Back in December 2012 a colleague shared some resources with me from Dan Meyer. Somehow at that time it really didn't hit me. Fast forward to an early Thursday morning in April 2013 when I woke up before my alarm to discover someone on my PLN shared the same video on Twitter. I decided my honors physics class needed a make over, and fast!
I was teaching the concepts of image formation by mirrors and ready to demonstrate how a concave mirror forms a real image of a distant object at its focal point. This is a demo I look forward to each year as the students can really see the light rays on a piece of paper when it is held at the focus of the concave mirror. This typically took about 10 minutes to do from intro to demo to the following practice problem from my slide presentation.
Now what were the students getting from me? Yes, Dan Meyer, a physics problem with all of the information given. When was the last time your boss asked you to solve a problem and gave you all the information necessary? I was ready for, "The Dan Meyer Challenge!"
My Honors Physics class learned these concepts via a flipped lesson online and then from a ray box and mirror activity completed in class earlier in the week. They were due for this lesson on Friday afternoon, but it was going to be a different experience for them than for students past. This time the students were going to be challenged to decide on what data to collect and how to use it to solve a problem. Here was my new "Dan Meyer-worthy" slide:
I did give them the hint that concave mirrors form images of distant objects at the focal point, but I did not demonstrate it to them. As I have a class of 20 students and 2 large concave mirrors, I put them in 2 groups of 9 (2 students were absent) and set them loose on the challenge.
First off each group had to determine the focus of the concave mirror. It was interesting to observe how each group went about doing this. One group, let's call them Group A, had a student far away from the mirror, then walked closer until she saw her image "flip." The other group, let's call them Group B, decided to use my hint. One student grabbed a piece of paper and started to move it back and forth in front of the mirror. Group B tried this for several minutes to no avail. I challenged them to be more dramatic in their testing of distances the paper was from the mirror (i.e. the focus of the concave mirror was 0.45 m and the closest they moved the paper to the mirror was well over 1 m!). Another student tried it with the paper this time and once the image of the trees outside were in focus he exclaimed, "Whoa!" The rest of Group B erupted as well and Group A stopped working to look over to see what all the excitement was about.
Now that both groups had a value for the focus of the concave mirror (f), the could have a student stand beyond a distance of 2C (two time the center of the mirror where the center is twice the focal length) away. They measured her distance from the mirror (do) and her height (ho). There was also some differences about how each group chose to measure the student's height. Group B group did her full height, while Group A did half of her height. Why would Group A chose half the height? Well, they knew the principal axis was parallel to the ground and went through the center and focus of the mirror. Thus, only half of the student would be above the principal axis. Well done!
Once the student (object) data was measured, each group had to determine both experimentally and mathematically the image data (di and hi). Here is Group B actively showing the location of the student's real image on the paper:
From here the students measured di and hi as best they could and compared it to their mathematical calculations from the mirror equation and the magnification equation. We followed this up with a class discussion on Monday where both groups demonstrated their technique for collecting data and explained their analysis. Students critiqued each other's methods of determining the focal length and also how to accurately choose the object height by using the definition of the principal axis.
What took me about 10 minutes to do in years past, now took an entire 50 minute class period. However, the difference is clear - the students had a more productive learning experience from working collaboratively on a problem. The students had to make decisions. This lesson went from teacher-drive to student-driven. I continue to look for additional opportunities in my physics teaching for this kind of learning.
I want to thank my math teacher colleague Nancy Hart for originally sharing this idea with me and my PLN for bringing it to my attention a second time. Thank you Dan Meyer for challenging teachers to do things differently!
Now are you up for the Dan Meyer Challenge? Please share your story in the comments section below.
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