A few years ago - winter quarter 2010 - I had the opportunity to get involved in theatre. I tell you this because I'm an egotistical bastard. No just joking; I tell you this because through my experiences over the last few years in the theatre I have refined my ideas about practice and how students apply the idea of hard work to learning to perform
(i.e. take assessments successfully). First of all, it seems clear to me that the math test is essentially an opportunity to perform (it's a shame that the standard paper and pencil test is the normative method for capturing information about what students know, but that's a-whole-nother bag of bananas). As I taught over the years I kept hearing about math anxiety -
this phenomena of "knowing" something but when faced with this opportunity to perform - it all went out the window. Since I was always good at math I had no experience in this department. It took theatre to help me understand how anxiety plays a role in performance and how practice (structured and methodical) is the antidote to that potential performance killer.
Here is my idea about how
practice is scaled up towards successful performance:
Now, as an instructor I can talk about this a lot, but my ability to give opportunities - structured in class opportunities to do independent or performance practice (here I'm assuming you've taken the time to look at the Phases of Learning document) is basically severely limited by the amount of content I'm faced with.
Now it would be interesting to throw a lot of content out of the window in lieu of just having the opportunity to work through the levels of practice to gain competence around something and maybe someday I'll do that in a class,
but for most classes the student will be responsible for taking the questions I provide and trying to do independent and performance practice. There are exceptions to this that I am developing (have developed). For example, I give diagnostic assessments in most classes and tell students to treat them like a quiz. If they follow these instructions then they are doing independent/performance practice (depending on whether they feel pressure in this situation).
Another idea which I have developed for getting the student to do independent work outside of class is called complete the loop (see link at left).
Returning to my original theme, I discovered through acting, that you start slowly, learning your lines and the blocking (where you stand on the stage). Over the course of time you pull back and layer this with directing but you build the knowledge and confidence about your lines and blocking by repetition.
Finally, there comes a moment when the safety valve is pulled off (during much of the rehearsal process you can call for lines or stop in the middle of the scene with questions). At this point you are supposed to stay in character and act through difficulties - you will forget lines and blocking and things will go wrong,
but you have to have a "due date" for actors to know their lines and blocking. Finally, right before opening night you go through tech week where all the pieces are put together, but most importantly, you insert the element of stress trying to produce the show in its entirety with all the conditions of a normal show (including the preview night when you may have a few friends or family members and at least the designers and director in the audience). That's not the same as having an actual audience there but what it does is it gives you plenty of practice (repetitions) and scales up the pressure and conditions of performance to mimic the real thing as closely as possible. Furthermore, you get practice during the independent and performance practice phases of experiencing that block that anxiety causes from time to time which both informs us of where our knowledge and familiarity are lacking and also just happens for no particular reason other than natural nerves. During these moments you have to train yourself to react correctly - as an actor that means staying in character and making decisions (maybe verbal/maybe non-verbal) that are consistent with the scene while you, one hopes, get ahold of the proverbial thread again. In math class, I believe that this is a skill which is not well understood or taught. I suspect that what students would be relying on is their innate mathematical sense and belief in their efficacy as problem solvers (which would have to exist in order to be relied on!) But this also brings up the interesting question about understanding and anxiety, namely how does understanding or lack of understanding intersect with the intensity of anxiety. There are students that have high levels of anxiety which - when facing new material - could not realistically put to rest in the course of a quarter - for them the question of performance practice becomes a sort of psychological investigation into themselves and their methods for dealing with stress and anxiety. But many students just flat are not putting in the appropriate level of practice or time investment to go to a level where they would be competent; another possibility, one which is tragic (not to be too dramatic) is that the student is working very hard but in ways which are not conducive to deeper understanding or development of confidence (copying notes, doing problems out of the book but staying too connected to the solution manual, working with tutors that don't know how to step back and let them develop confidence about the material without someone there to validate each step). My hope as an instructor is that by talking about and giving students opportunities to think about levels of practice I can improve their ability to practice in meaningful and useful ways. Furthermore, by giving them tools to validate and reflect on their understanding they can take more control of their mathematics education and develop skills in meta-cognition which will serve them in all aspects of the their lives (that's as ambitious as it sounds!).
