Different Strokes

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Different people learn best by different means because of their diverse strengths and weaknesses. Some people have better memories than others; some people are better at comprehending what they learn; some are better at applying what they learn; some are better at analyzing what they learn; some have greater capacity to synthesize ideas from different realms; some are better at evaluating the information they have. Furthermore, some people are more visual, some are more verbal; some people are more receptive to information from authority figures than others; some are more organized in their learning habits; some come to a topic with lots of prior beliefs; some have relatively few notions on the subject.

Unfortunately, in real life, the range of teaching methods is limited, and few if any are truly optimal for anyone. The discovery-type experiences just described are too expensive to be implemented everywhere. The traditional compromise that best supports discovery learning is classes with laboratories and homework.

It is pretty well established that a typical large lecture class, say 250 students in introductory astronomy, is among the least effective ways to cause conceptual change. The major reasons are varied. As you probably know, students respond to the personalities of their teachers. A boring or inarticulate teacher can make even the most interesting course drag. Also, teachers often teach at levels inappropriate to their students. Even if all instructors were stellar, intrinsic problems remain. They boil down to the fact that if students aren't actively involved in the learning process, they are exceedingly unlikely to retain information, incorporate it into their understanding of the subject, or replace their incorrect beliefs with more accurate ones. Typically, the individual in a group of several hundred is unlikely to get actively involved in class discussion. But such classes are necessary evils, given the numbers of students and the numbers of teachers, classrooms, and pieces of essential equipment available.

"But you teach big classes just like you describe. How can you live with yourself if you know your students aren't really learning what you teach?"

Once I realized that normal lecturing is relatively ineffective, I couldn't teach that way anymore. I still had the responsibility of such large classes, but I was determined to make the learning experience more effective. First, I needed to know what incorrect beliefs the students had coming into class. Then I needed to find ways of making them realize that these beliefs were wrong. And finally, I needed to find effective ways of presenting the correct information. This process took a decade. I would never claim that the result is a course as effective in teaching as small, hands-on classes are. Nor is it right for all my students. Nor did I see ahead of time all the twists and turns in the process. But eventually I did arrive at an approach that makes the knowledge presented in a large class compelling. And it all began innocently enough.

Show, Don't Tell

In order to help people deal with their misconceptions, we have to know what they are. There are at least two ways of getting this information: asking and taking. Asking for the information requires that students actively compare what they are learning with what they believe. Armed with insights from small discussion groups I held with students about their misconceptions, I realized that there are so many incorrect beliefs (both superficial and deep seated) that I would have to spend centuries interviewing a few people at a time to get at many of them. Or I could enlist thousands of volunteers and get most of the information in a few years. I chose the latter route and began the very next semester.

During the first class of each semester since then, I have begun with a demonstration designed to convince everyone that they have incorrect beliefs about science. I put an electric air gun, like the ones used to blow leaves off a driveway, on the table. The gun is fixed in a base that points it straight upward. I then produce a beach ball and throw it out for the students to bounce around for a while. Then I ask three questions:

1. What will happen if I turn the air on and throw the ball up into the vertical airstream?

About half the students have seen this demonstration and respond, correctly, that the ball will hover above the air gun. The other half expect that it will fly away. I then do the demonstration and, indeed, the ball hovers several feet above the air gun. Over the roar of the air, I shout the second question:

2. What will happen if I tilt the air gun over toward them at an angle of, say, 45 degrees?

Virtually everyone expects that the ball will be blown into the audience. I do this experiment, and the ball moves sideways and hovers over nothing about five feet to the side of the air gun. I then slowly rotate the gun around and the ball follows in a broad circle.

Finally, I ask: 3. What will happen when I turn the air gun off?

There is universal, if slightly more hesitant, assertion that the ball will drop. It doesn't, of course. As the air stream decreases in strength, the ball moves back to the mouth of the air gun, where I catch it (I've practiced).

This demonstration is truly effective in getting the students' attention. I go on to explain that they will be learning many things that contradict what they already believe. I give a few astronomical examples of common incorrect beliefs, such as that the cause of the seasons is Earth's changing distance to the Sun; that depleted ozone in the atmosphere is not replaced; that the primary purpose of a telescope is to magnify; and that Mercury is the hottest planet. Then I offer an incentive of extra credit to those students who provide me with a list at the end of the semester of 42 astronomical beliefs that I have corrected for them. (There are 42 contact hours in the semester.) Each item has to include a sentence stating what their original, incorrect belief was and where it came from, if they remember. This is how I get them to volunteer their incorrect beliefs.

Of course, there is a lot of duplication in the 50,000 statements submitted over the years. By combining identical items, I began developing a list of incorrect beliefs, which now number more than 1,560. As noted in chapter 1, you can find a complete list of them at http://www.umephy.maine.edu/ncomins/.

Some statements are given quite frequently, such as "I thought that Polaris is the brightest star" and "I thought the asteroids were close together, like in the movies." These are clearly common incorrect beliefs. However, even many of the less frequently cited statements are quite common. This becomes apparent when I ask questions on tests based on some of these less common beliefs. For example, only a few students have ever stated in their lists that they thought stars have molten liquid surfaces. I suspect, however, that this is a common belief; even after I have taught the correct science (gas all the way down), a large plurality of students choose the answer on an exam that stellar surfaces are liquid. This latter process of getting information by asking directed questions is an example of "taking" it. I will give another example of taking information shortly.

"It's not fair to ask loaded questions like that on tests."

I don't ask loaded questions as a common practice, but they sometimes are instructive in showing just how deep-seated some beliefs are. Also, keep in mind that I had already taught the correct answer. The fact that many people didn't "get it" was as much my fault as theirs. If I had done a better job teaching by helping them confront their prior, erroneous belief, more of them would have gotten the right answer.

Book Learning

Armed with lots of incorrect beliefs, I began reading the literature in search of ways to help my students in a large lecture setting. The results were disappointing. Most success in correcting wrong ideas has come in small classroom settings, especially, as noted earlier, when there are many resources available for students to use in their process of constructing new beliefs. One day, late in 1994, while reading the journal Physics Today, I came across an obituary for the astronomy writer William J. Kaufmann III. I was shocked and saddened. He was only in his mid-fifties at the time and was writing some very successful college astronomy textbooks, including one right at the level of the introductory course I taught. In an epiphany, I realized that here was an opportunity to help students in classes of all sizes address their misconceptions by writing about them in a textbook. Perhaps I could figure out a way to get students to think about their preconceptions before reading the correct science, then guide them through the reasoning that would help them unravel their incorrect ideas while making the correct ideas compelling.

The first big obstacle was getting the right to rewrite Kaufmann's book. I called the publishing house and talked to the editor in charge of acquiring astronomy texts and authors. She was a very pleasant, very sharp person. After sharing our sorrow at Bill's passing, I pitched myself to take over his paperback text, which I knew from the copyright date was due to be rewritten soon. I sent her copies of my previous book and trade articles. She then asked me to write some sample chapters for the revised text. While writing these, I worked out a way of addressing and correcting incorrect beliefs. I sent the sample chap ters off. Several weeks later, I got a phone call: "Neil, we'd like you to take over the book, but there is a real time crunch. We need a first draft in six weeks." They bought me a shiny new computer (66 MHz with an Intel 486 CPU, no less!), and six weeks later I shipped the first draft to New York.

There was deafening silence from the publisher for several weeks. Then my editor called, saying that while the draft would need some work, it was acceptable and that the misconception-based ideas seemed very promising. Then she told me that a normal revision of that text took eighteen months, so I didn't feel bad that my first draft "needed some work." The book came out on schedule, and the idea of addressing misconceptions in a text was quickly accepted by my teaching colleagues around the world.

My approach to misconceptions in the textbook has several parts. At the beginning of each chapter I ask a series of questions based on common misconceptions about the material in that chapter. The idea, of course, is to have readers thinking about their ideas as they read the material. When approaching the section of the chapter in which the correct information is presented, I try where possible to explain why some of the common incorrect ideas are wrong. A numbered icon appears next to each paragraph containing the correct explanation for each question. At the end of the chapter, the questions are repeated with brief summaries of the correct explanations given directly below them.

Student response to this feature has for the most part been positive. The only exceptions I have heard about are people who have difficulty with the fact that someone else seems to know what they are thinking. In other words, they feel uncomfortable being wrong and knowing that someone else knows they are wrong. This became particularly clear to me after a talk I gave about common misconceptions taken right from the book. A student came up to me afterward looking shell shocked. "I can't believe it. You were describing me exactly," she said. "I believed all of those things." I assured her she wasn't alone and that those incorrect beliefs didn't mean she was stupid. "We all have lots of misconceptions. They're unavoidable." I don't know whether or not she found that reassuring.

In Your Face

Having my own textbook that addresses common misconceptions proved a valuable first step in changing how I taught large classes. But addressing incorrect beliefs in a text is one thing; dealing with them in the classroom in order to help students retain correct knowledge requires active teacher intervention. I wish I could say that I planned what happened next in that regard, but it came unexpectedly as a side effect of the need to take class attendance. I decided to change my laissez-faire policy in light of reports that improved attendance leads to better grades among some groups of students. I made showing up to class worth 10 percent of the grade. This straightforward decision set into motion a chain of events that dramatically changed the way I teach.

The reality of college student life is that there are classes you have to take but choose not to attend very often. Sometimes you can learn the material from the book and don't want to waste your time going to class. Sometimes the professor is deadly boring. Sometimes you have a hangover. Sometimes it's too early in the morning. Sometimes you just hate large classes or discussion groups, or something else entirely. Nevertheless, many educators' experiences reveal that attendance improves many students' grades. The question for me was how to take attendance, knowing that some students will do anything possible not to attend and still get credit for being there. You can't just have students check off their name on a list or even sign in personally; they quickly learn that they can sign in for their friends, and attendance drops. So I came up with the idea of asking the students a question at the end of each class and requiring them to write it down, write an answer, and hand it in on a sheet of paper. Since I thought up the question as each class ended, the students would have to be there to know it and answer it.

In light of this book's subject, you won't be surprised that I decided to ask questions based on common misconceptions. Furthermore, they were on topics about which I had not yet presented any information in class, so the answers represented what students thought previously. This is the second way of "taking" information. I assured the students that during the semester I would only scan their answers to be sure they were responding to the question I asked

(and therefore had been in class). I also promised them that their answers would have no bearing on their grades and that I would never use their names in connection with any of their answers. I didn't forbid discussing the answer while they were writing, but I didn't encourage it. I answered each question at the beginning of the next lecture. Here are some of the questions I asked in the fall of 1998.

1. How did the Moon form?

2. a) How much of the Moon's surface can we see from Earth over the course of a year? b) Does the Moon rotate?

3. What causes the seasons?

4. What causes the tides?

5. What causes the phases of the Moon?

7. What is the shape of the Earth's orbit around the Sun?

8. How many zodiac constellations are there?

9. On which planet is the surface temperature highest?

10. What is the origin of the "face" on Mars?

11. Describe the rings of Saturn.

12. What fraction of the solar system's mass is in the Sun?

13. Why does the Sun shine?

14. How does the Sun compare in size to other stars?

15. What is the distance between the solar system and the star closest to it?

16. Which stars "last" longer, higher-mass stars or lower-mass stars?

17. How many stars are there in the solar system?

18. How many stars are there in the Milky Way galaxy?

19. How many galaxies are there in the universe?

20. If you go out at noon today, when the Sun is nearly highest in the sky, at which of the following angles above the southern horizon will you find it? Choose the closest angle: 30°, 45°, 60°, 90°.

21. How did the universe begin?

22. Please evaluate these questions. Have they had any bearing on how you think?

At first, many students were angry at having to write down their beliefs only to learn at the beginning of the next lecture that they were often wrong. This I had expected. What I hadn't anticipated was the evolution of their attitude toward this process. After two or three weeks, I began to see a noticeable change as they answered the questions and turned them in. Their resentment gradually decreased, and most students appeared to tolerate the questions. By the fourth week there was an air of anticipation for each question. I began seeing groups of students discussing how they had answered the day's question as they were leaving the classroom.

By the middle of the semester, the majority of the students were actively involved in the process of addressing their prior beliefs, driven by these questions. I mark the beginning of this period, which ran through the end of the semester, as the first time that loud cheering and moaning occurred in response to the correct answer I presented. I observed students who got it right raising their arms as they would when their team gets a touchdown or giving each other high fives. Students began asking me questions about why their own ideas were incorrect. The discussions among themselves were noticeably more intense. After each class, there were perhaps half a dozen groups of students standing around talking about the questions, arguing for one belief or another, even after I left. Several students told me that they went home after each class to research the question in the textbook or on the Web. Others told me that they would ask their families the questions when they went home for visits.

This attendance tool had morphed into two other things: a way for me to collect data on the percentage of students who held incorrect prior beliefs and a way to get students actively involved in thinking about their prior beliefs.

As the semester unfolded, the power of the attendance questions became even more apparent. This also gave me the opportunity to see if I had really changed anybody's misconceptions. I decided to administer a nongraded test near the end of the course asking the same questions as had been given throughout the semester. I gave this test in the penultimate week of classes, before anyone had started studying for the final exam. The idea was to see if after several, or even a dozen, weeks with the new concepts, students had changed their beliefs. Some typical results from the 1999 class follow.

Distance to Sun Earth's orbit Axis Tilt Time Sun is "Up" Axis Tilt+Distance Sun's Location on Ecliptic Dont Know

Precentage of Solar System Mass in Sun

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