Not long after I attended the conference I wrote about here and here, I ran across a blog post written by Fawn Nguyen on the Common Core State Standards in Mathematics. I was trying to find a good way to summarize my thoughts on the standards, and discovered that the always-eloquent Mrs. Nguyen had already done so in a way that I appreciate and agree with. And since she has many years of teaching experience compared to my 0 years, I’ll let her do the talking.
Focus, Coherence, and Rigor
These three words are the keywords (buzzwords/jargon, if you prefer) of the Common Core State Standards. The standards were designed with these three concepts in mind.
The Common Core standards were designed to focus on the skills that are truly integral to learning and understanding math. The writers actually cut out some skills that were determined to be less important.
One study that was performed recently involved determining the number of skills students are taught in their math classes all over the world, and testing students from all over the world with the tests we use here in the States. The researchers found that the US has one of the highest (if not the highest) numbers of skills taught. However, they lag behind other countries on the results of these tests. Note: you’d think that students in other countries would struggle with skills they had not been explicitly taught. Not so.
The writers of the Common Core believe that this disparity is caused by the “mile wide, inch deep” curriculum we currently have here in the US. We try to teach everything and don’t have enough time to teach anything well. (Take AIMS prep as an example – we spend months teaching students everything they could possibly expect to see on the AIMS tests, but lots of them don’t understand it well enough to actually perform on the test.)
Focus in the Common Core standards means attending to fewer topics in greater depth at any given grade level, giving teachers and students time to complete that grade’s learning. The focus in the standards means that we’re giving ourselves the time to work through the sophistication of the skills we are introducing. Once students have a complete understanding of a skill, they should be able to apply the skill in new ways, so we don’t have to explicitly teach those new ways.
Example: least common denominator. Students have been learning to add and subtract fractions using LCD for … I don’t know … a very long time. But does it really matter if a student uses the least common denominator? Isn’t it more important that she choose some common denominator as long as she can accurately find equivalent fractions? In fact, when she gets to algebra about 5 years down the road, she will have to add a/b + c/d, and will need to understand that the common denominator here is bd.
So the LCD has been removed from the CCSS. It’s not there. Common denominator is, of course (how else do you add fractions), but if you’re adding fourths and sixths, it doesn’t matter if you use twelfths (the LCD) or twenty-fourths (another CD). Even least common multiple in only mentioned once, briefly.
Right now, we teach math in a very disjointed manner. “Math” is basically a (very large) group of unrelated skills that students have to memorize. There’s no relation between the idea of splitting a cookie in half to share with your sister, the fraction 5/6, and the use of fractions in algebra. All of these are related concepts, but a select few of us can actually recognize them as related concepts. I probably couldn’t even have given this example until I started teaching math at a tutoring center 5 years ago.
Coherence in the CCSS refers to the idea that math tells a story, and we want students to see that story. We want students to understand how these concepts are interrelated within and across grade levels. Math is not just some random collection of things that we want students to memorize. It’s a process that gives order to our world, or better yet, shows us how to interpret the order that already exists in our world.
Now, there are two ways to approach coherence when discussing education standards. First, we can teach the math concepts in their logical order (what seems logical to people already fluent in math, that is.) Alternatively, we can teach concepts in the order that accounts for the natural development of the child. The writers of the Common Core attempted to balance these two options.
There are three main extremes that people will go to when discussing how to teach math – conceptual understanding (students need to understand the concepts of what they are doing), procedural fluency (students need to be able to compute accurately and quickly), and meaningful applications of mathematics (students need to see how math relates to real life and solve real-life problems using math). The “rigor” in the Common Core partly refers to the blending of all three of these goals.
It also refers to the challenge of the standards – they should be progressively more difficult to challenge students and keep them learning and moving forward on the continuum of understanding.
Yes, Common Core does require students to be fluent in their basic addition, subtraction, multiplication, and division facts. Yes, I am in favor of this. Yes, I know kids have calculators on their phones, but I don’t want them growing up and not understanding how “6 of one” and “1/2 dozen of the other” mean the same thing. Or not understanding that 5% off each item is the same thing as 5% off all the items.
Next post: How Common Core is attempting to change the way we teach math.
Last weekend, I attended a conference at the University of Arizona on the Common Core State Standards in Mathematics. We had the opportunity to learn more about the standards – how they were created, why they were created, and how to use them. Bill McCallum, one of the writers of the standards (also the head of the math department at UA) was our keynote speaker. I’d like to take some time to process the information I received at this conference.
CCSS – What they are, are not, and could be
The CCSS are standards (it’s in the name). This means they are what we expect a student to know at the end of the school year. They are not an assessment framework. Well, they’re not intended to be an assessment framework. Dr. McCallum used the analogy of a blueprint – the CCSS are intended to tell us where we need to wind up, but it’s up to us to determine how we will get there. A curriculum is a sequence of instructional activities intended to accomplish that goal.
The Common Core standards are not intended to solve all the problems of education in and of themselves. It’s up to us to determine how to solve those problems and implement our solutions. Furthermore, it’s up to us to implement the content so we can teach our students to solve problems.
Advantages of Common Core
The biggest advantage Common Core provides is the consistency of the standards across the country. Up until now, the only people who had influence on curriculum were the textbook publishers who had big enough budgets to research the 50 different sets of standards (one for each state) and create textbooks for each of them. What this actually meant in practice was that certain states (the states with big market share in the textbook industry) set the standards for the textbooks that were created.
Now, curricula and lesson plans and ideas can be created and shared by anyone with access to the Internet (blogs, Twitter, Facebook, websites, podcasts…). One teacher can post suggestions for how to teach a specific lesson that other teachers can use and modify to meet their students’ needs. One group can create scope and sequence documentation for the CCSS to show how the standards intertwine and offer one suggestion for what order they should be taught in.
Yes, I know I just ended a sentence with a preposition. Bite me.
We can share and improve upon one another’s suggestions, thoughts, and ideas. I don’t need to limit myself to just getting ideas from people in Arizona. I can gather ideas, suggestions, and lesson plans from people all across the country, knowing that their student are expected to learn the same things my students are. Yes, I will have to differentiate to meet my students’ needs, but THAT is the real work of teaching. Re-inventing the wheel does not need to be.
Next post: I will discuss the ideas of focus, coherence, and rigor in the Common Core State Standards.