The purpose of Math is to teach people to think. It teaches patterns that people can use in real-life situations to resolve problems. Unfortunately, I think a lot of that purpose is lost in today's world of worksheets and lists of isolated "math problems." Children (and adults) do not connect the value of higher level math to everyday life. It is important that you teach your child (or children) how to connect what they are doing to the world around them.
If you are using the Concrete-Pictorial-Abstract method of teaching, you are well on your way of teaching connections from "school work" to the "real world." When I teach parents how to teach, I separate the 3 angles into separate lessons. When I am using that method to teach children, however, they do not even notice that I've changed gears. They just know I am asking them to do the next step. Here's an example of a lesson I used this week with both my daughter and a 2nd grader whom I tutor.
I gave them the (abstract) problem of 17+26. I write it vertically on a piece of paper (small paper, actually - a note pad). I then asked them to solve the problem. Both girls struggled a little, even though we've done similar problems in the past.
Not waiting long for them get frustrated, I pulled out some dimes and pennies and had them show me 17 cents (one dime, seven pennies). Under those coins, I had them show me 26 cents (two dimes, six pennies). I then asked them to put the pennies together and see if they had enough to trade for a dime. They, of course, could and I physically got a dime to trade for ten of the pennies. We stopped and marked on the paper that we now had 3 pennies (in the answer spot) and added one dime (over the tens place in the problem). I then had them count the dimes and they added that answer (4) under the answer bar so that the answer was 43.
I then took it a step farther. In the past, we stopped at that point, but now we needed more to develop the concept. I had both girls write their own story problem for the math equation I had given them. I did the writing (no reason to make it more frustrating - they can do the writing after we've done this a few times). I asked them each to name something that there could be 17 of. My daughter said stuffed animals, my tutoring student said diamond rings. I then asked them to tell me who has the stuffed animals or rings. My daughter said they were hers, my student said her grandmother had them. I then asked if the addition symbol meant they needed more or less of the toys or rings, and they both said more. After writing 2 sentences, I told them the answer bar meant we needed a question. They both needed help coming up with a question related to the problem, but I happily helped them at that point by giving them 2 different questions which would be acceptable and let them choose which one to use. I know that in the near future, I will not always need to help them so much, but it's okay to give a lot of help when learning a new concept. Here are the Math problems we ended up with:
(1) I had 17 stuffed animals. I had 26 more in my tent. How many stuffed animals did I have in all?
(2) My grandmother had 17 diamond rings. She had a girl party and got 26 more. How many diamond rings did she have for the party?
(hmmm...If it's going to get me 26 diamond rings, I might want to figure out what this girl party is and have one myself -haha!)
We then read over the problem a couple of times, allowing the girls to each read aloud the story problem she had written and making sure they saw that it matched the numbers in the math problem we had solved first. After that, we did one more problem in the same way, though for my tutoring student, we chose a subtraction problem (with regrouping).
NOTE: these lessons were separate for each girl, but it would have been educational, also, if they had been at the same time so they could compare their story problems.
That was the entire Math lesson. It took about 20 - 30 minutes, but I believe they got much more out of it than if I would have given them a worksheet with 25 addition problems on it. I want them to understand how math connects to the real world, because when they become adults, I want them to be able to think for themselves, and math is a monumental piece to that incredibly complex problem of developing reason.
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