I worked in a high school for many years. Over time, my department reached a close consensus on curricular and pedagogical matters. One administrator, after visiting some math classes, expressed amazement on how similar our students’ experiences were, irrespective of who their teacher was.
I’ve also worked as a consultant. In that capacity, I visited many math departments, and offered many professional development workshops to colleagues around the country. One thing I learned was that many, many math departments are home to teachers with seriously divergent philosophies. While we cannot ignore teachers’ need for agency, we should also think about how these differences impact student learning. In this post, I will argue that striving for departmental consensus is well worth the required time and effort, even if the process is slow and challenging.
Philosophical differences in a department can be generational. A young teacher, fresh out of college, may join a department of oldsters who have always done it a certain way, and have no intention of making changes. They may even require the new hire to ignore what they learned in Ed School, and do everything their way. I will not discuss that situation here. Retirements and the influx of new colleagues can help gradually improve that.
A more common problem is philosophical tensions among well-intentioned and open-minded colleagues. This can look like a manifestation of the so-called math wars within a department: direct instruction vs. student intellectual engagement, skills vs. concepts, memorization vs. understanding, etc. In my view, these binaries are profoundly misleading. Direct instruction works best on a foundation of student intellectual engagement. Concepts cannot be acquired in the absence of skills, and vice versa. Memorization can help if it encapsulates understanding — not if it substitutes for it. Working for a departmental consensus is one way to work on embracing both sides of these false contraries and developing a local version of a balanced approach.
Every situation is different, but here is a possible scheme to get there.
1. Reach agreement on scope and sequence: what should be included in each course? You may not have a choice on this because of district or state constraints. If that is the case, that initial discussion should be about what should be emphasized in each course. The reason this has to come first is that without such agreement, resentments can develop (“They should have learned this last year!”) I share some big-picture planning ideas in this article, which can help structure that conversation.
2. Have teachers with different backgrounds, views, and experience teach different sections of each core course, in parallel. This should involve regular meetings to debrief the previous week and map out the next week, and the recording of notes of how things turn out. This is a slow but profound way for teachers to learn from each other as they share strategies in a fine-grained way throughout the course. I share ideas on teacher collaboration in Chapter 12 of There Is No One Way to Teach Math. (In fact, the book should help with this whole process: each chapter ends with discussion questions which can help develop the department into a professional learning community.)
3. For maximum impact, do not let teachers over-specialize. (“I teach Algebra 2.”) After a few years, teachers should move on to different courses. in the core sequence. Over time that will lead to joint ownership of the whole program. This mobility is mostly needed in the Algebra 1/Math 1 to Precalculus sequence. Elective courses are experienced by fewer students and need not be part of the rotation.
4. Take a few days each summer to make needed adjustments to the scope and sequence, and (probably more important) to introduce representations and learning tools that could enhance student learning of the most important ideas. (Administrators: make sure teachers get paid for this important summer work!)
Over time this process will yield a department that is more than the sum of its teachers. Students will appreciate the consistency and lose interest in comparing one teacher to another. Most importantly, their learning will be enhanced, as they will benefit from the combined contributions of the whole department, not just the quirks of their current teacher.
That said, it’s important that each teacher maintain their own individuality in the midst of this joint project. If someone is a history of math buff, or is enthusiastic about a relevant “enrichment” topic, or wants to make connections with social justice — by all means they should do what they can to squeeze that in, as long as they prioritize implementing departmental policies.
Henri's Math Education Blog 