes’ work on the subject, set by the tutor, with a sense of miserable obligation that is possibly worse than doing nothing.

We start the lesson the following week with the student having forgotten everything that happened in the previous lesson and maybe knowing even less that when it started.

Despite the immense value I have previously described in doing work independently, working with a tutor might even discourage this. The student, who despises maths in all its forms, feels they have done their time for that week. Why should they put in more? In reality, tutoring should be the icing on a cake made primarily of independent work.

The second issue of hiring a tutor for one hour a week is that it presents an apparent, but not real, solution to a student struggling with maths. A genuinely well-meaning parent works hard, makes sacrifices, sets the money aside and hires a tutor. They very reasonably feel that they have tried to help their child, so make the weekly payment and sleep well knowing the problem is taking care of itself. Only it is not, for the reasons I outlined in the previous paragraph. The hiring of a tutor may discourage the level of parental involvement I have advocated earlier in the series.

There are three cases that spring to mind when hiring a tutor is actually useful.

The first is the unrealistic case of the tutor effectively living in-house to oversee and manage the student’s free time, as well as doing some teaching. If the tutor is present to tell the student when to work, how often, the best study practices and when to relax, I do believe that would be effective. With proper enforcement of time management I believe a student can have the same quality of life, the same amount of fun AND see academic progress. This level of intensive tutoring, more akin to a governor/governess role, is not accessible to most families. In fact, this sort of thing is precisely what this blog series is trying to avoid. Note that the tutor responsibilities I have outlined in this paragraph are what I have suggested parents do in my earlier blog posts at a far lower cost of time and money. This series is attempting, through proper intent and cooperation of parent and student, to build the same habits and processes, and see the same results, as an intensive in-house tutor.

The second case of a useful tutor is one who is acutely aware of the need to cultivate independence in the student, and indeed sees it as the primary objective. This is a tutor that knows and can explain that progress comes from the student working independently, with encouragement from the parent, alongside help from the tutor. This is the type of tutor that I aim to be, not always successfully. “Well then,” you may be thinking “I’ll just get one of those tutors.” Sadly it’s not as simple as that.

For one thing, lots of tutors aren’t aware this should be their job. They think their job is the conveyance of information. Of course it is, in part, but a higher order goal should be growing the academic independence of the student. More cynically, a tutor pursuing this goal is effectively trying to put themselves out of a job. One can see how a tutor may be discouraged from taking this approach. Finally, even if a tutor does aim for the same things I do, it is painfully difficult. Each student is unique and the steps needed to get them properly working on their own are unclear. For all these reasons, such a tutor is rare.

The final case is the best and most legitimate application of a tutor. This is the situation where a student is putting in the work independently, and has been doing so consistently over an extended period. They have sincerely undertaken all the steps this series describes and are seeing results. In the case of this properly-oriented student, the use of a tutor can have a dramatic positive effect.

For this ideal student, most of the low-hanging fruit has been picked. They have learned the basic stuff themselves and are tackling the tough topics. A lot of their time may be spent problem-solving, Googling up alternative methods for difficult questions that they haven’t quite understood. Here, a tutor can save a lot time and facilitate some major progress. Rather than googling (a habit I encourage, but is time consuming) the student can direct those same questions at a tutor. The tutor can field those questions instantly, saving the web trawling, then move on to the next issue. The student can bring questions they have attempted and get instant feedback and corrections. I have worked with students like this and the sense of relief and almost-joy at being able to overcome hurdles that, though they could have tackled on their own, are more efficiently handled with the help of a tutor.

Essentially, a tutor is best used for answering a student’s existing questions, rather than teaching from scratch.

I must emphasise that this only works after the student has established the proper pattern of independent work. This type of student is exceedingly rare (in my belief because the existing education system does not develop students in this way) – probably somewhere in the region of around 1% of state school students. Do not kid yourself that your child is part of this 1%, because they are almost certainly not. A good way of testing this is as follows: does the student undertake 2 hours of independent work per week in addition to homework. Do they sit down and do some work on top of what their teacher has set? If they have been doing that consistently for 3 months or more, you should consider getting a tutor.

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

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

Practical Advice for Improving your Child’s Maths – Part 6 – Tackling a Topic

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

https://www.youtube.com/channel/UCStPzCGyt5tlwdpDXffobxA

To ask questions:

Reddit

Quora 

StackExchange.

Practical Advice for Improving Your Child’s Maths – Part 5 – Where To Begin

So you’ve negotiated some academic freedom for your child, you’ve put in a big Amazon order for their essential maths kit and you’ve explained to them what you are doing and why. As nice as it would be to lock them in a room with the textbook, that’s not going to work (just yet). We need to help them know where to begin. Let’s learn some maths!

It’s easier to find your way with a map

An issue I run into a lot is students viewing each topic from GCSE maths in isolation. They study one topic, then drop it and move on to another and onto another, failing to see the important interconnectedness of all of it. I don’t mean “maths is all connected” like some kind of maths spiritualist – I mean literally that students have to be able to see the connections between topics to successfully answer exam questions.

Likewise, they don’t know where they started and they don’t see an end point. To most students maths is a monolith that they half-heartedly chip away at for a few compulsory hours per week until at about 16 someone tells them they can stop. It goes without saying that this is no good for motivation.

I have always felt that students need to see the whole picture, a map of the maths course. In writing this article I was surprised that among the wealth of online maths resources available, something like I was imagining did not exist. So I made it myself.

A link to the full, interactive version can be found here:

https://atlas.mindmup.com/2021/04/a367e1509b5d11ebba1051f8eba5efa3/maths_gcse/index.html

If you use this link you can interact with the map and dig into each topic to see the subtopics that are part of it. Double click on any topic to see the subtopics underneath it. For example here is the top left topic, Non-Calculator Arithmetic, with its subtopics revealed:

Show this to your child! Print it off! It allows them to see the lay of the land, and how much there is to conquer.

Here are a few things to consider as you survey the terrain:

Firstly, it’s absolutely massive. As I pontificated in Part 2 of this series – The Problems – the volume of content in GCSE Maths (even the smaller Foundation tier) is absolutely monstrous. If you want to see it in all its glory, open the interactive mind map and reveal every subtopic at once. Is it overwhelming? Yes.

However, it’s more manageable than it looks. You don’t have to learn it all. It would be nice to do that, but a student could comfortably pass GCSE maths knowing two thirds or even a half of the content presented here. Secondly, you’re not going to attack it all at once, you’re going to take it piece by piece. This is why I broke it down into topics and subtopics. You can take one at a time.

The other reason I wanted students to see this is so they could plan how they would make their way through it. If your child has a preference on where to start and how to progress, great. Most students don’t. For the majority of students, who don’t know where to begin, I made the mind map in a specific order. Starting from the top left and going down the topics build one on the next, with the later topics needing the earlier ones to be understood. This also means they are in order of importance, with the earliest topics being the most important (and appearing on exams most often) and the later topics being the least.

Start at the top left and work down to the bottom, then go to the top right and work down to the bottom. Do not move on from a topic until you’ve mastered it.

Those two bold sentences contain some of the most important advice I am able to give. I’ll expand on it a lot in future articles, like how a student can know they have mastered a topic, but those sentences alone will take you a long way.

The subtopics on the map should correspond roughly to any decent GCSE maths textbook (and correspond exactly to the textbook I recommended in Part 4 – Gear Up). As each topic is mastered, they can be ticked off. The student can be familiar with the scope of the course, where they are in it and how they are going to move through it.

So now, you and your child have somewhere to start. If I stopped writing this series and the student stopped going to school, they would have a chance at knowing where to begin on their own. We are planting the seeds of academic independence. 

Of course I am going to keep writing this series and that should make everything even clearer. In the next part I’ll explain how a student should work through an individual topic and when they should move on. Stay tuned.

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

Practical Advice for Improving your Child’s Maths – Part 4 – Gear Up

In my last post I discussed how to set your child on the road to academic freedom when it comes to maths, and the importance of your role as a guide and supervisor at this stage. Now the real fun begins, as we get to discuss what work should be undertaken by your child to make the most improvement on their grade

Get a textbook

This is incredibly important. A good textbook will be the basis of your child’s independent learning. A textbook, if chosen correctly, will contain almost everything a student needs to complete GCSE Maths. But what is a good textbook?

To be blunt, it’s this one:

https://www.amazon.co.uk/New-Maths-GCSE-Textbook-Foundation/dp/1782944389/ref=pd_sbs_2?pd_rd_w=G39Tx&pf_rd_p=2cc879b3-0437-401a-870d-ced07a584039&pf_rd_r=NWVRDD85ZDWJ2EKQSBJN&pd_rd_r=0f095fd3-7dbb-4c53-ba68-b6281550707f&pd_rd_wg=iytEs&pd_rd_i=1782944389&psc=1

https://www.amazon.co.uk/IGCSE%C2%AE-Textbook-Higher-Course-Revision/dp/1782944370/ref=sr_1_18?dchild=1&keywords=gcse+maths&qid=1616402408&sr=8-18

(The first link is for foundation level and the second is for higher level. We’ll discuss later what the difference is and which is right for your child, but if you or child don’t know which their school was preparing them for, get the foundation book (first link))

There are lots of good textbooks out there so if for some reason you prefer another one, go for it. My advice regarding the book is going to be pretty broad. However, if you are like most parents and understandably don’t have a preference, you cannot go wrong with the ones I have linked.

What makes this textbook so good? It explains a topic, then shows examples, then gives students plenty of questions to practice on themselves. The answers are in the back for marking. It has almost everything a student needs to learn self-sufficiently.

Get moving with stationery

As important as the textbook is a student’s calculator. You are going to hear the following arguments about calculators from your child: “I can just use the calculator on my phone”, “I can use Google as a calculator” or the evergreen “I don’t need a calculator”. These are all things I’ve heard and none of them are true. Students need to get used to using the calculator they will use in the exam, so even if a phone or Google has the necessary functions, by using them students are not practicing with the actual tool they will use in the exam.

There is in my opinion one acceptable calculator for attempting GCSE maths and it is this one:

https://www.amazon.co.uk/Casio-fx-83GTX-Scientific-Calculator-Black/dp/B07L5YWTPH/ref=sr_1_3_mod_primary_new?dchild=1&keywords=maths+calculator&qid=1616582443&sbo=RZvfv%2F%2FHxDF%2BO5021pAnSA%3D%3D&sr=8-3

Even if your child already has another calculator, if it is not this one, get this one! Its functions and ease of use are unparalleled. Get this calculator.

The other essentials are:

• Pens and pencils

• Rubber

• Pencil Sharpener

• Ruler

• Protractor

• Compass

• Notebooks to work in (I’ll talk more later about how workbooks should be used)

Something like this will do nicely (all though I’m not as specific about the type of ruler you have!):

The Right Stuff

Basically, none of this stuff is negotiable. It is all essential. In my tutoring work I have constantly run up against students with missing, wrong or inadequate kit and it’s a serious drawback. GCSE Maths is hard and you want to turn everything you can in your favour – this is an easy way of doing it!

I’ve done the maths and (picking the most expensive version of everything I’ve suggested) the total to buy all of this comes to £34.77. Money should not be a barrier to education but I suggest you do everything you can to get the money together to buy these resources. It really matters. If you are in two minds, maybe I can convince you by adding that, apart from replacing pens and pencils and a bit of extra paper, this is all a student needs for five years of maths education. If we split that cost across all five years it comes to just under £7 per year.

Forgive me for spending 800 words talking about the importance of rulers, but because this stuff is basic it tends to get overlooked. Nevertheless, it is the foundation of learning maths so it deserves to be taken seriously.

In my next post I’ll explain how to help your child decide what work to do so they can actually get down to business and learn some maths!

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At this point I would also like to add to anyone reading this, if you have any questions please feel free to contact me directly at jake@jakeharristuition.com

There is a lot to take in from this series and you might have specific questions about your situation. I am very happy to advise.