Problem Types You May Find Useful

I’ve been writing exercises recently that Try to juxtapose concepts that are “related but different” and that can be difficult for students. Here are some examples from kinematics

1. Students are given the same shape graph and the same question, different vertical axis.

2. Students are asked create graphs for different motions where the number the 12 occurs to describe perhaps a position, a distance, a constant speed, an instantaneous speed, an acceleration.

3. Students are given different graphs without axes that all describe the same situation. They have to figure out what the axes are.

This is a nice contrast to “car sorting” where the focus is on how things connect. These exercises better focus on “what’s different” in subtle ways.

As usual, these exercises are fine to just do, but they are probably most useful for provoking certain discussions and/or formative assessment.

Magnetic Hooks for Doing Equilibrium on Whiteboards

This is basically what I was doing before.

I’m not convinced that the ones I’m currently using are best. Whiteboards are pretty slick and so the ones above only hold about 3.5 N. I’d like to get that up to at least 5 N, so I don’t have to reinforce anything.

And here is a slo-mo video of me using magnets with a horizontal spring.

Jigsaw Kinematics HW

In the hallway yesterday, we were talking about ways of better integrating homework into the flow of instruction. Here is one idea I came up with while sleeping last night

1. Students are assigned a 1D kinematics homework problems, where they are asked to work out a multi-representational model – diagrams, graphs, equations. Each individual problem is for a single moving object.

2. At the start of the next day, students get with a group of students who were assigned the same problem and they share and work on a consensus model.

3. The groups are then broken up. Students are then paired up with another student who worked a different problem. These students have to collaboratively work a problem involving finding when and where the two objects will meet up (or some other questions.)

Of course there are lots of details about the problems and the process to work out. But this is my initial thinking that I wanted to get them down before they vanished.

I see a variety of possible benefits, as well as a couple of logistical issues that would need to be ironed out, but I’m curious what others think. Has anybody tried something like this?

And finally, this is just a specific example of a more general notion. Lots of other ways to implement.

Motion Diagrams in Logger Pro with Motion Detector Data and Animated Displays

A lesser known function in Logger Pro is Animated Displays, which can be used to do a variety of things. One specific thing it can do is make animated motion diagrams from motion detector data. Below is one that I made for a cart given a quick push up a ramp, and then allowed to slow down before speeding back up the other way.

To get started, you will need to insert an animated display while you have a motion detector connected.

Then, on the screen double click the new display that has appeared. This will open up an options menu.

For scaling the display, you will probably want to select asymmetric coordinate systems so you can set the x (or y) axis to match the range of positions the motion detector will be sensing.

Then, you will also want to select “leave foot prints”. You can adjust how often a foot print is left.

Now you want to tell Logger Pro to link the animated point to the data coming from the motion detector. click the animate point button. This should open a window

Here you can set the horizontal and vertical variables. Set the horizontal drive to the position variable (this is name of the position data coming from the detector.) Doing this creates a dot on the display at the current value of the motion detector– and thus it animates the motion seen by the motion detector. The leave foot prints is what leaves a “breadcrumb” trail of this animation.

You can leave the vertical drive blank, but I’ll quickly show you how you can offset left motion from the right motion so motion that turns around doesn’t overlap with itself. I do this with a new calculated column that keeps track of whether object is moving in the + or – direction. I call this calculated column “sign” and is defined as

v / |v| (Velocity divide by its absolute value)

This will give a value of + 1 or – 1. By setting the vertical drive to this “sign” variable, motion in the positive direction will be plotted slightly above the axes and motion in the negative direction will be offset below. With an offset of +/- 1, a vertical range of +/- 10 seems to look decent.

Here is what the calculated column definition looks like.

Either way, whether you offset or not, you can also choose to add velocity vectors back once you are back at the display options menu. At the animated display options menu, click one of the vector buttons. This should open up a window where you can define a vector.

To give the motion diagram vectors. Set the horizontal component to track the velocity. You may need to adjust the scale down.

Anyway, you can also add acceleration vectors through a similar method, but it can’t get a little clunky on the screen if you aren’t careful about scale sizes for the motion you are observing.

Anyway, that’s the gist.

Magnetic Forces and Induction Setups

The setup below is pretty nice for induction across coils, done by either flipping a switch or varying the power supply manually. Here’s a short video. You can also grab the slinky coils and change the coil density to induce current. Here’s a quick look, and another.

This setup below is good for exploring how changes to magnetic flux can induce current. You can squeeze the loop, rotate the loop, or move it into and out the field. Here is a short video showing how it works.

This rails and rod setup can be used for either induction or a rail gun. It’s similar in look and feel to many textbook rail gun problems. Here is a short video I put up.

Below is the “classic” University of Washington Tutorials magnetic force on a wire set up.

Tiered (1D Forces) Problems

This semester I tinkered with writing problems that assess the same content but at different levels of sophistication.

I found this kind of thing useful in getting a better sense of students’ strengths and weaknesses, and hope to explore it more in the future.

Who taught me this racing game?

I’m guessing it was Frank who taught me this game, but from what I remember the rules are something like

  1. Your velocity vector updates your position.
  2. Each turn, you must accelerate your velocity vector by 1 square —  up, down, left, or right.
  3. If you crash into a wall, your velocity drops to zero, and/or maybe there is some penalty.

Screen Shot 2018-12-16 at 5.18.15 PM

Different Approaches as a Sign of a Healthy Ecosystem

I find it a healthy sign at the end of semester when there are many different ways that students approach solving a problem. Most students took an energy approach here (which is very sensible), but plenty of students also took various kinematic approaches.

Below are just a sample of my students’ work although I was not the grader for this problem.

Blog at WordPress.com.

Up ↑