MouseMatics: Unusual Math For 4 Year Olds (Volume 4) (Russian Edition)

You now have in your hands a far from ordinary workbook for the ordinary subject of mathematics.

There is a multitude of books and aids that help preschoolers become familiar with mathematics. All these aids introduce children to the world of numbers and geometric figures, teach them to tell numbers apart, continue patterns, and find identical pictures. The problems and tasks presented in all these books are more or less similar: connect identical shapes, find the odd one out in a set, count the number of objects, add or subtract, find the largest object, connect the dots to write the number 3, number 4, number 5, and so on.

However, the standard exercises conceal several dangers. First, they perpetuate unnecessary stereotypes to which the child quickly becomes accustomed. For instance, if the child needs to find an odd one out in a set, there may be only one correct answer. If the child is asked to match identical figures, there will be exactly one match for each figure, and the counterpart will be located in a different column. The child perceives the instructions and solutions as the “rules of the game” and learns to follow them, and is stumped by the smallest exception to these rules – say, there are two different ways to exclude an extra object or there are three matching shapes. There are also hidden, but pervasive visual stereotypes: children often memorize images and connect them with the required words; for instance, they know that a picture with dots drawn in the corners of a square is called “four”, and an identical picture with an extra dot in the middle is called “five”. But can they recognize the same number five if it looks different?
These stereotypes interfere with a child’s ability to master counting, and constrict the child’s freedom of thought. Therefore, in this workbook we try to break as many stereotypes as possible.
-In some problems, we have two correct solutions (a pair of friends can split a chocolate bar in different ways). After all, in mathematics no solution is also a solution
-A matching pair of shapes can be found in the same column.
-We build geometric figures using not only the usual squares, but also diamonds, trapezoids, and triangles
-When the child is asked to find a number value, we use a variety of shapes in addition to dots: diamonds, crosses, anything. Also, their arrangements in the boxes are random, unlike the standard dice configurations.

Second, often the same types of exercises do not change throughout the book, so children become used to them and complete them robotically. On the one hand, this is good: children master certain operations and gain useful skills. On the other hand, if they are subsequently asked to quickly switch to a similar problem but with a larger number range (1 to 10), they might have not had enough time to really master counting to five, so they will start trying to guess the correct answer. Their guesses will be based on what they learned from previous exercises, or on the look in the teacher’s eyes; or they will just try shooting in the dark. In order to avoid robotic guessing, we take the following measures:
-Quantity, numbers, digits, and their relationships to each other are approached from several angles, including unorthodox ones;
-Exercises of the same type become gradually more complicated;
-All tasks stay within the 1 to 5 counting range, so that the child has ample time to understand the concepts introduced and master counting these numbers.
Third, always doing the same exercises is just boring. Yet, mathematics includes so many beautiful and interesting topics! We have tried to create this workbooks as a compilation of unconventional, not obvious tasks that are easily understandable for four-year-olds. While doing so, we have focused not on counting itself, for its own sake, but on the fact that it might be interesting to think and find your own solutions.