21st Century Math Project
D. J. Fromal, CFF Math Coach, Hatboro-Horsham High School
dfromal@hatboro-horsham.org

What are 21st century skills?
According to the site http://www.21stcenturyskills.org/, these are some of the skills referred to as 21st century skills:
· Global awareness
· Creativity and Innovation
· Critical Thinking and Problem-Solving
· Communication and Collaboration
· Information and Media Literacy
· Flexibility and Adaptability
· Productivity and Accountability

My idea
In my AP Calculus BC class, I wanted to have students complete a project based upon parametric equations. This is a topic that has always been dealt with at a theoretical level only in my classes but is actually used by physicists to model real data. Because projectile motion is something we have all seen, it is relevant and relatable. Therefore, I wanted groups of students to complete a project dealing with projectile motion where they needed to compute and understand the similarities and differences between theoretical computations and real data that they collected. Then, they needed to be able to report their findings and be willing to have other people judge their work. What did we use? Water balloons of course!

Steps that I took
Once I had the idea of launching water balloons, I had to answer some questions:
1. How will students measure initial velocity?
2. How do I create a simple launcher with little money?
3. What should the students be able to change? What are the variables?
4. How can we document our results?
5. How will students be assessed individually if this is a group project? What will the rubric look like?
6. How much class time will this take?

I began to answer these questions by researching some of these on the internet. I was able to find some great resources.
·Projectile Simulations This site is not the one I originally used but is similar. Allows students to see the effect of changing variables such as launch angle, initial velocity, mass, and even air resistance.
·Equation involving height change This paper has an equation I posted that allowed one group to change the initial height the balloon was being launched from.
· Tracker AnalysisAfter a great conversation with one of our physics teachers, he demoed this program for me and I was able to use it to create videos for all of the student groups. It helped to verify student assumptions or to allow them to change pre-conceived ideas on the fly.

Planning/Prep
Because this was my first time trying a project of this type, I spent a lot time trying things on my own (like the launchers and the video tracker), constructing a rubric that I hoped would hold students accountable and creating the website that would hold all of this information. I did not log the hours but it was easily 3-4x as much time as I would spend creating a normal lesson (writing a plan, making up activity/worksheet, and preparing a test).

Some time was spent on trial and error and revision. But a lot of time was in production of the rubric, launcher, and video files. That time will be greatly diminished the next time I do this project.

How it ran?
At the beginning of the week, I spent half a period (40 minutes) explaining the project and assigning groups. One group would change the initial height, one would change the initial velocity, one would change the angle of launch, and one would change the mass. I provided them some resources for how they could simulate launches using websites and equations they would need to compute theoretical calculations. I also gave them a few minutes to start discussing their strategy for launch day.

Midweek was the actual launch day. We went to the stadium and brought launchers, water balloons (I filled them before school), tape measures, large protractors, and digital cameras. One group would complete three trials of their variable while another group was responsible for the recording and measurement of the results. Because of the small class size, we finished in less than 45 minutes and were able to get back to class to start talking about the results.

I gave the groups the responsibility of creating their reports by the beginning of the following week. Because I was attending a conference the day after the launch, I did sign out the computer lab so that groups could work on their presentation. This was a luxury, not a necessity. By the following Monday, each group had to have their final report posted on my Moodle site. Then, for the next 24 hours, the reports were available online and each individual had to read the other groups’ reports and post a rating with comments about each one. Completion of this was part of each individual’s grade.

Results
I was excited to see the students actually gathering real data and comparing it to theoretical computations. This was well done by every group. Clearly, they put thought into their reports. However, every group made their final report a PowerPoint presentation and for some groups, this was not the best choice. This was commented on by the individual students when they completed their ratings. It was good to see that even the brightest students still need some help and have to get a better understanding of appropriate media.

HH BC Calc Moodle

Improvements/suggestions
· More time on teaching students how to take decent video.
· Allow students time to do tracker analysis on their own.
· Switch the order of the project. Do real testing first and then use those values in theoretical computations.

How can you do something like this?
· Start with an idea and see what is available through the web or other resources (like other faculty).
· Find out how you can use equipment/resources you already have available (CFF equipment).
· Have a plan for assessment. Individual accountability will help maintain integrity of the project.
· Be willing to flop. Don’t worry about being an expert. It is an experiment. Failure is possible but not fatal!
· Find someone who is willing to work with you. It can be a coach or a colleague. Bouncing ideas and getting feedback is important.