31 March 2014

Common Core Mathematics

Plenty of people are still complaining about Common Core standards.  See this Yahoo! post for a recent example.

The complaints have nothing to do with the Common Core Standards.

The Common Core are simply a set of objectives.

Let's just look at one of the math standards for third graders.

Apply properties of operations as strategies to multiply and divide.

What would this look like in a student's work?  The answer to this question can vary from school to school and teacher to teacher.  Essentially the goal requires students to demonstrate they understand place value and basic number theory.

Here's an example to make it clear:

e.g. 12 x 9 =

If you were taught like me, you learned to solve this problem using an arbitrary algorithm that was very difficult to understand.  First, multiply the 2 and 9.  That equals 18.  Write down the 8 and carry the 1.  Now multiply 9 times 1 and then add the 1 to that.  Write down the answer next to the 8.  108 is the answer. 

Unfortunately most of us who were taught this method of multiplication could find the answer but had no idea why.  Calvin sums this approach up very nicely:

In bizarre routine of indoctrination all of us sat in classrooms and at kitchen tables scribbling away carrying ones and threes and adding and subtracting hoping we were getting close but not really ever knowing if we had the answer correct until we were given the answers.

There are plenty of alternative strategies to the old formulaic algorithm that students can use that also demonstrate their understanding. 

Let's take a look at the equation using a different approach.

12 x 9 =

12 is equal to 10 + 2.  10 x 9 (10 sets of 9 or 9+9+9+9+9+9+9+9+9+9) = 90.  2 x 9 (2 sets of 9 or 9 + 9) = 18.  90+18=90+10+8=108.


While for those of us trained in the traditional algorithm might look at this with incredulity, just think about how many problems we sat solving without ever really understanding what was happening.

We learned via rote practice.   Students today have the opportunity to learn via understanding.

The Common Core Standards have nothing to do with worksheets or homework or testing.  They are a set of objectives plain and simple that encourage deeper educational exploration by both teachers and students.

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