#MondayMathBite

So, I posted a few weeks ago about "talking someone off the ledge" of hating the Common Core State Standards in a casual coffee shop conversation.  It started simply enough, when an older couple I run into often simply asked me what I thought of the Common Core Standards.  If you know me, you know that conversation lasted through my caramel macciato, and then some.  Then, last week, I had a similar conversation with my grandfather over dinner.  I talked him off the ledge too, with the help of some choice textual evidence from a primary mathematics textbook first published in 1897 (for more on that, keep reading).  Since then, I have had the greatest of intentions to actually pen an article... something to the effect of, "How to Explain Common Core to Friends and Family Who Are Not Teachers Who Think You, As a Teacher, Are Ruining the Youth of America By Making Math Harder".  The title still needs some work, but you get the idea.  In the meantime, I am starting #MondayMathBite, a little tidbit of insight into the Common Core State Standards for Mathematics (CCSSM) for teachers and non-teachers alike to start your week.

Today, I present to you, a subtraction problem going around Facebook that has struck fear into the hearts of students, parents, and the general public at large:

First of all, can we stop using the descriptors "old" and "new"? Because, guess what?  The actual mathematics has not changed.  Not only that, but the idea that we want students to have a conceptual understanding of the mathematics behind what they're doing is not a "new" idea.  I recently started playing with Google Books and found a 103 year old primary mathematics textbook called How To Teach Arithmetic.  Yes, they taught math 100 years ago.  And yes, 32-12 was still 20 100 years ago.  The section in the book on teaching subtraction begins, "Addition and subtraction are so closely related that they may be taught simultaneously, particularly if the [additive method] of subtraction is employed. It advocates "subtracting by adding" rather than by "taking from" or "borrowing." (Brown & Coffman, p. 160)  So, the "new" way seen in the problem above is decidedly "old".  We all have experience with "subtracting by adding".  Primary students are often taught to "count up" when first learning subtraction, and the last time you shopped and paid with cash, the cashier most likely used this strategy (which Brown & Coffman claim dates to the sixteenth century) to count out your change to you.  The cashier probably even used a method similar to the dreaded "new way" in this problem, "$12 total, $13, $14, $15 (3 one dollar bills), $20 (one five dollar bill), $30 (one ten dollar bill), $31, $32 (two more one dollar bills), so why are so many people freaking out about this?  This problem shows ONE of the strategies for subtracting, a strategy which happens to be a pretty darn good one that is used by many people on a daily basis.  Other strategies could include using tape diagrams, number lines, base ten blocks, a 99 chart, estimation, etc;

Common Core aims to help students connect to the math through a deeper conceptual understanding, and therein lies the power of this "new way"... which really isn't new at all.  32-12 is not 20 because 2-2=0 and 3-2=1 (the algorithm shown in the "old way").  It is much deeper than that.  As we ask students to compose and decompose numbers, to contextualize and decontextualize problems, we are also going to be asking students to come up with multiple strategies and to explain their thinking.  Will it take longer?  Probably.  Will it benefit our students?  Absolutely, and the growth will not just in their mathematics.  Students who regularly engage in the Standards for Mathematical Practice, another facet of the Common Core State Standards for Mathematics will grow by leaps and bounds in their language skills as well; I've seen this firsthand in my classroom, made up of more than 60% English Learners.  Why are we doing this?  Because we're trying to prepare students for the real world, one in which they will have to think outside the box.  Imagine that.