What's the point of Common Core math? Why is it so confusing?

Question

When I get this question, typically parents are frustrated with the non-traditional math methods. Sadly, the point of these non-traditional approaches to math is frequently not understood by the classroom teacher. Thus, it leads students and parents confused while wasting precious classroom time!

There are 3 stages to a quality math unit:

1. Conceptual Understanding--This is the phase where teachers should explore concepts using manipulatives and other visual models. It is important to incorporate pre-requisite math skills for the concept about to be taught during this phase to ensure a solid foundation for the skill.
2. Representational Understanding--After students have developed conceptual understanding, it's time to transition them to Representational Understanding. This is where students further their understanding of the skill. This phase is the most misunderstood phase! Here are some examples of activities to develop Representational Understanding:
3. Drawing pictures (instead of using manipulatives) to make meaning
4. Using tally marks
5. Temporary methods of calculation: Partial Quotient Division, Lattice Multiplication, Box Division, Front-End Addition, and more.
6. Abstract Understanding--This phase is when students learn the traditional approach.

So many teachers struggle with the Representational Stage (and the non-traditional approaches) because it's not how WE learned math. They often teach a skill at the Conceptual level, then jump to the Abstract level (or if they are really old school, they might only teach the Abstract "traditional" way). When students don't understand, often, teachers will give "more worksheets" for practice (because that's how WE learned!). Then, after the skill is mastered, they backtrack to the non-traditional methods (which is no longer needed). The Representational Stage of Learning should be filled with fun, engaging activities to bridge the gap between Concrete and Abstract.

For example, if as a parent, you've ever seen partial quotient division (phase 2 of long division), it may not make sense why it is taught. The purpose of that specific strategy is to help students "pick" the number needed when doing long division. A student who has learned partial quotient division will transfer the learning to a problem such as 418/7 and "pick" 5 for the first digit of their quotient. Whereas without that skill, there's a ton of guess and checks going on.

Answer 1

"Common Core" was supposed to ensure that students could move from one state to another and not experience wide variations or gaps. If a concept is introduced in the fourth grade in one state (Let's call it "A",) but in the third grade in another (B), then a student that was in the third grade in the state "A" could move to state "B" for fourth grade and be a year behind. Common core was supposed to help with that. How exactly it became so maligned I'm not sure. It was a noble goal and, given the increasing mobility of our society as well as the increased meaninglessness of borders, a timely one. So that was the point of common core. Clearly something went wrong in its implementation.

Why modern Math seems confusing is exactly as the above poster described. For years our focus was on the manipulation of numbers, which are an abstract concept. We skipped the concrete and representational stages. I have only empirical evidence for this assertion, but there was and possibly is something fundamentally wrong with the way we teach Math. Think for a moment on all the people you have heard say, "I can't do Math. I'm just no good at it." These people would never admit to struggling with Reading. The shame in being illiterate is very real. But the shame in being mathematically illiterate is negligible at best. Why? Because there are so many people who ARE.

There is a very real correlation between Music and Math, yet when I was a college academic advisor back in the '90's 50% of our Music majors struggled to complete their Math courses. That told me there was something fundamentally wrong with the way we taught Math. But to those people who are able to instinctively understand the concepts, or who can successfully manipulate the numbers without understanding why, the need for the conceptual and representation phases is confusing. Teachers who never had that type of learning modeled for them as students sometimes have great difficulty implementing it.

For generations, we have tolerated a system of learning that results in failure for a significant part of our population. Trying to find a way out of that will inevitably result in some confusion.