I've always wondered how I might assess student understanding of projectile motion separately from the algebra. I've tried in the past to do this, but since my presentation always started with algebra, it was really hard to separate the two. In my last three posts about this, I've detailed my computational approach this time. A review:

- We used Tracker to manually follow a ball tossed in the air. It generated graphs of position vs. time for both x and y components of position. We recognized these models as constant velocity (horizontal) and constant acceleration particle models (vertical).
- We matched graphical models to a given projectile motion problem and visually identified solutions. We saw the limitations of this method - a major one being the difficulty finding the final answer accurately from a graph. This included a standards quiz on adapting a Geogebra model to solve a traditional projectile motion problem.
- We looked at how to create a table of values using the algebraic models. We identified key points in the motion of the projectile (maximum height, range of the projectile) directly from the tables or graphs of position and velocity versus time. This was followed with the following assessment
- We looked at using goal seek in the spreadsheet to find these values more accurately than was possible from reading the tables.

After this, I gave a quiz to assess their abilities - the same set of questions, but asked first using a table...

... and then using a graph:

The following data describes a can of soup thrown from a window of a building.

- How long is the can in the air?
- What is the maximum height of the can?
- How high above the ground is the window?
- Is the can thrown horizontally? Explain your answer.
- How far from the base of the building does the can hit the ground?
- What is the speed of the can just before it hits the ground?</li

I was really happy with the results class wide. They really understood what they were looking at and answered the questions correctly. They have also been pretty good at using goal seek to find these values fairly easily.

I did a lesson that last day on solving the problems algebraically. It felt really strange going through the process - students already knew how to set up a problem solution in the spreadsheet, and there really wasn't much that we gained from obtaining an algebraic solution by hand, at least in my presentation. Admittedly, I could have swung too far in the opposite direction selling the computational methods and not enough driving the need for algebra.

The real need for algebra, however, comes from exploring general cases and identifying the existence of solutions to a problem. I realized that these really deep questions are not typical of high school physics treatments of projectile motion. This is part of the reason physics gets the reputation of a subject full of 'plug and chug' problems and equations that need to be memorized - there aren't enough problems that demand students match their understanding of how the equations describe real objects that move around to actual objects that are moving around.

I'm not giving a unit assessment this time - the students are demonstrating their proficiency at the standards for this unit by answering the questions in this handout:

Projectile Motion - Assessment Questions

These are problems that are not pulled directly out of the textbook - they all require the students to figure out what information they need for building and adapting their computer models to solve them. Today they got to work going outside, making measurements, and helping each other start the modeling process. This is the sort of problem solving I've always wanted students to see as a natural application of learning, but it has never happened so easily as it did today. I will have to see how it turns out, of course, when they submit their responses, but I am really looking forward to getting a chance to do so.