In this article, Ferrera analyzes primary students' learning of graph motion by using CBR devices (which measure and make a graph out of motion) and assesses how this affects the way they present their understanding of mathematical relationships (mostly through distance-time graphs). In the first part of the paper, she discusses how the network of perception (body and imagination) affect student learning, and then goes on to describe a particular students' understanding as developed through graphing motion.
Two things struck me while reading this article:
Firstly, at the school I started teaching at, we had a class set of CBR devices - I had an activity where I had students walk towards and away from a wall and look at the resulting distance-time graph to have them analyze how slope increased/decreased as they moved faster or slower. Sometimes, if I was feeling ambitious, we would try to analyze the graph of a ball bouncing or other movements using the CBR devices. CBRs were clunky technological things that were hard to read and often malfunctioned. Still, the kids were usually impressed by the technology that could record their movements. I haven't seen CBR devices since leaving that school, but I'm sure there's an app that could be downloaded to an iphone, probably for free, that would do a much better job than the CBR did, yet I'd also be willing to bet that the kids now would not be as impressed by it as they were by CBRs 9 years ago.
The other thing that struck me was the idea that doing math can feel differently depending on how you are doing it. Is solving an activity on a board the same as solving it on paper? I knew a teacher who had a great deal of success giving his students erasable markers and having them write all over the walls and windows in the class - he found them much more motivated to solve problems and to work together. I know I lament the loss of my blackboard (in exchange for a whiteboard) as it's somehow not as rewarding to compute equations unless it's a bit gritty. I'd be interested to learn more about why this feels different for us cognitively.
David, there are certainly things you can do with a black board that you can't with a white board and vice versa. Either way, a few years ago, there were talks about allowing students to work on vertical surfaces similar to what you described. I too had a lot of successes with students working on white boards either individually or in groups. I never figured out whether it is the fact that they get to move about in the classroom or the novelty of writing on the whiteboards that triggered the excitement. I was at a math presentation on the concept of writing on non-permanent surfaces such that students are more bold to attempt questions without being afraid of making mistakes. Nonetheless, I am a firm believer in a positive relationship between kinesthetics and learning new (mathematical) concepts. Regardless the involvement of technology or not, allowing students to be out of their seats during a lesson can sometimes have a positive effect on student learning.
ReplyDeleteI have heard of programs that track bodily movements and generating distance, velocity, and acceleration versus time graphs. I first encountered one in my B. Ed. program at UBC in the room next door to our math class. I've heard countless issues with it and never had the chance to use it in my teaching. I do have used the ticker tape counter that tracks the distance an object travels per 60 Hz intervals. I used it in Physics 11 and Science 10 to calculate the gravity. However, it is fairly low-tech such that all of the computations and graphs and are done by hand. Also, the amount of work required to obtain a graph for calculating the gravity is extremely tedious. My speculation is that students would still be as fascinated about an applet that tracks movement as your students 9 years ago. However, I wonder if they would have the same level of appreciation for the mathematics behind the graphs if all the mathematics are computer generated.
Jubilee, David, the article I read this week touches on a lot of what both of you are talking about. In it, students use a motion tracking device called Kinect to record their movements and project a digital display (particularly, movements surrounding angles). The researchers also developed software for it so that Kinect would automatically measure and record the angles that the students produced.
ReplyDeleteSomething like Kinect sounds like an ideal medium instead of David's 'clunky' CSB devices, or Jubilee's ticker tape counter. Writing a program to convert movement into d vs t, or v vs t graphs would be very simple. I bet that there are apps that exist that could be used in conjunction with this.
Jubilee, I also love the idea of non-permanent surfaces. I frequently teach with all of my students standing, markers in hand, all ready to contribute to our whiteboard discussion (mind you, I do teach small classes, so this is more feasible).