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 21^st 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 9^th 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 9^th-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 9^th 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 9^th graders by the standards applied to 12^th 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.