image is taken from <www.nutristrategy.com>
Last week my principle, who is supportive and encouraging, came in to view my class and chatted with kids about what they were doing in grade 9 physical science class. One of the students explained, “I’m not sure why we are doing this. I guess we are practicing graphing of something.” Practicing graphing? – OUCH!
That sounds boring and apparently it was because students thought graphing is just about putting dots on paper. Why is it done? The assumption, which I did not change, is that it is done because that is what “scientists do” period. Nuts!
Graphing is so much more than make a picture from numbers. It is useful! The fact that my students did not know why they were doing what they were doing was both discouraging, but also a prompt to help them more directly. So we are now working on this data table (see top). Students are studying energy, heat and calories and calories used to run and walk is something kids have heard about before.
In this graph I assumed that the graph makers are providing data based on a mathematical model. The table does not say that, but I can dig into the data and find out! So I had students make two graphs: Graph 1-select a single running speed and graph mass and calories (students had to convert pounds to kg since we live in Malaysia.) and Graph 2-select a single mass and graph calories at different speeds. When both graphs are done then they need to draw a best fit line and calculate the slope.
Next day in class we practiced “interpolating” and “extrapolating” using the data set. We tried interpolating manually on their paper graphs. This turned out to be harder than it looks since students converted the pound values on that table (at top) to kg so they ended up with x-axis values on their graph of 49.1 kg, 92.7 kg and so on. This meant manual interpolation required a lot of “divide the space in half” between data points. Then “divide the space in half ” between those now marks and so on until you identify the precise point you are calculating. While easy at first this quickly seems tedious. Of course this is when one student raises her hand and asks, “Can’t we use the slope value to calculate these without all these small steps?”
“Are you sure that would work?” I ask, feigning surprise that there is a shortcut.
“Yeah!” she answers. So I invite her to show – on the whiteboard – how to use slope to determine the interpolated or extrapolated values. I review her method highlighting how “slope” can be used in dimensional analysis either “right side up or upside down” to help us get to the values we are trying to find out.
I assign several interpolation / extrapolation problems and ask kids to solve interpolation manually on the graph and extrapolation by calculating with the slope using dimensional analysis. Shortly I hear some complaining as the manual method is time consuming and painstaking to do carefully. I fake reluctance to permit them to solve all the problems by calculation, but ultimately relent.
Truth is, I am excited that they are beginning to see the power of grpahing to find meaning and patterns and not only that, they also WANT to calculate as a powerful method of producing meaning and knowledge.
Yep; one of those sweet spot lessons today!