Teaching young children math
ruth beechick talks about this in her book 'an easy start in arithmetic"!
The best way to begin teaching a young child math is with manipulative, such as bugs, rocks, pennies, marbles, m & ms, socks, any objects you can count with. It can be taught anytime throughout your day, when your doing laundry, putting socks together, counting them, setting the table, counting the silverware, glasses, plates etc. Remember to make it fun for you and the child!!
Using manipulative like this, the kids can then figure out some very hard problems! Just holding and seeing the objects clicks in their young brains. When most kids are young they don’t think of a math problem as we do 1+3=4 , they need something more hands on so they can touch it and feel it to understand its value, once they learn this way of doing math the other steps wont be as hard. This is the first step of how other types of math will be understood.
After the child gets use to using the manipulative she/he will be able to picture the things in their head, he/she will be able to see them and work out the easier problems. When he/she is ready to move on to the next step, you’ll know because the child will not be using the manipulative as much, she/he will start picturing the problem in her head, finding a faster way to figure math problems out!!! Then it’s on to step 2!!!
From ruth beechick booklet "an early start in arithmetic'
Levels of thinking about (example 3 + 2 = 5) or any other numbers
Real objects, with touching and moving: three plates or spoons, marbles, jacks, rocks, bugs etc, put two more with them. now there are five
Real objects, with only sight: 3 jacks in this group, 2 jacks in another group, there are 5 all together
Pictures: picture of 3 jacks in a group and 2 in another group. 5 total
Symbolic pictures: 3 dots in this group and 2 in another group. 5 total
Mental image mode-
Touchable objects: think of 3 jacks and 2 jacks. they make 5 all together. (story problems)
Non-touchable ideas: a team won 3 games and lost 2 games. they played 5 games all together.
Digits only: 3 and 2 are 5
Digits and signs: 3 + 2= 5