I’m grateful to Matt Brauer, a parent of two girls who attend SFUSD schools — one in elementary and one in middle school. Matt and I have been corresponding for almost a year about the district’s new Common Core math sequence, and I am very appreciative of the spirit with which he’s approached the change: cautiously, with an open mind and yet with some clear misgivings. I asked him to write a guest post about his “take” on the math changes and he obliged:
Some time ago I wrote a letter to Board of Education member Rachel Norton. I was concerned that my daughters were expressing boredom with math, and worrying that the in-class experiences they were having would diminish their joy of learning the subject. I was especially annoyed at some of the district rhetoric about differentiated instruction and an end to tracking. Also, I told her that while I’m a fan of what the CCSS is trying to accomplish, it was not clear to me that the curriculum necessitated heterogeneous classrooms, and that I felt like the district was using the curriculum change as an excuse to pursue other agendas. Finally, I wrote that the district has been notorious for talking a good game but not following through with the resources needed to implement the plan. (Differentiation is hard, and it’s not clear how much buy-in there is from the teachers, or if they have the training and prep time to do it well.)
It was kind of late at night and I may have sounded a bit cranky. Still, Rachel forwarded my concerns to the SFUSD math department, and as a result two members of the math department–the math administrator and the STEM executive director–contacted me to see if I would talk with them. We met for about an hour at a cafe near my daughters’ school. They listened while I laid out my concerns, and I listened while they told me about their goals and those of the Common Core State Standards.
I was already a big fan of the Common Core, but Lizzy Barnes and Jim Ryan convinced me even more of its value. Primary and secondary math instruction in this country has been caught in an historical eddy, and the consequences have been obvious to anyone who reads about student achievement across cultures. The problem has not been helped by merely jumping up the intensity of the curriculum: as Jim pointed out, the number of AP Calculus exams taken has been increasing every year, but the number of students entering STEM programs at the college level has been flat (and it’s even worse at the graduate level). Clearly, adding more challenging material is not sufficient to induce a love for the material.
The Common Core takes a pragmatic and empirical approach to find out what works to get students excited about math. A product of 15 years or more of research, the curriculum has learned from other country’s successes, as well as from innovative research in this country. On a personal level, as someone who applies my graduate statistics education on a daily basis, I’ve been impressed with at least the occasional extra-credit material my daughter has been bringing home. The material may seem confusing or rudimentary at times (the first unit in Math 8 is “Counting”) but there are deep concepts being taught, towards the development of strong mathematical intuition. The curriculum focuses on the creative, and less on calculation. As Jo Boaler—one of the strongest academic proponents of the Common Core—related in a recent talk, math consists of at least four parts: 1. asking the right question; 2. modeling the question mathematically; 3. doing the computation; 4. relating the answer to the original problem. Historically, it’s mainly been just one step—calculation—that’s been taught, while the other three steps represent the creative process that comprises most of mathematical insight.
These other steps can be highly social, and indeed, there is also a strong social component in how the Common Core is being implemented. Students do less of the endless timed worksheets and instead collaborate to address complex problems. In the process, it is hoped, students of all abilities and backgrounds begin to develop mathematical creativity. This heterogeneity in the classroom is supposed to allow students to dive as deeply as they are inclined and able.
But how critical a feature is heterogeneous instruction to the Common Core? There is an astounding level of variation among middle school students in interest, attentiveness, ability, even age. (For example, there is a nearly two year age range in my daughter’s math class). Even given the best curriculum in the world, why would we expect that a range of complex math concepts could be taught equally to all within a grade level? In another anecdote, Jim Ryan told me how in Singapore dividing-by-fractions is taught in fifth grade, rather than in fourth as in the US. “Why was this?” US educators wanted to know. It was because, according to empirical data, it “worked better” to teach the concept at a later time. The fact that this concept can be better taught by delaying it a year implies that there are developmentally appropriate times to teach various math concepts. I hope that no teacher would argue that all students in a grade are at the same developmental stage. So why would we treat them as if they are?
The district and many academic researchers assert that in teaching all students to a higher level, all students will benefit. The paper cited most often to support this is Burris et al.’s 2006 study, which does indeed show modest gains for all students taught in a heterogeneous classroom. But a couple of things have always bothered me about the use of this study. First, although the study neglected to report class sizes, it made clear that all students were given access to intensive algebra workshops every other day, in groups of four students. (Note that there is no comparable investment by the SFUSD.) Second, the study’s school was offering eighth graders a course equivalent to Algebra 1. SFUSD’s implementation of the Common Core appears to defer algebra to ninth grade. So in what sense exactly is this supposed to represent an “accelerating” of math achievement? It looks like the eighth grade algebra class is being moved to ninth grade, and all students are being placed in a heterogeneous “Math 8” course. Also, it’s troubling that this one paper is given so much weight to carry. In statistics-heavy fields like medical genetics or neuropsychology, the findings of a study are not worth committing to until they’ve been replicated—in another population, by other researchers with other agendas. Has nothing been done in this field since Burris’ 2006 publication? Have there been other papers that have not had quite as strong results? Has Burris given us the last word on heterogeneous classrooms and the achievement gap? Is this paper to provide the primary blueprint for instruction at all levels of achievement?
And this is the crux of my concern. SFUSD has had a laser-like like focus on reducing the achievement gap and, conversely, a very mediocre commitment to engaging with students who need extra challenges. My interactions with the district’s GATE coordinator have been particularly distressing: at one point she clearly stated that GATE-identified children are part of the cause of the achievement gap. This attitude is reflected in the resources allocated to the GATE program: beyond those needed to identify kids as GATE, there are NO resources allocated. (And GATE identification simply for the sake of labeling and lacking any meaningful follow-up, is about as toxic of a situation as could be imagined.) It appears that, for the sake of addressing the achievement gap, the district has abandoned a real sense of responsibility to make sure that “joyful learners” in math stay that way. As the father of daughters, as one who knows that girls face ever increasing social challenges to their innate interest in math and science, the implications of this policy break my heart. (Furthermore, for these kids math has become a challenge-free subject. The unrealistic sense of accomplishment that they have from effortlessly getting an ‘A’ every semester will not survive its first contact with a college-level course.)
The ideas behind Common Core are sound. And I do believe that–given good teachers–the curriculum has the potential to be transformative. The Math Department of SFUSD is in the hands of some very dedicated and skilled educators who also clearly love the subject, and it’s encouraging that they are very interested in engaging with parents. (I haven’t always found that to be the case with other parts of the district.) But I question the district’s ability to carry off such a profound change as this. Teachers have in some cases been given no more than three hours of professional development for implementing the Common Core: it’s hard to see how students can leapfrog over moribund attitudes towards math when their teachers have not been given the tools to do so themselves.
The district’s implementation of the Common Core is part of a gigantic experiment. It may be a worthy one, but it’s one in which we and our children are the research subjects. As parents we need to account for the possibility that the findings of Burris and others cannot be replicated, and that our hopes for the success of the program are in vain. We need to prepare our children by providing extra-curricular enrichment opportunities where the district is not willing to. We need to monitor the progress of the curriculum’s deployment, and hold the district accountable for claims stated and promises made. And we need to continue to engage with the educational visionaries driving the process, to make sure that they know, every step of the way, how the experiment is progressing.