Today’s activities did not go so well. I tried to adapt a cool lesson that looks at the basic ideas of refraction that is initially designed for a 1-1 iPad environment. The task is simple at first: you are on a beach and notice a taco cart down the road. Knowing that you walk faster on the road than on the beach, a less direct path is taken in order to minimize time in the slower medium. Students guess where to aim for the road so that their path takes the least amount of time. The full activity can be found here: http://blog.mrmeyer.com/?p=15186
This activity involves the use of the Pythagorean Theorem to calculate the distances traveled on both sand and road, plus the distance = rate x time formula to go from distance to time. Students could then compare times to see who picked the closer path.
There were several issues with attempting this on a paper format. First, students had to measure with rulers, instead of having the measurements pop up when they picked a path. This lead to a lot of rounding so that individual students did not have very different paths. It also made the initial set up portion of the activity take much longer because they had a lot more drawing and measuring to do. Another issue was that students then lost the need to calculate using the Pythagorean theorem because they could just measure with a ruler. This might be a welcomed adaptation for my next class because it makes the problem simpler, but it definitely through a wrench in today’s lessons. Finally, it is much less engaging to draw information out of paper than it is to touch a screen and watch information just pop up. Also, the ability to gather class data and project to everyone is taken away.
As far as this activity went, student’s problem solving skills were definitely below the level of going through this activity since many were unclear about what it means to take the square root of something. This activity would require some work with simpler tasks to practice the mathematical skills and could then be a challenge problem. For my next classes, I am going to just have them measure the distances so we can focus on the concepts while involving much simpler math (which was actually my original intent). Then, at a later time we could try a challenge type problem where the Pythagorean theorem becomes necessary, possibly in conjunction with their math class so they can work through the same problem with a focus on different parts in each class.
There was a definite behavioral change between this lesson and the previous TPR one, that I attribute partly to the lower level of engagement in the activity and partly to the difficulty. I think many students checked out because they were confused, and once that occurred, their lack of attention just led to more confusion. In the TPR lesson, each step occurred more slowly as students were instructed what to do and other students were able to watch examples. The overall intellectual load was less and there was a healthy balance of experience, social explanation time, and note taking time. This activity was more mentally demanding and since it took longer, it didn’t have the same repetition of one concept in multiple learning modes. Hopefully the simpler version with work better and with the savings in time we can talk more about the importance of what we are doing and make connections to our experiences.