## Alternative Ways to Teach Mathematics for Common Core – in response to video for TERC

03 Aug

Note this link comes from a site that clearly has a negative opinion about these alternative methods.  Is she justified?  Well, let’s not jump to conclusions and say, “Yes.”  I think the answer is “almost yes.”  I am a firm believer that nothing is ever black and white.  Common Core mathematics encourages students to learn alternative ways of thinking about mathematics.  They encourage students to delve deeper into the meaning behind the computation.  They want students to know the meaning behind an algorithm at a mature level.  This is a very LOFTY goal.  In fact, after doing my dissertation, I learned that many teachers don’t even have this level of understanding.  My daughter was taking 5th grade mathematics this past year using the North Carolina Common Core curriculum.  She was required to solve all her problems three different ways and then she had to write a journal entry that explained the WHY behind what she did.  This really isn’t too far off from what is in these videos.  Of course she was also taught or allowed to use the standard algorithm, but only in addition to other less effective algorithms that she had to learn.  These less effective algorithms were meant to build her conceptual understanding.  Was it effective?  I really don’t think so.  I don’t think you need alternative algorithms to build conceptual knowledge.  I think you can just build conceptual knowledge with good teaching.

For example, I have no idea how TERC might teach adding mixed numbers but when I look at how to teach this I know that some teachers (most) would teach it by just teaching the algorithm:

2 3/4 + 1 3/4

1.  Add 3/4 + 3/4  = 6/4

2.  Convert 6/4 to    1    2/4

3.  Add the whole number pieces:  2 + 1 + the extra 1 from step 2 = 3

4.  Final answer 3    2/4  or reduce to 3  1/2

However, a better approach might be to demonstrate this with a concrete approach rather than starting abstractly with just numbers.

Draw 2 and 3/4 a pies and another 1 3/4 pies.  Show how you can move one piece of the second partial pie to fill up the other partial pie, giving you 3 full pies and  2/4 left over pie (or 1/2 left over pie) – final answer 3 2/4 or 3 1/2.

From here you can now relate the concrete picture to the abstract numbers.