"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."
Posts
8 comments:
there's just as vocal and entrenched a silly group on the other end, though.
It's that old thing about the people who are smart enough to question their beliefs *aren't* the ones forcing them down everybody's throats.
I love direct instruction in small doses at the right time and place... but it's strong medicine. I loathe when it's done at the expense of that light bulb of discovery.
I wonder who is in that "vocal and entrenched and silly group on the other end?" I occasionally meet people who are teaching or, more likely, doing some sort of administrative function or other, who have the talk but not the walk of progressive reform mathematics education. A bit like teachers who thing manipulatives are magic bullets that somehow "teach" concepts, rather than objects through which students can model mathematical concepts and, if their thought processes are activated in useful ways, the students can then make connections. In other words, the manipulatives (or other sorts of models) don't teach, nor are they the concepts. It takes human minds to make connections and gain understanding. So okay, some folks are that naive and don't get it.
However, I find that such people can learn because they actually want to understand how to make things better for kids. If they're approached intelligently and with respect, they generally listen. Such is not generally the case with the people who oppose reform: hence the word "entrenched." They already "know" the "truth," and they're not prepared to consider that they haven't quite got everything neatly tied up into a ball.
I've made clear on this blog and elsewhere that I don't decry ANY instructional model when used intelligently. But the folks I'm talking about certainly don't advocate using it in small doses and they believe it's ALWAYS the right time for it. That's a very serious error. I have said that "discovery" - guided or free - isn't the best diet if it isn't supplemented with other approaches. The best curricula I've seen CALL for periods of direct instruction. They also call for whole-class conversations, reflections, summing up, etc. The bottom line remains that there simply isn't an instructional model that consists solely of one sort of activity that is likely to work well for many students or reach most of them often enough to be effective. My beef is with those who think they've got "proof" that direct instruction is the answer for everyone all the time. Such nonsense cannot be allowed to continue to control US mathematics classrooms.
Who are they? The ones who think that Direct Instruction is inherently evil and will turn teachers and children into automatons.
What is the difference between content and subject matter?
Your language preaching against divisiveness is... rather divisive.
Sioux, I'm afraid your questions and comments are not clear to me so I can't respond as well as I'd like. I don't know anyone who believes that direct instruction is inherently evil, any more than I know anyone who thinks that phonics is inherently evil. But there is no shortage of those expressing the view that anything BUT phonics is bad literacy instruction and anything but direct instruction is bad teaching in general. So it's those people whose views I'm opposing. If I'm "preaching" and causing division, it's not among people who haven't already chosen to separate themselves from the mainstream and portrayed progressive-minded educators as mad scientists practicing racist experiments that amount to "cognitive child abuse." All that terminology is actually used by people on web sites and discussion lists, some of which have been around for more than a decade. I didn't invent that language or decide to use it hyperbolically to win a debate. It's what these people say about those who don't share their views. Don't believe me? Read the attack pieces at mathematicallycorrect.com and the NYC-HOLD web pages and judge for yourself who is being divisive and who is trying to find common ground. Again, you will be hard-pressed to find progressives who say, "No direct instruction ever." What we generally say is, "Less lecturing, more student-centered lessons, please." Asking for a shift in balance and emphasis is most definitely NOT calling for the end of something, but that's the spin the MC/HOLD people put on the NCTM Standards and anything else that suggests that business as usual isn't working and needs to be modified. Sorry if after more than a decade of being called a racist by people whose politics (in general) would make them far more suspect of harboring such sentiments than people who have a proven track record of opposition to racism, I'm a teensy bit testy. Or if after over a decade of having such people complain to my employers or the University of Michigan in order to get me fired, reprimanded, or cut off from the internet, I'm a bit miffed by these people and their tactics. If you can find evidence of my trying to get them fired or cut off from free speech, let me know. But I can demonstrate that such has been done to me, and not just once or by one person. I guess that might make my language a trifle less sensitive and balanced and polite than you'd like, but then, read the description of my blog and its purposes. Making nice to the folks I disagree with is not my goal. Counteracting their lies and propaganda is. I don't see evidence that those dealing politely with such people has gotten them to be more fair, honest, or reasonable. I do see that I'm a frequent thorn in their sides. The personal attacks on me suggest I'm getting to them. So I'll soldier on, thanks, and while you and I may be more in agreement than not about teaching, I guess we'll just have to agree to disagree about language and tactics. On your blog, if you have one, you are free to be as unifying, kind, reasonable, polite, and diplomatic as you want to be.
I'm in another discussion with my doctoral cadre and the comment was made that k-12 hides behind tradition, whereas corporations are always having to innovate or go out of business.
The point I made in reply is that everybody agrees education must change; it's just that:
1. We have no consensus on direction.
2. The number of people who are passionately AGAINST a direction always outnumbers those who are passionately FOR a direction.
If you are an educator, you are always getting shot by somebody, but it's much less painful to stay and get shot routinely than it is to move and have opponents open with a volley.
Michael, I think to some degree you underestimate the effect the NCTM standards and reform math has had on classroom instruction. As an example, a substitute teacher in a Boston middle school asked a student to do a subtraction problem on the board. The student drew a number line and proceeded to answer the question correctly drawing on the number line. The teacher then showed the class how to do the problem using the column method. The class said they had never seen that before and a student teacher told the substitute that they were not to teach that method.
As another example, a Washington state state assessment test grading guide suggests marking a student down for using standard subtraction becuase it is an "algorithm." The implication being that it shows less understanding. Another example of the same question, but with the subtraction written differently was given full credit.
There may have been high minded goals behind reform math, but too frequently it seems, one rigid orthodoxy has been replaced by another.
Steve C.: maybe these things happened, but they don't reflect the thinking of the people I know well at NCTM. That would include current president Skip Fennell, and several past presidents, including Cathy Seeley, Johnny Lott, and Jack Price. In fact, I know no one who would subscribe to such rigid practice. I hear these anecdotes/horror stories, yet in nearly 16 years of observing classrooms, I've yet to see a teacher who did not teach traditionally in part, regardless of the curriculum/book in place, or who failed to teach "standard" algorithms in addition to alternative ones, IF s/he taught any alternative approaches at all.
Probably things are dramatically different in Michigan than in Boston or Washington State.
I can't prove that there aren't people out there with idiotic ideas about whether it's sensible to teach traditional algorithms. But I do read an awful lot of garbage that is put in the mouths of progressive reformers who say something different from that. The classic example, of course, is what is generally (and falsely) attributed to Constance Kamii. Nowhere in her work does she say that it is wrong to teach algorithms to kids. What she says is that it appears to be potentially (and in many cases actually) detrimental to the independent and confident mathematical thinking of young children if they are taught one orthodox way of doing arithmetic before they have had the opportunity to develop their own ideas about it. And based on my experience as a student, teacher, math coach, supervisor of student teachers, teacher educator, and researcher, this is not an illogical or crazy assertion on her part.
But the fact that opponents of progressive, student-centered mathematics teaching insist that she has made a blanket claim that "we shouldn't teach algorithms to kids" - PERIOD!!! tells me that many of these opponents are either very bad readers or very big liars. There's no third possibility (unless one considers that they're just sloppy "researchers" who don't bother to check the original source material and prefer to believe any nonsense they're told that fits their preconceptions and ideology).
Since I've actually bothered to read Kamii's work enough to know what she says and doesn't seem to be saying at all, I'll stick with my sense that she's not proscribing standard algorithms or all algorithms: she's suggesting patience, something that anti-reformers have very little of when it comes to reform, especially since they mostly appear to be sure they're absolutely right about everything.
As for my alleged underestimation of the influence of NCTM and the standards documents: would that were true.
On the other hand, there's always room for stupidity and doctrinaire thinking (where the latter is deeply influenced by the former; that is, the stupidity forms the misunderstanding and rigidity of non-doctrinaire ideas and codifies them into a bizarre mess). So perhaps some teachers or administrators have twisted the flexibility and sensible thinking in the NCTM standards volumes into what you describe. Or maybe these people are just "those sorts of folks" to begin with: that is, they're prone to look for the simplest, least-thoughtful views of things and will take a really entrenched position as long as they don't have to give much thought about whether it's right or reasonable.
If the rejoinder to this notion is that clearly NCTM and the standards books are culpable and should have known that some idiots would pervert their ideas, well, I'm afraid NCTM doesn't quite have the power to either make people follow their ideas OR ensure that those who think they're doing so are doing it well. That's a much more local matter. But if NCTM is culpable for bad math teaching in the name of their standards, who exactly is culpable for all the horrid math teaching we've had and continue to have that don't adhere and run counter to those standards? That's something critics of NCTM and progressive math education never mention in my hearing, for some odd reason.
I just want to concur with stevec's remark on the lack of cohesive vision in education reform in this nation of ours...
But, in defense of the progressives, reform must be made even if it means throwing darts at a board, for there will never be a shortage of critics... as long as the kids are learning, with both a grasp of the traditional and less conventional, who cares who's right or wrong? Time (and data-driven instruction) will tell what areas we can do built upon, just as Mike's column on "continuous improvement" as oppose to a one-size-fits-all philosophy, because I doubt that we can ever have a perfect, universal apporach.
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