Part I: Setting a Standard for Rigor
Standards. We all have them. We set personal standards for cleanliness around the house. We have workplace standards for what constitutes average or above-average performance. We have ethical standards governing how we behave as a society. We don’t always live up to our own standards, and we don’t always share standards with the people around us, but we definitely have them.
In K-12 education, we’ve had state-level academic standards since at least the mid-1990s, and now we have national standards for mathematics and literacy. We’re in the midst of implementing those standards right now, and feelings about them are…what shall we say? Mixed? Contradictory? Occasionally passionate and occasionally ambivalent?
Passionate ambivalence shouldn’t be all that surprising. As I said, we all have our own sets of standards governing different aspects of our lives, and sometimes we find that our standards aren’t the same as other people’s. Whether it’s the state department of education or the authors of the Common Core, we don’t like it when someone comes into our classroom and says, “You don’t tell me what’s good; I tell you.”
One problem with implementing new learning standards is that so many of the things calling themselves “standards” aren’t standards at all; they’re just To-Do lists. Teach this to your 3rd graders. Make sure 4th graders do that. This is curriculum mapping, not a set of standards against which we can measure and understand student learning.
We are told that the Common Core is “upping the rigor” on our teachers and on our students, but the standards alone can’t get us to that Promised Land, because the standards alone don’t tell us what rigor looks like. We need to decide that. It’s teachers and principals, working at the school level, who have to use the standards to define what constitutes rigorous work, and then create a culture that advocates and enables that kind of work across all subject areas.
What do we talk about when we talk about standards?
When we talk about standards, we are talking about two different things: what a person is doing, and how the person is doing it. We talk about content (the What) and we talk about form. But as it turns out, form has two components to it. Bound up in form are process (the How) and performance, or extent (the How Much).
As Grant Wiggins has pointed out in multiple blog posts, and as Paul Bambrick-Santoyo has demonstrated in his excellent book, Driven by Data, our learning standards do a good job of telling us what students are supposed to do (the content), but they rarely define either piece of the “form” puzzle: how they’re supposed to do it (the process) or the extent to which they need to do it to prove proficiency (the performance).
Wiggins, as usual, uses sports to create an interesting and insightful analogy. If I was judging an Olympics trial for high jumpers, I would have in my mind a description of what a proficient high-jumper does. I would compare each athlete against this mental standard. Did he execute the right steps? Did he do them correctly, and in the right order? That’s the content. Did he execute these steps with proper, accepted form? With beauty and grace? That may feel a little qualitative and mushy to you, but we’ve seen a lot of athletes in our time. We know what a high jump looks like when it’s done well. We know what a beautiful dive looks like. Our TV announcers freeze the video frame and show it to us again and again. Look—she sliced through the water without creating so much as a splash. Perfect form. Nobody disagrees. So there is clearly a standard in place.
Next, we have to deal with performance level or extent. If you can execute a perfect and beautiful high jump when the bar is set at nine feet, and I can execute an equally beautiful jump, but only at three feet, then you are clearly and indisputably the better jumper. At some point, we set a standard for what height a professional, top-rated high-jumper should be able to clear.
Do our learning standards set this kind of standard for process and performance? You decide. Here’s a sixth grade mathematics standard from the Common Core:
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
CCSS Math Content Standard 6.RP.A.3c
Now, borrowing an example straight from Bambrick-Santoyo’s book, let’s look at some questions “aligned” to this standard. Which question(s) would help us determine if a student was able to “meet the standard?”
1. Identify 50% of 20
2. Identify 67% of 81
3. Shawn got 7 correct answers out of 10 possible answers on his science test. What percent of questions did he get correct?
4. J.J. Redick was on pace to set an NCAA record in career free-throw percentage. Leading into the NCAA tournament in 2004, he made 97 of 104 free-throw attempts. In the first tournament game, Redick missed his first five free throws. How far did his percentage drop from before the tournament game to right after missing those free throws?
The answer is: we don’t know! The content standard doesn’t make clear to what extent a student needs to be able to apply his knowledge, as a sixth grader, or even what form (simple equation vs. complex word problem) we’re looking for. This is because, as it clearly states, it is just a content standard. Aligning textbooks and curriculum maps to these standards alone is no guarantee that anyone in your school is working at the same level of rigor, much less the desired or required level.
How can we set performance standards?
If we want to define more clearly what standards for performance the Common Core is looking for, or the world of college and careers require, we need to work together. If every teacher in the school sets her own standard for excellence, for rigor, for “CCSS-ness,” there is no standard at all. One teacher may be aiming for Question 1 from the example above, while another teacher aims for Question 4. We need commonly understood and accepted exemplars or anchors that tie performance to content.
Fortunately, we are not working in a vacuum. There is a lot of useful material surrounding the Common Core State Standards. We just need to make sure we’re aware of it, and know how to use it.
The authors of the literacy standards have provided a lot of exemplar material to help us understand proficiency at different grade levels. Appendix B to the standards provides text exemplars by grade band, listing appropriate literary and informational texts, and also providing excerpts that teachers can use in class to practice close, analytical reading. The exemplars even distinguish texts that are appropriate at the independent reading level from texts that should be read aloud. Personally, I find these exemplar texts far more useful than the three-part equation for calculating text complexity. When I look at the excerpts, I get a real, visceral feeling for what rigorous means—and I can go out to hunt for other texts that measure up.
Appendix B also includes sample “performance tasks” at different grade levels. We know that the complexity of a particular text depends, in part, on what you ask students to do with that text. Here, the authors give us some rich examples of what textual analysis should look like at different grade levels.
Finally, Appendix C provides us with exemplars of student writing at different grade levels, with explanatory annotations to show us what makes the sample a true exemplar of good work.
The exemplars, tasks, and writing samples give us a real standard of performance against which we can measure not only our students’ work, but also our own work, as educators. Are we assigning similarly rich and rigorous texts? Are we asking students to work at high levels of complexity with these texts, performing tasks of analysis, evaluation, and synthesis? When we ask students to write, are we seeing work similar to what we see in Appendix C? Are we asking for and looking for these same kinds of things that the annotations are pointing out? If we are teachers, these are questions we should be asking in our PLC or department meetings. If we are school leaders, these are things we should be looking for during observations and walkthroughs. Not to punish each other, but to help each other as we define a new standard of work and find ways, as a team, to reach the standard we have set.
The Common Core mathematics standards do not include tasks, exemplars, or other performance-related anchors, which is a problem, as we saw above. However, there are two places where we can learn about form—not just the steps of the high-jump, but what it should look like, and how high it should reach.
First, there are the Standards for Mathematical Practice—the eight standards that define how math should be used, regardless of grade level or specific content. These standards speak to things like abstract reasoning, constructing and defending arguments, working with precision, and making use of structure. In broad terms, the eight statements set a standard against which we can measure current practice and current materials. For example, it’s pretty clear that Question 1 from the Bambrick-Santoyo example above does not ask students to do any abstract reasoning or complex problem-solving. Even Question 2 is fairly basic, asking for nothing beyond computation. But which of the other two questions—the two word problems—is set at the right level of rigor for sixth grade? That, we can’t really determine from the practice standards.
However, there is another place we can look for examples. The two major testing consortia have worked hard to define grade-level performance and show us what it looks like. You can find sample test items from PARCC, the Partnership for Assessment of Readiness for College and Careers, here, and items from the SMARTER Balanced consortium here. Both sets of sample items make issues of form (process and performance) pretty concrete, and both sets do a nice job of depicting, in a visceral and inescapable way, what the combination of math content and math practice looks like. They can be enormously helpful when having discussions at department or PLC meetings about rigor and the Common Core. Are we asking students to use their math in the ways these test items are doing? If not, what’s the difference? What aren’t we doing? Is the difference simply in content difficulty, or is there something in the application that we’re missing? Perhaps we’re providing too much explanation and scaffolding. Perhaps we’re relying too much on classic equations and aren’t asking students to find problems themselves.
Whatever your subject area, and wherever you look for examples and exemplars, it’s clear that we cannot be efficient and effective at moving students towards higher levels of rigor unless we work together to set clear standards for what rigorous work looks like—standards that everyone can see, understand, and use to measure student performance. If anyone watching TV can know enough to judge high jump or a high dive, why can’t anyone in our school know enough to judge the quality of student work hanging on a bulletin board?