Two Communities of Practice: "Know That's" vs. "Know How's"
Ultimately, this web site is directed at enhancing and supporting teachers of mathematics. And, by profession, my focus has been on the education (i.e. preparation and professional development) of teachers of mathematics.
Thus, when I read something that hits home, I try to share it with anyone who will listen. And now, you are my "captive" audience.
Recently, I read a book by John Seely Brown...something I have wanted to do for decades. The book was The Social Life of Information, coauthored with Paul Duguid.
In Chapter 5, while discussing learning (and teaching), they refer to a research study by Jean Lave and Etienne. Their claim: Learning a practice (such as teaching) means "becoming a member of a 'community of practice' and thereby understanding its work and its talk from the inside." (p. 126)
I like that image. To succeed as a teacher, it is important that one "understand" both the "work" and "talk"...but I am concerned at the perspective of "the inside." The "inside" can be destructive relative to young teachers' ambitions, dreams, commitments, and approach to teaching.
For example, more than 30 years ago, JRME reported a study that documented how short the life was of a young teachers' commitment to openended problemsolving. When joining the community of practice (even as interns), the young teachers quickly gave up trying to challenge students, choosing to model their peer's approach, which was to follow the text book and not expect much from students.
This is sad...and does not always happen, though more than anyone wants to admit. But, if that is the standard "community of practice," then we are in trouble.
The authors continue with words from Jerome Bruner, describing the important differences between "learning about" and "learning to be." The latter is the focus of my methods class, but some students never get beyond the level of "learning about." Often, this is symptomatic of their belief that they are a "born teacher," and I am just one more "required" hoop in their quest for a job.
Philosopher Gilbert Ryle creates the same image...arguing that we must distinguish between "know that" and "know how." The former can be gained by accumulating information (i.e. some student's approach to a methods course), while the latter is much more important and can only be gained through direct experience and lots of reflection (years and years and...).
For example, I pose a simple situation and questions: In an algebra class, Stu Dent writes on the board: a/c + b/d = (a+b)/(c+d). How would you react? What is probably the source of the error? And, how would you help the student?
Unfortunately, the "know that's" immediately start grinding out a review of common denominators, while those starting to gain some "know how" connect the student's error with the process of multiplication, where a/c * b/d = (a*b)/(c*d)...and then work from there.
And perhaps the sad (yet happy) thing is that after 40 years of teaching, I pride myself in retaining my own commitment to working on becoming a member of the "know how" group. I will never reach the end, but that is part of the enjoyment of teaching mathematics.
