To me, the issue of creating several representations for the same phenomenon is interesting. I think that there are generally two approaches to the matter:
On one hand, in maths, when teaching functions, we train students to be able to translate between different representations, e.g. formulae, tables of values and line graphs. There is an assumption that they convey the same information, but in different ways.
On the other hand, there is the notion of affordances, introduced by Gibson (1979), reflecting the idea that each representation highlights certain features, but backgrounds others. This also reminds of Marshall McLuhan's idea: "The medium is the message".
Another association I had was Andy diSessa's idea of scientists being inventors of representations and that we should aim for our students to develop metarepresentational competence http://www.jstor.org/stable/10.2307/3233911.
In the following clip, the group has represented scenarios in pie charts and bar charts, reflect on their pros and cons and ended their discussion. Stamatis then asked them to try to modify the representations in some way in order to come to terms with their respective drawbacks, and they got more engaged with the exercise again. In particular, they think that it would be useful to introduce some kind of dynamics, showing the time dimension. Andrew suggests an animation, and Madonna (top right) brings up a series of snapshots. Allie (top left) mentions line graphs (which then is the upcoming task that Rachel asks for). I think Stamatis' little intervention allowed them be more creative and inventive, which also was motivating.
The idea of using animations is tempting, but there is no clear evidence that it is always better than still images for learning. It may at times convey too much information, so that there is cognitive overload: http://moodle.technion.ac.il/pluginfile.php/112657/mod_resource/content/0/winter_2008/articles/Hoffler_Leutner_2007.pdfI personally like the idea of a time series of snapshot images, alternatively a simulation with a lot of interactivity, so that you can pause, modify parameters, etc. By the way, in the Wednesday session, the class was introduced to a set of PhET simulations, which included such features in a nice way.
As suggested by Bradley, here's their drawings:
Are any of their drawings available to post on the blog as well? I think if we have pictures of their work (especially when it's on whiteboards), it would really be a great addition to our posts.
ReplyDeleteI'm really interested in conversations like these. I've been hooked on pie charts for the past few years, but I'm willing to open my eyes to other representations and start asking questions. I imagine that different scenarios must call for different reps, depending on the complexity and action. I like time series snapshots (which is a strength of pies and bars), because you can draw a physical image of the situation at different moments and show the associated pie or bars.
I will be interested to see how the conversations shift throughout the next few days as the teachers gain experience with diagramming.
I added their drawings in the main posting.
ReplyDeleteActually, in preceding discussion, Madonna says that she does not like pie charts and does not think that you can do much to improve them.
Awesome! Thanks for including their drawings. And be prepared to watch a fight at 3 pm in the parking lot. I'm gonna stand up for my pies!
ReplyDelete