Deconstruction: What you don’t say is what you do

I came across the document copied at the end of this post in the faculty room this morning.  I glanced down it and, perhaps prompted by a book I’m reading now (From the Ruins of Empire), I began to comment to myself on the questions picked and the wording used.  (If you want to repeat my naive experience, scroll down to the end now to glance over the questions before reading further.)

After noticing with favor that the questions started with asking about the meaning of the term under discussion (“globalization”), I noticed that that the question about the “positive effects of globalization” (question 4) preceded the one on negative effects (question 6).

Then there was the wording of question 5: “When people trade, how do both sides benefit?”  Having been reading about the run-up to the Opium Wars in China, my immediate response was “they don’t.”  Even a pro-globalization questionnaire might better word such a question as “… how can both sides benefit?”

Even in the Directions, the wording is “write the answers [my emphasis] to each question” rather than “write answers to each question” or (to my mind even better) “respond thoughtfully to each question.”

The overall tone of the questions seems to me to be pro-gloibalization (perhaps not surprising since the questions were copyrighted by the National Council on Economic Education in NYC).

I chuckled when reading the document as I made some of the above comments to myself, and a colleague in the faculty room asked me why.  I pointed out a couple of the examples above, and they replied with, “Well, it’s for ninth graders <pause> And the course moves fast. <pause> And we point out some negative effects during the discussion.”  I told him I wasn’t criticizing the course, merely noticing that even when people think they’re being neutral, there is usually a hidden perspective.  And of course, people aren’t necessarily trying to be neutral much of the time (in this case, though I didn’t point it out, it’s unlikely the people writing the questionnaire were doing more than trying to appear neutral).

All of the above show why, to me, studying a bit about deconstruction is useful.  It may often be presented using literature as a study vehicle, but people well beyond English majors can find its study quite helpful.




Directions: Write the answers to each question.  Use the back of this page if you need more space.

  1. What is globalization?
  2. How new is globalization?
  3. What has led to increased globalization?
  4. What are some positive effects of globalizatoin?
  5. When people trade, how do both sides benefit?
  6. Why {sic} are some negative effects of globalization?
  7. What roles do the International Monetary Fund (IMF), the World Bank and the World Trade Organization (WTO) play in globalization?
  8. What are some effects of multinational businesses?
  9. What are some of the issues involved with outsourcing jobs?
  10. What is the future of globalization?
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Classroom: learning environment or management area?

The article linked here has a number of points to make that I think are worth discussing:

I have discomfited people for years by maintaining that the role of a teacher is not “to teach” but to set up an environment in which students learn.  I mean “environment” in a broad sense, but mostly a set of expectations, attitudes, and tools.  To me, the physical space is secondary though not unimportant.

It is particularly difficult, sometimes, to inculcate the appropriate habits of mind we’d like to see in our students (or ourselves, as the article points out).  We all, sometimes, fall back on teaching algorithms because, frankly, it is so much easier.  For everyone.

I still remember years ago a student coming up to me in a calculus class and asking about a difficult problem.  I simply reeled off how to do it.  He was shocked, saying I didn’t usually do such things.  I agreed and pointed out that I was really tired and didn’t have enough energy to pose the thoughtful questions that could lead him to figure out the answer himself (as I usually did).

There is certainly a place for teaching algorithms as well as a few things that should be memorized.  After all, you can’t just reason your way into speaking a new language without memorizing at least some words.

And as a colleague pointed out, different kids from different environments may need more structured learning to get them started on a path from which they can then branch out by asking questions.  I am fortunate to teach at a place where such ground-work has mostly already been laid, much of it at home before kids even enter Kindergarten.  So, my teaching tilts heavily toward favoring inquiry, analysis, extension and reflection.

In a different school, the mix might need–and in some places–would need to be a different one.

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Unpersuasive writing about pedagogy…

Jennifer Barnett wrote in a blog for the Center for Teaching Quality about PBL and assessment.  In the course of her article, she says,

“Do you want students who can spout facts and vocabulary for an assessment? Or do you want students who have a deep ownership of their learning — students who can walk away with a learning experience? ”

I get her point and even mostly agree with what I think it is.  Nonetheless, there’s an implicit assertion that “deep learning” and knowing “facts and vocabulary” are mutually exclusive, which I reject.  And there’s also no definition/explanation of what “deep learning” is, and I’m pretty sure that there is a wide variation in what people mean by the term. Also, even when just memorizing, one ‘walk[s] away with a learning experience” albeit, I assume, not the one the writer has in mind…

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Discipline and implicit bias

What I particularly like about the article is that it’s not a rant and it avoids simplistic solutions.  It also acknowledges that even black teachers can have the behavior.  Which reminds me of the time many years ago when St. John’s was looking at the contention that teachers call on male students more than females.  As I visited classes, I found the contention to be generally true–even with female teachers.

At the time, I was surprised.  I have since learned that it’s very possible to be socially conditioned in spite of oneself (as it were).  Which, again, supports the need for reflection on, more than mere acceptance of, social norms.

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A Modest Proposal 2018

I asked my Differential Equations class  (mostly seniors, some juniors) to review what I felt the course content (as opposed to the course process/pedagogy) had been this semester.  It was a list of “things they should be able to do” followed by a second list of things they should be able to understand/derive/predict.

I told them to email me their self-reflection on this list.  I said the list was for THEIR benefit, but that I was curious about what they thought about the state of their own knowledge/abilities.

One student said, as he was going down the list, “I could do a lot more of this before [Thanksgiving] break.”

I’ve already told Eleanor (she’s sort of my accountability-person—if I say out loud to her what I want to do, I can’t pretend later that I never said it) that next year I want to start modifying my courses to minimize that sort of response.  I want to do less but have students get more long-term value from it.

I’m soliciting discussion/input from folks as to how to start this process effectively as well as how best to balance this approach with a more traditional curriculum/set-of-expectations.

I don’t, btw, subscribe to the currently fashionable idea that there’s no point in learning things you can look up.  Without some internalized knowledge, how do you know what questions to ask and how to evaluate the responses you get?  Nonetheless, most of us, teachers included, look up a lot of stuff to “refresh” our minds before class.  Or, we “work the problems” we assign in order to “make sure we can do them”—and it doesn’t seem to occur to us that there’s something odd about needing to make sure we can work problems we are assigning to teenagers…


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Assess the Essence

(and a second session from the 5.25 inservice)

With the move to get rid of “traditional exams” or “final tests,” there has been an exodus to “projects,” which term seems to mean many different things to many different people.  Final exams or papers are often meant to be comprehensive (either in terms of content or skills), but designing an exercise that sums up an entire course is a non-trivial exercise for most of us.

Projects can easily go astray if they are not carefully designed.  Requiring collaboration outside of class can be difficult for families where the kids don’t yet drive; disallowing collaboration can be difficult to enforce.  Sometimes teachers have a good idea but a less-than-ideal implementation.  Sometimes, we can get lost in the forest by focusing too much on the trees.  And sometimes, to continue the metaphor, we can stay on a well-worn path and miss the beauty of the larger woods around us.

It’s easier to come up with a good “culminating experience” (as a former headmaster at St. John’s once called non-traditional assessments at the end of a term) if we can answer the following questions:

  • What was the point of this course?
  • What skills were emphasized over the period of the course?
  • Is there any content that is critical for the student to retain?
  • If you interviewed a student in two years, what would you want her to remember from the course?
  • If your students took the “final assessment” next August instead of in May, what would they be able to do on it?

Maybe start with your department’s lodestone (if it has one).  (Some possible core ideas for several areas of study are jotted down on the back though your department may not completely agree or use different language to express the ideas.)

If you believe that “learning how to learn” is an important part of the value students get from your course, have you considered assessing “learning” rather than “having learned”?  How is that different?  Don’t we normally equate “what you’ve learned” with “how well you learn”?  Should we?

In each case, too, lurking in the background of the practitioners of the art (or in the minds of those who fund them) is the bigger question of “To what end?”  Neither funders nor practitioners agree on the answer to this question, so you need to be explicit in presenting different possible answers to your students.


Maybe some questions

  • To what extent should a “final assessment” be comprehensive?
  • Where should the balance of skills and knowledge lie?
  • The good–and the bad–of rubrics
  • Balance of merit of assessment with ease of grading






Scientists learn how to ask answerable questions (they’re called “falsifiable hypotheses” in science), then design ways to answer the questions (they’re usually called “experiments”) , and then present their answers in a way that’s persuasive to the intended audience (that usually requires background context, “data analysis” as part of a written article, and tie-ins to a broader context and steps for future work.)  Someone who “does science” for a living will not be impressed by work that doesn’t meet these basic conditions.

Mathematicians learn how to think deeply about very abstract questions, to approach the same question from multiple perspectives, and to prove their conjectures to their intended audience.    A step on the road to such mathematics is to be able to derive a result someone has presented you from basic principles.  Or to take an idea from one area and apply it to another one.

Historians learn how to construct a narrative from various documents/artifacts and to look at several different possible interpretations of such sources and their implications.  As a result, they can show how the contemporary United States might interpret (say) the Crusades one way, but people living near the Eastern end of the Mediterranean very differently. They may disagree both on “what happened” and “what we should do about it now.”

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Student choice, teacher enjoyment

(At our inservice today, I presented two sessions.  Here are the notes I used for the first one)

Power of Choice

We all like choices, but as students get older, it can be harder to manage the process of giving them choices while covering needed curriculum and skills as well as managing a classroom where people are doing many different things simultaneously.  There is also a movement afoot to encourage people to try different modes of expression to develop or show understanding of what’s under consideration in a class.

Choice Grids in Senior English

I have used the technique of a “Choice Grid” with great effectiveness.  Students like choices, and I like reading different responses in a class instead of many variations on exactly the same theme.

First semester, I had the following grid of choices for my “Style and Content Seminar”; students wrote four of the six:

Critiquing the Critic: Achebe’s essay on Heart of Darkness Changing modes of writing usingThe Grand Inquisitor as source text
Soliloquy: inserting new information in 25 lines of blank verse into Hamlet Imitating Style: inserting a new scene in Heart of Darkness
Critiquing the cinematographic elements of a scene of a previously unviewed production of Hamlet How do style and content reinforce one another in a class reading?


Second semester, students were expected to write 7 of the following 10 options in Literature and Philosophy:

Literature inclass: how do the processes of reading and writing mutually influence each other? “Merleau-Ponty[1] says that true philosophy consists in relearning to look at the world.”[2]  From Merleau-Ponty’s perspective, where is the philosophy in Calvino’s If on a winter’s night a traveler… ?
Literature inclass: how does Calvino’s style reflect the content of his novel? How and to what extent does If on a winter’s night a traveler… support a Nietzschean outlook on the contemporary world?


Critique Cavel’s definition of philosophy as “education for grown-ups” Critique Critchley’s assertions on the role of reason in argumentation
Where does meaning originate? Illustrate how we do—and do not—live in a postmodern world
Independent reading with evaluation/contextualization 2000-word paper on the social implications of a philosophy (counts as 2 choices)

Selection of ISPs in senior math:

Seniors have a choice each semester of a project from the following grid.  Each project requires work, reflection, and student evaluations if the student teaches.

Science: Molecular oscillations, Solving Schrodinger’s Equation, Maxwell’s Equations

Math and computer science: Group Theory, Coding in Mathematica, Number Theory, Complex analysis, Chaos  Non-Euclidean Geometries

Politics and Economics: Modeling the economics and psychology of war, An economics primer

Music: Fourier series

Into New Modes:  Teaching ;    Making manipulatives for math courses

The choices serve two different ends: in the English seminars, the students can gain flexibility in scheduling and a little control over the pace of their lives (important to first-semester seniors) as well as have the opportunity to try several things related closely to the course topic but outside the mainstream of their experience.

The math ISPs are designed to take only a week and to introduce the students to topics well outside the mainstream of all their math courses to date–or to let them delve much more deeply into an area that they found interesting.

Maybe some questions if you’re thinking “student choice”:

  • What should be required of all students?
  • Are all choices equivalent?
  • Do the choices emphasize breadth of possibilities or different means of demonstrating competence?
  • Are you comfortable in assessing “apples and oranges” and in defending your grades if they’re questioned?


[1] Maurice Merleau-Ponty (14 March 1908 – 3 May 1961) was a French phenomenological philosopher. At the core of his philosophy is a sustained argument for the foundational role perception plays in understanding the world as well as engaging with the world.  (from Wikipedia)

[2] From Simon Critchley’s Impossible Objects 2012 p44

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“Learning the material”

I had a senior make a presentation to me in support of her request for an alternative for a final exam. She didn’t want to “come to school to take an exam after school was over.”  While I’m sympathetic to the feeling, I told her that I didn’t agree with her premise that “school equals classes.”

She had a reasonable proposal: do her ISP in the course, produce a detailed study/review guide, and do test corrections on things she’d missed during the term so she would “learn the material [she] should have learned.”

In thinking over her phrasing, I realized that she and I had different ideas of the purpose of the course (it’s an advanced math course).    My response to her was the following:

Just as an addendum to your presentation, for me it’s more a question of learning to think with the material as tools rather than “learning the material.”

That’s why I try to have problems that require some thinking on tests/finals rather than just applications of things we’ve already done (or that students should have already done) in class…

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How math theorems really get discovered–maybe

This specific post is in response to a query about a derivation of what’s commonly known as Green’s Theorem that I had my MVC class work through, but the general ideas are applicable to a very wide range of ideas/theorems/developments in math and science–and even other areas.

Laura had a question about the “Changing Dimensions” lab that it might be helpful to send out to the rest of you.  Somewhat paraphrase, she said, “I get how it works, but why did anyone ever start to think with something like the partial derivative of L with respect to y?”

My response, somewhat abbreviated, was that even great mathematicians almost never start with something like that.  They usually have some idea of what the outcome will be, and someone (maybe Mr. Green) thought that, “Hmmm. I bet what happens on the boundary has to be the same as the sum of all the infinitesimal changes inside…”

And he might have then thought, “what happens on the boundary” is often a line integral around the circumference of a region.”  And, “infinitesimal changes inside often means the derivative of something.”  And, “the sum of infinitesimal changes sounds like the integral of a derivative to me.”

And then, the question is “which line intgral?” and “which derivative?”

Well, for divergence, you want “amount of stuff moving across a boundary,” and an amount is a scalar, for that’s why we wanted a scalar derivative for divergence.  On the other hand, if we’re talking about movement, rather than amount, we want a vector derivative.  Hmmm.  And if the stuff can’t move across a boundary but has to stay inside, we probably want the derivative of one component of the vector field with respect to the other.  Because when we wanted to know how much stuff was moving across a boundary, we did the derivative of the x-component with respect to x –change in a component with respect to its own direction and then the same thing for all 3 directions.  But if we want movement around within a boundary, it might make sense to look at the change in a component with respect to a different variable.  That insight caused someone, again perhaps Mr. Green, to think about the various ways you can take derivatives of components with respect to the other axial variables, which might eventually lead him (or you) to mess around with and other such “cross-component derivatives.”

And so, what looks like either brilliant insight or lucky pulling it out of his butt was probably actually neither.  It probably started with an idea of what might work and then formalizing a statement of that, and then working backwards to see how in the hell such a result might have come about.

In spite of how math is usually taught, the above is a much better schematic of what usually actually happened before it got “prettied up” for presentation to an audience—or for publication.

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After having listened to 10th and 11th graders running for student council for next year, I am struck by two things.  The first is that as a whole, they tend to be more creative without being offensive than they used to be.

More important, I am struck by the essential passivity of the large majority of them.  “Vote for me and I’ll see to it that changes happen” or “Vote for me and I’ll represent YOU” (one can usually hear the capital letters…).  While those are perhaps expected lines from a candidate running for office, and we certainly hear them in adult elections, I am struck by how infrequently the ideas being proposed (by those who have them) require student council action.

I’m sure having the support of the council wouldn’t hurt, but “getting lemonade in the cafeteria” is an idea that could be directly advocated without having to be elected to student council first.

“Listening to my classmates about what YOU want to do on the Great Lawn” likewise does not require an elected position.

While one could deconstruct many aspects of the speeches (including just how well off these students who want to improve their lives are and how few of the ideas put forth have any merit apart from self-indulgence), what most struct me after about 30 speeches in two days was the passivity of the speakers.

If you think something is worth doing, why aren’t you out there doing something about it?

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