If you do a web search, you'll find articles both supporting and stating manipulatives are worthless but I think so much depends on what you are doing. I've developed a way to use manipulatives that seems to help clarify process for my students while helping others connect things so they understand how to do the process.
For instance. in Algebra I, I pulled out my base 10 manipulatives to show them how to solve two step equations. I designated the 10's as x's and the ones as ones so when I had the problem 2x + 3 = 9. There would be two base 10 blocks with three singles on the right side and nine singles on the other side. I showed them how you take the 3 away on both sides, then divide the remaining singles into two groups.
I then had students try a couple of other problems using the blocks. Once they had the movement down, I began connecting the movements with the process so they could see when they took away 3 blocks on both sides, it was the same as subtracting. When they divided the remaining singles into two groups, it represented dividing by 2. I actually took away three with my hands, and wrote -3 on the problem. When I divided the individual blocks into two groups, I showed that I divided by 2 on the paper.
When I showed them how to solve x/2 + 3 = 5. I explained the 10's bar represented a half an X, like half a cup of flour with 3 extra blocks. So then we removed three from each side and were left with one bar representing half equaling 2. So we have to double the x's to get one so we double the other. It took a few times but the kids learned how to do it. Then we redid the problems showing the movement with the math step by step and they grasped it quickly.
I realize that I should probably let them explore all they want but due to having only 3 students in that class, I don't always have time so I work with them. I like the way this is going. Manipulatives can be used but it takes planning. Let me know what you think, I'd love to hear. Have a great weekend.
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