i3: Open courseware

As part of my online course, I was asked to explore a couple of sites with freely available educational resources.

The first was the creative commons page for educational resources.

As the site says, it partners with the Open Educational Resources movement, which makes materials available for teaching and learning. The point is that these materials are not copyrighted in the normal way; most of them have Creative Commons copyrights instead, which are much more flexible than standard copyrights and allow for works to be shared much more openly.

The first link on the Creative Commons site was for MIT’s open courseware. I’ve known for a few years about this, and it’s always been exciting for me. I teach computer science (programming), math and philosophy. MIT’s reputation in the area of computer science is one of the best in the world, and I assume it’s no slouch in math or philosophy either. The only concern I’ve had in the past is that, frankly, some of the courses I looked at were way over my students’ heads. I spent a little more time hunting through a course here and there today in my areas of interest. There is a lot more there than there was a few years back, and it’s organized more cleanly too. I found a class or two that had modules I might be able to pick and choose from for classes I teach. Other courses seemed to be more self-contained, only useful when taken as a whole.

The second link was to the Connexions web site. I’d never seen this before, and I like the idea a lot. The point of the site is to provide modules for small chunks of information rather than whole courses. That’s something I could use a lot more than just having a complete text book about a subject. I looked up a couple of modules in math and philosophy. They varied widely in how useful I thought they might be, of course.

Another link on the page that I found interesting was the one to P2PU (Peer to Peer University). I only looked briefly at it, but it had a link to a philosophy course that had as part of its components video lectures on specific topics from various universities. It looked like most of these were available legally for me if I wanted to use them for auxiliary material in my classes.

The second source of openly available material I looked at was College Open Textbooks. I didn’t spend as much time looking at this. It promotes the creation of entire open-source textbooks. For me, the usefulness of a site like this, at this point in its development, is very dependent on the specific topic and course I am thinking of. I’ve had bad experiences with inferior intro to philosophy texts. I really like the anthology I am using now, which has an excellent reputation; I wouldn’t want to go back to something less well-known. On the other hand, programming languages are taught the same way in almost all textbooks, and I don’t think it really matters much which text we use. Unfortunately I didn’t see anything for the specific programming courses I teach when I looked quickly through the lists of what was available. There is a lot more to the site than lists of available textbooks. I am looking forward to seeing how these movements grow in the future. I think we are moving toward an age in which it will be important for scholars to provide as many freely available high-quality sources of information as we can.

i3: Week 5 reflection (part 4)

(Part 3 is here.)

The rubric

I wasn’t really sure how to build the rubric. My real goal in the forum is to be able to detect when the students have “got” the concept or not. I am relying on my ability to prompt them further as the discussion proceeds. That doesn’t help the students know how I will grade them, though, and that is what will drive how they organize their own learning.

So I guess what I want students to focus on is:

  1. Answer the first question, thoughtfully.
  2. Participate in the discussion afterwards.
  3. Give me a final summary of their understanding at the end.

It seems to me that these three things reflect what the student is doing rather than what I am hoping the student will learn. Because the assessment and the objectives are at least fairly well aligned, there is not that big a difference, but I think of the rubric as being a checklist for the students to consult as well as a standard that ensures my grading is as fair and consistent as possible.

Anyway, the rubric I provided had categories for each of the three steps I mentioned above.

I chose the Yes / Yes, but / No, but / No format simply because I’m partial to it.

I am a little confused by the objectives / range / degree distinction, and how they connect with  the 3 x 4 matrix. In my case, is the objective that they answer the forum questions, and then the three rows (initial response, discussion, final summary) the range? Or are there three objectives — initial response, discussion, final summary – each of which has its own range and degree? Are the range / performance tasks supposed to be two alternative second components, or is range a synonym for performance tasks?

Another question: if a rubric is based on 3/2/1/0 then averaging 2 is already down to a D. Right? That seems harsh, but it also seems in the nature of rubrics. Am I supposed to think about that differently?

That’s all folks. That’s the last part. 🙂

i3: Week 5 reflection (Part 3)

(Here’s part 2.)

The instructional activities

My objective, briefly, was that students think of variables as boxes with names and values, and of assignment as putting something in the box.

In the classroom I have worked for several years to present this as clearly as possible. In my introduction to programming logic course, for example, I hit them with the following five components:

  • I have a section of a couple of different lectures devoted to the key concepts.
  • I continually trace programs by drawing the boxes and putting the values in them.
  • I have an entire assignment in which they practice doing the same thing.
  • I use an alternative version of the assignment statement to cement the idea of it before we move on to using the equals sign.
  • I continually tell them “be sure you are thinking of a variable as a box with a name and a value”.

In my online class most of this won’t be feasible, not only because it’s online but also because it’s only a 1 credit hour course, which changes how I have to prioritize the time. So I plan on using just four strategies:

  • They start by working through a tutorial in the textbook, even before I teach them anything myself. This will give them some initial exposure to the idea of variables. It isn’t as focused on what a variable is as I would be, but on the other hand they will actually be using variables in their code from the beginning. The practical experience that gives them will give me something to hook the correct concepts too later on.
  • Second, I will ask them the forum questions I discussed earlier. The point is to make them think about what a variable really is after they’ve read it in the book but before I’ve clarified anything. I’m relying on the idea that if they can get it by themselves, everything will fall into place without any further help from me. (I’m pushing them to clear a new space on their shelves for the programming variable concept.)
  • Third, I would like to prepare a couple of 5 minute video lectures/demonstrations on key concepts. There would be one on variables (“they are boxes”) and one on the assignment statement (“it isn’t an equals sign”).  Afterwards I’ll have them respond in the forums again so I can see if they really got it.
  • Fourth, as the course continues, I will continue to emphasize this concept whenever they seem confused about it.

The instructional activity I submitted in fulfillment of the i3 assignment is the forum questions, but I’d like to build the video lectures too. I don’t know how to do that at this point.

So that’s my second question, directed toward the i3 instructors: how do I create a 5 minute video lecture in which they can hear me talk but can see diagrams and pictures as I talk about them?

Part 4 discusses the rubric.

i3: Week 5 reflection (part 2)

(Here’s part 1.)

The objective

Students will demonstrate their understanding of the concept of variables by correctly answering questions about what variables and assignment statements mean, and discussing the answers with one another.

Here’s how I thought about it.

I know from experience that when the average person tries to learn programming, the biggest obstacle to that learning is a series of basic conceptual confusions. In a traditional course, one in which I lecture in the classroom, I have learned to structure my early lectures and assignments around correcting these misconceptions. Later on this becomes less important, but I still return to the same pattern whenever I introduce something conceptually new.

Here’s what I mean by conceptual confusions: when students first learn about programming, they don’t start from a blank slate. They start with a definite view of the world, and an approach to problem-solving, one that affects how they interpret what they learn. Whatever I teach them, they relate to what they already think they know.

Imagine that you have a big storeroom full of neatly labeled shelves. On each of the shelves there are neatly labeled half-full boxes of all shapes and sizes. Now someone gives you a strange object new object called a gizmo to add to your storeroom. What will you do if you have no box labeled “gizmos”? You’ll notice that it looks a little like a widget, and put it in the box labeled “widgets”.

That’s what students do when I teach them how to program. Every time I show them something new, they find a conceptual category that is familiar to them and put the new piece of information in that category.The problem comes when they need a new category. What they ought to do is purchase a new box, label it “gizmos”, find it a space on the shelves, and start collecting things for it. What they do instead is to squeeze what they’ve got into what they already know.

What I’ve got to do when I lecture is to push them to think in new categories. The problem is, the whole thing takes place on a largely subconscious level. Perhaps students comfortable with abstraction are good at deliberately overhauling their conceptual frameworks and expanding them, but most people just don’t think at that level most of the time.

In my experience, that’s OK. As long as I know what I’m doing, I don’t have to tell students: form a new concept. As a matter of fact, it would frequently be a mistake to do so. If I say something like that, it just confuses most of them. Instead, I approach the problem indirectly. I tell them to think using certain pictures; I insist that they use terms accurately; I carefully expose them to the questions that I know will push them to change their view in the most productive ways. They don’t know all of this is designed to change their conceptual map of the world, but it is.

So here is question number 1: in educational theory, one of the points of having clear objectives is to be as transparent as possible with students about what they are learning. So if I were to tell the students what my real objectives were, they would be this:

Students will habitually think about variables as boxes with names attached to them and values in them, rather than as unknowns.       (call this private objective 1)

and this:

Students will habitually think of the assignment statement as putting a value into a box, instead of as a statement of equality.            (call this private objective 2)

Instead, I said this:

Students will demonstrate their understanding of the concept of variables by correctly answering questions about what variables and assignment statements mean, and discussing the answers with one another.   (call this the public objective)

The public objective is much more helpful for the student. It doesn’t confuse them, and it tells them how they will be assessed. Also, it is really an objective of mine as well, albeit a secondary one. Because it is public and aimed at students I am more careful to be sure it is measurable and follows the “rules” for objectives than I was in stating my private ones.

It’s not what I think about when I plan my instructional strategy, though. What I think about is my private objectives 1 and 2. I design my instructional activities and assessments to teach and test private objectives 1 and 2. Then I examine the public objective to see if it is aligned with my instructional activities and assessments. If it isn’t, I change it until it is.

So, the questions are:

1) Does this commit some cardinal sin of objectives-based instruction?

2) What should my objective have been? The private ones, the public one, or something in between?

 I welcome responses from i3 instructors and general readers.

Part 3 reflects on the instructional activities I built.

i3: Week 5 reflection (part 1)

What is this post?

I’m taking a class (called “i3”) about how to teach online. Each week we write a blog post about something we’ve done for the class. In this initial post, I will summarize this week’s assignment and what I did to complete it. That way, those who aren’t in the class can have some idea of what is going on! In the next post I will put my reflection on the assignment.

The assignment

Anyway, here are excerpts from the most recent assignment:

Using [one or more objectives] choose instructional activities to meet the objectives and create an assessment … Write a blog post about what you have done. Please explain your choices in your reflection.

Create a rubric to assess an activity you may use … [I used the activity I had just created]

Notice that I am supposed to provide:

  • An objective
  • An instructional activity + assessment
  • A rubric to assess the activity (or some other activity – but I’ll use the one just created)
  • A blog post reflecting on my choices

My objective

This is my objective:

Students will demonstrate their understanding of the concept of variables by correctly answering questions about what variables and assignment statements mean, and discussing the answers with one another.

I have questions about the objective; I’ll ask them in the next post.

My instructional activity

For the primary instructional activity I chose to use a forum. In the forum I have questions about the important concepts in each chapter. The students answer once initially before they are allowed to see each others’ posts. Then they read each others’ answers and we all discuss them. I will prod and correct and clarify as needed. Finally, they will summarize what they’ve decided in a final post. (i3 instructors: The forum is created but hidden in topic 2 of my Fall CIS 299 course.)

The questions

Here are the two questions I prepared. I hope they will assess student understanding of variables and assignment statements:

== Question 1 ==

Consider the following assignment statement:
price = 10.95;

After this assignment statement executes, is it better to say:

a) price contains 10.95
or
b) price is 10.95

Explain why it might make a difference.

== Question 2 ==

Consider this statement, which adds one to the value in count:
count = count + 1;

Someone protests: “That doesn’t make sense. No matter what count is, it can’t be equal to itself + 1.” How would you answer them?

My rubric

Here is the rubric I would like to use to assess the students’ performance on this activity.

(3) Yes (2) Yes, but (1) No, but (0) No
Accuracy of initial answer Answer is substantially correct. Answer is not correct but is a reasonable response given the student’s knowledge at the time. Answer is clearly wrong but represents a real attempt to think through the question. No real attempt to answer the questions accurately.
Depth of subsequent reflection Initial answer and/or subsequent discussion reflects a thorough consideration of the question. Recognizes some key aspects of the question during discussion but also misses the point a lot. Participates in the discussion but misses the point for the most part. Little or no discussion.
Accuracy of final answer Conceptually and technically on target. Mainly correct, but some details or terminology is imprecise.ORSeems correct but imprecisely stated so that it is hard to be sure. The answer is partly correct but also displays some important persistent misunderstanding. The student seems lost.

I have questions about this too, which I will pose later.

My reflection on the objective (part 2) is here.

Should teachers lecture? Part 2

Part 1 is here.

A second thing I realize when I hear people dismiss lecturing as a valid method of teaching is that what they are rejecting is very different from what I consider an effective lecture.

What should a lecture be?

The podcast I listened to talked about needing to do more than lecture because students need to learn “more than facts and formulas” . What kind of lecture only gives students facts and formulas? Even the example used in the podcast, about physics lectures, was about lectures used to teach students problem solving techniques, which is a lot more than facts and formulas.

When I lecture, I am concerned that my students pay close attention to how I am thinking about the material. I am modeling for them how I hope they will think about it.

I tell them to look in the textbook for facts and formulas. Textbooks are polished, static things that can be trusted to always say the same thing and (usually) say it accurately. Lectures are different. Lectures are dynamic. They take place in time, so you can hear the reasoning process unfold in front of you. They are interactive. (At least a little bit: even a lecturer who leaves no time for questions will read the faces of his listeners and adapt what he is saying accordingly.)

The podcast said “people learn better when they’re actively engaged. A lot of the information in a typical lecture comes at people too fast.”

That probably explains why I like lectures better than the average student. I listen to lectures very actively. I’m always dialoguing with the speaker in my head. My notes are full of questions I want to ask about later. In addition, I reorganize the material as I hear it. My notes are also full of summary statements, attempts to capture the main point of a lecture as I listen. Finally, I make lots of connections in my notes to other material: “this is like such-and-such an idea in the other course I’m taking”.

I listen fast, by which I mean, I keep up easily with people’s spoken words. In the interests of full disclosure, one of my most consistent weaknesses as a teacher is that I speak too quickly for my students to follow. I have to work at slowing down for them. (I hate it when people speak too slowly. When I’m listen to audio recordings, I often put the recording on fast forward and listen to it at an accelerated pace if I can. I only wish all audio players gave me that ability.)

All this only works if the lecture is not just an information dump. The point isn’t to read the textbook to students or recite facts for them to copy and think about later.

Actually, I don’t even like my students to take notes very much. In certain classes I actively discourage it. Often when they are busy writing down everything I say, the important stuff moves from their ears to their fingers without visiting their brains along the way. I tell my students that it is important to be thinking with me as I lecture. I try to provide handouts and utilize the book enough that they don’t feel the need to record everything.

I don’t think that a lecture is always the best way to teach something. It depends on the material, as one commenter said, and on who the teacher and the students are too. We should try to learn good alternatives to lecturing. In the next part, I’ll talk about one non-lecture approach I would love to figure out how to use, not so much to replace my lectures as to enhance them.

 

Should teachers lecture? Part 1

As part of the how-to-teach-online class I’m taking online this semester, I listened to the American Radio podcast about the inadequacy of lecturing as a teaching method. (Articles that repeat most of the same information are here and here.)

I’ve heard this claim — that lecturing is a bad teaching method, and we should dispense with it — for several years and I’ve always been skeptical. I’m sure that lecturing is not the only teaching method, and often not the best teaching method. I’m also aware that lectures do not suit all learners. But it seems extreme to say that lecture is never a good method. (From the podcast: “Research shows that traditional lecture, where students sit and passively absorb information, is not an effective way for students to learn any subject.”) The reason I doubt that is because I learn really well from lectures. I love lectures. I definitely learn better from them than from hands-on approaches, for instance. So there must be something they do right.

The percentage of information retained from lectures

One of the reasons for the claim is expressed in this quote from the podcast: “Research shows it’s impossible for students to take in and remember all the information presented during a typical lecture.” I seem to recall that this is usually coupled with specific statistics to the effect that we only remember 10% (or something like that) of what we hear, 50% (or whatever) of what we see, but 90% (still making up the numbers!) of what we do. Therefore, lecture is the worst way to learn information.

When I hear this statistic, it makes me think of the flying lessons I took a couple of decades ago. The pilot who trained me said to me as we got into the plane, “Here’s how I will teach you. We’ll start flying, and as we go, I’ll just start talking. I’ll give a running commentary about everything that I’m doing as we go. Don’t worry about remembering it all; I’ll repeat most of it anyway. Eventually a lot of it will sink in.”

The funny thing is, it worked! For me, a strongly auditory learner, that was the perfect way to learn. Even though I only remember a small percentage of everything he said.

While that example may be extreme, the point still stands: a whole lot more information can be presented in a lecture than can be in, say, a hands-on activity. If I tell my students 100 things in a lecture and they remember only (say) 10%, and you show them 10 things in a hands-on activity, and they remember (say) 90% of that, they still learned more from my lecture than from your hands-on activity.

Furthermore, when I tell them 100 things in my lecture, the 100 things aren’t all of equal value. Perhaps I am making 5 main points, with 95 additional facts and illustrations to back it all up. All I really care about is whether you got those 5 main points. It doesn’t worry me at all if you forgot the other 95 things, once they’ve done the job of supporting your understanding of the main ideas.

When you use an alternative method — a hands-on activity, or collaborative approaches, or whatever — your goal is to get the same 5 main points across. That’s why it can certainly be a good idea to consider something beside lecture — the other 95 things to say are expendable, and anything that gets the chief concepts across can be considered a success.

But what it also means is, when you judge the effectiveness of a lecture, who cares how much the students have forgotten? The question is what do they remember? The point of a lecture isn’t to pour tons of information into a student’s head, it’s to make a few points very clearly, and it should be judged on that basis.

Do I think that lectures are always better? Of course not. I just think that they have their place in the world of teaching methods.

I’m not even saying lectures are effective all that often. I’m a pessimist about teaching. I think most of the time our attempts to teach fail. Teaching well is hard, and most of us (including me, for sure) fail at it a lot, no matter what methodology we use. Lecturing is one way I can often succeed, though, so I just wanted to defend it a little bit.

Part 2 is here.

i3: reflection on Week 4.

We were asked to respond to the following prompts:

  • Post a reflection to your blog regarding both the resource and activity you added to your course.
  • Also reflect upon the readings and podcasts for this week. How will the ideas you’ve explored influence your teaching?

I’ll respond to the first one in this post, and save the second one for another post.

In an earlier reflection from an earlier week, I said:

“… there were three things that I will remember from the week. The most important was finding the mindmapping Web 2.0 tool. I hope that will be something I’ll be using a lot in future courses.”

This week I explored the mindmapping tool further. Mostly it was frustrating.

To begin with, the class I am using for the assignment is going to have to be massively rewritten and redesigned in the next 7 days (well, just written and designed, really, since it’s basically barely started). I don’t really know yet what activities and resources I really want to put into the course, so I chose the mindmapping tool on the basis that a) it is likely to be useful in the course somewhere, and b) it’s something I want to know more about, and c) it was likely to be a little challenging to use it.

There are two different ways I want to use mindmapping, potentially. The first is as a lecture tool, i.e., to create a diagram for my students. For this, I used Mindomo. The free version of Mindomo doesn’t allow me to export a mind map, but it does generate code I can use to embed it into a web page. So I created the map on the Mindomo website and copied the code into a web page resource on Moodle. I had to switch to html mode and just figure out by trial and error where it should go. It works enough for now, but I would rather make it fill the window when students open it up.

Moodle has its own mindmapping tool available as an activity, and that’s what I used for my activity in this assignment.

The Moodle mindmapper is a lot more limited than the Mindomo one. I found that out by experience because at first I tried to use the Moodle mindmapper to generate the mind map for my resource. It has minimal help (clicking on the question mark for the activity produce a message saying it couldn’t find a help file for it). It didn’t let me change the positioning of the lines in the diagram. I couldn’t add additional relationships between widely separated entries in the map. I couldn’t figure out how to save or copy the map that resulted.

So I tried something else with the Moodle mindmapper. I created an editable mindmap. The idea is to let students build their own. I’m not at all sure that what I ended up with is the right way to go about things. I basically added a label about the activity giving a one-sentence instruction for students (I could find no way to put instructions into the mind map activity itself). Then I simply left the blank, editable mindmap in place for students to use.

That’s all I did for now. I’m not really done though. What I need to do is figure out how this works from the student’s point of view. Can they edit the mind map and save it? Will there be enough documentation for them to figure out how to use it, or do I need to create a document of video to show them how? There must be something already available somewhere, I suppose. Can more than one student share the mindmap and collaborate on editing it? I think that is what will happen by default, but I suppose it’s possible that every student gets their own copy. I think I have to have two different demo students in my course before I can test that. In any case, I would want to give them a lot more guidance before having them create their own mindmap. I still think it’s a worthwhile idea, but at this point it seems like it would be overly confusing for them.

A final note: I am only using some of the capabilities of mind maps at this point. The wikipedia page for mindmapping cites Tony Buzan   as suggesting that mind maps use color and icons to make things clearer, something I haven’t done.

(The wikipedia page is http://en.wikipedia.org/wiki/Mind_map, but its citation for Buzan’s comment is missing, although it probably comes from this:

Buzan, Tony. (2000). The Mind Map Book, Penguin Books, 1996. ISBN 978-0452273221

which is included in the bibliography at the bottom of the page.)

Is knowledge socially constructed?

An article I read for an education class I’m taking said that knowledge is socially constructed. In my written reflection, I said I was “not sure I want to say knowledge is socially constructed”. I’ve thought about it a little, and now I have more to say.

Disclaimer: I’m sure there is a philosophical context to this that I don’t know. In a couple of years, when I’ve learned more, I expect to look back on this post and be embarrassed by how ignorant I was of the real issue. If I waited until I understood things completely, though, I’d never blog anything! So here goes, based on my current halfway-complete understanding.

——————————————————————————————————————

What does it mean that “knowledge is socially constructed”?

Are the things we know socially constructed? Let’s take as an example, “I know that if I let go of this pencil, it will fall.” It seems to me that this is the kind of thing I could easily come to know completely independently of social factors, and that anyone in any culture would also come to know. I’m not sure what people really mean by saying knowledge is socially constructed though, so let’s take the possibilities one at a time.

1. Beliefs are socially constructed.

There is a difference between saying truth is socially constructed and saying knowledge is socially constructed. That something is true might be culturally independent, and still my realizing it and accepting it might be completely based on my culture.

Suppose we accept the traditional definition of knowledge, for example, as justified true belief: it must be true, I must believe it’s true, and I must have a reason for believing that it is true. Then even if it is true, independent of culture, that the pencil will fall, conceivably in a certain culture I would not have come to believe it. Maybe my culture doesn’t believe in natural laws, for example; it thinks that the pencil might randomly not fall next time.

If this is what people mean, I think it would be clearer to say “Beliefs are socially constructed”. That would make it clear just how social factors have an impact.

2. A lot of knowledge is socially constructed.

I am sure that some knowledge is socially constructed. In fact, I accept that there are some facts that I know that are themselves socially constructed (i.e., not just the knowledge of the facts, but the facts themselves). Rules of courtesy, for example, are largely a product of cultural conventions. So, for that matter, are the meanings of all our words. In turn, that means that many of the concepts we use to organize our experience mentally are socially constructed.

If this is what people mean, I’d rather they said “A lot of knowledge is socially constructed.”

3.  The way we organize and articulate our knowledge is socially constructed.

I am sure that some knowledge cannot be articulated without recourse to socially constructed conceptual frameworks. Even if I believe that the pencil will fall, I may not be able to speak of gravitational forces. Maybe knowing about gravity being a force requires a culture that has developed the concept of a force. In another culture, I would have to frame my beliefs about the pencil in other ways.

Nonetheless: even though particular conceptual frameworks may be culturally dependent, it seems likely to me that the general patterns into which some of our concepts fall are forced upon us by reality. Certain concepts may simply be the only good way there is to look at things. An alien mathematician would still have developed some concept of a circle, or of prime numbers, because these things are part of the way shapes and numbers work. The concept of force may very well be the only coherent way to frame our observations about things falling in a general way.

If this is what people mean, I think they should say, “The way we organize and articulate our knowledge is socially constructed.”

4. Knowledge of any subject is socially constructed.

We never know anything in isolation. If I know that “the pencil will fall” it implies I also know things like what a pencil is, and what falling is, and that we live in three dimensions. Every known fact is interwoven with a web of other facts. I am quite ready to accept that many of these other facts are socially constructed. That doesn’t mean that all knowledge is socially constructed, though – just that all knowledge is tied together with socially constructed knowledge.

In a way, I suspect this is what my education article meant. Educators aren’t concerned with our delivering isolated bits of knowledge, but with helping students to “know the subject”. It is this holistic sense that they have in mind when they say that knowledge is socially constructed.

In this case people should say, “Knowledge of any subject is to some degree socially constructed.”

5. The process of learning is socially constructed.

The process of learning, as a process, especially in a formal education setting, is social. Even independent study depends on the relationship of the learner to the books he reads, how his society defines the expert, and so on. So in that sense “knowledge is socially constructed”.

In this case, we should say, “The process of learning is socially constructed.”

This also may be what my education class meant.

As always, I welcome your comments/questions/corrections. Let’s construct some knowledge together. 🙂

Teaching and motivation

I am taking a course on teaching online right now, and in one of the assignments for the course I wrote this:

As I see it, teaching isn’t about the students, and it isn’t about me – it’s about the ideas. I love the ideas. I’m passionate about the beauty of truth and the adventure of thinking hard about things. My goal as a teacher … is to show that truth to students. If they catch a little of my passion for it at the same time, so much the better.

An instructor for the course responded with this comment:

Kevin, I think one of the frustrations of teaching is trying to light that fire under students to make them want to learn and do more than the minimum level to pass the course. I think the desire to see students achieve that and the frustration when they don’t is shared across curriculum areas.

So, the question is, in part, how do we create that desire? How can we wield that kind of influence?

I have two responses. I’ll mention the first here.

Suppose for a moment that I am standing in front of a class about to teach them the Pythagorean Theorem. I have, on the one hand, the Pythagorean Theorem itself – well, not just the theorem itself but also all the other ideas connected to it, all of which I find really cool. And I have on the other hand the students. They are supposed to learn all this cool stuff, but they don’t consider it cool. That’s OK – they don’t really have to –but how can I motivate them to learn it as fully as possible anyway?

Here’s what I’ve learned: when I try to motivate the students by focusing on motivating them, it never works. When I concentrate on my students’ attitudes toward math, I lose sight of the beauty of the math itself. All the joy goes out of my teaching for a few moments. I find myself scolding or apologizing. What I’ve learned to do instead is to maintain my focus steadily on the stuff I’m teaching. As long as I keep my eyes on the math, my love for it comes through. As I explain what I’m seeing, the students get a glimpse of the same thing. They start to see the ideas, just a little, through my eyes. That makes sense, when you think about it. It’s as though whatever I look at, the students look at. Their gaze will follow mine. The side effect is an increase in student motivation to learn the material.

A teacher I respect says that we should aim our teaching at the best students, not the weakest ones. That raises the bar for everyone, and the class does better as a whole. Another teacher says he focuses his teaching toward the hard workers. I do something similar, but in my case I focus on the curious students. I even imagine my audience as being more curious than the evidence suggests. I make the arbitrary assumption that they are already interested, that they all want to like math. The result, usually, is that they turn out to be interested after all. It’s a self-fulfilling prophecy.

I don’t think my approach is best for all teachers. Everyone has different abilities. Some teachers are really terrific at motivating students and my way of doing things would be needlessly indirect for them. For me, though, this is what works.