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Common Core or Common Sense?

4/9/2013

1 Comment

 
This evening I attended the Math + Science Teacher Forum hosted by the Philadelphia Education Fund and can honestly say my world was rocked.

The session I went to was about how to think about unit placement and place value for middle school students, but really applies to all students across the board. During the conversation we talked a bit about how the emphases in the Common Core curriculum are supposed to focus more on the conceptual basis for how we do things like multiplying 34x38 but on the ground in schools teachers are still using the same pedagogical tools.

The thrust of the argument is this: more often than not math teachers are teaching procedures and specific guided techniques instead of the concepts behind the mathematics. This might be so because our teachers are poorly trained or because the tests don't emphasize enough of the concepts or some other reason. Whatever it is, the problem exists and we are tasked with fixing it. 

So, now for the example:
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This session was run by Dr. Ellen Clay of the Math Forum, a wonderful group from Drexel University that tries to make sure math teachers do a good job. They have a lot of resources, including sessions like this one. 

The basic problem is multiplying 34x38, as I mentioned earlier. If you are like me, you learned to set it up this way and use the procedure where you multiply the 4 and the 8, then the 3 and the 8, then the 4 and the 3, then the 3 and the 3. If you complete the steps correctly, you will get an answer of 1292. 

This is all well and good, but it is such an isolated skill. With some deeper understanding, you can connect it to fractions, polynomials, and more. Let's take a closer look.

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Instead of thinking of the numbers as blocks like "34" or "38," Dr. Clay suggests we think of them in groups. 34 is 3 tens and 4 ones. 38 is 3 tens and 8 ones. So multiplication becomes a series of "unit matching" problems. 

If you see the text at the top, it says "3 tens times 3 tens = 9 hundreds;" then "3 tens times 8 ones is 24 tens" and so on and so forth. Instead of using a procedure, we are thinking about the units being used. Since we know that 3x3 = 9 and tens x tens = hundreds, we can conceive of 900 in a deeper way. We still get the same, correct, answer, but now we can apply it elsewhere.

This then extends to if you had a math problem like (x + 3)(x - 2). Now I am multiplying "1 x times 1 x = 1 x^2" and "1 x times -2 ones = -2 x's." It doesn't look so good in text, but I hope you get the idea. 


If we want to get some use out of the Common Core we need to understand the mathematics at a deeper level and learn methods to explain that deeper level to our students. Dr. Clay and the Math Forum will help that happen.

1 Comment
KD Davenport
4/9/2013 08:29:36 pm

The use of "procedures" for work involving fractions is something that has bugged me for a while. Fractions are hard, and by high school kids are "supposed" to already have mastered them. But many haven't. So one way to help kids to get the right answer to a physics problem, for example, is to teach them a procedure that they can use that doesn't involve understanding how fractions work.

I recently worked with a chemistry student who had a "procedure" (some kind of a box system) for solving dimensional analysis problem. It worked great until anything about the problem was SLIGHTLY different than what she was used to...then she had no idea what to do. She had no understanding these boxes even represented fractions!

I'm not blaming our chem/physics colleagues--I feel sympathy for what they're dealing with. If our bottom line is that a student will take a test on which their learning is measured by a few dozen right answers, then teachers are caught between giving students a method that WILL WORK for the few types of "standardized" problems they will see, and the messier world of working with concepts and ideas.

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    I am a math teacher in the New York Department of Education. I infuse technology and real-world problems into my curriculum in order to prepare my students for the future. I would love for people across the country to recognize we teachers can't do it alone. If you don't believe me, come visit my classroom!

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