In our last math class, my "aha moment" came when we learned how to use algebra tiles to uncover algebraic concepts. It took a couple of example problems, but once I saw how the algebra tiles worked I realized their potential as a learning tool - especially as a visual representation of rules like "FOIL" - rules that we were simply given and expected to memorize back in the day.
A question I have about using inquiry based techniques like algebra tiles for teaching math concepts is how to introduce them to a classroom with a scripted, direct instruction based, curriculum. My gut feeling is that these techniques would increase comprehension in my main placement classroom. However, I can see an inquiry based approach like algebra taking up more teaching time, therefore, the idea would meet with resistance.
In my main placement classroom, as stated, my feeling is that using manipulatives like algebra tiles would help some of our struggling kids "get it." Simply re-iterating the rule isn't working for them. We're currently using a FOIL technique called multiplication wrestling to teach double digit multiplication. The kids take each double digit number in the problem, separate it into 10s and 1s, and then multiply all the numbers together using FOIL. For instance, the kids would write out 32*49 as (30+2)*(40+9). Then the 30 and the 2 need to wrestle the 40 and the 9 (30*40, 30*9, 2*40, 2*9). The results are added together to get an answer. Many kids get this, but many do not, and going over the rules again isn't helping things sink in. I'd be interested to see whether these kids are helped by using a manipulative technique.
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