# Mathematics

## If you feel that however many long hours you study, your math grades never reflect your effort, you're not alone. ToppTutor specializes in facilitating good working routines, the core to all progress.

### MATHS IN GENERAL

“Maths doesn’t require understanding, just hard work like any other subject!”

NO!!! Work smarter, not harder!

Is your child not getting the results you were hoping for? If a student doesn’t “get it”, it is nearly always because it hasn’t been explained in a logical way. Remember, maths is based on four basic operations: + - x ÷

Everything else is derived from that and can be understood if explained in a logical way. Some teachers force feed formulas into students’ heads. And if they forget them, they are doomed. For some exams they get a formula sheet or even a booklet. Great! Even less reason to memorize. Understanding is the key word. If they don’t understand the formula, it is not easy to use it in a meaningful way.

Students who have been trained to reproduce formulas struggle when the questions get trickier. And some feel restricted by a narrowminded teacher who goes strictly by the “rules”. Even in maths (especially in higher level maths), it is important to think outside the box. We educate the whole brain, enabling them to see solutions to problems they thought they could never solve.

Maths is about UNDERSTANDING, not MEMORIZING! Even a student who is quite keen on maths may lose interest if he or she is told that it is all about how many formulae they can remember. The moments when our students exclaim: “YES, I GET IT” are our happiest. And it puts a big smile on the students faces. In some cases, so wide that they go on to university and take maths courses for extra credits, even though they do not need them.

### THREE KEY THINGS

### SELF CONFIDENCE!

01

The first thing we do is to try and make the student feel safe with the tutor. The tutor is not there to judge and condemn. We are there to get to know the student’s background in maths. What are the main obstacles? What have bad teachers done to their confidence? Where should we start?

### UNDERSTANDING, NOT MEMORIZING

02

Sometimes we ask a student: “What is 2 raised to the power 0?” That normally results in some stuttering and confusion. But some regain their composer quickly and reply: “1”. Only to lose it again for the next question:

“Why?”

“Because the teacher said so.”

“It just is.”

Sorry, not good enough. And after five minutes, they know why because we have made them see a pattern, a logic behind it all.

### TIME

03

Most students have a packed schedule most days of the week, so is it a good idea to make it even worse by adding a tutor?

That is one of our main concerns but let us do a little “maths”: Let’s assume that a student has 5 lessons of maths in school each week. How much of those 5 hours are affective? How much is spent looking out the window? Taking a sneak peek at the cell phone? Thinking about other things?

And last, but not least, not understanding what is going on at the board.

How efficient were YOU at school? How much of the time in maths class did you really pay attention? If you are reading this, it probably means that you think there is room for improvement. Let us assume a student is 40% effective. That means that 3 out of 5 hours are wasted. At ToppTutor we spend some of the lesson on key areas that the student is really struggling with, but we also try to find time to take a sneak peek at what is coming up in school next week, explaining a few of the basics that we know is ESSENTIAL to understanding the topic. That means that when the teacher starts on a new topic, the student hits the road running. “Oh, yes: I know this. I did it with my tutor last week.” So, the 5 lessons that week might suddenly be 80% effective! That is 4 hours out of 5! Not bad. Doubling! Why is that so important? Several reasons: The lessons are more enjoyable. The amount of homework needed goes down. And the grades go up! With a smile!

### MATHS LEVELS

YEAR 4-9

The foundation for maths is laid from an early age. We have seen countless students struggling to get through maths in secondary because their background is so week due to bad teachers or lack of follow up. Let us meet your child (we teach students from the age of 9) and make an evaluation. Is everything going in the right direction or is the basic understanding lacking. At an early age, this is easy to rectify. But the older they get, the more there is to catch up on to prepare for the tough syllabus they are facing.

YEAR 9-11

Did you know that IGCSE students must deduce the formula for cubic sequences? That is not even in the syllabus for IB high level maths! No wonder some students have a problem with it. And, on top of that, some students are still struggling with lack of understanding of the fundamentals in maths. We can rectify that before they get into the final couple of years in secondary.

YEAR 12-13

This is the real thing! Calculus, Statistics, Binomial theorem. Some syllabi cover parts of the first year of university! Many students have a constant bad continence during this extremely demanding period. Even when they do their homework. While studying Physics, they think that they should have done more English. While studying English, they feel they should have worked on their maths. We know this, and we always try to accommodate them with the best possible time slots to interfere as little as possible with their busy lives. And, like one student said: “I learn more in a week from you, than a week at school”. Good use of time? And what a compliment!

HIGH LEVEL

High level maths is tough. Really tough! Large parts of the syllabus are actually university level, so students struggling should think again about changing to standard level maths. Great course, even for those who plan on studying math related topics like engineering. But if applying to universities that require HL, let’s get to it!

It is no wonder that some students get lost when diving into complex numbers, planes in space, differential equations etc., so it is important to get some help as soon as possible. Most of the students here will have a good background at this stage but may get confused and disillusioned by the complexity of it all. There is some comfort in knowing that most will have the necessary background. It is just that the progress is a lot faster than what they are used to, so let us help them over the “bump”. It is very encouraging to see how fast they pick up speed once they are over the first shock. The word “speed” here is crucial. Some questions require a LOT of steps to get to the answer. Even though a forgotten bracket or minus sign may only be penalized with one mark, the continued steps may be a lot tougher with a wrong number and end up in an answer that seems highly implausible. Try again! While the clock is ticking. Here, more than in any other course, accuracy is of the essence. We try to get our students into better working routines: 1: Write down the question. 2: Complete each line of working. 3: Start the next one immediately underneath. 4: Include side calculations next to where you need it, don’t spread it all over the place. 5: Underline or highlight intermediate answers that may be needed later…….

The effect of good working routines in problem solving is amazing! It can mean the difference from a 7 to a 4! Or vice versa.

And, as with lover cases, understanding is the key. One example: A student, quite correctly, found the oblique asymptote for a function. When asked to explain, he said that he didn’t know, but the teacher had said so. The tutor pointed to the last term, one with an x in the denominator and asked: “What happens to the function as x increases”. Total silence for a few seconds while the student was thinking. Then suddenly he saw it! He literally got out of his chair and started jumping up and down in pure joy! (The tutor enjoyed it just as much but didn’t jump).

IB HL

Thinking about taking IB HL maths? If you are a maths genius, no worries. If you are simply good, you had better prepare for the freight train that will hit you. It is tough! We can help you to make the transition from IGCSE to Euler’s Formula (ei𝜋 = -1), the binomial theorem, calculus, planes in 3D a LOT easier.

Questions? Find some answers on our FAQ page or get in touch today!