This is my third post on the in-process revision of the California Math Framework. If you haven’t yet, please read the first two: The California Math Framework Revision, and More on the California Framework. I just reread them, and find that I stand by what I wrote: the revision attempts to address an important issue: low-track classes have had low expectations and are essentially dead-end classes. This is the broad professional consensus of math educators, as articulated by the National Council of Teachers of Math. Unfortunately, inequality in school reflects social inequality, and cannot be solved by educational reform alone. Still, it is our responsibility as educators to do the best we can to address it. This is easier said than done, which is why NCTM is at this point hoping mostly to launch a discussion rather than rush into making hasty changes.
Not having read much of the original draft of the Framework revision, I was careful to not endorse it. In both posts, I warned that no reform along these lines can possibly succeed if it is not done well. As I predicted, the resistance to the revision seems to be largely about the issue of tracking and acceleration. The Twitter response to my second post made me realize how polarized this conversation already is, and convinced me I need to spell out my views on these topics. (As for coming out for or against the Framework, that will have to wait until I see the next iteration of it. I just don’t have it in me to read that sort of document more than once.)
First of all, I agree with both the reformers and their critics that (almost) every student can learn significant math, and deserves to be treated accordingly. I also know that students vary widely, bring different backgrounds and skills to the classroom, and learn math at different rates. Denying a reality that every teacher, parent, and student knows does not serve the goal of equity. The question is not whether those differences exist, but what to do about them. The writers of the Open Letter offer no suggestion on this. This is not surprising, as they are among the people who have benefited from the status quo. (I have no animosity towards them: I too have benefited from the status quo! But like many others in NCTM, I have spent much of my career thinking about ways to democratize math education, which I would not have been able to do if I had pursued a career in STEM.)
In the remainder of this post, I will share a summary of my ideas about detracking high school math classes. Those are not ideas that just arose spontaneously in my head. They are based on decades of experience as the chair of an untracked high school math department, where we implemented those ideas. We were able to help students who would have been sunk by low expectations in a tracked system, without harming our strongest students who still managed to get into elite universities. This was in a private school, so you may want to exclude me from this conversation, which is your prerogative. I’ll just say that the range of our students’ math ability (as measured by standardized tests) was huge as they came into the ninth grade, and that the approaches described below were successful with the whole spectrum.
1. The least obvious and most important ingredient in detracking is the central role of an alliance with our strongest students. In a student-centered classroom, they are the engine that drives the class. If we do not keep our courses challenging and interesting to them, we lose their respect and their cooperation. Addressing their needs is paramount politically, ethically, philosophically, and pedagogically. Understanding this in no way harms other students — quite the opposite.
2. The sort of curriculum and pedagogy that best supports the widest range of students requires some departures from the traditional “I explain, you practice” approaches. It involves a combination of rich problems and activities, engaging classroom routines, teacher-led discussions and instruction, access to learning tools, and student collaboration. This is complicated and cannot be wished into reality by fiat, or merely by adopting a different textbook series, or a different state Framework. Teachers need training and support, and time to grow, not to mention buying into these changes.
3. We must combine forward motion and extended exposure. In a heterogeneous class (in other words, in any class) if we wait for every student to “get it” before “moving on”, we are sabotaging everyone’s learning, and undermining necessary “coverage”. But if we only move forward, we are only serving a small fraction of our students, and not doing even that very well. If we want depth of understanding and long-term retention for most, we need to use techniques such as lagged homework and assessments, quiz and test corrections for “points”, separation of related topics, and perhaps other manageable approaches to spiraling. This is what I call differentiation by time, not content.
4. We should offer outside-of-class math help to students who need it, and math enrichment to students who want it.
5. Students in a given course should span two grades. For example, a Geometry course can include strong 9th graders and not-as-strong 10th graders. This is quite different from tracking, as all students take the same classes — they just take them at different times in their school career.
Any approach to detracking in high school that does not include at least these ingredients is not likely to succeed. Worse, it could lead to a backlash that would set us back dramatically.
PS: Given the size limits on a blog post, I once again encourage you to see those ideas spelled out at much greater length in these three articles:Reaching the Full Range, Hyper-Acceleration, and The Assessment Trap. See also some of my other articles About Teaching.