Dr Cecilia Barnbaum
Although major and introductory science courses obviously require different teaching strategies and goals, they share a common purpose which is the students' achieving a new or broader perspective on the universe. In both types of courses I attempt to present students with a different view of their reality. To majors I point out with great enthusiasm the elegant beauty in mathematical descriptions of physical processes. I try to lead students to make what are truly astonishing connections between the vastness of space and the strange beauty of the subatomic realm. To students in introductory courses I try to show the connection among everyday phenomena and the same processes on the immense scale of space. There are some magnificent surprises that nature holds, and I hope to jar their worldview and dislodge their misconceptions.
For both groups I emphasize responsibility; they have not purchased an education with their tuition, they have paid for an opportunity and have taken on a great responsibility to themselves. This is an attempt on my part to awaken students who see college as extended high school where teachers run around after them which relieves students of the consequences of their choices. I make it clear to all my students that the responsibility for learning is theirs; I am just a guide. However, if they want help and are willing to work hard, I will do everything it takes to get them through; but ultimately the choice is theirs.
My classroom style is lecture based, although I use as many demonstrations as possible, especially ones that involve student volunteers. After explaining basic physical concepts, I try to lead students to assemble these concepts like building blocks and then have them use the structure to predict results for astronomical and other physical phenomena. Especially in the introductory courses, I try whenever possible to show how we know certain generally accepted ideas, such as the Earth revolves around the Sun. In advanced courses, I often find it useful to take a slightly historical approach to put students in the shoes of, for example, physicists at the turn of the century who found that Newtonian physics does not account for many observed phenomena. I take this approach to help them bridge their own recently-acquired knowledge of physics with the necessary but non-intuitive ideas of special and general relativity and quantum mechanics. How I implement these aspects of my teaching philosophy is detailed below.
Introductory astronomy courses are taken by students who are generally non-science majors; for these students, the course might well be their only encounter with a physical science. Therefore, I see their presence in the class as an important opportunity to offer them a new and hopefully enduring perspective on our universe. I attempt to introduce a broad view of: how science is done, how our every day perceptions can fool us about underlying realities, the fundamental nature of matter and space, and our place in the continuity of the cosmos. My strategies include asking students to apply different (and to them, unrelated) physical laws to a given system. For example, in a class discussion students used what they had learned about tidal interaction, centripetal force, and chemical and density gradients to rank-order the likelihood of four different scenarios of the formation of our Moon. In my lectures I emphasize process over phenomenology. For most part, students are overwhelmed by the science itself, and so I do not require them to memorize numbers or equations; although they are expected to have a relative sense of numerical quantities, e.g., distances in the solar system and Galaxy, and the relative strengths of the four fundamental forces of nature. Also, whenever possible I attempt to put a personal face on science by telling real-life stories about the often quirky people behind the ideas.
I have found that students need a way to pace their mastery of the material, so in addition to selected readings in the text, I give them study questions once a week followed up by a solution set a week later. The response from students has been very positive, and so every semester I tweak the study questions to improve them. In addition, I set up "recitation" sessions every week outside of class time, where we discuss the study questions and I can actively probe students' understanding of the topics. In these smaller groups, students seem more willing to ask questions.
On the first day of class I ask students to fill out a science questionnaire. The questions range from very basic astronomy-physics to specialized knowledge. This serves a dual purpose. First, their answers provide me a baseline of their knowledge in the field. I put the same questions on the final exam, which gives me some measure of how their understanding of the subject evolved over the semester. Second, the questionnaire becomes a tool for students' own self-assessment, since I return the questionnaire to them when they finish their final exam in the course. It is very satisfying to see their faces when they receive the questionnaires at the end of the semester. Most students read it right away and actually laugh at their answers, surprised that they ever did not know concepts which they now take for granted. ("How could I have thought that!")
In the majors' physics and astronomy courses my goal is to provide a strong fundamental background by requiring the same rigor that was required of me at UCLA when I was an undergraduate. I realize that this is a controversial approach since the preparation of our students is often not ideal. However, I feel very strongly that these students deserve the same quality of education as that provided by the most prestigious institutions, and that the more one expects of students, the more they will accomplish. When we set the goals this high, our students often need more direction and support to achieve at a higher level. To that end, I have provided specialized mathematics sessions outside of class e.g., calculus for PHYS 2211 and ASTR 3101, linear algebra and differential equations for PHYS 4411 and 4412. The material I present in these sessions is a distillation of the mathematics, that is, I design these sessions and material to emphasize the application of the calculus in a non-mathematically rigorous way. For example, after going over the mechanics of taking derivatives of various functions, I show pictorially why and how it works out that way, without the mathematical rigor of a serious calculus course. Several students have commented that as a result of those sessions and applications of the course material, they whizzed through their concurrent calculus classes with a more concrete understanding of the why and how of the mathematics. Beginning physics students (and some advanced ones, too!) do not employ a structure for approaching and solving physics problems. They write down equations willy-nilly without an apparent reason or goal, and hope things work out at the end. To help them build their own routine approach to physics problems, I have designed a step-by-step method and I require that they use the technique for homework problems. To date, I believe that I have succeeded in presenting the physics material rigorously and that the students were up to the task, given the extra support provided.
In general, I try to maneuver advanced students into finding inconsistencies or contradictions in classical physics so that they discover for themselves the need for the often surprising approaches and models of modern physics. I have found that students are much more receptive to the weird world of quantum mechanics if they first find the need and then see the success of model predictions. The challenge with advanced students is to wean them away from the limiting view of 3-dimensional models and toward abstract notions, such as multi-dimensional space. To this end, I try to construct a link between something in everyday life that can be expanded into the abstract. For example, I have used primary colors as basis vectors from which all other colors can be derived, creating a multi-dimensional space. It is also important that advanced students learn derive relationships from fundamentals, and so I emphasize these techniques in lecture and homework.
Teaching science on the elementary and secondary level is the most important job in this country. Students learning to be teachers will be responsible for our children's education, and ultimately for our future society. With that in mind, I insist my students know science content in any science-ed course I teach. A philosophy held by many is that these future teachers need only learn what they will teach and nothing extra is required; but "see one, do one, teach one" is not adequate. I call this my "Tip of the Iceberg" teaching philosophy. 90% of the mass of an iceberg is below the water line, with just the meager tip poking above. In the classroom, in order to get across to students the tip of the content iceberg, a teacher must have an understanding of the subject equivalent to the iceberg mass below the water line. This kind of in-depth understanding of science is what I expect of my students who will be guiding the next generation.