Methods of solving the problem of overloadin working memory when teaching mathematics

One of the reasons for the lack of progress in the teaching of mathematics is the overload of working memory leading to its “catastrophic failure”. As a result of this failure, information that is crucial for the current task in the working memory may be lost. For example, a sentence that a student tries to write down, a sequence of instructions to be executed, important relationships between the parameters of a mathematical object, and so on. The student cannot solve the problem, the learning process stops. This article lists known methods for reducing the load on working memory: training working memory, methodological aspects (using simple sentences, brief and timely instructions, available reference materials, reliance on long-term memory, load redistribution, multimodality and mnemonics), metacognitive installations. In addition, the author proposes to automate basic computational skills (arithmetic, trigonometric, geometric) using computer trainers created by him, available at: http://www.workingmemory.ru/htmls/trainers2. This makes it possible not to divert the resources of working memory to perform standard computational procedures when solving mathematical problems. These resources are released to search for the algorithm for solving the problem. As a result, the speed of solving the problem increases, the probability of errors decreases. The site contains four trainers. The Mental Counting trainer allows you to master the skills of counting in mind. The technical goal is the average time of multiplication a two-digit number by a one-digit number, dividing a three-digit number by a one-digit number, and subtracting a two-digit number from a three-digit number should be no more than seven seconds. The “Trigonometric Circle” trainer and “Reduction Formulas” trainer allow you to automate the skill of working with trigonometric functions. The technical goal is to learn how to perform correctly the exercise at maximum speed. The “Right Triangle” trainer allows you to automate the skill of solving a right-angled triangle: establishing the relationship between its sides through the trigonometric functions of acute angles. The proposed technique of working with the trainers is based on the principle of interval repetitions. After the first cycle of systematic training within a month, a break of two to three weeks is made. Then the cycle repeats. The average times achieved by individuals varies up to 80% due to individual differences in working memory in hum.

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