Teaching and active learning

I had a moment of insight today about teaching. When active learning techniques work, it isn’t because they help students intellectually, it’s because they help students emotionally. If I break students into groups to discuss a concept among themselves, for example, it’s not because that helps them to understand the concept better, it’s because it helps them become more emotionally connected to the material. This goes against a lot of the things teachers say about active learning. But I think it matches what actually happens.

In general, I think that a surprisingly large factor in the learning process is the students’ attitudes towards the material moment by moment. I think the most gifted teachers are those who are highly attuned to that attitude, and instinctively aware of how it can be directed and nurtured on the fly.

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Some surprising math

A state-wide college humanities committee has decreed that writing must be “integral” to any humanities course before it can automatically transfer to other colleges.

What does “integral” mean? According to the committee, “Integral is defined by the following: a student cannot successfully complete the course without successfully completing the writing requirement.

Sounds reasonable, right? Unfortunately, this innocent definition doesn’t really make sense.

At our college, “successful completion” generally means a C, or at least 70. One of the teachers in our discussion today suggested that by making the writing requirements at least 31% of the total grade we could make it impossible to get a 70 without successfully completing the writing portion of the course. That’s not right, though. That reasoning only holds if the student got 0 on the writing portion — a lot worse than merely failing to successfully complete it. If a student got 69 on the writing portion — just short of “successful completion” — then all he needs is 71 on the rest to get a C in the course.

So how about higher than 31%? Currently we’re considering requiring the writing assignments to account for the majority of points in the course. That doesn’t work much better. Now if a students gets 69 on the writing assignments, she needs more than 71 to get a C overall, but 72 will do.

As a matter of fact, even if the writing portion was 96% of the grade, it would be possible for a student to successfully complete the course by getting 100 on the remaining work:

(69 x .96 + 100 x .04) =  70.24

So to fulfill the requirements, the writing portion of the course needs to be at least 97% of the grade. If we round averages to the nearest integer, it will need to be at least 98%. If successful completion means 60 or above and we round to the nearest integer, then the writing portion needs to be 99%.

I don’t think the Humanities Committee really meant that.

Oh, well (sigh) … at least it wasn’t the Math Committee that said it. 🙂

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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.

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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. 🙂

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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.

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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.

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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
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.

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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.


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More about entanglements

Read the initial post first or this one won’t make sense.

There I said:

He’s pushed me to think of my secular job as being part of His calling for me and to care more about succeeding at it. He’s drawing me to pray more as I prepare classes, to ask His blessing on my students’ attitudes and understanding.

That’s not quite right. That is being entangled. What I should have said is that He’s pushed me to think of my secular job as being part of His calling for me, to discover its purpose, and to care more about seeing that purpose fulfilled.

Here’s the difference: I teach because I want my students to learn. I need to care about whether they learn. I shouldn’t be worried about whether they learn because of me, or in spite of me. It’s not my personal success that matters, it’s whether they learn. That’s why I pray for my students’ attitudes and understanding rather than for my own teaching. I think it was John Hopler, years ago, who said “Pray for the goal of the teaching more than the teaching”.

But that would put me in danger of becoming emotionally detached again. So having made that modification, I also need to add, “I think it pleases Him when I throw myself wholeheartedly into fulfilling that purpose with the confident expectation that He can use me.

Here’s the new difference: Although I care about seeing the students learn more than I care about having to be the one God uses to accomplish it, yet I also realize that God loves it when I try hard and trust hard to accomplish it.

Then if I succeed, great! If I fail personally, but God blesses the students around me anyway, also great! I know that my effort and heart was valued by him, even if He chose not to use me directly.

What if I fail personally and the students don’t learn? I want to say, “Great again! God is still in charge and I can trust Him to be working.” But, for me, that is another way of being emotionally detached from my students.

Instead, I think a better answer is to seek God more about it. That means first of all to let myself be a little sad that the students aren’t learning. Second, it means to wait on God in prayer, asking God what happened. Specifically I ask:

  • Did I set my goals too high? Was I aiming at something that wasn’t realistic, that wasn’t really His purpose for the job?
  • Is God trying to teach me something? Do I need to repent of something, or do I need to work at improving something in how I teach?
  • Are the students learning in ways that are hidden from me? Is God blessing in ways that I don’t see?
Finally, I can ask God to help me start over again, with a clear conscience and with renewed faith and joy.

Yet those who wait for the LORD
Will gain new strength;
They will mount up with wings like eagles,
They will run and not get tired,
They will walk and not become weary.  — Isaiah 40:31, NASB

Anyway, I guess this is the new version:

He’s pushed me to think of my secular job as being part of His calling for me, to discover its purpose, and to care more about seeing that purpose fulfilled. I think it pleases Him when I throw myself wholeheartedly into fulfilling that purpose with the confident expectation that He can use me. He’s drawing me to pray more as I prepare classes, to ask His blessing on my students’ attitudes and understanding.

I expect I’ll change my mind about it again tomorrow! 🙂 I think God keeps me thinking about this because I’m not very consistent in doing it yet.


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