Zhenya conducts master classes, igrotech, clubs, festivals and tourist gatherings, goes with children in water, hiking and ski trips, writes books for children and their parents. And most importantly, she knows everything about when you need to start doing math with a child and how to do it correctly. And Zhenya is a mother of two children and a happy wife.
How the idea appeared and how the unusual mathematician Zhenya Katz appeared – about this in our conversation with the author.
HAPPY PARENTS Zhenya, let’s start from the very beginning. A child has appeared in the family. Some parents are enthusiastic right away — when he doesn’t hold his head — to start learning letters and numbers.
Frankly, I myself was so – I hung the bed with training pictures. What do you say as an experienced teacher: when do you start to do mathematics?
Isn’t it harmful to teach, say, two-year-olds figures? And why is fun mathematics for preschoolers Zhenya Katz interesting in this sense?
Zhenya Katz: This is neither harmful nor useful. With the same success, you can teach a crumb at least to hieroglyphs.
If the child likes to memorize abstract pictures, you can play with it, but the numbers themselves are not needed in two years. It is more useful to teach him to say hello, to give a hand in a round dance, to play games by the rules, to build towers of cubes or sandpipers.
In 3-4 years, it is important to be able to “translate from language to language”: if I said “meow” four times, then I need to show four fingers, and if I said “woof-woof”, jump twice. After all, knowing the numbers does not mean being able to count.
Many children can count up to a hundred in order, but at the same time, if they need to show “six” on their fingers, they first recount five fingers on one hand, and then they add one finger on the other hand. This is normal.
In this case, it would be good to teach the child, say, to show 4–5–6 fingers in different ways (for example, “six” can be shown as five plus one, or four plus two, or three plus three). This is much more useful than memorizing the table of addition.
Just count – whether the cups and spoons are equal? Will there be enough apples for everyone?
Is it possible to split all the cakes equally? There is a good book by Leonid Wenger, where there are many excellent methodological ideas: “Home School of Thinking”.
You can also play with the child in finger games, in different constructors and cubes.
SR: But maybe, doing with the baby, and the account, and logic, and geometry, mother still works for his future, lays a strong foundation, gives impetus to its development?
Zhenya Katz: Not at all. It is possible for a 3-month-old baby to try to put on legs, but this does not mean that he learns to walk earlier and will fall less. When he grows up, matures, will get stronger, then he will go.
So it is here. The child may know the letters in two years, but start reading for himself, with pleasure, only after the first grade.
SR: Then, perhaps, such exercises develop memory? What does Zhenya Katz offer in this case, an unusual mathematics which was created for the youngest?
Zhenya Katz: Memory and attention can and should be developed – in different games, desktop and verbal. You can arrange five toys, ask the child to remember, and then, when he turns away, remove one toy (rearrange, rotate). You can play Memori or memorize five pictures, or add a pattern that is open for a while and then hidden.
All these games are also great develop attention and memory! And it’s not a problem if a child at four years old doesn’t see the difference between the numbers 78 and 87, 46 and 64 and even confuses the numbers 7 and 8 or 6 and 9. Mathematics is the ability to build logical connections, to reason and to understand where did “that”, and where does this come from.
In four years, few of the children cope with this. At this age it is too early to conclude whether the child has the ability to do mathematics or not.
Just talk with him on various topics, read aloud, discuss events from the life and books, invent funny stories. Now, if our front door to the house would be chocolate, would it be convenient? And what if we had milk from the tap and in all the buckets and in the washbasin there was milk, like in the cartoon Prostokvashino – would we be comfortable?
Or, for example, another exercise for the age of 4–5 years. A few chestnuts are put in a candy box with cells – not as horrible, but in groups of two or three. Say 2 + 2 + 1 chestnut.
Or from one edge one chestnut, three in the center and from the other edge another one. The child watches them for a while, then the box closes.
And he, presenting the picture in his mind, must calculate how many chestnuts there were. Some kids on their knees draw the location of chestnuts (as they saw them) and consider these points as a finger.
This is already a meaningful action – the child considers groups. He remembered the chestnuts in the box in this form, and if you shift them, it will be a completely different count.
SR: Russian mathematicians have long been famous throughout the world. There is even such a saying: in American universities, Russians teach mathematics, and Chinese learn from them. But this is a high school.
In the field of secondary education, Finland has shown brilliant results (it has been ranked first on international PISA tests in recent years). In which countries do they work best with babies?
Zhenya Katz: I can not say that I saw something amazing abroad, which is not with us. Yes, there is a Singaporean technique, there is a Japanese one (“Kumon”), there are various others, but.
All of them are more likely to develop perseverance, fine motor skills, but not mathematical abilities! But in our country there are very interesting methods. For example, the one that one St. Petersburg dad invented and develops now, Sergey Parkhomenko.
A psychologist by training, he previously conducted business training for adults, but at one point decided for his five-year-old son to organize a “home circle”, which he called the “Gang of clever men”. There they “played” mathematics: they developed a little memory, played a little board games, experimented, learned to reason (why the candle stopped burning when it was covered with a glass, why the ball did not fall out of the bucket, untwisted on a string, like blue and yellow paints get other colors). Here it is – real fun math for preschoolers, unusual math!
Based on these lessons, Sergey released several board games, and, believe me, these are great games for practicing math from 5–6 years and for the whole elementary school.
SR: How was your own methodology created and what is it? How was born the circle of Eugene Katz?
Zhenya Katz: It all started with the fact that I, at the request of my daughter’s teacher, came to school to lead a circle for second-graders. Gave tasks to the level of her daughter.
But it turned out that of the whole group, only my Galya and another boy solve such problems. The rest tried to guess the answer in my eyes.
I began to pick up tasks so that they were very simple, but interesting, so that children could easily solve the first and second tasks and “with overclocking” could cope with more complex ones. From these lessons, a collection of problems for elementary school “Mathematics in your hands” was born.
Can children study according to your books or parents should help them?
Zhenya Katz: Yes, many children do it themselves – we tried to do in the Myshematika (workbooks of the Unusual Mathematics series, the author Zhenya Katz – Approx. Ed.) The text of the tasks as simple and clear as possible. In addition, each task has an example, looking at which you can understand what is required to be done.
These are not school textbooks, so tasks can be solved in any order, skipping, and then returning again. My books were designed to show that mathematics is interesting!
Wouldn’t children be bored in school if they learn a lot before the first grade?
Zhenya Katz: No, it will not. In the classroom we preschoolers “build the foundation” and almost do not touch the school math.
We have fun mathematics for preschoolers! Simply in a game form we help to master the new information about the world of numbers, about geometry, about logic – using simple examples that are understandable to kids.
Are you involved in geometry with preschool children?
Zhenya Katz: Our geometry, of course, does not look like school geometry. We do not draw circles and perpendiculars, but we are engaged in puzzles, we put figures of tangram or Nikitin cubes.
Fold the pattern according to the scheme or from two triangles to get a rectangle – this is the real geometry. With two and a half years, you can perfectly “play” in it.
And at six, and at seven years old, you can also do tasks with cubes, if they are interesting to the child.
It is also important to encourage and praise the kids for the work done, do you agree?
Zhenya Katz: There are many theories. And no matter how you do, there will always be a theory that explains that you are not doing everything right. I praise a lot, I just like it.
But I do not put any marks, no stars, or flowers. When I give homework, someone performs, and someone does not, but to those who have done, I always say: “Great, you tried, well done!”. Even if everything is at random there.
But if you praise the child, it does not mean that the next time he will do his homework again. Rather, they like to be leading in the game, to be in the center.
And I try to encourage them.
- “Unusual Mathematics. Notebook of logical tasks for children 4 years old “, MCNMO
The first notebook of the series “Unusual Mathematics”, the main goal of which is to invite a child for an exciting walk into the world of logic and mathematics.
- “Pie with mathematics”, ICCME
A collection of “mathematical games” that develop children’s ability to think and reason, sort through options and look for different solutions.
- “Grandma Saws Raspberry Pie”, ICNMO
A cutter book that will help turn reading into an interesting fun game and teach you to “recognize face” new words.
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