Catchphrases

I’m done with my summer workshops, and I hope to resume blogging when the inspiration strikes. Today, a brief post about catchphrases, one per paragraph. (And no, this is not because this word has six consecutive consonants, which may well be a record.)

I started thinking about this topic when I learned that Annie Fetter’s catchphrase “What do you notice? What do you wonder?” had been trademarked by the alas now defunct Math Forum. The trademark is now owned by NCTM, which considers it community property, and has no intention of restricting its use by any and all math teachers. This is good, since in some situations, these two questions can jumpstart a worthwhile exploration, one which is initially driven by an actual expression of student understanding and interests. This is particularly important in a classroom that needs to move away from a rigid “listen to the teacher and then practice” model. Applied skillfully, these questions can honor student thinking and sense-making, and  launch a great lesson. Still, as I pointed out in this post, there are situations where this is not the best option. Like every other good idea about teaching, it cannot be expected to apply universally. Teaching is a complex enterprise, that does not lend itself to one-liner solutions.

And yet! I love coming up with my own catchphrases. For example, the point I made at the end of the previous paragraph is encapsulated in the catchphrase “Nothing works!”. I love this slogan because it is sure to get people’s attention, and it allows me to elaborate: nothing works for every class, every teacher, every lesson, etc. This is an important understanding in a culture of quick fixes and edu-fads. (Some links about this: “Nothing Works” article| blog post on being eclectic | “Art of Teaching”worksheet to help teachers and departments think about alternatives to current practices.)

A friend told me that “Nothing works” is self-referential, since it too doesn’t work universally: she claims that some things I believe in do work. (Alas, I’m unable to remember what she was referring to!) A related catchphrase, the motto for my Web site and for this blog, is “There is no one way” (as the Zen Buddhist said to the traffic cop.)

To elaborate: teachers sometimes look for the “best” way to teach something. That is the wrong question: for anything important, we should know many ways to teach it so as to have the needed flexibility when reaching a wall in a given class or with a given student. Thus the importance of learning tools and multiple representations, which make that possible.

My favorite among my own catchphrases may be “Constant forward motion. Eternal review.” This is aspirational, as it is sometimes necessary to pause the forward motion, and there may not be sufficient time or resources for eternal review. Still, it is a great thing to aspire to. Forward motion is essential to keep a course interesting, especially to our strongest students. Review is essential if we want ideas and techniques to stick. Each requires the other to work well, and in combination, they make for extended exposure, a must for heterogeneous classes (i.e. all classes.) Striving for constant forward motion and eternal review is facilitated by such practices as lagging homework, separating related topics, test corrections, and no doubt other techniques. 

Incorporating those changes, or any changes, into one’s teaching (or into departmental practice) is a long term project. This is captured in my catchphrase “Fast is slow and slow is fast”.

What I’m trying to say with this cryptic formulation is that if you try to make too many changes in a hurry, you may find that in fact the changes are superficial, and the underlying classroom realities are not affected. Or you may conclude that “it didn’t work” and go back to your old ways. If on the other hand you pace yourself, and make incremental changes one step at a time, you will find that on the one hand you reap immediate benefits, and on the other hand the changes will take root and become the new normal. Be the tortoise, not the hare. Even better if you do this in ongoing dialogue and collaboration with your colleagues.

You’ll notice that my catchphrases are largely aimed at teachers, not students. This is because I’m in general agreement with “Nix the Tricks” a great compendium of how to avoid catchphrases in our teaching. (Download the book, which was put together by Tina Cardone and the MTBoS.) Shortcuts like “cross-multiply” or “FOIL” usually obscure the underlying mathematics. They often reflect a cynical attitude: the students will never understand these concepts, so I’ll give them an easy-to-remember shortcut. 

Nevertheless, I do occasionally use a catchphrase in my teaching. For example, in geometry I might be heard offering the hint: “When working with circles, you should listen to the radii”. It is a good hint, with substantial mathematical content, so it’s not really a trick that should be nixed. Overall, my stance is that formulas and tricks should encapsulate understanding, not substitute for it. That is the catchphrase I’ll end on.

[Three more catchphrases in this follow-up post.]

Feel free to share catchphrases you love or hate in the comments!