Learning Addition with a little Montessori

Bug, who is about to turn 5, has been learning addition this year.  My background is in Montessori, and we emphasize the concepts of the various operations when the children are 4 and 5, so that's what I've been trying to do with Bug.  Addition is putting together; subtraction is taking away; multiplication is putting together the same quantity; and division is sharing equally.  When children understand these concepts well, they have a great foundation for future mathematics study. 

I showed him addition with the Montessori Golden Bead material first.  The golden bead material contains thousand cubes, hundred squares, ten bars, and unit beads.  This allows the children to have a concrete impression of our base-10 number system.  We added some 4-digit quantities this way.  I'm not sure it quite clicked for Bug at that point, but it's hard to say, as so much goes on with him internally that I don't know about.  It's very different working with this material at home than it is in a classroom, where he would have been watching the older children work with this material. 

He's also done some addition on his fingers, and this week I had him do some addition problems using seashells as counters.  Both times he did this, I wrote five one-digit problems on a colorful piece of paper and had him answer them.  At this point, it was clear to me that he understands the concept of addition. 

He has been very enthusiastic.  He's a tad too perfectionist about getting his numbers to look just the way he wants them, but I can deal with that.  Today, I was so happy because he made worksheets for his brother and his dad (and himself!).  His brother and dad were happy to humor him by answering the problems. 

Later this week, I hope to show him addition with carrying on the golden bead material.  This is not for accuracy, it's just to give them impression of what happens when we carry, and how we can't go over 10 in each place value. 

I do not think the Montessori materials are necessary for teaching children math at home.  I have them mainly because they have such sentimental value for me.  They are extremely helpful, but there are many good ways of showing math to young children.  I think the most important thing is that children have a solid understanding of how the operations work. 
He'll eventually move onto another Montessori material, called the Stamp Game, that allows children to work with 4-digit quantities in a concrete way.  We'll also be working over the coming months with memorizing his addition, subtraction, multiplication, and division facts, with a goal of finishing these by the time he finishes second grade.  I'm hoping that computer games will prove to be a good tool for him in the memorization process (as they were for me once upon at time), but these did not work for his brother. 

Hurray for math!  So far, it's been my favorite homeschool subject to facilitate.  I supposed that is odd, since I am a former English and Classics major.  My children's other parent is a mathematician; perhaps that motivates me.