I am not a fan of drills and I think that making kids do daily worksheets with x addition/subtraction problems is the sort of thing that makes kids conclude that math is a boring subject. That being said, I do think that the skills that the worksheets are trying to develop are essential for exploring more fun and advanced concepts. So how does one make a kid memorize basic arithmetic facts without doing drills? In my opinion the best way is to find games that the kid enjoys playing that involve basic arithmetic operations, or come up with games of your own.
One such game that Katie enjoys playing is Sum Swamp. The way I see it, it’s main purpose is to effectively drill addition and subtraction with small numbers, but the important thing is that Katie does not see it as such! The game consists of a board with a snake-like ‘path’ and three dice: two with the numbers 1-6 on them and one with three +’s and three -‘s. When a player throws the dice he/she has to solve the small arithmetic problem to figure out how many places to advance.
What fun games do you play with your kids that involve basic arithmetic?
Addendum: today we played the ‘how many did I hide’ game with dolls that were sitting on ‘chairs’ (aka, pieces of paper). Katie had to guess first. We had 8 in total and I hid 3 (leaving the chairs behind). She opened her eyes and immediately said three. I was surprised since usually it takes her somewhat longer to do the subtraction in her head, so I decided to ask her how she figured it out. “I counted the empty chairs!” was the reply :-).
Musings of a Mathematical Mom 
It is great that she figured out that empty chairs may be counted. What is even more important is the fact that nobody mentioned this idea to her, and she did it on her own. I agree with you that we do not need to give kids problem solutions immediately. It is much better when they figure them out on their own.
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We were just playing Sum Swamp this afternoon :-).
I was surprised to find that Hannah actually really likes arithmetic worksheets, but I think it’s because they’re kind of like problem solving to her. We didn’t explain borrowing and carrying to her, for example, so she had to figure out how to add/subtract/multiply those pesky two digit numbers on her own, and then test out her algorithms. But, doing those worksheets because you want to is so different from doing problem upon problem using a specific algorithm that someone has taught to you without intuition. Part of my strategy for keeping Hannah interested in math is by staying at least a little ahead of what’s being taught in school, so that she can encounter everything in an open, exploratory way first. And, for now at least, we let her work on whatever strikes her fancy, for as long or short as she wants.
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Kathy, I think that it’s awesome that Hannah comes up with her own algorithms. I also totally agree with you that worksheets aren’t inherently bad. It’s the forcing aspect of drills that I am usually against. If a kid likes doing them (which I must admit Katie often does too :-), then I think that they are often a good way of learning and reinforcing material.
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I think the other important thing to keep in mind is that you want to introduce the same idea in different ways so it really sticks and becomes second nature – so if the situation in which the question is asked changes, they’re not thrown off. Ari often likes to look for similarities between situations – this is like this type of problem, etc, and I think it helps them to understand the ideas in more depth.
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I totally agree with you. I am always on the look out for new ways of exposing Katie to concepts that I already introduced to her. It is also great to see them make the connections. Although I must admit that I often have to fight the temptation of making the connections for her, and not always successfully. Many times when I’m rethinking how I introduced something I feel like I might have said too much. It’s very much a learning experience for me too!
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For some reason, Valya likes to learn from computer games. I think the first one she learned arithmetic from was called JumpStart (free from our library), and the second was Dreambox Learning (web-based and not free). Your solutions sound much more creative, but these also worked.
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Katie plays some computer games on the ipad, although most of the time when we allow her to use it she opts out for the paint program. I think that computer games can be a great supplement, but not substitute, for learning with actual human interactions.
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I now remember that we used to play simple games with cards, e.g. find triples of cards where the sum of the first two is the third, or count a stack of cards, select 5 stuffed animals, and predict how many cards each stuffed animal will get after we deal them out. Another thing that works well is money. Predictably, addition and subtraction are easier when there are physical tokens to play with, but somehow Valya seemed able to predict how much money would be left in a transaction much more often than she would be able to do a subtraction problem correctly in the beginning.
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