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Thursday, March 19, 2009

Stoller’s Rules: Thoughts on Psychoanalysis and Education Research


In his 1985 book, OBSERVING THE EROTIC IMAGINATION, the late psychoanalyst, Robert J. Stoller, offers a number of rules for psychoanalytic research that could well be of usefulness in considering what exists and what is possible in conducting (and consuming) education research (as well as the research in other social sciences. I first give Stoller’s list of rules, without putting them in the precise context in which they were originally presented, for fear of prejudicing some readers about taking these ideas seriously. Note that words in brackets are changes I have inserted to make the rules more obviously relevant in the context of educational research. Original language being replaced is specifically psychoanalytic.

Rule 1: anyone can assert anything.
Rule 2: no one can show anyone is wrong, since no one can check anyone’s observations (including his or her own).
Rule 3: ignorance can be wisdom (“The way toward better understanding, then begins with our understanding how little we understand.”)
Rule 4: use [description of motives] warily
Rule 5: ease up, forswear rhetoric, love clarity, relax.
Rule 6: describe people as we see, hear, or otherwise sense them, carefully and in detail. Do not use [educational jargon] in the midst of . . . descriptive sentences.
Rule 7: When it comes to [using educational jargon], less is more
Rule 8: stop picking on students or teachers
Rule 9: let us then, regarding [education], start afresh.
Final note: this is not really a report about [psychoanalysis], but, rather, one that uses psychoanalysis] as an example of the failure of [educational research], so far, as science.

So, what is this? More bashing of education research but from an unexpected source? Hardly. In fact, it is a call for honesty on the part of educators (at various levels), administrators (from buildings, to districts, to states, to Washington, DC), researchers, policy-makers, politicians, journalists, talking heads, business leaders, think-tank pundits, foundation funders, ideologues, and various other stake-holders when it comes to what education research is, can be, or should be.

Like Stoller in his remarks on psychoanalytic research literature and its jargon, I offer this commentary out of concern that both practitioners and critics are destroying education research by trying to make of it something it is not: a scientific literature akin to that of physics. I will resist at this juncture the temptation to go further by looking at the work of Paul Feyerabend and other post-modern philosophers of science who are critics of the notion that even the hardest science is not devoid of subjectivity, judgment, and, for want of a better term, humanity. It suffices to state that it is an error to try to make a "pure" science out of an area of inquiry that cannot afford to lose contact with its essential humanness and humanity.

Thus, allowing those who think that "the answer" to problems in education and education research are the same, and that this alleged single answer is foundational, I suggest that we turn to the instructional precedent of the history of the philosophy of mathematics itself, where logicism (as exemplified by the efforts of Russell and Whitehead in PRINCIPIA MATHEMATICA) failed to establish purely logical grounds for all of mathematics, due to underlying problems with completeness and consistency revealed by the work of Kurt Godel. The failure of the Russell and Whitehead project did not lead to the death of mathematics, of course, but rather to the demise of foundationalist attempts at creating some "ultimate" underpinnings for mathematics. Among the implications of Godel's Incompleteness Theorem are the realization that there will always be unprovable but true theorems as well as false hypotheses that forever resist refutation. Is this a tragedy, or in fact, as I believe, a signal to mathematicians that new ideas and inventions in their discipline will never be exhausted?

Returning to education research, if mathematics, the "queen of sciences" cannot be ultimately grounded, why should it be necessary to ground education or its research literature strictly in quantifiable, statistical/mathematical terms? The fact is that no such grounding in some sort of absolute and objective reality is possible. Neither is such a chimerical pursuit necessarily desirable if it could be attained.

One of the peculiar things I noticed as a new (but hardly young) graduate student in mathematics education at the University of Michigan in July, 1992, was the on-going controversy and conflict in my newly-chosen field between those who advocated for purely quantitative research and those who supported primarily qualitative methods. Given that my adviser and the principal investigator on the project that funded my graduate work at the time was engaged in fundamentally qualitative research, it might seem predictable that I would be unduly prejudiced against quantitative methods. It bears noting, however, that I had already taken two graduate-level courses in statistics and quantitative methods and experimental design while doing graduate work at the University of Florida in psychological foundations of education. I was not ignorant of or intimidated by statistics. I did, however, find myself somewhat skeptical of the notion that educational issues would readily be settled through the kinds of experiments that could be well-analyzed by the quantitative methods I studied (somewhat ironically, the other students in the courses I took were all doctoral candidates in clinical psychology, many of whom planned to be psychotherapists, not research psychologists. And the text we used, the classic STATISTIC FOR EXPERIMENTERS by Box, Hunter, & Hunter, seemed to draw all its examples from industry: nothing could have been more quantitative and, seemingly, objective. I could make sense of it, but I didn't see it applying readily to educational research and still do not.

Neither, I suspect, would Robert J. Stoller. He makes clear in book after book that he feels obligated to remove a false sense of objective truth (conveyed in no small part through the use of psychoanalytic jargon, which he both decries and eschews) from his psychoanalytic studies of particular patients (several of his books deal primarily or exclusively with but a single case history) and issues of gender identity, sexual attitudes, practices, and feelings, etc. In the latter part of his career, he worked directly with an ethnographer/anthropologist, Gilbert Herdt, and even traveled to meet with and study the Sambia tribe in New Guinea that Herdt had been investigating (they co-authored a book on this collaboration). Stoller began doing a form of what he termed clinical ethnography that extended to studying several marginalized segments of American society.

Throughout this work, he makes crystal clear in the books he authored that in the sort of science he engaged in, he, the analyst, interviewer, ethnographer, IS the instrument of (not under) investigation, and hence cannot be kept out of the awareness of readers. The idea is not to guarantee a sort of false reliability by, in effect, telling readers: "Look, I'm drawing your attention to the fact that I'm the lens through which all of this is being filtered (it's important to note that Stoller made a major point of reviewing analytic notes and manuscripts with patients and those he interviewed for other studies before publishing and always got their explicit approval), and so you can trust me because I'm telling you this." Rather, he repeatedly states that the best he can do is to periodically remind readers of his own choices of what to report and how, and to do his best to get his viewpoint, biases, and methods "out there on the table" for readers to consider and examine. This practice doesn't make him right, or reliable, or objective, or anything of the kind. But it does make him much more honest than many other writers. And it does go a long distance towards demystifying and "descientizing" what he is up to.

On my view, this approach of Stoller's is precisely what educational researchers should be doing. While there are places where purely quantitative research may be possible, I believe those places are far fewer than many would have us believe, especially those during the last eight years who have pushed for so-called "data-based research" as the alleged gold standard. My sense of this move is that it has been a smokescreen for marginalizing research that looks closely at individual and small cases, the very sort of work that brings to life what happens in real classrooms with real teachers and kids. It may be possible that a blend of qualitative and quantitative research methods will emerge during this century that will allow research teams to include close studies of individuals with "bigger picture" statistical studies, the former fleshing out and giving real life to the latter. My fear, however, is that the biases both outside and inside the research community will continue to make such work difficult. The misguided desire to appear scientific will allow pressures from politically-motivated forces to keep qualitative researchers on the defensive, when in fact it may well be that it is purely quantitative research that we need to be most suspicious of. The idea that "data speak," that there is some objectivity about deciding what data to collect, how to collect it, what experiments to conduct, what statistical methods to employ, and how to interpret the results of statistical analysis, are all highly doubtful and dangerous. This sort of think is similar to that of people who believe that documentary films are somehow objective, when in fact every single aspect of them entail subjective choices by the filmmaker(s) that shape what the viewer gets to see and attempts to craft a particular sort of response. The fact remains that such films can be, if anything, less true, less honest than "fictional" movies.

If it were possible to do so, I would strive to convince all educational researchers to cast off the guise of objective science and to turn to methods similar to those employed by Stoller. I would urge them to put themselves and their prejudices and viewpoints more explicitly into their research reports, while preserving the sound tradition within social science research of examining alternative interpretations and hypotheses, something Stoller does with great frequency. And I would counsel that they abandon as much as possible jargon-filled writing that alienates teachers in the field, parents, and other stakeholders from being able to make sense or use of much educational research, jargon that primarily is aimed, I believe, in making the research appear to be weightier and more objectively scientific than in fact it is or could possibly be.

Like Stoller, I suspect that I am here trying to swim upstream. But if his work is as valuable to psychoanalysis as I believe it to be, and if he, a physician who could readily have hidden behind both psychoanalytic and medical jargon, refused to do so in the belief that his work would be far more meaningful and beneficial if written in more accessible language, then how much easier should it be for educational researchers to abandon much of the pseudo-scientific trappings of their work? And how much more effective would that work be, in the long run, if through honesty and simplicity they stopped trying to pretend to be physicists and stood up to those who demand that educational research produce theorems and laws to which the enormous complexity that comprises both teaching and learning can be supposed to have been reduced.

Tuesday, March 17, 2009

Making Pedagogical Choices in Algebra Class



From 2000 to 2003, I taught the same intermediate algebra course semester after semester to (mostly) high school sophomores whom I was trying to prepare to take and pass with at least a C the same course given by a community college mathematics department for dual-enrollment credit (this was at what is called a "middle college," located in Ann Arbor and serving a diverse population of students drawn from around eight counties in southeast Michigan).

I taught from a variety of materials during the nine semesters in which I taught this course, from very traditional to more contemporary and progressive textbooks, all with accompanying use of graphing calculators to varying degrees. Following the order of topics in the books always resulted in presenting quadratic equations, their graphs, and the relationships between their transformations and parameters before exploring the same issues with absolute value equations and their graphs in the Cartesian plane. And student understanding and mastery as evidenced by performance on assessments was often poor on the first topic and abysmal on the second. When we had to look at quadratic and absolute value inequalities and their respective graphs and transformations, things deteriorated further for many. (Of course, many kids "got it" all the time, based on their test results and occasional class participation, and overall my students did well both in my class and when they moved into the college course, but I'm speaking here of the ones who did not).

One semester, for reasons I don't recall, I reversed the order. Remarkably, or so it seemed to me at the time, many of the students I had at the time who had seemed indifferent and/or lost when we worked on linear equations gave evidence both in classroom discussions and on subsequent assessments of "getting" how the graphs of absolute value equations graphed and moved around as they played with the parameters (and vice versa). Later, when we looked at the same issues for quadratic equations, their understanding seemed to carry over. The overall success of the two units went up dramatically compared with past semesters. Had I inadvertently stumbled upon something of value, or was the result an utter fluke that could rarely, if ever, be replicated by other instructors or me?

Before considering that question, let me share my speculations on why things may have gone as they did. It struck me that for students who had some minimal understanding of the behavior of linear equations and their graphs, it might have been easier to move to a look at absolute value equations and their graphs because those graphs are comprised of two linear "legs" that meet at a vertex. A look at the interplay between the graphs and the algebraic expressions that produced them was easier to gain if one graphed by hand, because all that was needed once students understood the basic shape of these graphs was to find the vertex and one point on each leg. Naturally, with the use of graphing calculators (or computer software) it would be even easier to play with and think about the graphs, but for students who did not have access to these tools or who were expected to work with out them at the beginning of (or even entirely throughout) each unit, graphing a symmetric pair of line segments that meet at a common vertex is relatively easy by hand. It is also very easy to find the coordinate pairs needed to produce the graphs.

By contrast, calculating the y-values for quadratic equations can be more challenging for many students. And anticipating how the graphs will look seems to be complicated by how certain parts of the graph (e.g., for non-zero x-values between -1 and 1) will turn out because squaring numbers in that interval results in smaller absolute value outputs for simple quadratic expressions, a somewhat counter-intuitive concept for many students.

My sense was afterwards that students were able to deal with these absolute value equations and their graphs more easily when they saw them immediately after looking at linear expressions and graphs, and before they had been (possibly) confused by the quadratic ones. They were then more able to look at the transformations and subsequently apply what they learned to the quadratic situation.

Of course, it would be wildly irresponsible to claim that my experience with these students would obtain consistently or even in a majority of cases with other students and/or other instructors. While my analysis may be plausible, to know whether it's correct would require significant further research. To expect teachers, textbook authors, policy makers, and other stakeholder to consider seriously that this may be a more effective order to teach the topics in question, there would need to be reliable data that support the above. Indeed, for some, only controlled a double-blind experiment would suffice.

Unfortunately, it is not possible to conduct such an experiment. Teachers know the order in which they teach topics. Students know the order in which they are being taught them. If different classes in the same school are taught in different ways, it is extremely difficult to keep the differences between the approaches walled off from one another. Students have friends in other classes. These are only a few of the obstacles. Indeed, it would not be easy to conduct the simpler, non-blind experiment with controls. Because as a rule, parents are not happy about letting their children be subject to "educational experiments." And when it comes to investigating mathematics education, they are perhaps least inclined to do so, given the hostile propaganda against meaningful reform that has been spread by the American media, fed to them by conservative think-tanks, foundations, pundits, and propaganda groups like Mathematically Correct and NYC-HOLD. Testing even as simple a question as in which order is it more effective to teach two basic and related topics in elementary algebra would likely face real opposition, should it come to the attention of such groups. The seeds of suspicion have been sewn and in many places already have taken root.

Opposition aside, a sole practitioner would find it daunting to try to conduct research of this kind. Finding support for it within a public school setting would be far from trivial. Why, after all, should other teachers, let alone administrators, take the question seriously? And if they did, why should they take the risk of investigating it given some of the things I've raised above? Where would the funding come from, especially in these difficult economic times? Why not leave well enough alone?

Perhaps the most viable option for a single classroom teacher looking to investigate the sort of question I've raised here would be to connect with a university-based researcher who has or could obtain funding. With the funding and (relative) influence and authority of a professor, it might be possible to convince a district to allow such research, though many of the above-mentioned concerns and limitations would still obtain.

I'm not suggesting that research is impossible or that teachers shouldn't be reflecting on practice and using it to inform future teaching. But I do despair to some extent that in the recent and current educational climate, rhetoric about "data-based research" is probably the biggest obstacle to actually conducting meaningful research there is.