Navigating away from "mile wide and inch deep"

The analogy of math curricula as a river has been used frequently, with  the familiar "mile wide and inch deep" used often.  It is a compact way to describe a set of standards that tried to "cover" many different topics and left many students struggling to master math concepts.

With the Common Core, what is the alternative analogy?  Someone recently asked, "Is the curricula now an inch wide and a mile deep?"  That does not seem like an appropriate way to describe the Common Core.  I'm sure that many analogies will emerge as people become more familiar with the Common Core.

The big idea of the Common Core is to help students develop those important mathematical practices.  Children are naturally curious and wonder about many things.  We want to nurture this curiosity but all too often in mathematics students are taught a "rule" without understanding why it works.  The Common Core is going to push ALL of us to further consider the WHY things work.

For example, my son is in second grade.  Recently he came home from school and was proud that he could identify any number as either even or odd.  After giving him a couple of numbers to identify, I asked him whether he knew why 43, for example, was odd.  He recited the rule about the ones place having a 3 so it was odd.  We then had a discussion about why the ones place was important.  Any number that is a multiple of 10, 100 and so on will always be even because it can be grouped in pairs.  So if you think of 43 as 40 + 3 then you know there will be 20 pairs in the 40 and that there can only be one pair made from the 3 with one remaining.  We looked at several other numbers to test this theory and my son talked about what he noticed in the relationships of the numbers.

THIS is what we can do as educators to help implement the Common Core.  Think about WHY the rules in mathematics work.  If you aren't sure yourself, don't be afraid to ask your students.  They are curious by nature and will enjoy working alongside you to notice patterns and relationships in mathematics.