canceling terms

In my last post I talked about how I work with students with negative signs.  I thought I'd continue with some thoughts about canceling terms.  I'm a big proponent of having students solve problem algebraically first before plugging in numbers.  I usually reinforce that by asking follow up questions to problems like "what would happen if we increased the mass?", which are easier to answer if you can see whether it's in the numerator or denominator of the algebraic result.  On the way to an algebraic answer, though, there's many times when things cancel and I try to always be careful about those situations.

Here's an example: Consider a ball or block sliding down a frictionless ramp at the edge of a drop off.  The goal is to calculate the horizontal distance it will fly before hitting the ground.  Here's a quick sketch with the appropriate equations:

example problem with equations

Right at the point the particle leaves the ramp we can see that the mass cancels when considering the horizontal speed.  Right away with my students I would say "mass cancels!  That means you'd get the same answer with any block.  Cool!" or something like that.  The other major step in the problem is to figure out how long the flight will be.  Typically this is done by breaking the problem into horizontal and vertical components and finding when the vertical position has changed by the height of the drop off, as I've done on the left portion of the figure.  What's cool is that the final answer needs both major results (horizontal speed and time).  Both have "g" in them but together they cancel.  Here I'm often heard saying "g cancels! That means you'd get the same result on any planet.  Cool!" or something like that.

Doing the problem algebraically all the way before plugging in numbers lets students see what actually matters (in this case, the heights of the ramp and the drop off).  Students can then easily answer questions like "what would happen if you double h?" or "What would happen if you doubled the mass while tripling the strength of gravity?".  That last one causes groans for the students who've plugged their numbers in right away.

Another cool thing about this particular example is that the actual motion on different planets would be very different.  On the moon the horizontal speed would be very slow but the fall time would be long, exactly canceling each other!

When I push this method with the teachers that I teach (trying to get their physics license while already having another science license), most come to like the way that follow up questions are more fun and straightforward.  Some take a while to come around, though, as they like to grab their calculators right away.  The phrase "would it be the same on another planet?" usually works to get them to at least recognize the importance of canceled terms.

P.S. You get the same result for a ball that rolls without slipping on the ramp.  The horizontal speed decreases a little but mass still cancels (at least for spherically-symmetric balls) and the fall time stays the same.  "g" still goes away at the end.

SocCourt as a myth?

SocCourt is my favorite sport. I play with one friend at least once a week and I've gotten good enough now that I feel safe in offering extra credit to students who can beat me.  This semester no students have even scored a point yet (that's through six games so far) but they're motivated because I say that if a student beats me the whole class gets extra points.

In my "Hamline Mythbusters" class recently it was time to vote on what the full-class myth to bust would be.  This was after they'd already worked, in groups, on five different myths and they were wanting to all work together for the second go round (soon I'll post the YouTube videos of the five myths).   One student said it would be fun to bust the myth that SuperFly can't be beat.  At first we all laughed but it ended up being a lot of fun brainstorming how it could be done.  We realized that there was a lot of science that could be done including angle of reflection with spin, accuracy needed for controlled juggling, speed of ball necessary to break a light (this has, ahem, been done once already), and on and on.  We also realized that it would be fun to have some people investigate the value of trash talking (some would say I'm good at lots of things but awesome at that).  And of course, I'd be able to play lots and lots of SocCourt.

Alas, it got voted down.  Instead my students are working on the best way to lift someone with balloons. Some students are investigating the lift and leaking qualities of various gases.  Others are determining the best way to attach all the balloons.  Still others are working out the issues regarding weather (rain, wind, etc).  It'll be fun, sure, especially with the high speed cameras capturing things like balloons popping when filled too much, but it's sure too bad that I can't whup up on some poor students in the SocCourt court.

Negative signs

As a student I was very careful with my calculations.  I would hunt down every negative sign and make sure I didn't make any mistakes when doing homework and tests.  As a teacher I started out trying to get my students to do the same thing.  I would get crabby when noticing students trying to sneak in negative signs towards the end of a derivation instead of having them correct all along.  I found, however, that I wasn't teaching well when I did this.  This post is about how I teach now, specifically with those pesky negative signs.

For me, it's all about getting my students to trust their gut.  I figure if it's not in their gut, they haven't learned it.  So when I teach something with negative signs involved, I make a special effort to at least make sure the signs are in their gut, if not all the rest.  Here's an example: when deriving the potential formula for charged particles, you first have to teach about fields (possible negative signs), then about potential energy (more signs: should I integrate from infinity, is it me doing the work, is it the field doing the work?), then about potential (even more signs).  Now I just have students do the integral and separately teach about whether the result should be positive or negative.  I can be heard saying "don't write any signs down, just do the calculation and then ask yourself whether it should be positive or negative."

Knowing that like charges hate each other is often enough to help students get their signs right (though admittedly this is easier for potential energy than potential).  I've noticed that my students can get that concept pretty quickly but sometimes they'll still panic about how to go about doing a problem.  When they do I'll ask something like "does this charge want to be here?" or "would you have to move that charge or would it move that way on its own" and it's funny how often their confused faces turn to confident statements.

Charged particles are just one place where I do it (and have done it this semester) but I do the same thing in many situations.  I'd be interested to hear other's thoughts on this.

Recording students

This semester I'm trying two approaches in my teaching that both involve recording students. One has students using screencasting to turn in their homework and the other has students making pencasts of their group work.

Screencasting Homework

I've been teaching fully online classes for six years now. In the past my homework collection method has involved students scanning their homework and posting it to my Learning Management System (homebuilt using PHP/MySQL). This works pretty well but it was hard to ensure students were doing their own work. In my in-class courses I solve this problem with daily quizzes based on a randomly selected problem from the assigned set but I couldn't find an easy way to do this online. One option would be to do timed quizzes in Blackboard or something but students don't have nice pen mice like I have and so they could only type their answers without the ability to easily write equations and draw figures. This year I decided to do things a little differently.

At the beginning of the week I provide the students with screencast solutions to six problems from the chapter. I make myself available until Friday morning to answer questions in the discussion board and in my online office hours about the concepts of the chapter and the posted problems. Then on Friday morning I post a single homework problem that is due Monday. The students need to solve it, scan it, and then do a screencast of their solution to turn in.

Here are some of the benefits of this method:

• I only have to grade one problem per student per week.
• I can hear the students thought process about the problem.
• Even if they work together or cheat somehow they still need to put it in their own words.

It's been very interesting to see how a screencast often gets a different grade than the plain scanned document would have. It goes both ways. Sometimes I see a paper that seems technically correct but I hear them describe certain aspects incorrectly. I've also heard a student say all the right things while what they have written isn't technically correct.

I've gotten some good feedback from the students doing this (who happen to be teachers working on their physics teaching license) so I think I'll continue the practice. I've also branched out to in-class students, offering this method as a way to make up for missed in-class quizzes.

Group work pencasts

My newest toy this semester is a LiveScribe smartpen (actually eight of them). These pens are incredible! They record both what you write on the page and the audio happening at the same time. When you go back and click on a word it'll queue up the audio from that moment. You can also post "pencasts" that work the same way only on a web page so that students can access them. Even since I got my first one I've found plenty of ways to use it in my work. I originally wanted one to help me take better notes in one-on-one meetings with students where, in the past, I've found that I sometimes lose track of promises made by both parties. I certainly use them for that but I've also used my pen at campus-wide speakers, doctors appointments, department meetings, and yes classes. What I want to write about here, though, is how I use them in class.

Here's a breakdown of my hour-long general physics class periods:

• 10 minutes for a quiz on a randomly selected problem from the previous class period.
• 10 minutes to recap the material for the day (often prompted by a randomly selected summary posted by one of my students).
• 15 minutes to answer all the questions posted by my students on the material for the day.
• 20 minutes for groups to work on the problems assigned (one of which will be randomly selected for the quiz next time).
• 5 minutes for the groups to record a pencast of a roadmap (not a solution!) for the problem they worked on.

After class I post all the pencasts so that all the students have at least a sense of how to do all the problems when studying for the quiz. A typical day's daily outline will then have links to all the pencasts along with links to screencasts I've posted on the material and any resources I've found useful.

The students seem to have fun with these pens. They've made several suggestions for how best to use them including hitting the record button when I come around to their group as they're still trying to understand the problems. I now have eight pens in total and I look forward to finding more ways for students to use them in the future.