I employ a highly unscientific, but I think also highly defensible, approach to evaluating most proposals for changing how a particular course is taught. I talk to an experienced colleague who actually teaches that subject, and teaches it well.
Blog readers will know by now that I don’t have a lot of time for much of what passes for pedagogical theory, especially as taught in education schools. But I have enormous respect for pedagogical experience, and for teacher reality checks.
So as I continue my posts on the common core standards, I reached out to Stephanie Sawyer, a fellow teacher at Juan Diego Catholic High School in Utah. She has been working very hard to figure out how to improve her students’ math understanding, and performance. I asked Stephanie what she thought of the common core math standards.
Here’s the first part of her thoughtful response. I’ll post the second part soon.
Should the state of Utah adopt the Common Core Standards for Mathematics and English Language Arts? That’s a moot point now because they have. The Common Core Standards for Mathematics (CCSM) were adopted in 2010. The right or wrong of that is worthless to debate at this point, because it’s a done deal. Mathematics teachers throughout the state will have to deal with the fallout from that decision.
Utah has chosen to adopt, for mathematics, what the CCSM folks call the “international model” for meeting the standards through curriculum. What this means to most high school mathematics teachers is that the traditional Algebra I, Geometry, Algebra II sequence is gone. It has been replaced with the rather vague-sounding Secondary Mathematics I, Secondary Mathematics II, and Secondary Mathematics III sequence. Not to worry, though; you will still be teaching the same material, just in different courses. Sounds good on the surface, doesn’t it? But it doesn’t quite work out that way. More on that later.
As a parochial high-school teacher, I am often asked if we have adopted the Common Core Standards. The answer is yes and no. Yes, we think the standards are okay – more than a little ambitious, but they are good standards. But no, because we don’t think we need to adopt them as they are presented sequentially, nor do we think we need to teach all the standards (the ones without a + next to them) as a minimum. I believe that these standards attempt to do too much in too little time.
The lesson from the last TIMMS (Trends in International Mathematics and Science Study, 2007) assessment was that the US mathematics curriculum is a mile wide and an inch deep. These standards seem to indicate that we are to expand our curriculum to two miles wide and six inches deep…in the same amount of time that we were unsuccessful in teaching the previous standards. We are supposed to provide more depth to the old topics, and add in a whole new strand of Probability and Statistics that used to comprise an entire high-school statistics course. While the new standards certainly spell out what our students need to know to be college-ready in the 21st century, the recommended curriculum for how to accomplish mastering them is decidedly UN-realistic. At least as how things now stand.
When Mary asked me to write this post, I wasn’t sure how to approach it. To me, the standards-assessment-college-ready discussion has become a hydra: every time you address (lop off) one head, two heads grow to replace it. I think that in lopping off the standards head, we must now confront pedagogy and grades.
The new standards are very focused on conceptual understanding. In the early elementary grades, I’m not sure one needs to understand the concept of addition to add, or the concept of multiplication to multiply. While understanding these concepts becomes essential when approaching word problems and applications utilizing these skills, I don’t think one needs to understand WHY something works in order to be able to understand HOW something works. In the elementary grades, could we please teach the students HOW to do things, like add, subtract, multiply, and divide integers, decimals and fractions? And in the middle school, could we please teach them how to comfortably move from decimal to fraction to percent? And how to apply decimal, fraction, and percent to the real world? I know this material is taught; my contention is that it is not mastered, precisely because there are just too many standards to hit in these grades.
You don’t have to go to college to get a certification to sell real estate, but you sure as heck have to be able to do math to pass the test that allows you to sell real estate. I understand that CCS have this built into the standards, but I’m not sure that education schools have trained teachers to go beyond the “fun of learning” into the necessary drill required to master these skills. The term “rote learning” has become synonymous with “not thinking.” But don’t we want our students to be able to handle basic operations without having to really think about it? Because drill is what it takes to actually master anything – mental, physical, emotional. No citation here, just life experience. And “drill” has become anathema in education schools.
I suppose I see mathematics education a lot like I see learning a sport. In baseball or basketball, there are “fundamentals” – things you have to have mastered in order to progress to the next step. If you want to play basketball, every practice, regardless of how long you have been playing the game, includes lay-up drills and wind sprints. Do the kids who have made the varsity basketball team already know how to do lay-ups? And how to run? Of course they do! But the point of drilling is to make it second nature – something they don’t have to think about so it is automatic.
Likewise, my 8-year-old son is a baseball player. He pitched for the first time this week. He’s never had a pitching coach, but he understood that his main goal was to get the ball in the strike zone. Which he did. Sure, his pitches were slow. But to my mind, this is fine. He can pitch. He can learn about the nuances – the WHY – of pitching now that he has his accuracy nailed. Now he can worry about things like how high up he needs to cock his front leg on his lead-in, or how much his back leg has to follow for velocity, and if making these adjustments will change the accuracy. He can now focus on these issues because he has mastered the fundamental getting-the-ball-where-you-want-it-to-go.
If I may, I’d like to give one more example of this mastery from drill idea, but back in the math realm. When I talk to parents and colleagues over, say, 35, and ask them how to add fractions, they can actually tell me. Most of them haven’t had to add fractions in 20 years or more, but they can still tell you things like “the bottoms need to be the same” and “you multiply the top and bottom by the same thing.” Why is it that these folks can still, years after they learned this skill, recall how to do it? Yet we have students in Honors Geometry who have been looking at and reviewing fraction addition for at least four years, and they will say “I don’t remember.”
If one wants to be able to do, much less understand, high-school mathematics, there are just some things that have to be automatic. And you get to automatic by drill.
Until we in mathematics education acknowledge that mathematics is a combination of skill and understanding, it won’t matter how great the standards are, or how cool our classes are. If our kids can’t do the most fundamental math, it’s pretty much a waste of everyone’s time.