I’ve engaged in discussions trying to answer this question ever since I started teaching AP calculus in 1995. Since 2001, when the No Child Left Behind assessments and high school graduation exams were implemented, this question has become even more relevant. In fact, it has raised more questions than answers. For instance:
- If the students are administered a good assessment that is written to the standards, then is it bad to teach to the test?
- Since the majority of questions on the exams are multiple choice, are we cheapening the math by boiling the answer down to a, b, c, or d?
- By teaching to the test, are we narrowing our curriculum? Is this always bad, since most math curriculum is known to be a mile-wide?
- Are we making the curriculum more shallow by focusing instruction on what is easily assessed?
- As the saying goes, you can’t fatten pigs by weighing them all the time. So how are we strengthening education if we’re taking significant time away from instruction to assess?
You’ve no doubt heard multiple answers to these questions coming from multiple perspectives. Unfortunately, none of the answers to these questions come easily or are definitive.
But this past Saturday, while attending the California Math Council’s Asilomar conference, I heard something that crystallizes my thinking about the difference between teaching to a test and teaching to the standards. (Admittedly, I bristle when I walk into classrooms and see “test prep” work being done, so I have my own bias.) At the conference, I heard Phil Daro—a Common Core author—present the structure and reasoning behind the Common Core State Standards. One of the data points he cited was the difference between how American and Japanese teachers approach lesson planning. According to Daro, as teachers look at the math problems they assign to their students:
- American teachers ask themselves: How can I teach my kids to get the answer to this problem?
- Japanese teachers, on the other hand, ask themselves: How can I use this problem to teach the mathematics of this unit?
As I see it, the difference in those two questions embodies the difference between teaching test prep and teaching math standards.
For example, if I’m teaching students to answer problems correctly, then my stopping point is much shallower than it would be if I were teaching to the standards. With this answers-based approach, I would be less likely to extend a lesson beyond the correct answer or have a student present an incorrect solution—because both are distractions from arriving at a correct answer.
But if I view each problem as a tool to further my students’ mathematical development, then my approach to teaching will change. I will be more likely to extend the problem so that students’ depth of understanding is enhanced. Additionally, I will be more likely to have a student who did the problem incorrectly explain his/her thinking to the class because diagnosing misconceptions is imperative to fully grasping concepts.
So as you plan your lessons over the next few weeks, ask yourself, “What will this problem allow me to teach my students?” Let me know if it changes the way you approach your teaching.