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Can everybody learn to do mathematics?
My answer is a resounding YES! There's this idea going round that some people are born with an in-built ability to do maths while others aren't – and that's just so wrong. Learning maths is like learning a language. If you grew up in Slovenia, surrounded by Slovenian-speakers and practising Slovenian every day, you'd be able to speak Slovenian, right? If you are open to the idea of getting better at maths, and prepared to put in the practice to do that, then YES YOU CAN.

Are there limits to how fast and how far a person can improve their maths?
Reaching a high level certainly takes time. It all depends on (a) your current level of maths (b) the level you want to reach (c) your attitude and the effort you're prepared to put in. Maths is 'hierarchical', which means it's essential to practise each stage and feel comfortable with it before you go on to the next. For example, you must be comfortable with counting before trying addition, you should be comfortable with adding before doing multiplication, and so on. It all takes time… but if you've got the patience and the determination, then ultimately THE SKY'S THE LIMIT!

What's the best way to prepare for a maths exam?
Just like other subjects, it's a good idea to organise your notes, read them through, read examples in textbooks and so on. But ultimately you have to be able to answer maths questions, so it is essential to prepare by… ANSWERING MATHS QUESTIONS! Diving into a past paper can be daunting, so first try exercises on individual topics and make sure you are getting good scores on these.

Should I mark my own work or have someone else mark it for me?
I'd recommend you mark your own. Maths is easy to mark, because the answers are either clearly right or wrong (well, most of the time at least*). The key thing about marking your own work is that you can try any corrections without delay.

(*Sometimes in algebra you might get an answer where it's not completely clear, e.g. if your answer is b+a and the answer in the book is a+b. If you're doing a lot of complicated algebra, it helps to have someone you can ask to double-check any occasional iffy answer.) .

Is there much benefit from trying corrections?
Absolutely YES. First and foremost, it prevents the learner learning the wrong thing. If you write "7 x 8 = 54" a hundred times and don't correct it, you reinforce the wrong idea. In this case, it is absolutely essential to do the corrections and write "7 x 8 = 56" a hundred times AS SOON AS POSSIBLE after doing the exercise.

A second benefit comes through "error analysis", which is a fancy way of saying "work out what type of mistakes you're making". Maybe these are something fundamental, maybe they're just silly slips. Whatever they are, you need to think about how to avoid these mistakes in future… and especially in any exam.

A third benefit of doing corrections is for your morale. No one likes getting a low score – that's just human nature. But if you can analyse your errors and correct them, then certainly you should take pride in that.

What's the best way to do past papers?
Past papers are essential practice for any major exam. Follow three stages:

STAGE 1: OPEN BOOK. Keep notes and textbooks to hand and refer to them as needed. Use the mark scheme and mark each part of each question directly after doing it. This is also an excellent opportunity to organize your notes! While doing this, think about what formulas and key information you need to know, and start a list of 'key facts' to memorise.

STAGE 2: CLOSED BOOK. Close up your notes or textbooks, except for any official formula sheet you are allowed in the exam. Mark each full question after doing it. DON'T RUSH – allow at least as much time as the real exam would allow. Corrections are vital here, so refer to your notes as needed when trying corrections.

STAGE 3: FULL DRESS REHEARSAL. Do at least one paper under conditions as close as possible to the real exam. If the exam is at 9:30 a.m. and finishes at 11 a.m., then you should start and finish at those exact times without a break. No music, sitting upright at a desk. If you can hire a hall with a few hundred nervous perspiring teenagers in it then do so. (The last bit is going a bit far, but you get the idea.)

How many past papers should I do for each exam?
How long is a piece of string? Every individual is different, and some need more practice than others. It all depends on the goal you want to reach. If your target is 80%, then keep doing open-book papers (stage 1) until you get 80% or better, or at least close to it. Then switch to closed-book papers (stage 2) until you're hitting the target, then go on to stage 3. The absolute minimum is three papers – one at each stage – in theory anyway. In practice, a few more may be needed.

A common observation among teachers is that those kids who do many papers get much better results than those who only do a few. Well, that's probably true, though doing twenty practice papers for each exam is a big commitment of time! My last word on past papers is this: a few papers done thoughtfully can be much more effective than lots done in a slapdash way. Do the corrections carefully, think about what mistakes you're making and how to avoid these, and you can save time in the long run.

Can individual tuition help me to improve my maths?
I'm a maths tutor, so I'm obviously going to say yes. To back this up, I would say that one-to-one lessons can (a) help identify weak areas that need to be addressed (b) help the student to understand new ideas and methods and (c) give encouragement and guidance in doing the necessary practice.

Having many years of experience of tutoring, I know various "tricks of the trade". For example, if a younger student were to make the mistake 7 x 8 = 54, I get them to write down

5 6 7 8, 56=7x8

ten times, while reciting "five six seven eight, fifty-six is seven times eight". That always seems to do the trick!

In general, for tutoring to work well, it is essential for the student to have a clear goal. For students studying towards GCSE or A level, then the goal is to get the best possible result in their exams. For others, the goal might be to move up a set at school… or at least avert any threat of moving down…

Are there down-sides to individual tuition?
Yes. The most obvious one is having to pay for it, though most parents are willing to part with their hard-earned money if it helps their child's future.

Some parents worry that the child might get confused by being shown different methods from the ones shown in school. As a tutor, I always allow students to use a method they know already, PROVIDED they are getting the answers right in a reasonable amount of time, and can use that method to answer the full range of possible questions. On the other hand, if they are getting lots of questions wrong… which is most often the case… well, they just have to adapt and learn my methods. In practice, this is hardly ever a significant problem.

A much more important consideration is that of the time-commitment of the student. It's essential for the student to allow time to do additional homework, and to do it properly, including marking it and trying corrections.

Have you ever given tuitions without giving homework?
In the past, yes – and the results were not good – the student had difficulty remembering the methods covered in the previous lessons. By contrast, whenever a student does a piece of homework independently and gets most of it right, I am fairly sure that they will remember the key points for some time to come.

These days, homework is compulsory not optional, without exceptions.

Do you tutor all ages and abilities?
My speciality is GCSE and A-level maths. I also tutor other secondary school ages (years 7 to 10), but not primary-schoolers.

I'm not an expert regarding students with specific learning difficulties, but otherwise I've worked with a very wide range of abilities. I have seen students on the verge of dropping out of sixth form turn themselves around to get A grades in every modules. Others have gone from hating maths and being far below average in GCSE, to not only passing that but going on to A level maths and completing that too. Given time and effort, IT'S ALL POSSIBLE.