### Inverting the Lecture

I'm teaching Ay20: Introduction to Astronomy of the Galaxy again this year. Last year I prototyped a bunch of non-standard teaching techniques, and this year I've put the lessons learned to practice for my second time around.

Lectures are a medieval form of teaching in which the knowledgeable individual (presumably, the instructor) conveys their knowledge through a one-way verbal communication to the students. This worked well back when only a handful of people in a village or church could read and rapidly acquire new knowledge. With the invention of the printing press, it's time to empty out the lecture hall.

Along with my excellent TAs Melodie and Trevor, we get the students out of their seats and into a more active, collaborative learning environment. I take the examples I would cover in a traditional lecture and lay them out in order of increasing complexity/difficulty on a worksheet. Students then form groups of 3-4 and work on the problems at the board. This is the technique used at the Missouri University of Science and Technology's Learning Centers, at the MIT TEAL centers and the UC Berkeley TALC astronomy homework sessions.

With the students working at the board, the instructors can hang back and watch for conceptual errors, providing us with a real-time assessment of student learning. Conceptual difficulties can then be addressed on an individual basis, with customized assistance. In the photo above, TA Trevor David carefully stands behind the group and avoids picking up the marker. He instead prompts the students to think about their work by using the Socratic method. After helping this group, the students started discussing their misunderstanding and corrected their work. Trevor was then free to assist another group.

Here, Melodie assists the group next to Trevor's. After helping the students, she referred them to the neighboring group so they could compare techniques and answers. Our collaborative policy is that students must collaborate!

Here's an artistic shot of two first-year graduate students working on an Ay20 problem related to blackbody radiation. They participate in the Ay20 class voluntarily in order to shore up their basic astro knowledge, which pays off later in the day in their graduate level Radiative Processes class. Their eager participation demonstrates their desire to learn the material deeply, and the collaborative environment puts them, as grad students, in close contact with the undergrads, providing them with opportunities to enhance interaction within the department.

But do they learn? you might ask. Yes, yes they do. We know they learn because we can see and hear them learn in real time. We don't have to make assumptions about what the students know. We perform "rolling oral quizzes" throughout the week, taking students aside for one-on-one discussions of the key class concepts. These quizzes are evaluations of student learning and our teaching effectiveness. WE can make on-the-fly adjustments to our teaching methods and course material based on how well these quizzes go.

We also had the students take a concept evaluation exam at the beginning of the term, which we can compare to their results from the end-of-term performance on the same exam. Stay tuned for the results!

For more, check out our course website:

honestjournal said…
Excellent. I am thinking about doing similar experiments if I will have a chance to teach in the future. See also:

http://www.npr.org/2012/01/01/144550920/physicists-seek-to-lose-the-lecture-as-teaching-tool
jcom said…
Please tell me you do the hand motion when you say, "I inverted the lecture".

Great to see that the first-year grads voluntarily go to this undergrad class. That they chose to spend their time there speaks to the effectiveness of the approach.

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…

### The Long Con

Hiding in Plain Sight

ESPN has a series of sports documentaries called 30 For 30. One of my favorites is called Broke which is about how professional athletes often make tens of millions of dollars in their careers yet retire with nothing. One of the major "leaks" turns out to be con artists, who lure athletes into elaborate real estate schemes or business ventures. This naturally raises the question: In a tightly-knit social structure that is a sports team, how can con artists operate so effectively and extensively? The answer is quite simple: very few people taken in by con artists ever tell anyone what happened. Thus, con artists can operate out in the open with little fear of consequences because they are shielded by the collective silence of their victims.
I can empathize with this. I've lost money in two different con schemes. One was when I was in college, and I received a phone call that I had won an all-expenses-paid trip to the Bahamas. All I needed to do was p…