What do I want students to learn?

Background:
As a graduate student in astronomy at Columbia, I was required to teach an undergraduate astronomy lab course that's a companion to the introductory astronomy lecture course for non-science majors. I enjoyed teaching this course very much, and I did it for 6 semesters. During my last year of teaching, I was the named the head teaching assistant, which is sort of a misnomer for this course, because we don't assist anyone in teaching it but instead design and teach it ourselves. In my capacity as head TA, I was at least nominally responsible for monitoring the curriculum that other instructors came up with for their classes. Although I didn't really like the feeling of monitoring my peers, I am very interested in pedagogy, and I've read a fair amount about science education and have attended several conferences on it, so I liked thinking about the relative merits of different kinds of curricula.

Just a little more background — Barnard students are required to take a year of lab science courses, and the Intro Astro Lab course that I taught is one among many lab science courses that fulfill this requirement. So, most of the students in the class are Barnard students who want to get this requirement out of the way.

In fact, I know this is true: At the beginning of every semester, I passed out a questionnaire that asked, among other things, why the students are taking the course. Occasionally I'd get answers something like, "I've always been interested in astronomy." But, by far the most common response was, "To fulfill my lab science requirement." To my students, astronomy had for some reason seemed like the least painful way to pass this hurdle on the way to graduation; or maybe, since astro lab meets at night, it was the only course that fit into their schedule.

Teaching Non-Science Majors:
I have spent hours, weeks, and years of my life thinking about what I want to teach the predominantly non-science majors who took my Intro Astronomy Lab course. Unfortunately, I'm still not confident in an answer.

(a) Since my students were not astronomy majors, there wasn't really any specific astronomy knowledge or set of astronomy skills that it was critical for them to learn by the end of the semester.
(b) Furthermore, since biology lab or geology lab would also have fulfilled the lab science requirement, clearly Barnard isn't interested in making sure that all of its students learn any astronomy; instead they must hope that the students will get something out of the course beyond specific facts or skills relevant to one particular field of science.

These two realizations gave me a great deal of freedom to shape the course. But, as Spiderman reminds us, with great power comes great responsibility.

There's a relatively easy way to teach an astronomy lab course. As the instructor, decide on some astronomy facts, principles, and skills that one wants to impart to one's students. Then, each lab class will consist of lecturing to the students for long enough to explain all the nuances of the lab, and then having the students work through some procedure for figuring out the answer to some question. Along the way, they will learn some astronomy, and they will reinforce some skills. The instructor will more or less hold their hands along the way, making sure that the students feel comfortable while they work out whatever it is they're working on. I don't pretend that this is easy — there are major questions the instructor must address, about what content to teach and what exercises will be best (most efficient? most fun? something else?) for teaching this content. But it's easier than the alternative.

The relatively hard way to teach an astro lab course involves figuring out a way to get the students to think scientifically, and to be scientists.

Motivated both by what I think Barnard hopes its students will learn and by what I think the students will be capable of remembering 1, 3, 10, or 30 years from now, I arrived at the following goals for my course — during my course, students should:

1. learn the scientific method: science involves observing the world, making hypotheses (falsifiable models or predictions), and observing the world again to see to what extent it matches the predictions.
2. become investigative practitioners of the scientific method, specifically,
3. (i) observe the world, (ii) think of questions about the world, (iii) hypothesize answers to the questions, (iv) think of methods to answer the questions, (v) carry out the methods, and (vi) analyze the results of investigations.
   
4. become more comfortable talking about science.
5. learn to think about the meanings of numbers. This means,
6. (i) think about how many digits are significant, and, as a matter of scientific integrity and honesty, don't report more digits than are significant, (ii) understand what a margin of error or uncertainty is, (iii) think about what physical thing is being described every time a number is reported, and finally, (iv) don't reach for a calculator every time you have to do some simple calculation.
7. learn how to use a telescope.
8. come to enjoy thinking about science in general and astronomy in particular.

I don't care if they learn how far away the Large Magellanic Cloud is, or if they can reproduce a Hertzsprung-Russell diagram a year from now, and if I don't care about those things a year from now I don't think I should be too concerned if they learn those things now, either.

But how do I teach a lab that results in them becoming better scientists?

It's very hard to get students — especially students with a rather weak science background — to pose interesting, tractable questions about astronomy. So, I often eschewed astronomy in favor of more tractable scientific problems that were inspired by astronomy.

Basically, everything we do in lab as fits into at least one of three categories:
Exercise (e.g. point the telescope, or calculate this distance using parallax)
Experience (e.g. watch this demonstration)
Investigation

And, there are two kinds of investigation: guided or open-ended. In a guided investigation, the instructor poses the question, and the students think of how to answer it. In an open-ended investigation, the instructor provides a rough topic or framework, but the students think of the questions they want to answer and the methods by which to answer them.

If I tell the students how to answer a question, then I've turned what they're doing from an investigation to an exercise. Although there is certainly some benefit to exercises (they help reinforce knowledge or skills), I cared much more about developing their investigative minds (goals 1., 2., and 3., above) than about developing knowledge or skills. So, I spent as much time on investigations as possible, and I assiduously tried to avoid telling the students how to answer questions, or even what questions to ask. I worry that too often in lab courses, items 3. (ii) and (iv) above (in italics) are almost entirely overlooked; I tried to give the students lots of opportunity to do both.

But it's very easy for an investigative lab to make the students feel that the instructor is passive-aggressive. The instructor holds information that the students need, and yet refuses to give it to them. Why won't s/he just tell them how to answer the question? And the students have a response: stall. When the students stall for long enough, the instructor can feel forced to give them what they want so that they can complete the lab before the 3 hours are up. Doing this can have a terrible effect: "Oh, that's what you wanted us to do? Why didn't you just say so?" Well, I didn't say so because there wasn't anything in particular that I wanted you to do; what I wanted you to do was to think and come up with a solution on your own. But the damage is done.

Teaching a lab in an investigative manner can also make the students feel less comfortable, and it can therefore be less fun for them. I'd hate to think that I worked much harder than I otherwise would have, I made the students work harder and feel less comfortable, and in the end they have learned less astronomy and learned that astronomy is no fun. I'd hate to think that 3 years from now their memory of astronomy lab will be, "that time when that passive-aggressive teacher made me suffer pointlessly for 3 hours each week".

Jacob Noel-Storr, who was the Head TA when I started graduate school, had some excellent advice when I was in my first year of teaching: Never lecture, never use the blackboard, and be aware of how much time you are spending talking relative to the students (and make sure this ratio is small!). Of course, it's practically impossible to avoid ever lecturing or using the blackboard, but, if you go into lab with the intention of never doing these things, you end up doing them a lot less.

I believe it's safe to say that in my entire time teaching the lab course, I never spent more than 10 straight minutes talking at the students, and practically never spent more than 3 or 4 minutes talking at them. Many labs, I didn't even talk for more than a minute straight. I kept my blackboard usage to what felt like an absolute minimum, maybe venturing to the board on average 6 times in an 11 week semester.

This advice goes a long way toward addressing goal 4. Instead of me explaining things to the students, I had them explain things to each other. I had them present their results in every class. I often noticed students who were shy at the beginning of the semester become much more comfortable talking about science by the end of the semester, and I feel very good about this.

Goals 5.-7.: I explained why significant digits are not just a procedure for truncating answers so as to make teachers smile, but rather a matter of honesty (I hope they apply this concept to the terribly innumerate world out there); in general, I always made sure they were aware when they were not being adequately attentive to the meanings of numbers; and I had them observe with a telescope as often as possible. I hope that these lessons stick with them as they go through their lives, encountering political polls, descriptions of the efficacy of one medicine versus another, etc. And I hope that using a telescope is at least somewhat like riding a bicycle, and when they have a house in the suburbs someday they can show their kids how to point a telescope at Saturn.

Goal 8? This gets back to my huge fear. Was the extra effort (on my part and theirs) wasted? Did I make them suffer and at the same time lay the groundwork for a future of loathing science and astronomy? Gosh, I hope not. I'm sure that in plenty of cases my students felt very positively about astronomy by the end of the course. But, on the margin, could I have taught them roughly as much (or more) — while along the way making more people feel more comfortable, have more fun, and ultimately feel more positively about astronomy — by teaching the class in a more traditional manner?