Mathematics Teacher Education

"Stay away from that unproven experimental stuff. Much better to stick
with the Moving The Furniture Until He Gets Better approach." Gregory
House, MD.


The on-going debate about content, pedagogy, and pedagogical content
knowledge as they pertain to mathematics teaching and the education/
training of future mathematics teachers continues to produce more heat
than light in venues where one side continues to insist that we need
to focus on mathematics content only, that questions of pedagogy are
closed ("One way to rule them all, One way to mind them, One way to bring them all and in the darkness bind them: direct instruction!), that pedagogical content
knowledge isn't worth discussing, and that in fact all questions of
mathematics teaching and learning are closed (or at least that there
are no open ones on the table).

Contrast that attitude with what is likely to be gleaned from the
following presentation, which I plan to attend tomorrow:

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Systemic school improvement through teacher learning:
The case of Japan


International comparisons repeatedly show that Asian countries such as
Japan excel in the teaching and learning of mathematics. This
presentation will consider how teacher education and professional
development in Japan contribute to these outcomes. Specific
mathematics tasks designed for “research lessons” in lesson study
groups will be examined to reveal aspects of Japanese professional
development critical for teacher and pupil learning of mathematics.
Beyond features internal to lesson study, the presentation identifies
the role lesson study plays in systemic school improvement. The
presentation compares American conceptualizations of school “reform”
to Japanese models of “continuous improvement.”

Jennifer Lewis completed her doctorate in teacher education at the
University of Michigan in 2007. She currently works on a number of
mathematics education projects in the School of Education. Jenny is
especially interested in ways teachers learn in their practice
settings, and how might they best be prepared to do so.
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Educational conservatives and anti-progressives pay enormous lip
service to Asian mathematics education - in China, Taiwan, Singapore,
Hong Kong, and Japan - as long as no one looks to closely to what
actually goes on in these countries. These Americans prefer to pick
out anything that looks like it supports their viewpoints (whether in
fact it does) and ignore or spin everything else. Few of them, if any,
spend time in these countries, of course. Why bother to observe real
classrooms, kids, teachers, or teacher education? Why look at such
innovative professional development models such as Japanese-style
lesson study? After all, such practices cost: serious investments of
money, time, and personnel are needed, either through extending school
days while reducing individual teaching hours, or by paying for
substitutes to cover classes while teachers are participating in
lesson study. Wouldn't buying a set of books from, say, Singapore or
Oklahoma and throwing them at teachers suffice? Or making pre-service
teachers take more and higher-level mathematics courses taught by
professors of mathematics with little or no experience or interest in
pedagogy or pedagogical content knowledge? After all, if we're going
to spend money to pay professors to work with pre-service teachers, who
is better qualified: a mathematics Ph.D whose primary experience and
interest is in pure mathematics research, or some pretender from a
School of Education whose main claim is a minimum of three years'
actual elementary or secondary teaching experience? Clearly, wasting
time in real classrooms with kids and teaching colleagues is not as
valuable (or as lucrative for the math department) as Partial
Differential Equations for Kiddies.

Of course, this is not necessarily a meaningful dichotomy, as we see
throughout the country: there ARE mathematicians who are deeply
interested in and knowledgeable about mathematics teaching and
learning. And there are mathematics educators who know the requisite
mathematics for the relevant band(s) in K-12 curricula deeply and
well, and who can communicate it to teachers and would-be teachers
effectively. Ideally, future teachers get the best of all worlds:
enriching mathematics content courses designed specifically for future
teachers, not future Ph.Ds in pure mathematics or future engineers or
future physicists, as well as mathematics methods courses, field
experiences, practicums, and supervision from experienced and
reflective instructors with knowledge of teaching and pedagogical
content that is grounded in work with real kids out there in the
world. Both sorts of courses should be taught by people whose
knowledge crosses between the disciplines. Ideally these instructors
will have some practical knowledge of applications of the mathematics,
will have knowledge of and competence with a spectrum of the
mathematics and applications that the actual grade-level course
content points towards And also ideally, these instructors would view
one another as colleagues, rather than with fear, suspicion, or
contempt. Naturally, for such collegial relationships to work, neither
the math department-based teachers or the ed school-based teachers can
view their perspective as either best or complete: they must instead
work intimately with those from the other "world," and value the very
real contributions that each sort of teacher can make.

As long as a small, vocal, entrenched minority of mathematicians and
like-minded individuals continue to denigrate the import of teaching
knowledge grounded in subject matter knowledge, and instead pretend
that content knowledge alone, along with a slavish devotion to direct
instruction as the sole approach to teaching school mathematics, and
as long as such people have the ear of influential politicians, policy
makers, parents, and colleagues who are prone to believe what they are
told by fellow mathematicians about the "evils of Schools of Education
and those who are educated there," we're in for more years of foot-
dragging and wasted energy. Or as Gregory House so wisely observes:
"Stay away from that unproven experimental stuff. Much better to stick
with the Moving The Furniture Until He Gets Better approach."