Post date: Jun 8, 2012 5:10:19 PM
We did this activity on the same day as our discussion of the syllabus so we only spent 30 minutes on this activity. I started them off without introducing it at all - I just showed them the two cylinders (one taller than other) that they would need for the activity. This turned out to be a mistake - I should have mentioned something about pouring water into the cylinders as that was not mentioned in the activity (we will fix this in the activity). They were confused about how they should be considering the water - discrete or continuous basically. Thinking about that now though it's actually not a bad point of confusion and maybe something I should have talked to the whole class about (I only had the conversation with one or two students as they were working). As a result I think they probably spent too long on the very first question. I let them work on it for about 10 - 15 minutes - asking them to try it by themselves first and then to come together in small groups. I also used this opportunity to set up how I wanted them to work in general. As they were doing this I walked around the room and talked to various small groups to see what they were thinking and how they were working. We then spent 15 minutes in class discussion - I pulled some sample graphs from around the room and put them up on the document camera - on each one we discussed what was good and what needed improvement. (When I took the graphs I told students if there was something not quite right about their graph - not what it was - just that there was something that needed to be adjusted and then asked them if they were ok with me putting it up for the whole class to discuss.) We then settled on a linear graph for each cylinder and discussed why. At this point I asked them about the definition of proportional. I was running out of time so I gave them the definition in terms of y=mx and then told them that they graphs we had drawn (which went through the origin) were proportional and to think about why. This is not my ideal way to do this but I think it ended up working ok. It was really good to follow this up with the question in the synthesis questions on proportionality which almost everyone answered incorrectly. I didn't get to moving to another container on this first day but I think this is actually better at the beginning of Part II anyway so we will move it there for next time. Overall I think the activity went pretty well. One great thing about this activity is that it is not what students are expecting and it tends to set students who are worried about the class at ease. It also allows for lots of time for the instructor to interact with the students in a relatively stress free situation which is a good thing for the first day.