In our society, the division into "humanists" and "mathematicians", "physicists" and "lyricists" is accepted, focusing on people's ability to understand (and love) mathematics. What's happening? Why can't you be both a physicist and a lyricist at the same time?

And what is dyscalculia? Translated from ancient Greek δυς - "bad" and Latin calculāre "to count". Bad count. It's hard to count.

Officially, dyscalculia is defined by the following features:

• the presence of difficulty in understanding mathematics

• these difficulties are not caused by a lack of education in this area

• the level of knowledge of mathematics does not correspond to age

Just like dyslexia, dyscalculia often occurs in people who do not think verbally (you can read about this in my previous article: “What is dyslexia: a gift or a problem”, but with the help of images or feelings. And just like people with dyslexia, the problem is a feeling of confusion or misunderstanding, uncertainty. With dyscalculia, confusion creeps into numbers and mathematical logic ... At the same time, dyscalculia does not affect mental abilities in any way: people with dyscalculia can be successful and talented in other areas ... Dyscalculia can be of varying degrees: depending on the level of confusion.

In mild dyscalculia, confusion comes from misunderstandings on just a few topics, and tutoring can easily alleviate these problems. Officially, this condition is not even recognized as dyscalculia, it is so easy to get rid of it. But it is necessary to say about it, as it reflects the essence of the phenomenon.

At the level of confusion of an average degree, a person seems to be able to complete tasks in mathematics, it seems that he understands what needs to be done, but he does not have the integrity of understanding. But there is a set of local algorithms: in order to complete this task, you need to do this and this, and why it happens this way and why it was invented, he cannot explain. This gives rise to a feeling of confusion ... For example, when multiplying fractions, the numerators are multiplied and the denominators are also multiplied. But why is this happening? Where did the formula come from, and what if a person forgot it? How to remind yourself? It is easy enough to "remember" the formula, visualizing how it works in real life, understanding the physical meaning of the process. In this case, there is no correlation between mathematical algorithms and physical processes (or understanding the meaning of this process).

Moderate dyscalculia is also characterized by the absence of causal relationships between mathematical phenomena in general. For example: common fractions, decimal fractions, percentages, proportion, ratio and all actions with them are all division of the whole into parts based on common fractions.

Usually the average degree of dyscalculia manifests itself as follows:

- dislike for mathematics;

- a person does not always understand which of the algorithms should be applied in this case;

- can forget a couple of algorithms, but easily remembers if you give an example of its use;

- can easily be trained for the test, but after the test everything is forgotten;

- difficulties with understanding and solving words problems, since one needs to know the physical application of mathematical concepts;

- can only solve problems of a certain type, that he has already encountered (and remembered the algorithm);

Thus, if you create an understanding and an “image” of the mathematical process physically, show the mechanism for the emergence of a formula in the real world using different three-dimensional objects, then confusion will disappear, and ease and confidence in choosing a mathematical algorithm will appear, and, as a result, even love may appear. to math!

And finally, the most difficult degree of dyscalculia . And here you can’t do without a program for correcting dyscalculia according to the author’s method of Ronald Davis! But let's first understand what's going on.

Very often, mothers of children with this degree of dyscalculia say that:

- the child could not learn to count or recognize numbers for a long time;

- or learned, but can not write down;

- or counts well up to a hundred orally, but cannot write down and name the number correctly; - confuses tens and units (for example: 45 and 54);

- tries to add and subtract on the fingers, while the transition through a dozen causes a lot of errors;

-makes a lot of mistakes even in the simplest arithmetic operations;

- confuses arithmetic signs;

-can't figure out what to do;

- cannot remember and learn the multiplication table or learns it by the method of associations;

- can't solve problems

-cannot count the change in the store;

- can't deal with time;

- quickly forgets even the already studied algorithm;

-often forgets everything literally to the state of a “blank” slate, for example, having solved 9 examples, by 10 cannot remember how it is done;

- over time, there is a persistent aversion to mathematics ...

This happens thanks to:

1. Lack of correlation between number and figure (see photo #1).

The number is the number of real objects, and the number is the symbol of this quantity, written on paper (in the photo, from plasticine). The numbers were invented so that you do not have to constantly draw objects. In a child with dyscalculia, when looking at a number, the image of the number does not arise, but instead extraneous images or emotions appear, preventing the child from learning, distracting and defocusing him. Approximately, as in the picture (see photo No. 2).

2. Lack of understanding of the basic mathematical concepts.

Understanding the logic of the mathematical language and the principles of construction mathematical algorithms is vital. This is manifested in the absence of such concepts as change, cause-and-effect consequence, sequence, importance or priority, the concept of order and disorder, the lack of an internal sense of time and the connection of time counting with the rotation of the earth ... All this makes understanding the system of interaction of mathematical algorithms rather problematic.

The Ronald Davis Mathematics Correction Program establishes all of the above concepts and concepts, and then lays down basic arithmetic and mathematical operations on this solid foundation.

This program is one of the longest.

The main stages of the correction program:

- obtaining internal tools for controlling attention;

- with the help of tools, a person learns to explore the material to identify confusion and ways to eliminate it;

- mastering the missing concepts for understanding mathematics (change, consequences, cause-effect, before and after, time, order and disorder, 5 types of sequences: by size, amount, time, importance, arbitrary order);

- and only after that, we proceed to the creation of three-dimensional symbols - numbers from plasticine with mandatory binding to numbers;

- visualization of all principles of arithmetic (decimal system, addition, subtraction, multiplication and division, multiplication table, division with remainder, fractions, decimal fractions, equations, operations with fractions);

-creation of images of the physical world for words used in mathematical tasks and problems, the beginning - remains for homework;

- work on certain topics that are not included in the official part of the correction program, but cause great confusion for the client.

As a result, there is a correlation between all arithmetic operations: addition and subtraction mutually transfer and complement each other, addition in groups turns into multiplication, subtraction in groups turns into division. Then a fractional part appears in the division: common fractions, decimals, percentages, proportion and ratio ... Then you can organically impose simple geometric concepts: perimeter and area, as well as run algebra, for example: the formula for calculating the area of rectangle is suitable for any rectangles, but how can we write it down? - with the help of letters (the lengths of the sides change, but the calculation of the area remains constant), so for the first time letters appear instead of numbers ...

The dyscalculia correction program according to the Ronald Davis method, however, stops at the stage of common fractions, since it is limited in time (30-40 hours). But on such a solid foundation, a wise tutor will lay the rest of the base ...

Thus, summing up the above, I think that it is quite possible to become both a physicist and a lyricist at the same time, if you suddenly want to ...

I wish you success and love for mathematics!

Elena Nikulina

© Copyright 2020

Elena Nikulina, a licensed DDAI (Davis Dyslexia Association International) specialist in the correction of dyslexia, dyscalculia, dysgraphia, dyspraxia, Attention Deficit Disorder with or without Hypo/Hyperactivity, and other learning problems using the original method of Ronald Davis, Director of Dyslexia Correction and Support Center , London, Great Britain. www.fixdyslexia.com

For more information on how to correct dyslexia, ADD, and other learning problems, see Ronald Davies's The Gift of Dyslexia and The Gift of Learning.

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