Tom's Tutoring

What to do if you miss your grades for uni

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Tomorrow is A-level results day. While many will get the results they need some won’t and will feel upset and confused about what to do. Here are a few suggestions for students who don’t get the results they expect.

Don’t assume the university won’t take you. Universities are expected to be over-subscribed for many of their courses and so it’s more important than ever that you get the grades specified. But universities do often get this wrong – even on popular courses – so always check with the university if they might still accept you as they will always want to fill their places with good candidates. When speaking to the university do always emphasise any special considerations that might apply – e.g. illness or bereavement – or impressive achievements you can point to – e.g. sporting or debating success.

Don’t be too hard on yourself. Just because you don’t get the grades you wanted doesn’t mean that you have failed. The university system is incredibly competitive (much more so than when your parents went to university!) and makes mistakes. Every year I see excellent students rejected from courses for reasons which are hard to fathom. It is certainly not necessarily a reflection of your ability or suitability for the course.

Be realistic about why you didn’t get the grades. Having said this it is very important to be clear why you think you didn’t get the grades you needed. Did you just have one bad exam? Were there special reasons why you didn’t get what was predicted? If so, then you might be best taking a year out to resit and reapply. On the other hand if you think that the grades you received are a good reflection of what you can achieve, then you need to consider applying for a different course or elsewhere. This is not an easy decision to make and involving as many people who know you as possible (parents, teachers, tutors, friends) will help you get to a clear conclusion.

Do consider clearing. Many people feel that going into the clearing process is some sort of desperate step only taken by very weak candidates. This is wrong. Clearing is just a way of universities and students trying to fill courses that are under-subscribed. Many excellent courses are under-subscribed simply because they are slightly odd combinations of subjects, because they are not well known or because results were weaker than expected. Sometimes you can find a better course of study through clearing than you might have found originally! So it’s definitely a good option to consider.

Do consider re-sitting. If you genuinely feel that your grade does not match your ability in the subject and have a strong desire to attend a particular university or course, then do consider taking a year out to re-sit your exams. Many people do this and there is no shame in it. In the long-run an extra year studying is no great loss to your future career prospects. Once you have made the decision to re-sit you then need to consider whether you will a) self-study, b) use a tutor or c) attend school / college. It is important to choose the right option which will maximise your chances of securing the grades you require.

Retain a sense of perspective. It’s understandable that not getting into the course of your choice might temporarily lead to despondency or even hopelessness about your future prospects. Hard though it might be it’s important to see it in perspective. Ten years from now it’s unlikely that your employer will care that much about the university you went to or course you did. There are many different routes to the same career destination and often it’s possible to specialise or retrain at a later date (e.g. training in law after a degree in history). Lastly, it’s just possible that the ‘bad luck’ of not getting in might lead to you choosing a different course that suits you much better – you never know!

Best of luck!

Do you understand it or just know it?

In English there is no word for ceasing to understand something (“ununderstanding”) but there is of course a word for ceasing to know something i.e. ‘forgetting’. This points to something vital about the process of learning that is very often lost by both students and teachers – that the foundation of deep learning is understanding, not knowledge. This is because understanding is a usually permanent gain in insight, whereas knowledge is often temporary and fragmentary.

But what’s the difference? And why does it matter? Here’s an example that may help to illustrate the point. In A level maths you may be taught that there is something called the discriminant (b² – 4ac) which can be used to determine the number of roots of a quadratic equation. (If the discriminant is positive it is has 2, if equal to 0 it is 1, and if negative it has no real roots). I once had some students that knew this but did not know why. I explained to them that the formula for solving a quadratic contains the discriminant (highlighted in red):

x = [-b ±√(b² – 4 ac) ] ÷ 2a

And then I asked them: Can you square root a negative number? To which the answer was no. So then I asked them: Well if the discriminant was negative, would that formula give you any answers? And then I saw the PENNY DROP moment! And then I said: And what if the discriminant was equal to 0, what would happen then? And one answered: “Well then it would just be √0 so x would just equal -b ÷ 2a! So just one answer.” And then of course they could answer for themselves what happens when the discriminant is positive.

This illustrates what I believe is central to effective learning: that students not only knowing what is true, but vitally, WHY it is true. It’s clear to me that those students will now never forget the meaning of the discriminant, because they can’t ‘ununderstand it’. What’s more the understanding they’ve gained would lend itself to being able to handle other more complex situations. For instance they would be able to use this insight to answer questions of the form: “Prove that quadratics of the form kx² – 2kx + k always have exactly one root.” Whereas students who only ‘know’ the discriminant might well struggle.

So my job as a tutor is always to inculcate understanding in my students, not simply knowledge. And for students, your aim should always to be to understand what you are being taught, not simply to remember it.

What’s so good about tutoring?

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Do you really need a tutor? Maybe your teacher at school is very good and you are very bright, so perhaps you can get the grades you need without the help of a tutor? Certainly some students go through their school years without any personal tuition and still get very high grades. However in my view, in the UK, this is now a small minority. But why is this? What’s so good about tuition? And why is it worth the trouble and expense?

In my view there are some aspects of tutoring that can make it invaluable in helping students achieve their potential. In essence, personal tuition is the foundation for deep understanding, and true mastery of a subject. As such it is no surprise that it forms the basis for teaching at places like Oxford and Cambridge! Personal tuition has some huge benefits when compared with other methods of learning. These are the main ones:

The tutor is able to meet the exact needs of the student, and pitch the questions and tasks at exactly the right level. So, unlike at school, the student need never feel ‘left behind’, or alternatively bored and unstimulated.
The tutor can focus on those areas where the student needs most help. A good tutor will be able to identify and concentrate on those areas causing the most trouble, so maximum progress is made in a minimum of time. In school students often find that too much time is spent on some topics and not enough on others.
Tuition enables the tutor and student to form a close relationship based on mutual trust and respect. This trusting relationship then allows the student’s barriers to learn (distrust, anger towards authority, fear of failure) to be recognized and removed. In school these barriers are usually ignored and teachers are unable to form such relationships with their students.
Tuition ensures that students show they understand. If tuition is effective the student will be constantly thinking, answering questions and solving problems (the foundation for understanding and long-term memory) under the close watch of the tutor, rather than simply ‘hearing the teacher speak’, which too often occurs at school. This means that while at school students often think they understand what has been taught, in tuition they will know they understand.
Students always have the opportunity to ask tutors the questions that are bothering them. In school environments this is often not possible, due to the number of students and constant need to get through the syllabus.
Tuition encourages students to take responsibility for their learning. Effective tuition encourages the student to consider what they want to learn from the tutor and why they are facing problems in a subject. But at school students are encouraged to see learning as the ‘teacher’s job’, which undermines this sense of responsibility.

Don’t get me wrong, schools are not all bad, and of course not all tutors are good! But, done right personal tuition can be a truly transformational experience for students.

How to write a good personal statement

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It’s that time of year again when students often start thinking about or even drafting their personal statement for their UCAS application. For those planning on applying to Oxbridge or for medicine or dentistry, an early start on this is likely to be necessary.

But what on earth are you supposed to write? And how do you make your personal statement have maximum impact? Some people believe that there is some magic formula or structure which will guarantee them the offers they want. There isn’t.

Remember that the people reading these statements are very intelligent and experienced and have probably read hundreds of such statements. They will not be ‘wowed’ by some fancy story-telling, anecdote, or clever structure. What they want to see is something truthful, personal, specific and aimed at the course you want to pursue.

The most important thing is to keep in sight your aim which is to convince your future supervisors of your merit and suitability for your chosen course of study.

So what are they looking for? This statement captures the essence of it:

Strong personal statements convey the applicants’ passion for and growing insight into the chosen subject and course. They also convey personal attributes such as diligence, organisational skills, and leadership qualities.

“So what?” you might say, “everyone knows that.” But the truth is that so many candidates are trying to do this that the job of the admissions officer is very difficult. Increasingly people are saying the things they think will get them the place. So instead admissions tutors have to read between the lines to find the people that are really interested in the subject, and really read outside the syllabus. This brings me to one of the most important principles to follow.

Show, don’t just say

This means that it is simply not enough to say things like “I enjoy reading the Economist.” The admissions tutor has no way of knowing that it is true and it may well by the 10^th time they’ve read that line this morning. Instead you need to show that you read it (or even better some other publication) by saying “I particularly enjoyed a recent Bagehot column in the Economist newspaper which compared David Cameron with the Prime Ministers of the 19^th Century. It had never occurred to me that the style of politics of the 21^st century might be so similar to that over a hundred years ago.” This shows that you have read it and had your own ideas about it. It shows a passion for politics and current affairs and a desire to learn more.

Be personal

It’s no accident that it’s called a ‘personal statement’. The rest of your application will be contain the more impersonal information e.g. grades, educational background, references and so on. But this is the one place where you get to as it were ‘speak directly’ to the people who may well be teaching you. And so they want it to be packed full of personal details which really tell them what sort of person you are and what you’re interested in. After all not only do your future supervisors want you to do well on the course, they also want people on their courses who are interesting, engaged, and fun to teach!

So by all means read other people’s personal statements and maybe get some ideas from that. But above all the statement needs to convey who you are, what interests you and how you approach your studies and your life more generally. Stories or information about your family, your background, your education are all potentially excellent ways of doing this. Ask yourself: is there an event or occurrence that shows something important about me and why I want to do this course? How could I use that in the statement?

I had a student who told me how once dropped into conversation that he used to bore his sister with his extensive knowledge of capital cities of the world. What he didn’t realise is that story – if told in the right way – conveys to a potential supervisor that he is someone with a thirst for knowledge! So look at your own life and experiences and think of what shows you in your best light.

Show them how you think

Most students think it’s a good idea to talk about books or articles you have read that are relevant to the course. And it’s true that it can often be useful. But many students are missing the point of it. What the tutors are looking for is people who are interested in the subject and have the capacity to study that subject in the very different environment of a university. So they’re not that interested in how many books you’ve read. Rather what they want to see is your interest in, and critical engagement with what you have read. After all it is these students that are likely to do well in the subject at university.

So for example saying “Reading Karl Marx’s Communist Manifesto I could understand how nineteenth century British capitalism must have seemed unstable and unfair.” is ok but it’s a bit generic and doesn’t given any insight into your thought processes. This is much better: “When I read Marx’s Communist Manifesto I was struck by his argument that capitalism inevitably exploits workers. However it did raise for me the question of whether trade unions and legal rights could in practise prevent this exploitation. This led me to read other books on this topic such as..” This shows that you are thinking about and engaging with what you have read – vital skills for anyone studying at university.

Just a final warning – don’t try and fake it! You might be tempted to write things that you think ‘sound good’ or are what they are looking for. But there really is no point. Chances are the tutors will be smart enough to see through lies or pretence. But even if they’re not then all you will have done will be to cheat your way onto a course that probably doesn’t suit you – which won’t be any good for you in the end!

So as a summary, here are the main dos and don’ts. Good luck!

SHOW your qualities
Be as specific as possible
Use real and novel examples
Show you thinking and ideas about your subject
Be personal
Be different

Don’t

Just say what you want them to think
Simply list your achievements or interests
Duplicate info available elsewhere e.g. your subjects or grades
Be vague or general e.g. “Adam Smith’s ideas interest me.”
Copy other people’s ideas

5 Top tips for solving maths problems

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Many maths students find that even if they are able to solve the problems set to them at school or in the textbook when they turn to exam questions they often get stumped. This is often because exams require students to solve problems not simply show they can do certain techniques (like differentiate, or factorise). And problem-solving is often not taught at schools at all! Obviously a lot depends on the exact problem you have, but if you are stuck on a particular maths problem, there are a few quick things you can try which might help get you ‘unstuck’.

1. Have you used all the information given in the question?

Because it must be possible to solve maths questions and the examiners are not deliberately trying to confuse you, maths questions always give you exactly enough information to answer them. But if you don’t use all that information then it’s unsurprising if you get stuck! So check that you have used all the information given and if there’s something you have missed that could be the clue you are looking for. Go back over the question carefully and check you have incorporated everything, no matter how small, included in the question. Also check that you have written everything down correctly – you’d be surprise how many times students make an error here!

2. Have you paid attention to the key words in the question?

Similar to the above, maths has its own language which is very precise but often ignored by students in their rush to get to the answer. Some particularly important terms to look out for:

– Hence: means you need to use the result from the previous question.

– Hence or otherwise: means that although there are other ways of doing it the easiest is to use what you just found!

– Exact value: means no rounded decimal answers are allowed. So answers must be either whole numbers, fractions or use constants such as e or ln3.

– Show / Prove: this means you have to take the information given and using maths and logic get to the answer they have provided. So you must not thing they are asking you to prove!

3. If it’s the later part of a question, have you tried using the earlier answers?

Maths questions in exams (particularly at A Level) are in the form of problems which have interconnected parts. Usually the easier, earlier questions are used to provide the basis for answering the later, harder parts. But too often students behave as if every part of the question is separate, when they are not.

Ask yourself what have I just found? What does that mean? What could I use that to find? Very often this will help solve your problem.

4. If you can, have you tried drawing a diagram or graph?

They say a picture paints a thousand words. Well in maths you might say a diagram paints a thousand equations! Graphs or diagrams are a brilliant way of combining the information given in a single picture. Very often this quickly provides the clue you are looking for, so it is almost always worth trying if possible. Just be careful that your diagram is neat, clear and not misleading (doesn’t suggest things that aren’t true). By looking at the diagram, sometimes from different angles or perspectives, the insight you need will often suddenly appear.

5. Could you solve a simpler version of the problem? If so, can you adapt that approach for this harder one?

Exams will only test you on topics you have (hopefully) already covered in class. But very often the questions in exams ‘look different’ or appear harder than the ones you have solved before. But often that appearance is largely illusory. If you can spot the type of question you are being asked and focus on how to solve problems of that type then very often this helps overcome this obstacle. Once you have noticed that a problem is still, say, factorising a quadratic, or still determining the maximum point on a curve, then you see you can still use the approach you have already learned.

I hope these methods help you solve more of your maths problems!

The dangers of studying too hard

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The title of this post might seem a bit odd, after all surely most students are not working hard enough! Well, not usually! While there are many students who would benefit from working more, in my experience a large proportion are actually working too hard and this is one of the reasons why they are doing less well than they could. In fact I would go as far as to say that one of the main reasons students under-perform in their exams is that they have worked too hard.

Why is working too hard bad for you? Primarily because it makes you tired. As you get more tired your ability to learn falls significantly. A common pattern is that overworking leads students to struggle to concentrate in lessons and when doing their homework. As their performance drops they then (wrongly) conclude that they need to work more and so the cycle continues. Usually this only ends when the student falls ill and has to take time off school. That time-off then leads the student to fall further behind, causing even more difficulties.

Another reason working too much can be a problem is that when you work too hard this is usually at the expense of other important activities like spending time with your family and friends, relaxing, doing sport or other hobbies. While they can sometimes seem like an optional luxury, in fact they are crucial to your health and happiness and should not be neglected. And while doing those vital things your mind assimilates the information you have learned and your body recharges its energy stores. When those activities get dropped the tendency is to feel more tired, bored, and irritable which is not conducive to working productively. Also the more you work, the more your life is centred round work which can make it seem all important and very stressful.

So how do you know if you’re working too hard? These are some important signs to look out for:

– You struggle to concentrate during lessons or homework

– You sleep poorly and wake-up feeling tired and sluggish rather than refreshed

– You find yourself feeling unmotivated or lacking interest in your work

– You keep making the same mistakes in your homework or exam practice – your grades are not improving

– Homework seems to take you several attempts and much longer than it takes others

– On the weekend all you want to do is sleep

– You frequently get colds and flu

If you are experiencing several of these then WATCH OUT you could be approaching exhaustion or burnout, meaning you will need to take time off school / college to recover.

So what do you do about this? How much should you work?

No one can say exactly how much or when you should work, as it varies enormously from person to person. However there are a few principles you can follow which should help prevent this problem:

– Don’t work for longer than 1 hour at a stretch and even better, 40 minutes. Then have a break where you do something that doesn’t tax you like go for a walk or have a snack before re-starting.

– Few people can cope with studying for more than 6 hours in total in one day. If you have also been at school then it is probably 2 hours in one evening.

– As you approach exams you should be steadily reducing the number of hours you work as you approach the exam, not increasing it! This will ensure that you are fresh for your exam.

– If you have a revision timetable you should also block in time for fun, exercise, relaxation and treats which you look forward to. Don’t cut these out!

– If possible, don’t study in your bedroom as this can make the room associated with work and stress, making it harder to sleep well at night. (If you have to work there then make sure you pack away books and notes at the end of the day so that it feels finished before trying to sleep).

If you commit to these things what you will find is that your work is no longer the chore it once was, that you come to it refreshed rather than tired and that you see that work is part of life, not all of it! You will work much more productively and achieve better results. Sometimes less really is more!

One easy way to boost your exam results

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Exams are tough. Too often students work really hard up to the exam only to find that the exam itself doesn’t go as well as they expected because of poor technique. Of course there is no substitute for hard work but there are some small but very effective changes you can make which can help improve your exam grades, regardless of your subject. One important one is to change the order in which you approach the exam.

All exams are presented to the examinee in a particular order: in Mathematics you are usually presented with 7 or 8 questions starting at 1 and continuing to the last one. In Economics A-Level you are often given a multiple choice section followed by a data response. And 90% of students will answer the questions in exactly the order they are presented. Even though you don’t have to! And even though there are good reasons to approach them in a different order!

Why do it in a different order? Well the main reason is this: questions that require the most energy and thought should be approached early on in the exam while the mind is still fresh and you are not pressured by time. Most exams are structured so that the easiest questions with the fewest marks are given first and the hardest questions with the most marks are towards the end. If you answer the questions in order what usually happens is that you are tackling the most difficult questions (which usually have the most marks) at the end of the exam when you are getting tired and flustered. That is not a recipe for success.

So should we do exams backwards then?! Well in general that’s not such a great idea either. The reason is that if you start an exam with the hardest questions there is a chance that you will struggle and then lose confidence. This could make you panic and also reduce your chances of doing well. No, before you do the hardest questions you should first do a few easier questions you are confident with.

This is how I suggest you approach your exam:

1. Flick through the exam making a note of a) easy questions to start with, b) hard questions with lots of marks.

2. Tackle 1 or 2 easy questions which you can do quickly. That will boost your confidence.

3. While you are on a roll and still fresh get stuck into the tough questions with lots of marks.

4. Once you have done those go back and complete the rest.

Many of my students have tried this approach and it has improved their exam performance significantly.

Just a few caveats about it. First, the important thing is to get as many marks as possible, so always focus on doing those questions second whether or not they are very difficult. It is normal that they are the most difficult, but if not, you should go for where the marks are. Second, sometimes you have to modify this approach slightly if doing a harder question depends on, or would be much easier, if you had first done the earlier, easier questions. (This is why you don’t apply this within e.g. an A-level maths question where the earlier parts of a question almost always lead you towards the later, harder parts.) Finally, do make sure to present your answers in the correct order for the examiner – usually this is just a matter of filling in the right places in the answer booklet. Otherwise he will get confused and might mark you down!

But other than this, it’s an approach that is applicable to almost any exam and should help boost your grades immediately. Let me know how you find it.

How to be a better student

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At this point in the year students seem to put their heads down to focus on understanding all the difficult new topics they need to learn. Many have exams in January which they are anxious to do well in. But more often than not the barriers facing students are not within the subject they are learning but within themselves! Focusing on addressing those can yield benefits across all subjects and significantly improve grades. The following are the habits I have observed in my most successful students, regardless of their subjects. How many are yours?!

Taking responsibility for both their achievements, and failures

This is the single most important habit, but the one which can be most elusive. When things go well most of us are happy to take the credit and bask in the approval of others. But when they don’t go so well we generally seek an excuse: “I wasn’t feeling well”, “The teacher is rubbish”, “It was a tough exam”. But the danger of this is that we miss a major opportunity to learn and adapt our approach in order to improve in the future. If you find yourself reading this and thinking “Nah, that’s not me” then maybe just pause for a moment!

Highly effective students always know that they are responsible for their own learning, successful or not. They don’t look for excuses but instead seek ways of changing their approach and understanding things better. I once had a student who repeatedly made small errors in algebra which would lead to her dropping a lot of marks in maths exams. For a long time she ignored the problem and pretended it was because her teacher was inadequate. When she eventually accepted that this was her responsibility it quickly stopped and her marks improved hugely.

So use failures and disappointments as a launchpad for future success!

Always wanting to understand, not merely remember or reproduce

The problem with lots of teaching and learning is that the teacher and the student remain content with the ability to reproduce the material covered in class, rather than for the student to truly understand why it is true. But it is only understanding that will enable you to answer the unpredictable questions you will face in the exams. There is no word for “ununderstanding” because it doesn’t exist!

So when in class or reading a textbook always ask: “What does this mean?”, “Why is it true?”, “How does it connect to other things I know?” Challenge your teacher or tutor to answer these questions! Challenge yourself! Use all the resources available to you to get you to a state of deep understanding. Then you will be able to tackle anything thrown at you and you won’t have to memorise anything (well almost)!

Always reflecting on and learning from experience

We all make mistakes. They are a fact of life. And in fact they are a crucial means by which we learn. But if they are ignored or their lessons are disregarded then we risk repeating the same mistakes over and over again. I once had a student who kept sitting exams and running out of time, so his marks were never as he should have achieved. We discussed techniques he could use to improve this but then they would just be forgotten about or dropped and he would revert to his old ways. So he never improved.

If an exam or test doesn’t go as well as expected, the successful student will always ask themselves why, and seek a clear answer to that from their teacher or tutor if necessary. They will then act on the answer. So if the answer is “I don’t understand conditional probability” they will then go away and make sure they work on it until they do understand.

Being organised

You can be highly intelligent, motivated and hard-working, but if your notes are not filed properly, you are always late for your classes and you don’t know what’s in the syllabus then you are not going to achieve much.

Getting organised is a matter of being in control of your studies rather than letting it control you. It means: always being on time for lessons and never missing deadlines, keeping your notes organised and accessible, always knowing what you need to know and by when. It means doing this not just periodically when it has all got out of control but always, as a matter of habit.

Knowing how to rest, relax and enjoy themselves

If this is all sounding like hard work then it’s important to emphasise that the most successful students are not necessarily those that spend the most hours studying. The ones that spend the most time are usually wasting their time because they are disorganised, bored or tired.

In fact successful students know and appreciate the value of time spent playing sport, resting, or just having fun. They know that this time is not only valuable in its own right but also provides time-off for the learning mind to recuperate and assimilate new information. People forget that when you are not thinking your unconscious mind is still learning! Time spent on hobbies and pastimes also helps put studies into perspective and avoid the stress and anxiety associated with over-work. So it’s vital to build in regular times for rest, sports, social activities and fun in and around your studies.

Time spent developing these habits might just be the best thing you ever do!

New job

I am very happy to announce that I am about to start working part-time as a teacher of Government and Politics and Mathematics at Ealing Independent College.

This is a new venture for me and the first time I have worked in a college environment. I’m very excited to get to know my new students and colleagues. So far it seems a very nice place to teach. As it’s only part-time most of my work will continue to be private tuition but inevitably I have much less time for that than before.