Meets Thu. 2–2:50 PM in SERF 329 Fall quarter, 2018 (SERF is east of and adjacent to Price Center)

Tuesday 12:30–1:30 PM and Friday 10–11 AM: in SERF 336

In order to receive a P (pass) in Phys 87, you must:

- Attend class: two absences will be permitted, (so attend 8/10). E-mail notification of planned absences are appreciated.
- Submit a weekly question (see below for more detail)
- Come to at least one office hour some time in the quarter (will have a sign up sheet in class to spread out visits)
- Though I can't as easily grade this part, please engage in the class, contributing ideas and questions of interest.

This Freshman Seminar is meant to free the minds of our students so that they approach problems with flexibility, intuition, and quantitative estimates. You think that's π you're smelling? It is also meant to provide a mental framework that makes the material learned in future classes more tractable and permanent, by facilitating contextual links.

Students in physics classes often have problems transitioning from lower division courses into upper division courses. Many reasons contribute, but one observation is that students have developed a habit of solving problems by pattern-matching. This can come in the form of equation-hunting or relying on exposure to essentially identical problems from the past.

Human beings are powerfully adept at pattern recognition, and this
versatile tool can get us rather far—all the way to
upper-division physics. At this point, *concepts* begin to rule, and
students must have a well-stocked toolbox of mathematical techniques
at the ready—and know which tools to grab for the problem at
hand. Sure, identifying relevant concepts and applicable tools also
constitutes a type of pattern matching, but at a higher, more flexible
level.

A related problem is that material (e.g., tools, concepts) presented in classes does not end up in long-term storage in students' brains. This may be due to insufficient contextual ties, so that information ends up in a jumbled pile rather than in neatly organized shelves cross-referenced by real-world connections and relevance. It becomes much harder to access and utilize such information if it's in some poorly-exercised junk heap.

- Equation-hunting and formula-wedging are increasingly prevalent in physics majors: historically more characteristic of engineering students
- Over-reliance on pattern matching
- Stiff and formal relationship with numbers (relax, and let π = 3 = 10/3 = sqrt(10))
- Difficulty adopting concept-driven, first-principles approach
- Under-developed intuition; infrequent application of symmetry arguments
- Infrequent use of sanity checks, unit checks, estimation for scale
- Lacking intuition on basic units: how much is a N, J, W, C, F, etc.
- Students can't remember basic math tools, because insufficient contextual linking at the time of learning

- The educational system places emphasis on testing
- Many secondary education teachers don't really "get it"
- Changing population of majors: pragmatic, STEM-driven job-seekers who don't want to be left out of the emerging world
- Increasingly inaccessible world: urban environment with x-box and wifi vs. farm/woods, repair/dissection of simple equipment
- What I call the "Dora the Explorer Syndrome"—where
emphasis is on the
*idea*, not on challenges and practical feasibility of implementation. Kids come away thinking*any*idea constitutes a victory. - Insufficient connections being pointed out by instructors, so that information is disjoint and seems random—thus harder to retain

So let's try re-programming the way students approach problems
*before* reaching the upper-division whiplash moment. That's
what this Freshman Seminar aims to do. No guarantees that this will
be successful, but let's try building comfort and versatility in
thinking about problems so that students have better intuition and
alternate ways to sanity-check their answers. Among the approaches,
we will:

- Learn that there are often various ways to approach a problem
- Learn to ask: "How do I know if this is
right?"—and to answer
*on your own*without the aid of an outside source (like answers in the back of a book, or online solutions to a problem) - Build estimation skills to assist sanity checks
- Apply intuition to anticipate the outcome, and apply feedback to refine intuition when it is found to be off
- Check for symmetries or end-runs to potentially save time
- Check symbolic results in limiting cases to verify proper behavior
- Identify reliable, basic concepts (e.g., conservation laws) and build your own formulas from there
- Encourage exploration and daily life problem creation/solving

Famous physicists like Fermi and Feynman frequently forged formidable feats 'festimation. Less alliteratively, good physicists tend to have well-developed estimation abilities. Seldom are these skills learned in classes, but "learned on the mean streets," as my colleague George Fuller puts it. Maybe it's a selection effect: those who are good at estimation are more likely to succeed in physics/science.

For me personally, I learned at *least* as much in my
explorations outside of class as I did in the formal classroom. I
almost always had some problem I was chewing on, and my eagerness to
understand and make progress drove new discovery. What's more,
because I had problems in mind (many of which I got stuck trying to
solve), when new concepts and tools became available in the classroom,
I would think, "Aha! That's the piece I've been waiting
for!" and I could return to the problem and do it less clumsily
than before. By having context in mind already, I had carved out
space waiting to be filled by classes. By exploring the problem
before and after new techniques came along, I *owned* the
material. It was personal. It meant something to me.

Examples of problems that occupied me during high school and college appear in the list below (not chronological). I'm sure I am forgetting numerous lesser problems, but these are the ones that stand out in memory. And yes, my tendency to actually carry out these schemes brands me as an experimentalist. But just because kid-me did some stupid things does not mean that adult-me condones these activities!

**Why is the time between successive new moons not always 29.530589 days?**—led to a successful science fair project- In the process of working out the above problem, I needed
essentially instantaneous changes in some quantities, so
**I invented the derivative**to accomplish this. Granted, it was a crude quantitative construct formed by differencing two values as the independent variable (e.g., time) suffered a quantitatively very small change. Later that year when derivatives were introduced in my math class, you can imagine my excitement and personal connection. That whole "limit as delta-x approaches zero" business? Totally understood why. I owned it. **What math describes the distance between lines of longitude on the lunar map hanging over my desk?**—when I first encountered the sine function as a junior in high school, I had another Eureka moment: I had been waiting on the sine, and had an immediate friend.**What is the circumference of an ellipse?**— the formula for area is easy. The circumference is an introduction to*elliptic integrals*, unbidden.**Is the trajectory of a thrown rock a parabola or the end of a very long ellipse?**—and how to reconcile the math that says parabola with the intuition that says ellipse?**How does gravity vary as a function of latitude?**Can I reproduce the curve shown in my undergrad textbook by a combination of Earth's oblate shape and centrifugal force?**How should I throw a water balloon from the back seat of a roller coaster to hit the front car as we go around a loop?**Elliptic integrals again?!**Can I compute Sun and Moon positions accurately enough to produce an eclipse track to kilometer accuracy?**—associated with my journey to the 1991 solar eclipse.**Can I measure the radius of the Earth myself armed with a theodolite?**— yes, to about 10%. Variations in atmospheric refraction limited accuracy.**Can I use the same theodolite plus a timing signal get my position on the Earth using star sightings?**— yes: could tell whether I was in my yard or my neighbor's, after a few weeks of calculations!**What is the "muzzle velocity" of a three-man sling-shot?**—based on measuring "hang time" and figuring in drag**Building a telescope**also exposed me to many practical problems requiring thought, calculation, solutions, design, implementation.

The lesson should not be to copy what I did. I'm not trying to say
that I'm a rock star, but will point out that emulating a rock star's
visible behavior is not effective (and will probably land you in jail!).
Countless hours practicing and honing the basic skills is where it's at
(which is utterly boring to most people). Concert pianists spent years
perfecting excruciatingly uninteresting scales before spinning off
masterpiece performances. Emulation is not in itself a likely path
to success. Rather, find your *own* interests and ask your
*own* questions. Let your curiosity guide you. Plunge in to
solve problems or go as far as you can while you wait on pieces to fall
in place. Don't be afraid to explore. It's stumbling into the dark
that lets you build a picture of what you can't see by staring into
that darkness.

Recognizing that questions were an important part of my learning, and allowed me to build instant contextual links to new material, I want to help you do the same. Let's think of your brain as a warehouse where the college experience will bring daily deliveries of new material. Don't let it all pile up on the floor in an unordered mess. Let's make some shelf space with labels already in place. For me, this is what having questions/curiosity did.

So each week, I will have each student turn in a question (part of basis for grade). The question should be genuine and personal: something you really care about. I will select among these questions to guide class discussion, in which we use tools of physics to make progress in answering the question (maybe sometimes only partially or tangentially). By sharing questions, you might adopt others' questions for yourself as well. This just means more shelf space for future classes, where you're waiting for the day when a relevant topic is finally covered in a class. Now you know where to put it: fills a ready-made void in your brain.

The questions are not meant to impress me or other students: don't waste time thinking in this direction. I'll respond best to questions that ring true in terms of some personal connection/interest, and less so to deep philosophical questions. And more importantly, they'll serve you better in the future if they have genuine personal meaning. The questions most likely to get attention in class are those that involve some quantitative answer/approach.

While it might sound like psycho-babble, *metacognition* is thinking
about thinking. It's reflecting on what goes on in your brain when solving
problems. It's recognizing when distracting thoughts are getting in the
way (why can't I do this; maybe I should check for messages). It's
tracking the wrong and right turns and learning effective mental
strategies. In my role as instructor, I'll try to unpack thought processes
in my own head so you can see some of the wrong and right turns and use
that as a model. Whether or not it's useful, it is through metacognition
that I have come to think that a framework of questions can pre-load the
brain with order/structure making learning more meaningful and permanent.
At the end of the day, learning involves the physical process of
rearranging neural connections in your brains. So I'm trying to operate as
a brain mechanic, in some sense. That's why it makes sense to think about
how to facilitate this mental development—and that's metacognition.

All the stuff above may give a false sense of what the course will be about. It won't be a course in cognitive science or learning. It will be physics-based, focusing on fun, relevant problems as a way to expose you to how physicists think about and approach problems. In the course of tackling the questions posed to the class, we are likely to cover topics from the following list:

- Estimation techniques: finding familiar contact points; geometric means (bounding by the absurd)
- Approximate and flexible quantitative math (ignore digits/precision)
- Fermi Problems and coming up with list of sub-questions to solve overall problem
- Developing context for units of measure
- Energy content of familiar materials
- Human metabolic capabilities
- Drag in air and water
- Thermal properties of matter and heat transfer
- Energy in our Society
- many other topics that will surface in the course of chasing all manner of problems.