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Mercury, September/October 1999 Table of Contents

Teaching science in general, and physics and astronomy in particular, is difficult in an era of decreasing attention spans and increasing extracurricular activites and responsibilities among students. But engaging and involving them is certainly not impossible.

Victor M. Montemayor
Middle Tennessee State University

I have a confession to make: I love teaching. By this, I don't just mean that I love to teach people. I do, but what I mean is that I love to lecture. To me, heaven is a giant blackboard, not freshly washed, with a nice layer of chalk dust distributed uniformly over the surface to make erasing easy. The group of people gathered to hear me talk, be they students, other faculty, or laypersons, have a passing interest in what I am about to say. But by the time I'm done, they're going to be hungry for more!

Yes, that would be heaven. Okay, there might be other things there, too, but that's beside the point. The problem is that my idea of heaven is becoming a thing of the past, at least in the introductory physics classroom, and I have been working very hard over the past several years to make sure that it remains a thing of the past. Lecturing a course was always like performing on stage for me--it was kind-of a well-scripted play (the lecture) interspersed with impromptu sketches (questions). One had to project to be heard clearly, vary the intonation of one's voice to remain lively and not put the "audience" to sleep (yes, that happened anyway...), and always stay in character (the "sage on the stage," as it is now often derogatorily referred to). Pedagogy research has clearly shown that lecturing to people is by far not the most efficient means of getting them to understand the material at hand, especially in the sciences. By understand, I mean learn and be able to apply the fundamental concepts and skills associated with the subject material.

As has been discussed previously in Mercury, it has been shown that students must take an active role in the learning process. Periodically breaking up a class into small groups of three to four students and giving them a non-trivial concept or problem to work on appears to be time well spent in class. Walt Bisard and Michael Zeilik ("Restructuring a Class, Transforming the Professor: Conceptually-Centered Astronomy With Actively-Engaged Students," Jul/Aug 1998) and Douglas Duncan ("What to Do in a Big Lecture Class, Besides Lecture?" Jan/Feb 1999) have discussed their approaches to incorporating group learning into the lecture format in large astronomy lectures. They point out that even very basic concepts often are not understood when presented in the traditional lecture format. This problem is just as prevalent, if not more so, in the introductory physics classroom.

Wherefore art thou, Newton?

A couple of years ago I finished writing a text for a "pre-physics" course that we call "Discovering Physics." The course takes a discovery-learning approach in which the students are guided through a series of "discoveries" of concepts, relations, and skills associated with basic physics. One of the investigations involves a classic exercise that might help demonstrate active learning (in this case, discovery learning).

The students are asked to perform fifty "reaction-time" measurements in which one student holds a ruler at the top (the 30-cm end) while the other student holds his or her thumb and index finger, separated by about one inch, at the bottom of the ruler. The second student tries to catch the ruler as quickly as possible after it is dropped by the first student. The catch-position reading on the ruler then gives a measure of the second student's reaction time. (We discuss how we can talk about time when we are measuring a distance.)

After all the measurements are made, the students are asked to make a histogram of the results, having just learned about histograms in the previous class. They are also asked to compute the average catch position, and to draw and label a vertical line on their histogram showing the position of the average. As you would expect, a roughly bell-shaped curve is obtained, with the average about at the center.

The students are then asked why the catch positions were not all the same (as the average value, for example), since each of the catches were supposedly performed under the same conditions with the same people dropping and catching the ruler. They readily come up with the idea of "human error," and that, although they try to duplicate the conditions each time, things are not always exactly the same. Hence the spread in the data. They are then asked if they would expect to get exactly the same average catch position if they were to perform the fifty catches again, exactly as before. They again readily answer "No!" due to their favorite error.

The students are then told to go back to their histograms and to draw in a region around their average, which we call the "window of acceptance." The significance of their window of acceptance is that, if another series of "reaction-time" measurements were made and the average catch position were to fall within their window of acceptance, then they would claim that, to within their uncertainties, the average of the new series of catches agrees with the average from their original series of catches as represented in their histogram. The investigation so far takes about one 50-minute class period. The remainder of this exercise takes another class period.

Next, the students are asked the following question:

Let's say that a mass were hung from the bottom of the ruler such that the total weight of the ruler plus mass were four times the weight of the ruler alone. How would you expect the "reaction-time" results to change if they were performed with this new ruler-plus-mass combination? Be as specific and quantitative as possible.

I've tried this question out on students who have had no physics, on students who were taking physics, and on those who have completed one or more years of physics, all with about the same result: They tend to believe that the catch position will be significantly greater (most commonly either two or four times greater) on the ruler with the mass hanging from its end than on the unweighted ruler. This is a dramatic demonstration that they still believe that heavier objects fall faster--after all, heavier objects are pulled on harder by the Earth than light objects, right?--despite the fact that students who have completed as little as three weeks of a traditional physics course have "learned" that the acceleration due to gravity at the Earth's surface is constant, independent of an object's weight (assuming that frictional effects can be ignored). The point is that the traditional lecture/problem-solving format simply does not affect their world view--it does not change the way they believe the world works.

On the second day of the "reaction-time" investigation, the students are asked to commit their thoughts about using the weighted rulers to writing and to discuss their thoughts. They are then given rulers with weights attached to them and asked to perform another set of catch-position measurements, following the same format used in the original (unweighted) measurements.

A number of students are shocked when they start to realize that the catch positions are the same as before. Some students are so convinced that they won't even be able to catch the weighted rulers that they don't catch them! The groups tend to conclude that the new average catch positions agree with their old catch-position results to within their windows of acceptance; that is, they are forced, by their own observations, to conclude that the extra weight did not affect the results.

You might be interested in finding out the main purpose of this investigation: It is a discussion of the scientific method. At the end of the investigation the students are asked to summarize the steps that they took in following through the investigation. What they end up with is the "scientific method." The idea that the acceleration due to gravity at the Earth's surface is independent of mass is hit on several times throughout the semester in various investigations.

By the pricking of my thumbs, something wicked this way comes

The previous discussion demonstrates two important points. First, a concept as simple as the constancy of the acceleration due to gravity with mass slips by many of the students in a traditional lecture physics class. Second, it can take a significant amount of time to address these simple but essential concepts in a more meaningful way.

Introductory astronomy classes are often taken as a general-studies science elective. The students often do not go on in the sciences, let alone astronomy. If all of the material that is traditionally covered in a survey-of-astronomy course is not covered, the students will usually not be hindered in their future studies (unless, of course, it is part of an introductory sequence in astronomy).

Very few students take physics as an elective, however-they are there because they have to be there. Many taking the physics courses will need at least some of the material in the future (for example, pre-meds who will have to take the MCAT exam to get into medical school). So what is the physics instructor to do? On the one hand, if we do our traditional lecture, then, at least according to research, the students are not really learning the material the way we think they are. On the other hand, if we adopt major shifts in pedagogy, there is no way for us to cover the material that will be needed by some students as they pursue their career goals.

Certainly one good way to approach this problem is to do periodic group problems in the lecture. The problem with this approach is that it is very instructor-dependent. I don't know as well about astronomers, but not many physicists have sufficient chutzpah to carry this off successfully in a large lecture class.

For the past year or so I've been working on a new approach to teaching introductory algebra-based physics. This new approach has several goals:

• to make the time spent in class more meaningful for the students and instructors;
• to provide the students with the skills necessary to appreciate the results of experimental investigations (be they in physics, astronomy, or any other science);
• to develop a working understanding of the fundamental concepts associated with introductory physics; and
• to develop skills associated with working successfully in groups, both in completing analytical and experimental tasks and in reporting results orally as well as in a more formal written form.

On working on the new pedagogy, I threw traditional pedagogy out the window. This is not because it didn't work for me or because it was bad, but because it simply wasn't efficient enough. We have essentially six hours with the students each week (normally three hours lecture, three hours lab), and I simply do not believe that the traditional lecture and lab meetings are time well spent.

Something is Rotten in the State of Denmark

Consider first the traditional physics lecture: About an hour is spent with the instructor trying to get as much information presented on overheads or through computer presentations as possible. Meanwhile, the students try to write down the same information along with as many of the instructor's comments or explanations as possible.

Then comes the weekly lab, usually having very little or nothing to do with what is being done in lecture that same week. The students work with their partners to try to once more verify that a fundamental equation in physics really is true or that the fundamental constant being studied really does have the correct value. The amount of detail provided in the form of procedure steps varies, but the students tend to be able to work through the lab whether they are in the lecture class or not.

In general, the students show up to lecture and copy down the lecture notes. They leave lecture. They try working on the homework problems (at least the good students do) and tend to have much difficulty; they page through the corresponding chapter in the book to find examples similar to the homework problems. They find equations that seem to have symbols for the same quantities as they have in their homework problems, so they try applying the equations to their problems and sometimes they even get the right answers. Then they go to lab and follow steps through an experimental procedure for an exercise whose significance they don't really understand. But, again, the procedure steps seem to be written clearly enough that it really doesn't matter that they don't understand what they're doing or why they're doing it; they get the "right answer," and they're outta' there!

Welcome to the new physics experience. The URL for the web-based lecture material is physics.mtsu.edu/~phys231. Image courtesy of the author.

The previous discussion is a bit harsh, but unfortunately it is not too far from reality in many introductory physics courses. Equally unfortunate is the fact that many physics and astronomy faculty simply do not have the time or desire/expertise to go about the enormous task of revising the course pedagogy. I am not being derisive here. The simple fact is that teaching and research are two related but time-consuming and often mutually-exclusive lines of work. The way the physics and astronomy departments are set up and the way tenure/promotion decisions are (realistically) made often mandate that a faculty member devote the overwhelming majority of his or her time to either teaching or research-circumstances simply do not often exist to permit both.

That it should come to this!

The new pedagogy that I've been working on for the algebra-based physics sequence has four primary components: web-based lectures, spreadsheet-based exercises, hands-on activities, and out-of-class projects. I will describe and discuss each of these in turn.

web-based lectures

Lecture time in the old regime was essentially a time of conveying information. Relatively little time was spent in discussion or in answering questions. I now fully acknowledge that fact by placing all of the lectures on the web. There is no textbook for the course: The web pages serve as the course text. The web lectures are very focused; the material is what the students need to know to do well in the course.

A typical web-lecture starts off with a brief introduction to the few main points of the lecture. A definition or concept is then introduced, and an example is given to show how the concept is applied. The answer to the example is given beneath the example statement, as is a link to a very detailed discussion of the example solution. The best students will be able to work out the example without looking at the solution, although everyone is encouraged to read through the solution hints to more difficult problems. Students that need more help should be able to work through the detailed solution.

Putting the lectures on the web definitely places a large burden on the students. They are held responsible for working through the appropriate material by the assigned deadline. Of course, not all students do this. There is also the problem that some students simply cannot learn by reading, no matter how clear or straight-forward the writing. These students have a chance to hear the instructor discuss the lecture material and some examples during a (mini-)lecture time which is scheduled once per week for about one hour. This time is also used to administer exams to all students taking the lecture course.

It is important that one hour per week is assigned to "lecture." Many students do not show up at this time, as all material that they need (everything being discussed during the lecture time) is on the web, and they can look at it whenever they wish. Since we have six contact hours per week with the students and one hour goes to lecture, we are left with five more hours to work with. These five hours are divided into two Problems Lab meetings per week, each meeting lasting two and a half hours.

spreadsheet-based exercises

These Problems Labs are really the heart of the course, and are where the learning really starts to take place. There are up to 32 students in each Problems Lab.

The typical Problems Lab starts off with a very brief, very basic quiz to check if the students have at least attempted to understand the lecture material assigned for that day. The quiz lasts five minutes and tends to be multiple-choice. The quiz solutions are discussed immediately after the quizzes are collected. Students then move to their computer tables, where, working in groups of three or four, EXCEL spreadsheets guide them through conceptual and analytical questions and problems associated with the lecture material (see the sidebar "A Few Sample Spreadsheets.")

Not merely a series of steps to be completed, the spreadsheet exercises bring the groups together to work on problems that will be addressed by hands-on activities.

The spreadsheets start off by reminding the students of some of the basic concepts and definitions from the lecture. They are then guided through a series of conceptual questions and analytical problems. The questions start off easy and eventually work up to a level at which the students should be able to solve traditional textbook or exam problems. The classroom quickly becomes alive with discussion as the students work their way through the spreadsheets. The instructor at this point is merely a consultant if the student groups get stuck on a problem or cannot resolve a point of contention. But more often than not, the students are able to work out their own difficulties and solve the problems at hand.

It should be pointed out that the students are not graded on the spreadsheet problems. It is made clear to them that this is a chance to work through test-like problems, and to get all of their questions answered and their difficulties ironed out without being penalized. They tend to take these spreadsheet exercises very seriously and earnestly discuss their ideas in trying to solve the problems at hand. It is in discussing their ideas with their fellow students that many of their misconceptions are brought to light and debated.

hands-on activities

Once the students have demonstrated an ability to work with the concepts, definitions, and mathematics associated with the material du jour, they are told (by the computer) to go to their activity tables and perform the corresponding Activity. The Activities are the experimental part of the course where the students get their hands dirty by working on an experimental problem solution. The Activities are usually graded in class as the students complete them, so they get immediate feedback on their work.

Each Activity contains a "background story" (which usually has nothing to do with physics!) that motivates the "challenge," or experimental problem, that they are to work on for the Activity (see the sidebar "Sample Activity"). There are in general no procedure steps. Only hints and precautions are provided for them, along with a list of results and conclusion statements they should have by the time they are finished. Again, without any procedure steps to follow, the discussion starts among the groups as they try to decide how they should proceed.

The students soon figure out that, since the Activity is directly associated with the spreadsheet problems that they just finished solving, they should examine the challenge within the context of the day's lecture and spreadsheets: Indeed, many of the spreadsheet problems are designed to give them hints of how to solve the Activity challenge. Because the Activities tend to use very simple equipment that the students can readily get their hands on outside of class, the students tend rather quickly to get the idea that the material they are studying applies to the everyday-world around them. This idea is reinforced by the out-of-class projects.

out-of-class projects

There are two out-of-class projects that the students must perform during the semester. The projects start with a Project Proposal. Each group must submit a formal proposal for their project. Some time is then allotted in the Problems Lab when the proposals are returned for the students to discuss their proposals with their instructor. This usually means focusing the proposed study (stating, "We want to study 2-D motion," doesn't quite do it) and making sure that they are hitting on the required skills. It is important to mention that the Activities part of the course emphasizes graphical analysis of data, all done by hand, and a straightforward error analysis which does not bother with a detailed propagation of error, but forces the students to acknowledge all errors they can identify in their measurements. Both of these skills must be addressed in the projects.

The students usually have about four weeks to complete their projects. Some time is provided in class for the students to discuss the progress of their projects with each other and with the instructor, but the projects are primarily out-of-class work. On the due date, each group must present an oral presentation to the class of their project and its results, and each student must submit an individually prepared formal report on the project. The total project grade is a combination of the group oral-report grade, the individual written-report grade, and a factor determined from a group honor statement that each member must sign.

Scheduling two projects is really a pain because there's just not enough time to do everything, but it's really worth it. The reason for two projects is simple: The students are to take the feedback from their midterm projects and use this to improve their final projects and corresponding presentations. It is made quite clear to them that it is expected that the quality and thoroughness of the projects and presentations will drastically improve for the final projects. We find that they really do tend to improve.

All's well that ends well

Student response to the new pedagogy for the algebra-based introductory physics course has been mixed, but is primarily positive. Some students, of course, resent the active role that they must play in order to make it though each class. The Problems Labs keep them very busy. They are expected to work on all of the homework problems on the web. There are also sample quizzes and sample tests that many students tend to work through. The projects challenge them to work within the constraints of their chaotic schedules to reach some sort of finality with their project and to arrange an oral report as a group. They have to learn how to deal with some students who are apathetic and don't want to do their share of the work (this is one of the motivations for the honor statement).

On the other hand, the majority of the students seem to react very positively to the new approach to learning physics. It is also rewarding to see the students really take ownership of their projects. They tend to stick around after the oral presentations and discuss their presentations with one another, comparing and contrasting their work with that of the other groups. They want to know how their projects compared to those in other sections. They rightly seem to feel very proud of the work they did in completing their projects. It also gives them a new perspective on science and research-especially when they realize that their instructor doesn't necessarily know what's going to happen with their project. A lot of times we just have to say, "Try it and see what happens!" When something unexpected comes along, we all work together in trying to figure out what's happening. Sometimes this is beyond the scope of the course, but some of the students want to follow it up anyway.

In the activities, students work with simple set-ups - indeed, nearly all of the "equipment" is inexpensive and available at department or toy stores. Photo courtesy of the author.

The new pedagogy has been sufficiently successful, both among students as well as their instructors, that all sections of the first-semester of the College Physics sequence at our university follow the new format starting this semester. During this same time, I am starting work on the second semester of the sequence. Developing these materials is an awful lot of work, but it seems to be worth it in the long run-it saves much time for the other instructors (and eventually, for me), it increases uniformity among different sections and semesters of the course, and it significantly improves student attitudes and decreases the drop-out rate in the class. Hopefully the second semester course will follow suit.

So how does all of this come to bear on astronomy teaching? Consider it as a template, perhaps, for your efforts to vitalize your subject and improve your students' learning. Whatever your approach in the classroom, you certainly have to be very comfortable with it. I would just entreat those teaching astronomy or any subject, for that matter, to seriously consider three questions:

• Who is taking the class?
• Why are they taking the class?
• Is class time being used as efficiently as possible? (or is class time even necessary?)

With the plethora of information now available on the web, it is no longer reasonable to assume that if students don't see it in your class, they're not going to be able to see it at all. Think about it.

VIC MONTEMAYOR is an Associate Professor of Physics at Middle Tennessee State University in Murfreesboro. He is a member of Project Kaleidoscope's Faculty for the 21st Century, and serves on its national task force on Incorporating New Pedagogies and Research in Learning. His email address is vjm@physics.mtsu.edu.