Common Core. Those are naughty words in a some circles. These are just a few thoughts about Common Core Math. (Common Core English has totally different issues that are beyond my purview. )
I’m not a math teacher. I don't even play one on TV. My experiences with the evolution of the “new” math of the Common program is gathered through working with my children and my tutorees. This is my fifth year tutoring, and each year I’ve experienced the curriculum change through my students. I primarily work with 5th through 9th graders, and the way my students are spaced, I have a nice cross-section of materials and the way they are evolving. My thoughts about the math program are my own, and are based solely on my own observations.
First off, Common Core took a harpoon gun and nailed both of it’s feet to the deck of the Titanic when they utterly failed to include parents in the how’s and why’s of Common Core Math. I’ve seen some really interesting and thoughtful reinventions of how math is taught as the new lessons have been fleshed out, but I can’t name a single (non-teacher) parent who has any idea what their child is doing, or why. I sincerely LOVE some of these new innovations, but by not educating parents with their children, the designers of this plan have lost their best supporters. Are all parents interested in the details of how math is taught to their children? No. But, those parents who distrust mysterious re-writing of techniques they were raised on, or who actually want to help when homework is frustrating? Those are the parents who make up the icebergs that sink unsinkable education programs.
Through my layman’s observations, the Common Core’s mission is to deepen the understanding of students in mathematical thinking. They want students to understand the greater how’s and why’s of numbers and functions. Instead of taking on faith or blind acceptance, they want young people to have a profound knowledge which is backed up by a framework of mathematical thinking. For example, when I was in grade school we were taught to divide by fractions using the mystical axiom: “Invert and multiply, ours is not to wonder why.” The new curriculum seeks to teach division with fractions by first teaching multiple ways of seeing fractions, then to teach the interrelated relationship of multiplication and division through a range of activities. Only with this base do you encourage the students to formulate their own understanding of division with fractions. All of this teaching is done through multiple methods, which might include physical objects, grids, arrays, coded shapes, words and, finally, numbers.
This brings me to my second serious issue with Common Core math. I love learning multiple ways to solve math problems. I love the ideal of deeper understanding. I am a person who can wake in the night thinking about how many different ways a sum can be calculated, BUT, as much as I appreciate the very thoughtful building of ideas that I see coming from this program, I am often frustrated that there is too little time left to consolidate ideas. When the day ends, and the understanding has been built, the student must be able to do the simple conjuring of facts. They must be able to numerically divide fractions. The algorithm of invert and multiply must be known. It is not prudent, in higher math, to need to draw illustrations to divide fractions. I find students who understand the Why, but they cannot just Do. The Guess and Check process lingers way too long. There isn’t enough emphasis on just Doing The Math. And this lack of nitty gritty doing is another element of this curriculum that frustrates parents who were raised to simply solve the problem.
My third issue: testing. Give me the latitude to use this comparison. The ideals of Common Core Math are akin to the ideals of Communism. (Wait, take a deep breath.) There is beauty in the idea of Common Core Math, just as there is beauty in the idea of true, pure Communism. Communism, the idea of co-ownership, of communal living, of pure-hearted workers striving to live together with the single goal of doing their best, what is not to admire? The rub is when Communism becomes a reality and all of that lack of freedom and poverty kicks in. It doesn’t live on a large scale like it does in theory. Common Core Math, with its goal of deep, fluid thinkers who fully grasp mathematical theory is utopian. The dissolution point is testing. How do you test thought processes? If you encourage multiple paths to understanding, how do you demonstrate that you’ve all arrived at the same destination? Because on the Common Core tests, you can't just given an answer and show your work, they want you to say "WHY". I would say the majority of school children simply do not have the capacity to explain how they think with clarity. Just as Communism strips it’s participants of rights and freedoms, Common Core Testing undermines the tenants it tries to instill. It says, "Think in the these grand expansive ways, and then give me this specific wording as you jump through institutional hoops." If you could remove the tests from the equation, perhaps Common Core could be as idyllic as it intends to be.
I have other, wee beefs with individual elements of curriculum here and there, but these three issues are the big ones for me. Educate and include the parents, make sure the algorithm can be used after the base is built, and let go of the testing.
My intent is to follow up this blog post with other posts hi-lighting techniques in the new Core that I LOVE. I mean, seriously, love. As in, I could build little shrines to. The build up to quadratic equations? I am filled with envy that I did not learn them this way. It’s like finding out that you don’t have to worship a math God that mocks and requires flesh sacrifices. Instead, there is a kind and benevolent Goddess that just wants you to understand. (Of course, I firmly believe that quadratics should be able to be factored without divine intervention. My point is, now that is possible.)