What different students meet. I keep wondering how different the level of preparation for the USE can be between two students with the same conditions. One of them, a math tutor in 10th grade, tells me about integrals and differential equations (I’m currently studying such a prodigy), and the other one can’t explain what a square root is. And the roots are not the worst option yet. Approximately at 0.5 pupils per year in preparation for the USE in mathematics, the tutor spends time on opening parentheses, on actions with fractions, and sometimes on the multiplication table. What are the reasons for this delay? Is it really only in the abilities?
There’s a widespread belief that a mathematician has to be born. Yes, of course, there are talented children whose abilities are manifested from birth. They are prone to learning and finish school without the help of tutors. They prefer reading or problem solving to entertainment. They pay attention to what the schoolteacher tells them, love to work and often develop well ahead of the program. When I started out as a math tutor, it seemed to me that the laggards were the only category of tutor students.
A lot has changed with the arrival of a strong and quite unique student. Her name was Rada. From 5th to 8th grade, we solved with her only olympiad problems in mathematics in large numbers. Most of them she clicked them like nuts. In the 6th grade I was asked to tell about the determinants and matrices, and in the seventh trajectory of training passed on the concept of power of set. She was madly interested in the whole thing. Later I learned that my uncle Rada is a mathematics teacher at one of the prestigious universities in the United States, and my father has 3 higher education in Russia.
The pull to science in such children is genetic, and they are certainly born talented. But what is talent without development? If it was not closely engaged, if parents did not orientate a tutor in mathematics to a certain level and type of problems, it is unlikely that it would have been possible to take first place in the Olympiad at Moscow State University among sixth-graders (I do not remember in what year) and enter the Department of Mathematics, Faculty of High Technology, one of the very, very serious universities in the states.
My experience of classes and observations of students allows me to say that it is possible to become a mathematician without any special brilliant abilities. It simply requires a full commitment to the subject. It is possible to compensate for the lack of abilities with long and hard work, spending considerable time on mathematical development. It all depends on what your head is packed with and what you do each in your spare time. You can lie on the sofa for a long time and play with your mobile phone, or you can open the problem book and solve all day and night tasks. And not only those that the tutor has brought in mathematics, but additionally. It is necessary for years “to sit on books” with a sheet of paper and a pencil. To solve a lot, to think, to think. Is this how your child does it? How to get better at math? How does he use his spare time (when there is no tutor or school)? What is his inner world filled with?
All major mathematicians on the planet carried science within them, paying maximum attention to it. The same will be required of you. A school or private maths tutor is only a means of organising and planning your development (you don’t have to know in what order and what topics to study). Everything else is in your hands. Math tutoring techniques are only additional “accelerators” and “optimisers” of the movement, but they only give tangible results when you are the one who is driving it.
How do future mathematicians learn today?
A strong student came to me recently. The aim of the classes was to prepare me for the USE in mathematics and to pass the exam for admission to Mehmat at MSU. We studied vector algebra with him. Once I made for him homework on one of sections of the additional textbook “Polyhedrons”. I gave him the book. What was my surprise when, at the next lesson, I learned that the student completely photocopied it and in addition to my 8 tasks solved 10 of it additional. In almost every lesson, we dealt with questions about tasks outside my D/S (from different collections). The boy passed the internal math exam at MSU for 100 points and got the coveted budget place.
Common core math example. No one will force a child to solve problems outside the plan if he has no internal attitude towards mathematics. If the purposeful pupil also is engaged with the tutor on mathematics, knowledge to it will come faster and in greater volume.
Knowledge is always proportional to the time spent on them. The only difference is that a capable (brilliant) student is faster to capture the main thing, to see the decision a few steps forward. But everything is in your hands. Any properties of objects can be independently verified or proved, and most of the movements of numbers can be opened on paper. To solve complex issues, there are specialized tutorials and, after all, a tutor. If you wish, you can always understand anything. The main thing to do, not to be lazy.
Most students do not withstand significant mental stress in the study of mathematics. However, in itself I know that persistence and stronger than any difficult topic.
How did I become a mathematician myself? Common core math example.
I didn’t have tutors, but I compensated for their absence by working hard independently. I also solved problems and repeated evidence. There was such a period at the turn of the 7th grade – the beginning of the 8th grade, when I felt uncertain about my understanding of geometry. What was done? Every day I either read the passed paragraphs or mentally ran the proofs through myself by theorems together with the formulations of the objects participating in them. I even did it lying in bed. If something was forgotten, I could climb up at 12 at night and see the evidence in the dim light of the lamp (so that my parents wouldn’t notice). When I understood or remembered the proof, I went to bed with a feeling of satisfaction. And so about six months. At some point, the proofs began to be remembered by themselves, and I confidently passed the final oral exam on geometry in 9th grade for excellent.
Tutor’s advice to future mathematicians…
1) Solve and solve the tasks yourself once again.
2) Do not stop in development having achieved good results.
3) Do not abandon a task if you fail. Approach it after a while or change the solution method.
4) Try to prove everything and everything. All the theorems that you use that come to your attention.
5) Find a math tutor with knowledge of additional subject chapters. Ask him more questions.
6) Show observation. Many methods use features of the object that you can see.
7) Learn the results of your transformation and calculations. Theorems are nothing more than observation.
8) Attend math Olympiads at different levels. They will give you extra interest in learning the subject.
9) Do not focus only on preparing for the EGE. Consider the subject more broadly. Look for interesting tasks on the Internet and in printed publications. Their resolution will have a positive impact on your development.