# Teaching Philosophy

My teaching changed substantially in the past years, informed by my research in physics education. Working in a public university in Brazil, a country with one of the highest school failure rates in the world, I taught introductory mechanics classes using the same standard lecture-recitation format that I remember from my schooling. I believed that if I made my lectures better, an improvement in student's learning would follow. However, advancements in my lecturing skills did not bring about corresponding advancements in student learning. As is common with introductory physics courses, students who passed it did not approach their work scientifically and lacked basic conceptual understanding needed to think of everyday phenomena.

Aware of the need for changes in physics instruction at my university, I started researching physics education and reading about learning theory. As a teacher, the best evidence I have seen of student learning has been with activities that engage students to interact in ways that more closely resemble scientific work. I began to regard learning as a process of adaptation, but rather than viewing it as an individual adaptation, I agreed with situative learning theorists in thinking of learning as a process of becoming a member of a community of practice, where newcomers model their work after that of experts, gradually learning to use shared vocabularies, techniques, and concepts. Following this model, I encourage interactions among students, engaging them in discourse modeled after scientific work. I believe that students must practice working with ideas to truly learn them - through context-rich activities or participation in original research projects - and that interactive classroom work should be designed to foster critical thinking and inquiry, and to confront contradictory conceptions of nature.

In 2000, as the Program Coordinator for the Physics and Physics Teaching undergraduate majors at my university, I introduced a pilot class to experiment with some physics teaching methods that I thought were consistent with situative learning theories. I incorporated group work and peer-interaction, and instructed students to focus more on the process and less on the outcomes of their discussions. Students were encouraged to challenge their own ideas and discouraged from referring to instructors or books before thinking about a question themselves. I also used materials and methods developed by physics education researchers in the U.S., like the Tutorials in Introductory Physics from the University of Washington's Physics Education Group, and materials aimed to build metacognitive skills. The activities I chose fostered interactions among students that mimicked those of working scientists and prioritized conceptual understanding over fact-recall. The outcomes of the teaching methods were, by most measures, significantly better than our previous methods.

As an example of how this work improved introductory physics teaching, one group of pre-engineering students was having trouble understanding why no force needs to act on an object when it is moving. The activity they were working on was designed specifically to bring impetus misconceptions to the surface, and to lead the students to understand the contradiction within their own world views. After engaging this group in a Socratic-style dialogue, one of the students, upon realizing how Newton's Second Law worked, looked at me and said: “So,... there is no need for a force. Force causes acceleration! Man, physics is cool!” These moments of discovery, in which students realized that physics in the classroom is the same as the physics in the real world, show that we may lead students to stop doing school and start doing science.

After the success of the pilot program, the method was adopted by the physics department, and expanded to all introductory mechanics sections. A Physics Education Group was formed at my department to conduct research on student learning, to work continually on adapting teaching methods to the population of students with whom we work, and to work on training pre-service teachers and providing research opportunities for undergraduates.

My research in introductory physics instruction has changed the way I approach all of my teaching. For instance, in an advanced mechanics course, students worked in small groups throughout the semester and did more tasks aimed at building metacognitive skills. Students collaborated on projects creating detailed models of complex physical situations. In one semester, students worked on explaining tides via Newton's theory of gravitation. By trying to make models on their own that could explain tides, they were able to recognize that most textbooks oversimplify, often making mistakes, the problem. Students learned a great deal of how to create physical models and to be critical of apparently simple and widely accepted explanations.

Traditional lecture-recitation methods alone have been shown, through extensive research in physics education, to be ineffective in helping students develop a consistent conceptual framework. Peer-interaction and active-engagement can help bridge the conceptual gap, but doing science is more than understanding concepts. In my classes, in addition to engaging students through peer-interaction, I choose activities that require the construction of auxiliary hypothesis and detailed models that apply students' theoretical and conceptual knowledge to situations that are close to their day to day experience, thus imitating the work of scientists.

## Courses Taught

### SF State University

**Concepts of Physics and Chemistry (SCI140).**

**Fundamental concepts of physics and chemistry, from motion, forces, and energy on to atomic structure, molecules, bonding, and chemical reactions. Basic organic and biochemistry.**

**Concepts of the Number System (MATH165)**

**.**Designed for prospective multiple subjects credential candidates. Understanding operations with whole numbers, fractions, and decimals. Problem solving strategies, numeration systems, and elementary number theory.

**Physical Sciences for Elementary School Teachers (LS309).**

**Designed for prospective elementary/middle school (K-8) teachers. Understanding through inquiry the structure and property of matter and principles of motion and energy.**

**Perspectives on Liberal Studies (LS300)**. Basic preparation for interdisciplinary study. Draws on language arts, mathematics, science, social sciences, humanities, and creative arts to prepare students for advanced work in Liberal Studies and for careers requiring breadth and depth of knowledge.

**Liberal Studies Senior Seminar (LS690)**. Interdisciplinary theory, research and practice. Examination of key questions and complex problems from multiple perspectives through preparation of a substantial piece of work.

### UFJF

**Physics I.**Introductory Mechanics course with calculus as a prerequisite. Taught to freshmen students at the Federal University at Juiz de Fora, majoring in Engineering, Physics, Chemistry, Mathematics, and Computer Sciences. I taught this course for 7 semesters.

**Physics I (Keller).**This is the same as the Physics I course above, but it was a joint project with Prof. Jose Luiz Matheus Valle and Prof. Luis Carlos Gomes to test the Keller method at Juiz de Fora. The Keller method is a self-taught self-paced method where student's progress is closely followed by a TA under direct supervision of the Professors responsible for the course. I taught this course for 2 semesters.

**Physics IV (Física IV).**A one-semester course to sophomore students covering wave propagation in electromagnetic theory, optics, and modern physics. Usually taught to freshmen students majoring in Engineering, Physics, Chemistry, Mathematics, and Computer Sciences. I taught this course for one semester.

**Experimental Physics I.**A one-semester course with experiments in mechanics that complement the lecture part of a one semester course usually taught to freshmen students majoring in Engineering, Physics, Chemistry, Mathematics, and Computer Sciences. I taught this course for one semester.

**Experimental Physics II.**A one-semester course with experiments in thermodynamics, waves and sound, that complement the lecture part of a one semester course usually taught to freshmen students majoring in Engineering, Physics, Chemistry, Mathematics, and Computer Sciences. I taught this course for one semester.

**Experimental Physics III.**A one-semester course with experiments in Electricity and Magnetism that complement the theoretical part of a one-semester course usually taught to sophomore students majoring in Engineering, Physics, Chemistry, Mathematics, and Computer Sciences. I taught this course for one semester.

**Analytical Mechanics.**I was a TA for an analytical mechanics course taught by Dr. Nelson Pinto Neto and Dr. Bartolomeu D. B. Figueiredo at the Brazilian Center for Physics Research (CBPF). This course was required for students belonging to the Masters in Science program at CBPF.

**Advanced Analytical Mechanics.**One-semester Advanced Analytical Mechanics course taught to physics graduate students at the UFJF/UFMG joint program. The students had prior contact with analytical mechanics, and this course had a strong emphasis on the Hamilton and Hamilton-Jacobi formalisms, in particular its relationship with wave theory. I taught this course for one semester.

**Quantum Mechanics.**Two-semester required quantum-mechanics course taught to senior students majoring in Physics, at the Federal University of Juiz de Fora. For this course we followed Park's quantum mechanics textbook, but included extra material from Cohen-Tannoudji, Diu & Laloe, Schiff, and from Peres. I taught this course twice, over a period of four semesters.

**Statistical Mechanics.**A one-semester course required for students majoring in Physics. This course is taught at the level of Reiff, and covers the basic of statistical mechanics.

**Quantum Optics.**One semester Quantum Optics course for physics graduate students at the UFJF/UFMG joint graduate program. We were mainly interested in the properties of the quantized Electromagnetic Field that are considered purely quantum mechanical properties, as for example squeezed states or quantum mechanical correlations for entangled states. This course was taught jointly with Prof. J. P. R. F. de Mendonca.

**Research on Physics Education.**A one-semester course aimed at senior students from our physics teaching certification program. We covered basic topics in physics education, with particular emphasis to misconceptions in physics and evaluation, as well as active engagement methods in physics education and how to implement them in a classroom.

**Physics of the Brain.**A one-semester course aimed at senior students interested in biophysics and physics of the brain. In this course we started with detailed analysis of the physico-chemical processes that lead to a membrane potential in a cell. After that, we described the models for the action potential in neurons. From the behavior of individual neurons, we showed neural network models that could model associative memory. At the end of the course, we discussed measurments of macroscopic collective behavior of neurons, like EEG and MEG. This course was taught jointly with Professor José Paulo R. F. de Mendonça. .

**General Relativity and Cosmology.**A one-semester Gravitation course for senior students majoring in Physics. This was an introductory course in General Relativity, with a strong geometrical approach. During the semester, we made an effort to cover most of the interesting solutions to Einstein's field equations, including the Schwartzchild solution, the Friedman cosmological solution, and also gravitational wave solutions.

**Foundations of Quantum Mechanics.**This was a course aimed at senior or graduate students that already completed at least a semester of quantum mechanics. We covered topics like the measurement problem, decoherence, consistent histories, Bell's inequalities and the GHZ theorem, contextuallity vs. nonlocality, and quantum computation. Alternative interpretations to the Copenhagen interpretation were also discussed, as well as its advantages and problems.

**Special Relativity.**A one semester introductory course in special relativity, with particular emphasis to its geometrical interpretation. This course was aimed at freshmen students and up, and followed Taylor & Wheeler's Spacetime Physics.

### Stanford University

**AP Mechanics.**This is the AP Physics: Mechanics course that I help develop at the Extension Program for Gifted Youth (EPGY) at Stanford University. This is a distance-learning computer-based course aimed at gifted students that cannot have access to this course at their school. I was responsible for writing the computer lessons and, at the software's initial stage of development, I was responsible to give supplemental lectures to students. I was also the responsible for tutoring remotely the students. I tutored and developed the course over a period of two years.

**AP Electricity & Magnetism.**An AP: Electricity & Magnetism course that I helped develop at EPGY. My work was similar to that that I made with the Mechanics AP course at EPGY, described above. I tutored and developed this course over a period of one year.