How We Teach Math
Alexander Shilmover M.S. in Math from Moscow State University. Lifelong experience teaching Math.
Our math programs are designed to fill the gap between the requirements reflected in the recommendations of the Curriculum and Evaluation Standards for School Mathematics made by the National Council of Teachers of Mathematics (NCTM) in 1989, and the existing practices in most of public schools. Some of the shortcomings of current practices are the tendencies to focus on the acquisition of rote skills; to cover many topics superficially; and to be highly repetitive without in-depth learning.
Nearly every subject has a shadow, or imitation. One can learn imitation history -- kings and dates, but not have the slightest idea of the motives behind it all; imitation literature -- stacks of notes of Shakespeare's phrases, and a complete destruction of the power to enjoy Shakespeare.
Many traditional programs and textbooks reflect disconnected orientation, focusing on the end results, omitting the important notion of the process, the association of different topics and concepts between each other.
The result is often a feeling of dissatisfaction and even a fear of math, the notion that mathematicians are a race apart, and feeling by the students that they will never be able to understand math.
We are convinced that these perceptions do not lie in the nature of the subject, but are caused only by the poor tradition of teaching math.
The fear of mathematics is a tradition handed down from the days when the majority of teachers knew little about human nature and nothing about the nature of mathematics at all. (Walter Sawyer).
What do we emphasize in our programs?
Mathematics as a language, mathematical reasoning and proof, which includes deep understanding of the differences between theorems and definitions, ability to draw logical conclusions, to make and test mathematical conjectures.
When a student realizes that he actually deals with the same phenomena when he looks at the things from the various angles, the fear of math is replaced by the pleasure that comes with deep understanding.
To master anything requires effort. But it does not require unpleasant effort, drudgery. The main task of any teacher is to make a subject interesting. (Walter Sawyer).
Significant efforts are dedicated to teaching the student to communicate and express mathematical ideas coherently. We teach the student to listen to herself, to become aware of the way she is thinking. We emphasize the aspect of math being a language, and for the student to understand that this concept really implies an ability to express it (using verbal and symbolic ways).
Our Russian background and traditions of the Department of Mathematics and Mechanics of Moscow University reflects somewhat on the school curriculum and selection of permanent and guest teachers, but the philosophy of the school is defined in the first part of this proposal and is very much in the spirit of the new approach developed in the Curriculum and Evaluation Standards for School Mathematics, and MCAS requirements.
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