While working as a tutor I realized why students who start learning math at schools with English or American educational system are often bad at this subject.

- Using calculator at the lesson is allowed.
- The way of studying is not thorough and, as it is known, superficial knowledge can easily be forgotten.
- Test form is often used at classes.
- For students, who enter a new school with foreign teachers, sometimes it is hard for them to ask a question. There can be different reasons for such a behavior, like culture gap or fear to show their lack of knowledge.

If student’s knowledge about certain topic is quite poor, for the first time we thrash it out in Russian.
It is necessary for student to get basic conception for him/herself. On the next class we repeat the material,
but all the tasks are already given in English.

If student already knows the theme, he is supposed to solve the problems in two languages
(the first task is in Russian, the next in English and so on). We usually take 2-3 different
mathematical themes during one class.

Evidently, if student is a native speaker, all the material is given in English.

Every 30-40 minutes we have a 5-minute break. During this time the room can be ventilated, and my student can solve a brainteaser or discuss some interesting and challenging mathematical ideas. These breaks are vital, as it is hard even for adults – to concentrate on a certain subject longer than an hour. After the break students revive their spirits and do the tasks eagerly.

Due to the frequent use of calculators students do not feel the scale of numbers. I teach simple methods of Speed Mathematics. It will enable your child to make lightning calculations in his head. If problem needs big calculations we use long arithmetic.

Light calculations:

$32^2 =\ ...\ $ (from Grade 8);

Convert to decimal fraction: $({1\over 5})^ 2=\ ...\ $ (from Grade 9);

Calculate: $\sqrt{2}\sqrt{50}=\ ...\ $ (from Grade 10);

Calculate: ${8}^{7\over 3}=\ ...\ $ (from Grade 11);

Convert to decimal fraction: $\log_4 8 =\ ... \ $ (from Grade 12);

Evaluate: $\sin{45^o} =\ ... \ $ (from Grade 9-10).

Tiresome calculations. You may use the tool :)

Calculate: $(2.1-0.079)^{18}$ giving your answer correct to 4 s.f.

Find: $244.5+1954.56+12045.1+$

$+997.333+4366.01$

(part of statistical problem);

Evaluate: $\sin{40^o} =\ ... \ $ (from Grade 9-10).

It is especially noticeable when we speak about geometry, when the whole answer is marked on the drawing without any reference to theory. That’s why sometimes students do not get everything about certain problems. At my classes students have to write every detail while solving a problem. So they understand the rules better and their knowledge becomes quite deep. This way of education is profitable as firstly students began to think precisely and secondly it is a good way to repeat the theory.

It is common knowledge that the only way for clear math understanding is independent work. That’s why all the
students get compulsory homework, that includes the themes they
studied at class and some brushup tasks. I have to point out that doing
homework is not just a simple traditional pattern. After the lesson student must think over the
material on his own, so on the next lesson they could comprehend new tasks without repeating
familiar material once again.

My method includes some peculiar features, that I invented during my teaching practice, and I am going to tell you about them at first class. Due to these aspects students get the material quicker and better than at usual school classes.