Teaching 2015 (1)

I was inspired yesterday by going to see the actual furniture I’ll have in my “innovative classroom” next fall.  As a result, I decided to put down some thoughts on how I’ll bring to my teaching some of the innovations I thought about for quite awhile.  We’ll see if there’s institutional support for the teaching as well as the furniture!

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This document is an attempt to put together some things I know about student engagement, collaborative learning, and “education for the 21st century.”  Some of the observations seem to me to stem in significant part from basic human nature; others seem to me to reflect how we have taught our students to behave.

In the last part, I will note include some potential problems I foresee with implementing certain aspects of such a program in our Upper School.

Observations

  • Students tend to like problems or issues with which to grapple, and mostly they prefer the grappling to the preparation needed to grapple with them effectively.
  • For the greatest engagement, issues considered in class need to be things of interest to the students in some context.
  • Students need to feel supported in class—not necessarily comfortable, though.
  • Students need to feel comfortable to disagree with me or with other “experts” in order to facilitate the development of independent thinking.
  • For the greatest success of the greatest number, there needs to be a variety of permissible learning paths: some kids like to work together; others like to work independently; some want quiet; some want to feel free to walk about the room and argue; most want to hear what I have to say, whether from a desire for guidance or a desire to have something to challenge.
  • Students like a measurable outcome—they want to know if they “got it right.”
  • Engaged students do their best work when they feel challenged but not overwhelmed.
  • Although extremely valuable, abstractions are difficult for students. Moving between abstraction and reification—in either direction—is difficult.

Commentary and Implications of Observations

Preparing vs doing

In humanities courses, students often like arguing/discussing/debating more than they like doing the work necessary to prepare to be persuasive “arguers.”

In math courses, they’d usually rather do “find something out” problems than proofs; and in math and science they almost always want to use a theorem, property, or natural law rather than prove or derive it.

Issues of interest

In humanities courses, this term means things of interest to them.  Yet, in high school, they are rarely willing to verbalize things of too much importance to them in front of peers, probably for fear of ridicule.  Certainly, tying discussion points of literature and philosophy to the contemporary political scene is usually effective.  Tying highly emotional issues to their personal lives takes some level of trust and a supportive atmosphere and can be quite risky.

Supportive atmosphere

Teachers sometimes mistake “supportive” for “comfortable.”  Students (like all of us) perform best in an atmosphere that is supportive yet not too comfortable.  Just as some teachers won’t do new things until pushed, some students won’t try to think seriously about new ideas or acquire new skills unless pushed out of their comfort zones.  Once outside those zones, however, it’s important that students (again, like teachers) feel that when they stumble, they will be helped to rise.  It’s also important that they believe that failure at a task is not correlated with the judgment of “failed as a person” (or even “failed as a student”).

Students are (rightly) skeptical about an atmosphere wherein there is no judgment whatsoever.  If we seem to think “all opinions are as good as all other opinions,” students see that for the cop-out it is.  Misogynistic or racist opinions, for example, are not ones that should be treated as having as much merit as more inclusive ones.  However, discussion of such opinions can happen effectively.  We can even talk about them in some detail from the perspective of the people who hold them.  It’s important for students to realize that trying to understand something does not mean approving of it.  Neither they nor I believe that tout comprendre, c’est tout pardonner

In math courses, “issues of interest” seem to be tied most commonly into “real-world problems.”  For instance, with vectors in Honors Geo/Trig, I not only have questions about sailing, but I use maps of Galveston bay, with realistic speed and winds in the questions.  Such an approach grounds the question in something at least some of the students can relate to: even if they’ve never been sailing, they’ve mostly been to Galveston.

Disagreement

While all the people in a class (students and teachers alike) are entitled to their opinions, they are not necessarily entitled to spout them without being willing to defend them intelligently (again, true for both students and teachers—“because I say so” is ultimately an appeal to coercion, and it should be used as sparingly as possible).   We say that we value critical thinking, but if we do, we have to be willing to have it turned on ourselves.  A colleague once told me that “no 16-year-old has anything to teach me about British literature.”  Even if that’s so, they had things to teach him about how to teach British literature effectively to them.

The 9th grade Geo/Trig book has a number of statements in it that have been simplified (presumably to make the ideas easier for 14-year-olds to understand) to the point wherein they are no longer actually correct.  I like taking such statements and having students critique them to determine under which circumstances they are and are not correct.  As they’ve told me, they love “showing the book is wrong.”

While I don’t deliberately make mistakes or mislead students, mistakes and miscommunications obviously happen, and they need to be made into learning opportunities when they do. Modeling how to recover from failures is a critical component of helping students learn how to develop enough self-confidence to take intelligent risks.

Different learning paths

I have always been a proponent of individualized instruction and independent learning.    One thing that teaching 9th-graders this year has reinforced for me is that different people really do learn best in sometimes very different ways.  And whereas we should all be exposed to different teaching/learning styles, unless the School’s goal is enforced socialization or conformity, a classroom should as often as possible allow different learning styles to flourish.  Having a classroom in which some kids want to walk around during class, some want to argue with each other or the teacher, and others want to work quietly is a challenge.  Letting students who want quiet plug in to music is one way to help allow different environments.  The writing walls of the innovative classrooms should be another.   Letting some students read extra texts instead of being in class discussions is a possibility for those who learn better from independent reading or who have interests not shared by the rest of the class.

Measurable outcomes

Like all of us, students like to know “where they stand.” Sometimes that desire is expressed in wanting to know their grade at any given moment (regardless of how incomplete-and thus potentially misleading—it may be).  More realistically, they want to know how their work will be graded, but they don’t understand the assessment process. There are a number of consequences of such lack of understanding.  One is that they tend to think grades in math and science courses are more “objective” than grades in humanities courses.  Many also tend to like “multiple choice tests” since those appeal for two reasons: they seem more objective and thus fairer; and in many cases (especially when such tests are ill designed), they either lead the students to the desired answer or allow students to “guess and check.”

Challenge

There are two aspects to this point, maybe more.

The first is the nature of the challenge: sometimes the challenge is simply to beat someone else.  In sports contests or courses or competitions in the arts, for some people the goal is to win.  Sports teams want to win SPC; a student wants to get the highest grade in a class, a violinist wants to be concertmaster.  Lesser goals are accepted as stopgaps or when reality steps in too strongly: maybe we can’t win SPC, but we can at least beat Episcopal; maybe I can’t be the best in the class, but I can at least get an A (or beat my friend/arch-rival); I can at least make All-State Orchestra even if I’m not First Chair.

Other times, the challenge is to do something worthwhile or interesting: instead of simply doing twenty math problems faster than anyone else or getting more of them right, I can come up with a computer  program that graphically shows how the derivative of a function is the limit of the slopes of the secant lines at a point.  Instead of writing another essay on color symbolism in The Red Badge of Courage, I can write an interior monolog for the protagonist to be interpolated at some point in the text.   Instead of finding the pH of some solution my chemistry teacher gives me, I can get water samples from the effluent of an oil refinery and see if they are more acidic than those of the rest of the bay into which they are dumped.

Abstractions

Abstractions are powerful concepts—it’s the ability to abstract from specific individual experiences that allows us to formulate natural laws/scientific principles, mathematical theorems, philosophical ideas, and ethical principles (among other things).  But producing neat results from a messy world is unsettling and potentially harmful if we oversimplify in an inappropriate way.

Caveats and Challenges

Issues of interest

I mentioned under the humanities part how one has to deal with potentially embarrassing or explosive issues of race, sexuality, and power.  In the humanities, abstract questions are often easier to deal with than concrete ones:  “What should society do about racism?” is sometimes an easier question to answer than “What should I do when I’ve just laughed at a sexist joke or tolerated racist behavior in others?”

Under the math part, I mentioned briefly “real-world problems.”  Yet, at some level, which I am better at addressing in math than humanities (perhaps because we differentiate math instruction here both earlier and more successfully than English instruction), I think that abstract questions become important.  It’s generally considered, by mathematicians anyway, that the concept of proof is critical to their profession.  And while we don’t produce too many people who will become math majors, let alone math professors, the concept of proof vs plausibility seems pretty important to me for an educated citizen to have.  Presumably, that’s the reason we teach it in geometry.  So, advanced math courses need to have an element of abstraction that, perhaps, other math courses do not.  These abstract components are not necessarily going to tie in easily to “real-world situations.”

Disagreement

Many students, especially younger ones, want certainty.  And most of their training before me has taught them implicitly if not explicitly that “the teacher is always right.”  And if not actually right, then right in the context of school or the classroom.  Our entire school is set up to reinforce this point, and the more we do so, the more we raise children to distinguish between school and life (where no-one is “always right”) or to see what goes on in class, especially when it’s presented as clear or already pre-determined—the way much math is taught–as divorced from the messiness that is life.

Measurable outcomes

As long as the school tolerates, and by some of its policies (such as quick turnaround on course grades at the end of the year) even encourages, such behavior, it’s unlikely that there will be a sustained movement towards having students produce more original work.

Many teachers use rubrics either to provide an illusion of objectivity or in the belief that by doing so they are actually being objective.  A joint grading exercise in 9th English several years ago, however, showed that different teachers armed with a commonly agreed to rubric gave fairly different grades to the same student papers. The phrase “a strong thesis” or “an arguable thesis,” whether in history or English, is simply interpreted differently by different teachers and, in fact, means (and should mean) different things at different grade levels.  Do we really, for instance, want to judge 9th graders by the standards applied to 12th graders?  Or vice versa?

But an overly specific rubric has problems of a different sort (though at least its issues are more obvious).  If a student needs citations to support assertions in a paper (say), is there any distinction in the quality of the sources?  Is a quote (as it is in debate) from a racist web site equally valid as one from a peer-edited article in a book from a University Press?  If a student needs 8 sources for an A and only has 7, what lesson is the student being taught?  I can tell you both from my own experience and listening to students:  a) quantity is more important than quality, and b) the paper is being assessed mechanically rather than thoughtfully.

Challenge

As a rule, students here may enjoy, but they have little respect for, those teachers who do not challenge them intellectually.

The other end of that spectrum is that few students have the self-discipline and fortitude (I suppose one could say “masochism” if one took that attitude) to continue to work at challenges that they believe (whether erroneously or not) to be ones they cannot surmount.  As a number of people have said, worthwhile challenges need to be out of the immediate grasp of the student yet in a region that the student believes is ultimately achievable.  That range, in my experience, is elastic.   Students will often try something harder for supportive teachers, whose judgment about the achievability of the outcome is trusted.  And, of course, different students have different sizes and locations of the “not immediately but ultimately achievable” area.

Abstraction

People often have strong opinions about what someone in a specific situation should do.  Generalizing those opinions into a self-consistent world view is often difficult.  Likewise, people who have fairly axiomatic systems of judgment often have trouble applying their principles in more complex situations.  As one of my students put it, “Society pretty much agrees that killing any morally and functionally competent member of society is wrong.  Where we disagree is over whom to include in that category.”

In a math example, students almost always (though it’s particularly obvious at the younger level) prefer to work on questions involving numbers rather than symbols.  As an example, the question “Show that the lines   x = y  and x = -y and are perpendicular” is almost always preferred by the majority of students to the question “Show that the line between the origin and (a,b) is perpendicular to the one between the origin and (a,-b) ” because the former is less abstract.

 

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Collaborative learning (aka “group work”)

A very interesting piece from an NAIS blogger on cooperative learning.

My experience was the opposite of that of the author of the blog.  As a science major, I had lab partners from Middle School through graduate school, and exactly three of them enabled the “us” to work better than the “me.”  With all the others, I had either to do most of the work or double-check their work if I needed to rely on their data.  Otherwise, we tended to work independently even if in proximity to each other.
As a result, I came to the conclusion that group work is only synergistic if I get to choose the group.  I’ve heard a variant of that insight from others, mostly from friends talking about their college and business school projects:  The group is more powerful than the individual when each member brings a different strength or skill set to the mix–which is more likely in professional settings rather than K-12 ones–particularly in a school like this one which has in a number of areas (in US, at least) often been much more focused on having small standard deviations in grades than in creativity or output.
Put these experiences together with what the author describes, and I have to agree that collaboration that is designed in from the ground up is much more likely to be effective.  Assignments that are adapted from those expected of individuals will probably not work as well as those designed to be collaborative from the get-go.  I also suspect that work designed to answer specific questions or solve specific problems is easier to turn into effective group work than assignments focused on the individual–but maybe that’s an erroneous conclusion drawn from a small sample size.
I’d love to hear your thoughts on the issue if you’re willing to share them.
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Grading (1)

Purpose of Grading

Presumably, the purpose of grading is to assess how well a student knows something or can do something (or both).

Historical background

When I was a student here, the average grade was around 75, and the high honor roll (average over 90) was about 10% of the class (ish).  A few years ago, the median senior average was 92.  Part of the discrepancy is probably because seniors can take mostly electives if they choose, and part is probably because the quality of the student body is academically higher than when I was here (standardized test results support the latter claim).  Nonetheless, I think part of the discrepancy is from what is commonly called grade inflation.

Relative or absolute standards?

It’s fairly easy for a seasoned reader, for instance, to read a set of English papers (say) and put them in rank order (or rank “piles” if several are similar).  Assigning grades, then, for relative merit is usually easy—though see the caveat below.  The question becomes, then, where to peg the relative ranking on an absolute scale.  What grade should the median paper be given?  Determine that, as well as the desired spread, and the grades usually fall into line fairly easily.

Ideally, at least, one could use “standards-based grading,” where some external authority (like AP) sets the criteria for grading rather than the course teacher.  Except that after setting these standards, College Board carefully “norms” the scores so that the grade distribution stays relatively constant over time.  But in theory, one could set standards and judge each student’s work accordingly.  The question of whether and if so how those standards should change is one we can defer.

One could also use relative grading, where one grades a student compared to the work produced by other students.  Traditionally, this scaling is done for the current year only, but there’s an argument to be made for also taking into account how well students have done on similar assessments in the same course in years past.  Maybe this class is weak compared to others and so its median grade should be lower.  Maybe it’s better than most of the ones in the past, with the result that a higher median is appropriate.

Comparative arbitrariness of assessment

So, how are grades arrived at?  In spite of what many people think, grades are just as arbitrary in math/science courses as in humanities courses.  An example I commonly use is that if you give me any topic in math, I can write a test where the average will be 90.  I can also write one where the average will be 40.  The difference is that students don’t see what goes into the construction of the test, so they are not as aware of the arbitrariness of what’s tested.

What goes into an individual grade?

Now, let’s look at the components of a graded assignment.  Rarely is only one skill or knowledge of one specific fact measured.

Take an English paper.  In general, the desideratum is a persuasive paper that’s well written and, if an analytical one, supported by examples from the literature.  Often, the student who thinks well writes well, and so there’s not a large discrepancy in the two aspects of the grade (which are often called “content” and “mechanics”).  Still, if you’re assigning one grade for the paper, how should one balance the style of writing with the merit of what is said?  25% mechanics and 75% content?  Should the proportions be different at different grade levels?  Or in different courses?

Take a math test.  Somewhat analogous to the English paper situation, there are the conceptual aspects of the material and the “working-out-the-details” aspects.  You don’t, for instance, want to drive over a bridge designed by an engineer who typically makes computational errors.  But without someone who understands physics and engineering, you’ll never make any progress in designing new bridges.  So, how should the trade-off (if there is one) between conceptual understanding and computational accuracy be handled?  Some partial credit?  No partial credit, where only the answer counts?

Risk-taking and entrepreneurship

We (SJS) often say we want students who are intellectual risk-takers, who are creative, who are entrepreneurial.  Such people have historically not been treated well by traditional schools.

Part of the reason for that situation is that for teachers to encourage students to take risks, they themselves have to be encouraged to take risks.  Taking risks means ipso facto that failure will occur.  As long as teachers are “called into the office” when something they try turns out to be politically unpopular, few will be willing to take such risks except in a very minor way.

Another part of the reason for the situation is that teachers tend to like to control things and to be perceived as experts in a subject or skill area.  Thus, some won’t take “off-topic” questions because of the risk of being wrong or looking foolish in front of students (or peers or superiors).  Creativity involves risk-taking, which we’ve already said requires tolerance of failure.  And most entrepreneurs fail one or more times before doing something amazing.

Caveat from above:  assigning grades for relative merit is difficult with outlier students: those who have brilliant ideas but poor execution, for instance.

 

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Excellence in teaching

The headmaster sent an article from Inside Higher Education that dealt with excellence in teaching at universities.
I thought it was interesting and  handed it out  to my senior English class (those that were here, anyway), and after they read it, I asked them to think about really great teachers they’d had and what qualities they shared.  Here’s what they came up with:
  • communicate clearly
  • match curriculum effectively to different students
  • “a certain level of frankness”
  • admit their ignorance and mistakes and then do something about them
  • stimulate individual thought
  • make least interesting parts of the course interesting
  • are self-critical and not dead-set in their ways
  • are on your side
  • are well-rounded (so they can bring in examples and ideas from outside the course material)
  • have a sense of humor
  • match teaching style to different students
  • not averse to taking risks
  • show “fairness in grading”
The last led to a discussion about grading that we will continue tomorrow.
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Letters to a freshman

A friend of mine in his first year of college periodically writes to get my opinion on things he hears and talks about at college.  He sent me a recent email questioning some statements from one of his courses.  His points are in blue; the quoted material in black is apparently taken from class notes or paraphrased from a discussion.  My responses are in red.

Here are some of the aphorisms I specifically wanted to hear your opinions about:

 “Your professors can make you a good engineer, a good historian, or a good reader of ancient Greek; they can’t make you a good person. Some will try. They will fail because there is no necessary connection between mental and moral strength. ”

 -Can any teacher make you good at anything?  And is there really no necessary connection between mental and moral strength? What even would you say morality is, anyway?

 Interestingly, I just mentioned this idea in an application for an “innovative classroom” for next year.  I think you can only be “taught” things that are essentially algorithmic.  Other things have to be learned more independently, and for those sorts of things, a good teacher is more a mentor than anything else.  Sometimes, there are things that can be modeled without our understanding them at a detailed level (think basketball lay-up shot, for instance).  While that might not normally be considered algorithmic in the same way a free throw is, nonetheless, someone who does it really well can show you how to do it, and do it repeatedly well in the same manner.  After enough practice, you can (potentially, at least) do so as well.  Repeating the same process over and over makes it algorithmic in my mind, even if the performer can’t explicitly state what the steps are since s/he *can* demonstrate them in a nearly identical fashion over and over.

I think there is no necessary condition between mental and moral strength in the sense that many people who are mentally strong are certainly not morally so. Those people tend to be showcased on the pages of the newspapers nearly every day.

 I think there is a reverse connection, however.  I don’t think you can be morally strong without being mentally strong because no matter what you think for yourself, if you can’t act on your morals, you might as well not have them.  Of course “mentally strong” in a university setting tends to be equated with “getting good grades with ease,” and I don’t think there’s a correlation between that kind of mental strength and morality.

 “Be a joiner. College is about belonging to communities. Join things. If your school doesn’t have a club for the activity you want to celebrate, create one, and watch them join in droves.”

-am not sure what to make of this. Seems okay, but perhaps one of the most meaningful compliments (or at least I took it as such) I have ever received was when you told me, after  not being elected to SAC second semester junior year (LOL), that “Amigo, you’re not a joiner.”

There’s a very popular adage these days–almost a mantra in high schools.  “All the important things are done by people in groups” is how it often gets phrased to encourage teachers to encourage student collaboration.  To a point, it’s correct.  Five good people working together can accomplish more or more difficult things than one good person.  But the effect is certainly not linear (though it is, occasionally, synergistic), and it definitely depends on who the group is and what perspectives people bring to it.

And being able to motivate people to work with you to accomplish a goal you can’t accomplish yourself is a very useful life skill

 Attend to actions, not people. What we do is who we are. There’s no such thing as a “good person” or a “bad person”; there are “good actions” and “bad actions,” and anyone is capable of either. You will set yourself up to be proven a fool the moment you think you know what someone will do because you think you know who someone is. We aren’t anything; we just do.”

-Thoughts? To me seems to echo your metaphor about character as the area under the curve of our actions…but IMO misses the mark by seemingly denying the existence of a character/self.

Yes, I agree with you that to say “we aren’t anything” is extremely reductionistic and simplistic–and hence, almost undoubtedly, not correct.  I do agree with the part about “what we do is who we are” in a social setting.  I only agree with the idea that there’s no such thing as a “good person” or a “bad person” in the sense that no-one always acts well or always acts badly.  “There is some good in the worst of us and some bad in the best of us” is an old saying that is, I think, correct.

In practice, we tend to judge people by the sum of their actions over time.  If you usually screw me over, you’re a bad person to me and I need to exercise great caution in dealing with you.  Note, however, that actions don’t take place in a vacuum.  Killers are often talked about as having been “such a quiet person, never caused anyone in the neighborhood any trouble” when neighbors are interviewed, for instance.  We are faceted individuals, and the facets aren’t symmetric.  Who you are to me isn’t, probably, who you are to your family or lover (although there’s probably a significant overlap).

I remember a student’s telling me once that I was completely predictable. I was offended by the comment because I thought he meant I was shallow.  His explanation, when I called him on the comment, though, was that I was predictable because I was so principled: once he figured out my principles, he said, he could predict my actions in new situations because I so rarely deviated from them.  Put that way, it sounds better LOL

 On another note, he put as the course thesis that “rhetoric, understood as the study of modes of interpretation and persuasion, is a prerequisite for the successful pursuit of knowledge.” Then in class he asked if I disagreed. I put out that Newton, who often wasn’t in the habit of telling people about his work(i.e. did not need “persuasion”), is still considered by most to have “successfully pursued knowledge.” My TF got annoyed and said that he thought that if one discovers something of value, one is obligated to share it, and then another kid chimed in to say that one can only pursue knowledge by communication because each person has their own individual truths. Perhaps I am carping over details, but much as I agree that sharing knowledge is highly important, I do not think that pursuing knowledge requires sharing it, and thus feel that my challenge to his thesis (which he asked for!) is still valid. I don’t think pursuing this conversation with him would be beneficial for my long-term performance in this class, but I was wondering if you could share any insight?

I agree almost completely with you.  I disagree that one is obligated to share knowledge, though some of my colleagues at least partly agree.  I remember once I had a senior who said he had never, in three years of high school, gotten anything out of class discussions in English.  So, I called him in after class one day and said he didn’t have to come to class anymore if it was truly pointless for him but that since I didn’t want him to use his statement as an excuse not to work, he had to read every day during English while the rest of the class was stuck in class discussing.  So, while we were discussing Catch-22, he was reading The Trial, and when the kids wrote a paper on Catch-22, his paper had to combine both Catch-22 and The Trial.  After he turned in the paper, he told me that he wanted to come back to class because when he heard his friends discussing topics for their papers in senior country, he realized he had in fact missed a lot of stuff.

The colleague with whom I taught at the time was not pleased with the action because she thought that a classroom is a social setting and that people in the class have the obligation to share insights with their classmates in order to help with their mutual education.  Phrased that way, I see her point, but I see the sharing as an advantage rather than an obligation.

 I’m pretty sure the deal I made with that student would not be allowed now, but since I was US Head at the time, I allowed it LOL.

There are several points to the story.  One of them is that sharing knowledge is a way to generate insights.  To that extent, your quote above is correct.  But the student was indeed pursuing knowledge on his own, and he got knowledge without sharing it with his classmates.  So, the mere pursuit of knowledge does not, in my opinion, require communication (unless you considering talking out loud or thinking to yourself to be communication, in which case it probably does–there are few things we can learn without words except, perhaps for basic physical actions).

 Finally, in a section called aphorisms on the humanities, he basically asserted that all knowledge depends on the trivium/humanities, and even railed against our modern focus on stem. Much as I agree that we ultimately only study our human experience (as that’s ultimately all we know), is it not fair to say that the scientific method, in some way or another, is the basis of human knowledge, making a STEM-based education system pretty logical?

 To me, the validity of your conclusion depends on what you mean by “the scientific method.”   If you mean gathering data, formulating a hypothesis about how the world works, and then testing the validity of your hypothesis by your actions, then repeating that set of actions in a process of step-wise refinement, then I pretty much agree with you.

 If you consider “logical thinking” to be a part of the scientific method, then I would say no.  As Pascal said, “the heart has its reasons which reason does not know.”  (Only he said it in French, of course, but I’m not going to be pretentious and quote the French to you since I don’t think you read French.)  Learning from experience is certainly a necessary part of learning, but sometimes in math, science, and engineering, people minimize the importance of things they can’t explain with a universally applicable natural law or formal system.  When such is the case, then STEM does indeed fall short.

 Moreover, he asserts that “If we define a text as “something created,” an author as “someone who creates,” and interpretation as “explanation of an author’s creation of a text,” then the Humanities are the only form of academic inquiry that interprets things.”

 With such a broad definition, scientists are authors because they interpret experiments others create as well as, in your point below, interpreting things created by nature or God.  Is your speaker unaware that science was originally called “natural philosophy” and was simply the application of philosophy to the natural world?  In a broad sense, I think that’s still true.

 However, if one just tweeks author to “something that creates,” couldn’t you just consider science the interpretation of how natural laws have created our natural world?

Yes, of course.  See above.

In class during a discussion of this (he was asking if a tree was a text) I put out that botany could just be defined as the “interpretation of plants” as it analyzes how their structure fits their goal (to live and reproduce). I’m not sure if I’m just totally missing the mark, but I was wondering if you had any insight on both my thought and his?

I think I’ve already answered this, but unless a text has to be “human created,” your point is valid.  And given genetic engineering, more and more formerly “natural things” are being modified by people.  When does the modification become significant enough to merit being called a “new creation”?  

And if he were to argue that all these things started with something found in nature, you could riposte that all texts are, in some sense, reworking of the same “basic texts” made by other authors.  If on a winter’s night a traveler supports that idea pretty well….

P.S. Here is his full aphorisms on humanities below to put my last two questions in context:

“Ancient Greek and Roman universities were organized around what was called the liberal arts, the seven fields of knowledge a student needed for a life of learning: logic, grammar, rhetoric, arithmetic, music, geometry, and astronomy.”

Notice that all of these, with the possible exception of parts of rhetoric and music, are now considered sciences, which seems to me to weaken his point about how “purely humanities” they are 

“In medieval European universities, the liberal arts were categorized into the trivium and the quadrivium. The trivium included logic, grammar, and rhetoric. The quadrivium included arithmetic, music, geometry, and astronomy. Students would proceed sequentially through these fields, starting with the trivium and then proceeding to the quadrivium, because the fields dealt with in the trivium were (and still are) seen as a necessary foundation for success in the fields that constitute the quadrivium. That is, the skills developed in the trivium – the skills of thinking, reading, writing, and speaking – allow a student to deal with other kinds of specialized knowledge, namely those of the quadrivium.”

Yeah, so the only way I agree with the medieval viewpoint is from a functional one.  Understanding anything abstract requires language (I think).  Math is a language, so in that sense, you need to know the “logic, grammar, and rhetoric” of math to understand arithmetic and geometry.   But the “logic, grammar, and rhetoric” of math are not necessarily those used in human language or in systems more complex or more poorly defined than math.

Using the terms of the trivium, I would say that, essentially, proof is the rhetoric of math.  And while all math is supported by logic (probably), that (Boolean) logic isn’t necessarily the same logic that applies to our interactions with the natural world or with other people.

“Modern American universities face a unique educational challenge in the context of the tradition of the liberal arts. American society has elevated careers (and therefore skills) stemming from the quadrivium above those stemming from the trivium. Consequently, American education has decreased attention on skills stemming from the trivium.”

Simply not true in many ways.  First, the challenge is not unique either in time or space. He should remember as well that rhetoric and logic were extolled by Cicero (for instance) mostly as means to win arguments in legal cases, which to many in contemporary American society would seem to make “careers (and therefore skills)”  the driving force even of the trivium in some cases.

“This push has been led, we must say, by President Obama and his “race to the top” educational policy, which really means “race to the top of STEM fields”: Science, Technology, Engineering, and Math. This very moniker, “STEM,” attempts to replace the trivium with the STEM fields as the foundation or “stem” from which knowledge is built or grows. It is explicitly not knowledge, however, and even less so something like happiness, but “economic prosperity” that, according to the STEM Education Coalition, is our goal, a position epitomized in the Obama administration’s decision to use graduates’ starting salaries as one matrix in a college and university rating system.”

The “race to the top” may well emphasize STEM fields, but the idea was dominant in the early 60’s as well (well before Obama’s time)  right after the Soviets launched Sputnik, so Obama certainly did not lead the push.  He may agree with the push and have supported funding it in this incarnation, though.

I think your writer is reading a fair amount into the acronym.  It starts with “science and technology” because that’s where the concerns originally were, and if you start with ST, there aren’t too many more combinations that make catch-words in English. When he says that STEM is explicitly not “knowledge,” I’m pretty sure that even in the humanities, it’s now considered to be more important to think about things rather than simply acquire knowledge.  Prioritizing “knowledge” is more a function of a time period (pre-ubiquitous internet) than of discipline.  When knowledge was the limiting quantity, then having a lot of it was an advantage.  Nowadays, knowledge is important in the sense that without some basic knowledge it’s hard to make informed judgments about other knowledge that can so easily be sought out.

I agree with his point that comparing graduates’ starting salaries is a poor way to rank colleges–but so are SAT scores, traditionally a very common metric.  And in defence of the position (even tough I don’t agree with it) are two significant points.  One is that many other people in the general population *do* in fact agree that monetary success is an important metric of success (and even happiness).  And starting salaries are much more objective than surveys of “happiness” or “feelings of success.”  A second point is that with many universities’ charging amounts of money out of the reach of “average” families, it is important for people to be able to get a cost/benefit analysis of their education since it costs so frickin’ much.  Also, many for-profit schools, where the federal govt pays up to 90% of their tuition costs, are basically money-making scams intent on bringing in tuition, keeping costs low, and have little other interest in their students.  So in the sense of “where does my tax money go and why,” it’s useful to know the starting salaries (or even whether they can get a job in their field of training) of graduates.

“Economic prosperity” is an easily quantifiable metric, which makes it desirable in areas of public policy.  Why else do we use IQ scores, for instance?  And, honestly, a lot of people want economic prosperity more than other things that a college education is supposed, traditionally, to provide.

“In other words, the trivium that was traditionally treated as a foundation for the quadrivium – not as grade school stuff, nor as a frivolity or an added bonus to be gained if there is enough time after dealing with the important stuff, but as a necessary prerequisite for success –  has been devalued at precisely the time when it is most needed.”

See earlier points.  The trivium is indeed alive and well, simply not in the specifics as known to those living in the European Middle Ages  (except perhaps in law schools)..  Far from being devalued, logical thought is alive and well in STEM.  Communication (a modern aspect of rhetoric) is incredibly important in terms of getting papers published in science, which is close to the be-all and end-all of getting tenure in those fields.  Grammar is simply the rules by which a language works, and as so it’s alive and well as a set of formal rules for constructing proofs in mathematics.  Insofar as “natural laws” (which are the desired goal of generalizing from data sets in science) are concerned, then grammar is alive and well in science as well–to physicists, it’s essentially *the* most important aspect of their work.

“In modern academic parlance, the field of “rhetoric” and the disciplines collected under the banner of “the humanities” have acquired the significance of what was classically called “the trivium.” That is, “the humanities,” and especially “rhetoric,” is the name we use to study the arts of language pertaining to the human individual (i.e., our subjective experience in the world) in contrast to the sciences that study the arts of quantity pertaining to matter (i.e., the objective reality of the world).”

His ignorance is amazing.  “Rhetoric” is the use of language with the goal of persuading others, *not* with the goal of studying “our subjective experience in the world.”

And the sciences study much more than “the arts of quantity”–while the amount of something matters, so does its essential makeup.  No matter the size of the quantity of granite you have, for instance, you don’t have the capacity to transmit electricity found in the smallest piece of copper.

” Institutionally speaking, the humanities is an umbrella term that refers to a set of academic disciplines usually including (more or less) Classics, History, Philosophy, Religion, Law, Literature, Linguistics, the Visual Arts (such as Painting, Photography, and Film) and the Performing Arts (such as Music, Theatre, and Dance).

“Conceptually speaking, the humanities are based in the notion of textuality – that is, in the idea that the world is full of texts, or things we humans have created (whether those things are material objects like a poem or immaterial events like a war), and that we can interpret those “texts” in the same ways that we interpret “texts” more traditionally understood (as in works of literature).”

It’s an interesting way to define the humanities , and not one I’ve thought of before.

“If textuality is the condition of having been made by humans, it is no throwaway platitude to say that the world is full of poetry, from the Greek word poiesis, “making.” The world is full of things that we’ve made for this reason or that. The textuality of the world around us means that we must acknowledge the interpretability of well nigh everything, at least everything that we humans have made. You might love, hate, or fear the idea of poetry, but all you need to study “poetry” – understood as the making of things – is an intense curiosity about the way humans make things to get what we want.”

Without disagreeing about his point, I’ll just say that defined in such a broad manner, the idea applies to all of engineering and most of the fields of math and science as well.  Nearly everything STEM promotes, for instance, is an engineering approach rather than a “pure” approach.  And engineering is quintessentially concerned with  poiesis.  The original point of science, as indeed of religion, was to learn how to predict and control (to the extent possible) the natural world in order to make human life better/easier.  Which is pretty much what many people think is the purpose of studying philosophy or literature–to make their lives better.

“The notion that we can study what we have made is the basis of humanism as an intellectual tradition and the humanities as an academic discipline: both study what, how, and why humans create things, leaving the many aspects of existence that humans did not create to other modes of inquiry, such as the natural sciences. Indeed, not everything was or is created by humans, and not everything is available to the humanities for interpretation: humans did not create the rocks and the stars, so the humanities have nothing to say about such things, though the humanities certainly do have something to say about the interpretations and discourses we humans create in response to those naturally occurring objects.”

The second part of the paragraph is something which which I agree, but whoever wrote these aphorisms does not understand mathematics or science except in a very superficial way; and he definitely doesn’t even know what engineering is (and certainly has never seen a good STEM program at work) .

“As such, the paradox of the humanities is that it studies the most important, but not the most basic, feature of existence. Human experience is the most important feature of existence for the simple reason that existence is meaningless and irrelevant unless we humans are alive and kickin’ to experience it.”

As they say, to be in the game, you have to show up.  Science and engineering make it more likely that more people will survive (consider advances in medicine and agriculture) and so more likely to have the time (and leisure) to experience the pleasure of the humanities.

“But human experience is not the most basic feature of existence. The most basic feature of existence is matter (protons, neurons, electrons, and so forth) – in other words, the things that are studied by the natural sciences and disciplines such as physics. Because matter is more basic, it seems to have acquired the status of being more important, but it is experience in the world, not the reality of the world, that matters most for human being.”

I get this point and even agree that understanding people is in some senses more important than understanding group theory (for instance).  But he doesn’t seem to know that as natural philosophy, science originally started out wanting to understand the world as way to help define and control our place in it.  And that today, studying human “experience in the world” is the goal of a fair amount of science and some math.  It’s just that humans are so complex that the methods pioneered by “science” are only now beginning to be able to grapple with problems so complex.

“The problem with too scientific an approach to existence is that no one will ever meet and shake hands with a proton or electron; yet we deal with human beings all the time. Human being is the event that necessarily mediates – that is, stands in the middle of – existence and any experience of existence that may occur.”

True almost by definition, but it scarcely means that “human being” is not amenable to study by formal processes.

” If we define a text as “something created,” an author as “someone who creates,” and interpretation as “explanation of an author’s creation of a text,” then the Humanities are the only form of academic inquiry that interprets things. The Humanities study the things humans have made, from art and literature to language and culture. When we study such things in the Humanities, we are serving as messengers conveying the meaning of the authors who created those things. To be sure, other academic fields perform invaluable kinds of analysis and inquiry. Interpretation is not the only game in town, but interpretation belongs to the Humanities. Interpretation is what we do. For us in the humanities, it is our responsibility as well as our justification.”

Some mathematicians see themselves as creating mathematical ideas rather than discovering them.  And, to be sure, in some ways they are more like humanities majors, especially in graduate work, than scientists and engineers.

Also, while linguistics may have started as a humanity and still be classified that way in universities, its methods are much more those of science than is interpreting a poem, for instance.  

 So, again, a pretty over-simplified view.  

 

 

 

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Student and teacher learning

My senior English class is reading Italo Calvino’s If on a winter’s night a traveler and I’ve assigned sections to various people to present.  Listening today, I was struck by a couple of things:

  • what the students pick out as “important” has less overlap, even in this Honors seminar, with what catches my eye than I would have thought
  • (The observation that some are better prepared or more articulate than others is correct but so common as to border on educational cliche [to paraphrase Dr. Beverly Hofstadter])

Only the first is really worth commenting on, but it gave rise to some other speculations that I’ve had in other contexts from time to time.

  • To what extent is there a body of knowledge or skills that need to be transmitted from a course?
  • To what extent is there a body of knowledge or skills that traditionally are considered necessary to transmit from said course?
  • Why?
  • Who sets them?
  • When is it appropriate to encourage student independence of thought and when not?
  • When is it useful/interesting for students to hear what I got out of the reading and when is it useful for them to listen to peers’ insight?
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“Curving tests”

I had a colleague opine yesterday that if you have to curve a test, it’s not a good test.  I would say that’s only true if your goal is to write a test that doesn’t need curving.  If you have experience with a course and a very homogeneous class, then I agree that you might not need to curve tests.  Absent either of those conditions, it’s very difficult to make a really good test (ie, one that doesn’t aim for the lowest common denominator) and not scale the scores.

I think of college tests: the reason they’re scaled is so that the best students can be challenged without overwhelming the weakest.  Such is always my goal as well.

I think the practice of aiming for tests that “don’t need curving” has several bad effects in practice (though I don’t attribute these bad effects as motives to the people writing them, of course!):

  • it implies that we’re aiming for a collection of a standard body of skills (which by definition have to be algorithmic or not everyone will have mastered them equally at the same time, even in principle) or body of knowledge rather than aiming at developing people’s ability to think creatively
  • it suggests that students should be fungible units, where each one is capable of doing exactly the same thing in response to the same prompt as every other one
  • it further implies that if a student *can’t* perform just like every other student on a given prompt the student failing to do so is inferior in some measurable, and presumably valuable, way

I acknowledge this post may be controversial, and I apologize if you are offended by it, but that’s how I see it.

Posted in 21st century learning, Assessment, Creativity, failure, Implications for teaching, Reflection | Tagged , , , , , | Comments Off on “Curving tests”

Teaching and Training – 1

I’ve been thinking recently about the difference between teaching and training.

Some of you may be familiar with my occasional idea that there’s not really any such thing as “teaching” in the sense teachers are supposed to do: there are merely environments (and states and habits of mind) that are more or less conducive to learning.  But leaving that question in abeyance for the nonce…

There definitely is such a thing as training, and since that seems to be what many teachers do for much of their time, it might be worth thinking about when we want the one thing (teaching) and when we want the other (training).  Let’s accept a provisional definition that “training” is the repetition and internalization of an essentially algorithmic process.  The algorithm need not be explicit: one can train to do basketball lay-ups effectively, for instance, without having anything other than a good feedback process (though the training is facilitated by a good model and coach).

As most really good athletes know, it’s the automatic and internalized responses that are the hallmark of success.  If you’re going to have to think about how to hold your racket, where to start your swing, how much follow-through you need, and so on, you’re rarely going to hit a fine shot in a fierce tennis match.  Anything that can be internalized, should be in order either to free your mind to think strategy (maybe tactics) or to blank out “in the zone” where your body works at its best, free from the distraction of conscious thought.

Such training is eminently feasible in many academic areas.  Students used to spend a great deal of time learning to spell words.  Some still spend a large amount of time learning how to “solve” many kinds of problems in math courses.  It is not necessary, and perhaps arguably undesirable for the purpose at hand, to learn how languages evolve and how the history of a word may, in a language like English or French, be revealed in its spelling.  It may be counterproductive if you’re trying to get people to prepare for the math part of the SAT, for instance, to learn how to think mathematically.  Learning how to do as many kinds of problems that are likely to show up is, perhaps, a better strategy to train for the test.

It is arguable, however, the extent to which learning to score well on a math SAT test is tied to mathematical thinking.  And it is certainly not clear to me why “good schools” push all students to take math all the way through basic calculus without teaching a fair number of them much of the beauty or joy of creativity in mathematics.  It is quite possible for a student to leave even a good school without knowing how “a mathematical approach to reasoning” is applied to other than “math problems.”  It is almost likely in some places that a student may learn many interesting facts about biology, for instance, without learning how to come up with a hypothesis about something she doesn’t know, then design and carry out an experiment to test the hypothesis.

Interestingly, and perhaps it’s because most of us start talking and even reading well before we do much with numbers other than counting (and maybe grouping), English courses tend to do a better job at teaching students how to write and support their conclusions with evidence than math courses (perhaps outside of geometry?).

While every three-year-old I’ve known has an insatiable curiosity about the natural world, somehow high-school science courses tend to teach “facts” and “formulas” and “how to solve problems” as their main goals. Maybe English/Language Arts courses have a head start on other disciplines; maybe there is also a cumulative effect of more hours of ELA instruction in the younger grades.  And my experience is biased toward what used to be called middle-class households where parents (or other caregivers) read more to their children, ask them more questions, and just generally interact more with them verbally than families from lower economic groups are sometimes able to do.

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Ten influential books

The “10 influential books” meme is going around Facebook right now, so here are mine.  They’re not all on the list for the same reason(s), and after Lord of the Rings, in no particular order.  It is definitely the single most influential non-sacred text in my life.

Some of these might be exchanged for others, including something by Bertrand Russell.  These do represent works that I “come back to” in the sense of rereading periodically. Lord of the Rings I re-read every year from when I was a teenager until about a decade or two ago.  Have just finished re-reading it for the first time in a number of years.

It’s interesting to me that as interested as I am in philosophy, no “philosopher” made the list except for Cornel West.  It’s quite possible that something by Thoreau should be on the list, though Walden is awfully long/repetitive.  But some of the quotes from it are superb and have resonated with me ever since I first read it with Robert P Moore (founder of Chinquapin School) when I was in 9th grade.

The challenge: in your status, list 10 books that have stayed with you in some way. They do not have to be great works of literature. Tag (10) people to do the same, plus me so I can see your choices. So here they are in no particular order:

  •  The Lord of the Rings  (Tolkien)
  • The American Evasion of Philosophy  (West)
  • The Bible
  • Catch-22 (Heller)
  • Ajax (Sophocles)
  • Hamlet (Shakespeare)
  • The Warden (Trollope)
  • The Fall (Camus)
  • The War Prayer (Twain)
  • Stranger in a Strange Land (Heinlein)
Posted in American lit, Learning, Philosophy, Reflection | Tagged , , | 2 Comments

Not a history teacher…

During a discussion with a colleague yesterday, I was asked what my goal was for a new elective that she and I will be proposing this fall for next year.  I said, “to get students to see that race is not an issue that was “fixed” in the Civil Rights Movement, that the election of a black president does not show we live in a “post-racial society”–but that, on the contrary, race is an issue that informed most of the history of the United States before there was a United States and that it is still present, as an issue, in a huge part of every-day life today–in 2014.”

She liked the idea–the course, if approved, will be a joint history-English interdisciplinary elective.  I went on to say that I would love to teach American history by getting students at the beginning of the year to brainstorm some “big issues” in current American politics and then use the rest of the course to show how those issues (or a couple of them, anyway) have been with us since the founding of the nation (or before) .  Sort of a “looking backwards” approach.  She pointed out to me that most history teachers love “the content” and would be leery of the kind of non-chronological approach I proposed.  I dryly added, “Yeah, I’ve found that out.”

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