The fifth myth of education The calculator

The fifth myth:               Pupils with good and cheap calculators have no need for mental arithmetic.

5                   Miniräknaren ger bara en uträkning av vad som har matats in på den. Den lär eleven ingenting om räkning, mer än på mycket låg nivå.

Nowadays you often meet math teachers in school, who believe that the pupils can make math without mental arithmetic. The pupils have the calculators.

Pedagogical research often stay out of easy project, like showing the effect of bad or even worse skills in mental arithmetic.

You can easily divide the pupils into two groups. The first group is all the children that are going to have difficulties with math early and also have a bad self-image for their results. This group has low results on speed tests in mental arithmetic. The result is black and white. No chance to misunderstand and with no need of calculating any significance result.

I will below try to explain how it works and also how the school sometimes do wrong. But also, how you as a parent easily can help.

I will also tell you about the automatic processes in your brain and the subconscious work in it and how this goes with the pupils learning of math.

Building Math knowledge and math skills is like building a house. Basic knowledge of things like numbers, quantity and ordinals and the understanding of the position system are using mental arithmetic as concrete and then we build further with logic. We can build up to any height. But if the ground is bad prepared, the house will soon fall down.

We give children very different opportunities when they grow up talking about learning counting. Some talk about talent. I have never seen any proof of that. But my observations made it very clear for me that all children have the resources for learning counting. Even children with Down syndrome and their likes.

All children are born with simple ways of observing the change of one item for two of the kind, and maybe more than that.

Through the use of language and communication around the baby, they notice quantity “look, two cars” or order “This is the second time today”.

When later the baby starts more active to take part in communications these knowledge is getting stronger. Quite early we have communication with quantity.

If the family is child oriented, will storytelling, rhymes and songs every day deliver knowledge with counting. If the parents also use movements with the body by rhyming and singing, learning is even faster.

The chance to take part of activities is also unfair distributed between children. In a children friendly family, the child can always take part on their own conditions. Hereby they learn a lot of basic math quite early. Other children are told to go out and play and not to be disturbing.

Games in many forms train math much better than beginners’ math books, the kinds that are used in the schools. But it of course matters what games they play. They include many different forms of counting and train very different.

Please compare the use of computer game, where you are supposed to shoot down soldiers or monsters with a card game, where points are to be counted together and compared.

Almost all children’s outdoor and indoor games give time for learning counting. Especially when there are children at different ages taking part. Sometimes you have to have the knowledge and skill to be able to take part. Remember that children always learn what they see as important.

Parents and personal in pre-schools can easy help the children to learn the pattern of the ten numbers we use. Take all chances to use big and clear numbers. Don´t miss to use the numbers in your communication with the small children. “Our house is number 29”, “Your birthday is on the 14^th of June”.

Also, calculators can be used by the small children. I myself learned a lot of counting and calculating with my mother’s mechanical computing machine operated by a crank. The problem here is that the baby has to realize what´s going on. This means that it has to first be training with what´s called laboratory material in the school. Actually, anything countable. I counted my mother’s cooking things in the kitchen, but also wooden toys.

We are now talking of simple addition from 0 – 10. Most children master this rather early. Attending school later on, they are often treated as if they didn´t understand anything in the math books. Children who play many board games, often control the counting in the space of 0 – 1000 before entering school.

Subtraction is often a part of the game. You have to pay taxes in Monopoly, you buy things and so on.

Simple division is also a part of the games. We divide all children into teams or groups.

Multiplication has often been said a tough thing to learn, but in the game, they learn it easy. A lot of useful laboratory material are rather cheap to buy, but can easily be produced in the family. “So, you want to buy 4 bananas. They are 50 cents each.” Most children like to play shopkeepers and customers.

The earlier the children meet all forms of math and the use of math, the more skills and knowledge they build up.

I strongly go for not using math books. Not at home, but also not in school. There are several reasons for that. Math is to be used and trained hear and now together with the children. Math is a tool to discover the world with and to calculate have things really are working. The most important reason is that the math books underestimate most children, and tell the rest that they are no good.

Working with our brains to learn something or to use knowledge or skills, that we already master, there is one slow, carefully and conscious way. It´s useful when you are trying to learn something or to understand something. But for normal work it´s useless slow. We need automatic memory functions supported in our fantastic brain. This part of our brain is unconscious. They are working like highways with a flying start.

To get your driving license, you re trained until you have got automatic processes for most of your driving. The idea is that you have no time for thinking, when a child runs out in front of you. Mastering all this in a test and the license is yours.

The same goes for walking, running, biking and counting, but no license.

To add 12 and 23 you need to understand what the numbers are, the position system with the base of ten they work in and addition between 0 and 10. Both numbers and also the sum is greater than ten, but you make it here with simple addition.

A pupil who under many years use the slow method in his brain, is also slowly telling himself that he is no good compared to others. In the same manner, it works when they all the time have to pick up the calculator or ask the teacher to borrow one. The slow pupil will do less work and is getting more and more behind.

If this pupil had played Yatzy with his family, there would be addition skills ready.

We measure the automatic processes of mental arithmetic with speed tests. The tests show if the pupil lacks anything in the knowledge and skills with mental arithmetic. Rather many pass the school without that kind of tests. Thereby there is a dangerous lack of information.

Some mental arithmetic knowledge is rare that you get from playing games. The school must always calculate with that every pupil has some learning to do when starting school. But please let all children start where they are, they are individuals. Throw the math book into a museum!

Instead of math books pre-school and school should go for talking about measuring and calculation to solve problems they find by themselves. “I wonder how much water we need when we change water in our aquarium”. Adults around that child gather all in the group and start a discussion. How can we get to know? How do we measure? When do we do it? We bake a cake och look at the recipe. That is real math. It´s all around us every day. The body measures, measure of time and time itself.

But every child has also an own individual development. In the future, through international cooperation, we must produce good material for presentations and training for the individuals in all math areas. Place all on the internet, so it can be reached whenever the pupils want it and need it. Some is graded into levels coming after each other. But with the possible choice of the pupil.

Much of that kind of material, films of instructions, slides with explanations, small apps showing results, is possible to be produced by older pupils, who thereby get broader knowledge and skills in math.

Later, further analyses will be published in this area.

Goa the 12th of February 2017              Lennart Warenius