Constructivism? We Don't Need No Steenking Constructivism! (or do we?)

In a recent post on math-teach@mathforum.org in response to my comments about pedagogical content knowledge, Jonathan Groves wrote, in part:

Perhaps it is tricky to define constructivism precisely and to know exactly what it is. I am not even sure if I know exactly what it is though I do have at least an idea of what it is. I have learned some about constructivism in some education classes I took at Austin Peay State University when I originally was trying to become a high school math teacher (which I later abandoned so that I can graduate in four years and teach college instead).

But the constructivism I learned I remember vaguely, and I learned some more about it when I was completing my online faculty training for Kaplan University, where I will begin teaching math online on March 25. The faculty training consisted not only on
information on how to use their online system for their online classes and about Kaplan University itself and some of their expectations for faculty but also about some of the theories of online learning and how online learning differs from traditional higher education learning. Constructivism is used a lot in their classes since direct instruction can't be used well in online classes. Even with live seminars, instructors still can't use direct instruction as their primary teaching method since the seminar is only one hour once a week.

The constructivism I learned from the training is very general; it says nothing about constructivism in mathematics or in any particular subject for that matter. That is perhaps not a good idea, but the faculty training course is designed for all the new faculty, regardless of what subjects they are teaching.

It is extremely important to know how constructivism is relevant to mathematics learning and teaching not only for those discussing it but also for those teaching mathematics. This knowledge can help us fellow mathematics teachers discuss constructivism intelligently and without confusion to others and to teach mathematics more effectively. We first need to learn exactly what constructivism is and
how it is relevent to learning and teaching mathematics.

[F]lexibility and content knowledge of mathematics itself is extremely important for teachers. I myself would hate to lead a discussion and it sidetracks into another related interesting topic but then find myself not knowing how to handle this situation. Class would then become a disorganized mess, and no students would benefit from it in the least bit. Lesson plans don't have to be followed rigidly and shouldn't be; the teacher should allow for digressions if they are relevant. But if the teacher cannot handle these digressions, chaos will reign, and chaos never works in any classroom.

I would also hate it if this new related interesting topic is something I know little about. I doubt that will happen with the classes I will soon teach in the next few weeks. One such course is Basic Algebra (Developmental Mathematics) for the Spring 2 quarter at Florida Tech (starts March 9) and Math 103 College Mathematics for Kaplan University (starts March 25). Kaplan uses 10-week terms, and they have new terms starting about every 3 weeks or so. Thus, one of your colleagues' classes may start
at the beginning of one term and yours start at the beginning of another and yet your colleague hasn't finished teaching his class yet. If I am wrong and something does arise I know little about, but since the courses are online, getting around this problem will be easier since I will usually have time to think about such posts
before I reply to them.

It seems obvious that subject knowledge is required for the mathematics teacher, yet the lack of mathematics knowledge potential teachers have when they graduate and then get their teaching licenses later makes one wonder if it is as obvious as it seems. At least that is a major problem in states like Tennessee and Kentucky that are known
for providing education that is not so good.

That leads to an extremely important question: What content knowledge should math teachers have? Of course this depends on the grade level or level of college they are teaching.

If new topics are related to the curriculum but not part of the curriculum itself and there is little time to devote to them, then having students think about it as homework or to lead a short class discussion or as extra credit research assignment are wonderful options to pursue. The last one is good since it encourages students to become curious about mathematics and to learn to study it on their own, which is a great benefit for them. And it teaches them that mathematics studied do not have to be topics restricted to what is learned in the classroom; in other words, it encourages them to learn whatever mathematics interests them, even if it is not discussed in the classroom.

Being able to make these decisions effectively is vital for preventing classrooms from turning into chaos and into doing what is best for the students.

[W]hat is best depends on who the students are, what the required curriculum is for the class, what math classes the students will or are likely to take in the future, and too many other factors to list here. Depending on the experience of other colleagues, whether in your school or not, when facing a tough decision in
teaching is vital. Kaplan University encourages us instructors to ask our department chair and our mentor and other colleagues when we face difficult decisions and other problems in teaching. And reading widely about teaching and discussing with others may
help prepare us for these difficulties later and to make good decisions. That is why several colleges I have seen take professional development seriously. Kaplan University does.

We definitely need better teacher education and professional development programs in this country. This will help not only in mathematics teaching but in the teaching of any subject. Like mathematics, most other subjects aren't being taught very effectively
these days. For example, schools didn't teach me much world geography or world history (our high school world history class was really European history; our teacher skipped all the chapters on history in the Americas, in Africa, in Asia, etc. except when the history pertained directly to European history. Even then, that was really
history on European colonization). And our U.S. government and economics classes weren't very good either. I wouldn't be shocked if that is the case throughout the U.S. since somehow I get the impression that many young American adults these days don't know much about how economics (except maybe business and economics majors!)
and the government work. I could give more examples, but I think these suffice in illustrating my point.

Where we start these improvements, I am not sure. One idea is to make sure our mathematics teachers have enough subject knowledge and knowledge of teaching to get started. And we should make sure mathematics teachers at all levels appreciate and enjoy mathematics. I have heard this problem is most severe at the elementary school
level, and I am not surprised since these teachers are forced to teach math,
regardless if they want to. Higher up, they can choose whatever subject they want. And I suppose elementary school math is harder to get excited about than more advanced math. And a lot of these teachers who don't like math may too have had teachers in elementary school who didn't like math who turned off their interest permanently, which in turn hurt their ability to learn the mathematics they ought to know to teach elementary school math effectively. If students learn to dislike math early, say in elementary school, they may learn to dislike it the rest of their lives. Exactly how to fix these problems, I don't know, and I strongly wish I knew! Does anyone have any ideas here?

My reply

I think the relevant ideas from constructivism are not complex. From my point of view, constructivism simply asserts that people construct their own individual understanding of anything they learn (in or out of formal instructional settings) through an INDIVIDUAL interaction between past knowledge/experience and new information.

Why this is important for teachers, most particularly for teachers of subjects in which there is a propensity for many instructors to think that "it is obvious" that something is true, or that it suffices for them to state a logical sequence of definitions and reference to previously-taught axioms and theorems in order for students to learn a new theorem, is that very little is obvious to many students, and it's lousy pedagogical practice to assume otherwise. Further whipping through the carefully constructed steps of a proof, while it may be beautiful to those who understand and are capable of appreciating it aesthetically, is lost on most students seeing the ideas for the first time and just learning to grapple with proof-theoretic mathematics. This approach not only leaves most students in the intellectual dust, but gives them the VERY false impression that if they were mathematically competent, all would be clear, just as it is to the instructor and must have been to the mathematician who first constructed the proof.

But of course, that is precisely NOT the case. In all likelihood, the professor did NOT grasp the workings of the proof (if it was of any depth and complexity) at first blush. And it is certain that the mathematician who constructed the proof didn't have it spring from her/his head like Athena from that of Zeus. There were generally a series of fits and starts, a good deal of creativity, intelligent/inspired guess work, going up blind alleys, retracting steps, and much frustration requiring sustained effort on the part of the mathematician or mathematicians who ultimately succeeded in constructing the proof in question. (Yes, there are "simple" proofs at various points in the development of any mathematical subject, but it's not long before those are left behind, and those who are going to follow the development of the topic will need to be able to juggle a host of definitions, axioms, previously-proved theorems, and, of course, abstract concepts, in order to make sense of new material and proofs). We do an enormous disservice to many students by hiding ALL the rough edges as if they never existed and as if we "got it" first time and every time.

At a lower level (namely K-14, where there is a lot less formal or even informal proving and a lot more teaching of definitions and procedures, much of the same still holds except that it's conceivable that the teacher has at best a tenuous hold on what's being taught, making many lower-grade or poorly-qualified higher-grade teachers loath to go off the reservation of any lesson plan. Hence, they are wont to fail to offer alternative explanations for concepts and procedures, often holding to the dreaded "my way or the highway" philosophy, sometimes from fear, sometimes from laziness, sometimes from just being a rigid character, but in all cases failing to serve well many students.

Teachers who have recognized the usefulness of the constructivist approach to understanding how we learn are less likely to come at teaching as a "one-size fits all" process. Constructivism doesn't tell anyone how to teach, but it surely points towards the notion that we can't pour our own understanding of anything into anyone else's head. That's simply not how folks learn. There is NO unmediated learning. There is NO way to get through the filtering and processing EACH individual will do every time we teach and s/he tries to understand and learn. Any teacher who gives a "dynamite" lecture and leaves the classroom with a confident belief that the students must have learned (if they were prepared and paying attention) is likely deluding him/herself. It's not that no one learned: everyone who WAS paying attention learned. But just what each one learned is unknowable, and to have ANY idea at all requires doing more than simply lecturing, no matter how well.

That is not to say that all lectures are equally good (or bad) or that lecturing doesn't have its place. But it does suggest that there needs to be a lot more. And given how much lecturing and its variants (so-called direct instruction, teacher-centered instruction, and similar approaches in which teachers can say with straight faces, "Boy, I taught good, but they learned lousy") dominate math teaching in this country, we might expect that mathematics teachers at all levels would welcome ideas about how to be more effective by varying instructional strategies and styles. If a group of mathematics teachers and teacher educators called for a shift in emphasis towards more student-centered instruction and less of the sage-on-the-stage approach, folks could look at what has been going on (and not going on) for decades honestly, recognize their past successes and failures, take some ownership and responsibility for both, and respond fairly to the 'new' ideas (of course, many of them actually aren't new, but rather are a return to some things that fell out of fashion for various reasons, not all of them because the methods didn't work).

Thus, it would perhaps shock a neutral observer to note how some mathematicians and K-12 math teachers responded, and the vehement attacks that have been launched on various notions that were introduced in the 1989 NCTM standards volumes (though not necessarily solely there, as there were individual practitioners using a host of more student-centered practices in their classrooms long before the first of those volumes was published). Twenty years later, the same distortions, lies, misinformation, epithets, etc., about this call for a shift in emphasis continue to appear on the internet, in the media, and in public and private discourse. Reform is portrayed as utterly wrong-headed, extremist, throwing babies out with bath water, ad nauseum, with little sign that the original opponents and those allies they gained will ever lighten up at all.

We're a long way from seeing broad-based and meaningful reform practice in math classrooms in this country, but it is clear, too, that reform ideas aren't going to go away, despite the best (or worst) efforts of its hard-line foes. And so it becomes necessary to go over a lot of the same ground periodically to try to sweep away the enormous amount of dreck about reform ideas that spews from a few persistent sources.

The necessary content knowledge for teachers is a majr focus of the research and writing coming out of the University of Michigan's mathematics teaching program, particularly that of Hyman Bass and Deborah Ball and their colleagues. Indeed, it is the major research question they've been looking at for about a decade.

Of course, part of the issue here goes beyond simple concerns about curriculum and towards questions about "the system." Recent calls for a national curriculum, national standards that apply to every state, etc., are simply an extension of the idea that there's some blueprint we could devise that, if followed to the letter or nearly so, would produce a mathematically competent country. I think this idea is in fundamental conflict with constructivist theories of learning, and these calls are an attempt, well-meaning or not, to make it increasingly impossible for individual classroom teachers to make the sorts of pedagogical judgments which in fact should be a major part of what they do. I have argued here and elsewhere that no one is better-positioned than the individual classroom teacher to make such choices about his/her students. Rather than managing curriculum from the top down in some blindly monolithic fashion, the people in charge should be putting energy into ensuring as much as possible that teachers are well-equipped to make those decisions as they arise.

The phony "accountability "movement would appear to be all about finding out which practices work and which don't and rewarding the successful and "dealing with" those who are not, but the real agenda is to reduce teaching to formulas: a wacky stop-watch brandishing "management science" approach out of the worst nightmares of those of us who realize that there's no such formula. A genuine accountability effort would entail creating structures in which teachers are helped to make better choices while not hamstrung so that they can't dare do anything that isn't "by the book." A real approach to accountability would entail ensuring that teachers give "accounts" of some of the important choices they make, both to encourage reflective practice on the part of each individual teacher and to collect a body of knowledge that can be shared with other teachers. Of course, when education is viewed as a business and creativity, originality, and any sort of "risk-taking" behavior is likely to be punished, this sort of model can't happen (and it's hard not to see the irony in these management notions coming from various executives whose companies may have been burning through money like a '65 Buick badly in need of a ring job burns through oil, while the genius managers are collecting millions of bonuses and perks. Apparently accountability is only for others).

What pedagogical content knowledge is, exactly, would take books to contain. What it is in small part is some of the choices I pointed to previously when I looked at roads not taken by Bill and by each teacher every time s/he chooses to either stay on the prescribed path of the lesson (and of course in constructing the lesson in the first place) or not. It's unlikely that I or anyone could cover every possible choice (even just the reasonable ones and some examples of less reasonable ones) that could arise. However, there are books starting to appear that, if their titles are to be believed, focus on mathematical pedagogical content knowledge. I don't have any of them and can't comment on how effectively they accomplish any of this. If and when I get my hands on some, I will try to report on what I see.

I don't think there are any simple or exact fixes to the current state of mathematics teaching and learning, naturally, but being open to real reflection on the issues, one's practice, and much else makes for a good start. The closed-mindedness exhibited all-too-often in response to constructivism and its relation to mathematics education helps no one, not even the entrenched.

Pedagogical Content Knowledge: The Missing Link In Math Education

In a recent post to the math-teach@mathforum.org list-serve, Bill Marsh wrote, in part:

I continue to think that guided discovery can be a powerful teaching tool, of definitions, as well as of proofs, but I should emphasize that in GUIDED discovery there will be a teacher in the room who knows the theorems that are coming and some of the pitfalls on the way to getting them.

If you don't know how to use them, power tools can dangerous. If you don't like them or have to use them, you won't use them very much. Unless you use them a lot, you are unlikely to learn how to use them well. If you don't know how to use them well, you may underestimate what can be done with them.

Suppose students arrive in a seventh grade math class to see 1+2+3 = 6 on the board. After a moment or two, the teacher might mention that numbers like six are called perfect and ask if anyone can say what's going on. I'd expect that pretty quickly someone would suggest adding up all the divisors, which can then be tweaked into a good definition. The class could look for another perfect number less than a hundred. If this were done near Valentine's Day, amicable numbers might be mentioned.

At a higher level, I might, on the first day of a real analysis course I was teaching, say that we were going to be looking at things like the epsilon-delta definitions and proofs they saw briefly in calculus. I might ask them to consider, for a real number a, the sequence the intervals defined by |x-a| < dk="" education="" 01330="" pdf="">http://www2.mat.dtu.dk/education/01330/Chapter1Math3.pdf

I don't claim that guided discovery is the best way to teach. I will claim that it is a good way, and that it is an especially good way in K-12. But only for those who like it enough to be willing to try to do it well.

I think Bill's post points to something far more important than "constructivism" (a topic that generates lots of heat and virtually no light here, in my experience). Who is and who isn't a constructivist, and what comprises applications of constructivist learning theory to mathematics lessons is rather useless to talk about amongst folks who can't even approach the slightest agreement about what "constructivism" actually is or what its theorists have to say that is relevant to mathematics teaching and learning.

What Bill's post touches upon, however, is the issue of pedagogical content knowledge. A teacher who proposes to teach a lesson on perfect numbers and offers the example Bill originally posted may well, as Dave Renfro subsequently pointed out, find herself in the middle of a conversation about triangular numbers (though it's quite possible that no one in the classroom, the teacher included, may know that term). Or perhaps (though less likely) the reverse situation takes place, with a lesson on triangular numbers potentially branching off towards a conversation about perfect numbers. One important consideration is, as always, what do teachers do when the unexpected or unplanned for arises? And clearly, one consideration in that regard is whether the teacher has the requisite content knowledge (awareness of the mathematics being pointed to, the mathematics that leads into what's arising, and some of the mathematics that is pointed to by what's under consideration AND being raised by the "surprise" issue). But more than that, the teacher must be able to make quick but reasonable choices as to how to respond to what arises.

Bill's proposed response seems to me to be one exemplary option. And in order to produce it, a teacher would need to be prepared to deal with the math that comes up, and also have a strong sense of whether it is a better idea to continue with the plan or to go down the new road. That means pedagogical content knowledge and knowing the class and what is most likely to serve them well, collectively and individually. If the original plan is chosen, how is the new idea addressed (never? in the next class? by the teacher raising it? by the teacher asking the class to think about it as a homework assignment? by asking the student who raised it to report on it or lead a class investigation/discussion, etc., as an extra credit assignment? some other option?) If the new opportunity is pursued, what happens to the previous plan?

My view here is, of course, that content knowledge alone and general pedagogical knowledge alone will not suffice. While strength in both these areas is necessary and contributes to making good decisions in this and many other situations in math class, they are not sufficient. There is a third kind of knowledge pointed to in what I raise above that is peculiar to this domain of teaching (and so saying does not preclude the idea that similar but different specific pedagogical content knowledge is needed in other subject areas) without which teachers are less likely to make choices that adequately serve the vast majority of students.

None of the above is intended to imply even remotely that there is a single "correct" decision to be made in the situation Bill describes. I'm perfectly comfortable that he made a good one, but there were other possibilities that, depending upon information that only the teacher has access to at the point the decision is made, might have been as good. There's no way to know with certainty what the results of these other choices would have been, but experienced, reflective teachers who have the requisite knowledge and use it actively are the ones most likely to pick from a "menu" of better and more productive options. Naturally, there are worse, less effective choices, based on previous experience, observation of and/or conversations with colleagues, consultation with the literature, interaction with coaches, master teachers, etc. It is naive to think that without reflective practice and competence in the three domains of teaching knowledge mentioned here that teachers will "naturally" make better choices when these situations arise, based simply on content knowledge alone. It is for this reason, among others, that effective teacher education and professional development is vital if we are to improve mathematics teaching and learning in this country.

Are "Both Sides" in the Math Wars Dogmatic Absolutists?

In response to one of Wayne Bishop's usual assaults on someone who deigns to write or speak positively about progressive mathematics education, Bill Marsh wrote, in part:

Wayne follows Wu by starting with one way of doing something, then dogmatically claiming and perhaps believing that it is the only way. This happens on both sides of the math wars, usually in the weaker form of merely claiming there is only one best way.

I wrote back to Bill, a mathematician with whom I generally agree about educational issues:



I wonder what you mean when you say "This happens on both sides of the math wars." Assuming that the antecedent of "this" is "claiming and perhaps believing that it is the only way," I would suggest that I've yet to see someone on MY side of the Math Wars debates take the view that there is only one way to do or think about anything, particularly when it comes to teaching and learning mathematics.

The anti-progressive side has been pulling a cute trick for a long time by citing a couple of types of things that make it appear that those they oppose are just as outlandishly rigid as they are themselves. One sort of evidence is teachers who are not involved at all in the sorts of debates that arise here and in similar places, but rather are rank-and-file folks who have "caught the reform bug," so to speak, but haven't given it a lot of thought. They may have caught it because their district mandated a particular curriculum, or because of a conference session, or from a colleague, and suddenly they are True Believers in the worst sense. They become just as rigid and unreflective about their latest religion as they are about every previous one and as they will be about the next one. Such folks are not, on my view, progressive teachers, and their lack of reflection and insistence that they've found some new panacea (be it manipulatives, problem-solving curricula, technology, games, a particular math textbook or series, small-group work, project-based learning, or anything else) makes them simply folks who will likely jump on many more bandwagons with just as little thought and understanding. They are not really any different from unreflective teachers who glom onto Saxon Math, programmed instruction (back when that was the fad), or a host of other things that don't happen to be part of the progressive/reform menu. Approached with little or no thought or reflection, such things aren't answers either, but of course a True Believer always thinks s/he has found magic, not realizing that magic doesn't exist (at least not of that sort).

Another major sort of evidence anti-progressive ideologues have used is to find little snippets of things people associated with reform say that they can build into ultimate proof that the REAL progressive reform agenda is racist, fuzzy, watered-down, inferior, extremist, and so forth. A classic example is what was culled from a radio interview given in 1996 by the then-president of NCTM, Jack Price. Wayne and his Mathematically Correct/HOLD friends have come back to that little bit of decontextualized spoken prose as damning evidence of patronizing racist and sexist attitudes not only on the part of Jack Price, but the entirety of all progressive reformers. While this is hardly the only example of such things, it serves as the archetypical one to my mind.

A third example, somewhat similar to the second, is taking lines from articles by progressive reformers that are clearly intended to shock people out of their complacency about mathematics education and, again, use them to attack EVERY progressive reformer and progressive idea. Two cases in point are Tony Ralston's piece, "Let's Abolish Paper and Pencil Arithmetic," suggesting the seemingly radical idea in the title (his very sensible call in the same article for increased emphasis on teaching estimation skills and mental arithmetic is conveniently ignored by the critics, of course), and Steve Leinwand's 1994 piece in EDUCATION WEEK, "It's Time To Abandon Computational Algorithms." A fair reading of the article makes clear exactly what Leinwand proposes, but it's more effective rhetorically for critics to cite the eye-catching opening paragraph rather that the reasoned argument that follows, especially when in the third paragraph Leinwand makes crystal clear that he isn't calling for an end to teaching basic computation skills, but rather asking that we take a much-needed critical look at WHICH computation skills we teach and what alternatives exist for kids who don't necessarily "get it" as quickly as conventional wisdom says that they "should" (always a word that is popular with the MC/HOLD folks and others who wish to trash progressive reform notions).

While the above three sorts of maneuvers hardly exhausts the list of what anti-progressive reform attackers are very wont to do, they are the ones most immediately relevant to the question of whether Bill's comment above, if I've gotten its intent right (and it's quite possible that I haven't), applies equally well to "both" sides (of course I think there are many more than two such sides) in the Math Wars. And in my experience, it's simply not the case in any meaningful way that progressive reform theorists, advocates, and reflective practitioners are guilty of the sorts of dogmatic absolutism that so thoroughly characterizes the views of their vehement critics and opponents as seen on the websites of Mathematically Correct and NYC-HOLD.

It's About Time: Obama On Science

Sometimes there's nothing to add other than my wish that the speaker succeed in not only being heard, but heeded, and my gratitude for having been around when an intelligent, articulate, and above-all humane person once again holds the most powerful elected position on the planet.

Reducing Class Size VERSUS "Best" Instructional Practices (and other rants by yours truly)

A recent commentary "It's Not All About Class Size" appeared from Ken Jensen on the discussion list of the National Council of Supervisors of Mathematics (NCSM):

I agree with the assertion that, "it is possible that smaller classes will actually widen the domestic achievement gap between the haves and have-nots." and the explanation as to why this may occur is well thought out. However, the article is void of any suggestions as to how we might increase achievement for all- both raise test scores and close the gap.

I would like to propose that a teacher with a well developed sense of best instructional practices does much more to increase achievement for all students than lowering class sizes. In fact, I would want this teacher's class to be full to the brim so that as many students can take advantage of this learning environment as possible, and I would expect this teacher to raise the achievement level of all his or her students in spite of the large size.

So much has been written about what makes for good instruction and yet it is so elusive in America's schools. Let's take the money the politicians would use to lower class sizes and instead use it for in bedded professional development. The coaching model as developed by Lucy West and Catherine Casey is making a difference in the district where I work, and I promote it everywhere the conversation comes up.

My response, which of course is to more than just what Ken wrote above:

Seems a bit puzzling as to why this is an "either/or" situation. EITHER we decrease class sizes OR we try to improve the quality of teaching? Why not both if each is important?

Effective classroom coaching is an important part of the story, no doubt. So is, I think, reduced teaching hours per day, more opportunity for collegial observation and interaction (as long as the school creates and supports actual professional development during the non-teaching hours, rather than offering more planning periods that are spent grading or talking about baseball (not that I oppose giving teachers time to grade, but not INSTEAD of meaningful collegial interaction and professional development. And much as I like baseball, I've sat as a guest in far too many math teacher lounges where that was the main subject, when bashing individual kids or certain "kinds" of kids was not, and no mathematical or pedagogical issues were ever raised at all)). So is lesson study, which incorporates features involved in coaching, planning, collegial feedback and observation, etc.).

As to the idea of cramming as many bodies as possible into the classrooms of the "good teachers." How long before they become burned out by their increased grading load? How long before you destroy the classroom culture by making the carefully-crafted dynamics impossible to rebuild or sustain? I think that's a rather questionable suggestion at best, unless of course you assume that the "magic' this teacher is doing is completely grounded in some sort of fabulous lecturing, a doubtful proposition in my experience.

And as long as I'm scatter-gunning here, I am for some reason skeptical of the phrase "best instructional practices" for a couple of reasons. First, I think teaching remains far more an art than science (not unlike pretty much everything else in the social sciences. I'm working on a blog entry about the relationship between psychoanalytic practice and jargon and educational practice and jargon. Suffice it to say that the more the jargon, the less impressed I am by the what's being spoken of, assuming I can piece out what that might be). The notion of "best" instructional practices sounds a little too smug and reminds me of how the word "authentic" gets used in the writing of some educational researchers and pundits: if what YOU are doing is "best" or "authentic," where does that leave me? I have this same reaction to the Core Knowledge Foundation gurus, who tout the solution to our educational woes as "teaching content." Obviously, since I don't subscribe to their religion, I must not be teaching content. Or at least not the "right" content.

I prefer to think about instructional practices as a palette from which we choose depending on the vicissitudes of daily teaching reality. It is not a scientific process. If it were, I could mail in my lessons (and my instruction). Yes, there are some things I choose quite consciously not to have on my particular palette. And some things I have in very small supply and use sparingly by design. Beyond that, I can't claim to know in advance what classes will be like other than in broad strokes, and the rest comprises details that emerge as part of an organic process that cannot be accurately foreseen. Stuff happens when you're dealing with human beings. And lest we forget, the main instrument we use to both teach and to assess the effectiveness of that teaching on a moment-by-moment basis as well as upon latter review is a flawed one: ourselves. That's fine, since we're all in the same boat. But I for one am tired of being asked to pretend that teachers or educational researchers, teacher educators, coaches, curriculum developers and authors, administrators, or others involved in the instruction process are objective scientists or anything of the sort.

Set rant to [OFF].

Core Knowledge: Who Are the Snake-Oil Salesmen?

The following was recently posted on math-teach by the always-remarkable Professor Wayne Bishop, who never saw a progressive educational idea he didn't despise:

http://www.coreknowledge.org/blog/2009/02/03/21st-century-snake-oil/


21st Century Snake Oil

Published by Robert Pondiscio on February 3, 2009 in Core Knowledge, Curriculum and Education News. Tags: 21st century skills, Alfie Kohn, content knowledge, critical thinking, Curriculum, Jay Greene, Tony Wagner.

Yesterday, Alfie Kohn; today Tony Wagner.

Jay Greene goes after the education guru on his blog and in an op-ed in the Northwest Arkansas Morning News. The Fayetteville Public School system has purchased 2,000 copies of Wagner's The Global Achievement Gap and is holding a series of public meetings, according to Greene, on how Wagner's vision for 21st century skills "might guide our schools." Be afraid, says Jay. Be very afraid.

It's hard to get people to think critically about people who push a focus on critical thinking. To be for critical thinking is like being for goodness and light. The tricky part is in how you get there. To the extent that Wagner has any concrete suggestions, he seems to be taking folks down the wrong path. He wants less emphasis on content and less testing. But he shows no evidence that higher levels of critical thinking can be found in places or at times when there was less content and less testing. In fact, the little evidence he does provide would suggest the opposite.

Joanne Jacobs weighs in as well, pointing to a Sandra Stotsky op-ed on Tony Wagner, and noting succinctly: "I don't see excess knowledge as a big problem for today's students."

Cultural Literacy Bonus: Check out the illustration atop Jay's blog post. It's Bugs Bunny dressed as a Wagnerian Valkyrie from the cartoon, What's Opera, Doc? Can you imagine a kid's cartoon using Wagner's Ring Cycle as the basis of a parody today? It's a bromide to suggest that entertainment has been dumbed-down over time, but it's hard not to notice the difference in the vocabulary of Mary Poppins, for example, or the Rex Harrison version of Doctor Doolittle compared to contemporary kids' fare. Quantifying the change in cultural references and vocabulary level in children's entertainment over the last 50 years or so would make for an interesting study, if it hasn't already been done.

Well, pardon my lack of excitement at the above from Bishop and his Core Knowledge buddies, but I felt compelled to craft a response:

Just reading the name of this blog and the first few lines had me in hysterics (the fun kind).

"The Core Knowledge Blog

Closing the Achievement Gap: Teaching Content"

Funny. And the rest of us are, of course, NOT teaching content. Sez the Hirschies.

Of course, they have a very narrow definition of what comprises "content": namely just precisely what THEY say it is, and nothing else. Beware! Fascism lurks here.

Then, the blogger quotes Jay Greene in order to attack Mr. Wagner (whose ideas are not particularly appealing to me, but clearly any enemy of my enemy deserves my consideration):

"It’s hard to get people to think critically about people who push a focus on critical thinking. To be for critical thinking is like being for goodness and light."

Yeah, and being "for content" is not a pile of equally empty baloney? Doesn't "which content" matter? Oops. See above. THEIR content, of course. Want to know which? Pay Mr. Hirsch and pals and they'll sell you all the books you don't need to find out what a narrow-minded old white guy thinks your Nth Grader "needs" to know. And just as a reminder: this is the "educational expert" whose credentials are being a literature professor at University of Virginia who suddenly decided he could make a lot more money shilling guides to K-12 educational content. And whose literary theory is that there's one right interpretation to every literary work, based on the "intention" of the author (apparently he managed to ignore the notion of the "intentional fallacy" or simply figured no one would notice that his view was outdated and for the most part irrelevant). This is the guy you want telling you what you and your kids need to know? I think you could do just as well to get advice from MEIN KAMPF, THE LITTLE RED BOOK, and THE EXECUTION ORDERS OF JOSEPH STALIN (okay, I made that last one up).

And then we have this bit of sophistry:

"Cultural Literacy Bonus: Check out the illustration atop Jay's blog post. It's Bugs Bunny dressed as a Wagnerian Valkyrie from the cartoon, What's Opera, Doc? Can you imagine a kid's cartoon using Wagner's Ring Cycle as the basis of a parody today? It's a bromide to suggest that entertainment has been dumbed-down over time, but it's hard not to notice the difference in the vocabulary of Mary Poppins, for example, or the Rex Harrison version of Doctor Doolittle compared to contemporary kids' fare. Quantifying the change in cultural references and vocabulary level in children's entertainment over the last 50 years or so would make for an interesting study, if it hasn't already been done."

I wonder if this genius actually bothers to watch today's cartoons. Of course, first he pulls a little bait and switch: cartoons and Wagner (and who does he think was supposed to 'get' that joke? Four year olds? No more than the writers of Rocky and Bullwinkle expected little kids to know that Boris Badenov was a play on Boris Gudenov. There have ALWAYS been jokes in kids' cartoon shows that are for the writers and other adults. And such things are far MORE widespread today than ever. I could cite dozens of shows and movies ostensibly pitched at kids, from SPONGEBOB SQUARE PANTS to RUGRATS to Disney's ALADDIN to BILLY AND MANDY (and on to more sophisticated fare for older kids and up, like SOUTH PARK, AQUA TEEN HUNGER FORCE, ROBOT CHICKEN, FAMILY GUY, etc.) in which the references are multi-layered, culturally sophisticated, and fraught with vocabulary and references my son constantly learned from and continues to learn from. As he gets older (nearly 14 now) he sees levels of things in these shows he missed when he was younger. No kidding: just as I am amazed at things in those old WB cartoons and CRUSADER RABBIT, BEANIE AND CECIL, etc., that went right by the much younger me at the time they first aired or I first saw them). And then suddenly we're talking about Mary Poppins and Doctor Doolittle. Nice. So then let's compare the vocabulary in those books (as well as the sophistication of ideas presented) with Harry Potter and Philip Pullman's HIS DARK MATERIALS trilogy, to be fair and accurate? Or would that ruin the sales pitch for Core Knowledge?

Let me sum up: Wayne and his Core Knowledge pals are the snake oil salesmen. Don't buy it, it's really bad for you and expensive as well