My answer to a question in Quora: What should we do to stop calculators hindering children’s math learning?
It is the best kept secret about mathematics: mathematics is done by the subconscious. Learning mathematics means learning to communicate with, engage one’s subconscious. I wrote about that in my answer to As a mathematician, how would you mentor your child and help her to learn, do and live mathematics in her free time as she is growing up?
Calculators do not help child to engage his/her subconscious. There is a class arithmetic problems that help: these are word problems. An easy example:
A girl said: “I have three more brothers than sisters”. How many more boys are there in her family than girls?
Is calculator needed? No. Is thinking needed? Yes.
If you think that word problems are so-o 20th century, let us add a twist more suitable for the 21st century. Why not give children a toy programming language, say Scratch, and ask them to produce their answers as a code in Scratch which solves all problems of that type.
For an example, let us consider a simpler problem:
A girl said: “I have two sisters”. How many girls are in the family?
On the screen, it will be child’s favorite sprite (a term from
Scratch , a programmable object, usually chosen to be some cute animated object, say, a cat, or dog – very easy to control and manipulate) who starts data input dialogue by asking
- Are you a girl or a boy?
- How many sisters do you have?
And returns: “aha, you have [output] girls in your family!”
Please notice – what we have here is (a) creating a model of a real life situation, and (b) implementing it as a computer algorithm. And it is doable in Scratch. And also notice: at no stage calculators are needed.