The depth and skill density of high school mathematics competitions (especially at the league, cmo and even the imo level) are well above the level of mathematics. Contesters are not simply “smart”, but because they follow an extremely efficient, systematic and intensive training system。
In short, it is a process that goes from “accumulation” to “internalization” to “creation”. Here are the core paths to their mathematical skills:
1. Building high-level knowledge architecture (ground and tools)
The skills of the competition are based not on the sky, but on a deeper and broader knowledge than in high school textbooks。
Advanced learning and university decentralization: tools in high school mathematics textbooks are often inadequate (e. G., when they are processed, they are only average, while competitions require cosy, sorting, ginseng and even condensation). Competition students systematically study “competing textbooks” that are specialized in primary mathematics, combination mathematics, plane geometry, complex numbers and multiple formats。
University tools fall-on: when they process high school algebras or solve them, they master such university tools as calculus (conductors, points), vector algebras, linear algebras. In many cases, the so-called "godic skills" actually see the nature of the problem in a more advanced perspective (e. G. By killing traditional geometry in vector seconds)。
Accumulation of “violence” in classic thematic and modelled methods (shows)
This is the most basic and obligatory stage. Competition techniques are largely “model recognition” capabilities。
Books and subject training: competition students don't come up and do simulations, they eat books. The great geometry, the osei book, etc. They will learn by theme: today, for example, they will learn only “draining techniques in the array”, and tomorrow they will learn only “chromosomal problems in the graphics”。
“second-level conclusions” and “formats”:
Geometry: a coding of dozens of common quotes (e. G., root axes, dots, menelaus, ceiba, simón). When you see a graphic structure, you react instantaneously to which guide you connect。
Algebra: proficiency in rationing methods, coefficients to be determined, metallurgical (triangular exchange, incremental exchange) various maximum uses。
Combining: complicated variations that capture the principles of drawers, extremes, rebukes。
Purpose: in the event of a problem, it is "decomposed" into a combination of known models. If this is done, it will not require creativity, but proficiency。
Deliberate “faultful reflections” and “reverse” (heart method)
This is the key to distinguishing between “brush machine” and “skiller”. It's over when the regular student finishes the answer, and the contestant's play is over。
After a difficult one, they try to find a second, third solution. By comparing different solutions, understand which techniques are at the core here, which are general and which are stunts。
The method is summarised and refined: they create their skills index. For example: “the essence of this question is the most valuable value for which discrete variables are handled, and the core technique is `adaptation' (i. E. Gradual adjustment of the state of the variable to the optimal solution)。
I'm going to study the designer's intentions and think, "how did this come out?" “understands the logic of the subject matter, often with inverse techniques。
High-intensity “deliberate exercise” and stress resistance training (actual)
Skills require the transformation of "short-term memory" into "muscular memory"。
An advanced version of the tactical: not a blind brush, but rather a high-quality one (men-yen, cmo, national team test)。
Time-bound training: competitions are demanding time. They will force themselves to come up with their skills in a very short period of time during normal training. In this high-pressure environment, the brain forces a combination of known techniques, which greatly increases the speed of extraction。
When you can't think of it, they can read it. But instead of reading it out, i asked, "why didn't i think of it? What kind of knowledge fault is it?" so we put the skills chain on。
5. Intuitive and deep-thinking training in mathematics (internal work)
That's the best feature of the best. The so-called “teaching” became “intuitive”。
Sensitivity to beauty and symmetry: many algebra techniques are derived from observation of symmetry; many geometry techniques are derived from perception of graphic beauty. This intuitive recognition is based on a pattern of automatic brain formation after extensive training。
The construction of the logical chain: competitions (especially digital theories and combinations) often require complex logic. Through long-term training, they are able to operate multiple logical branches simultaneously in the brain, thus acquiring advanced skills in “situational discussion” and “logical construction”。
Abstract capabilities: it is also a top-level technique to quickly abstract a specific practical problem into a mathematical model (e. G. Abstracting the rules of the game into a graphic model)。
6. Communication and high-profile points
There's usually a strong circle for contestants. The discussion between the students was the fastest way to exchange skills。
A seasoned coach who can point a finger at the nature of a technique and keep students away from the curve for months。
Summarizing: the skills of high school contestants can be compared to the skills of martial arts masters:
Practice: deep-seated mathematical principles, high-dimensional perspectives。
Remember a lot of models, quotes and classics。
Fight: forced into a flexible combination of boxing through intensive practical and time-bound training。
The go-go machine: to internalize the skills of others into their own instincts through a rehearsing and reflection。
For them, the technique is not a “guilty”, but a “linguistic”. They have enough vocabulary (basic models) and grammar (logical principles) to write fluent articles (problems)。
