[The following post refers to the newly-published article found here: https://www.tandfonline.com/doi/full/10.1080/07370008.2018.1539736]

Imagine you are a typical eighth grade student. Maybe you know a lot of science facts and terminology, but haven’t quite put it all together yet. You’re given the following graphing challenge: in the graph space below draw four x’s in places that would represent objects that would sink in water and four o’s in places that would represent objects that would float in water. When you’re done, draw a line to separate all possible x’s from all possible o’s. Go ahead, sketch it out on some scratch paper.

How did your typical eighth grade self do? Perhaps you drew a smiley face or played tic-tac-toe. Maybe you put the o’s on top like they floated and the x’s on the bottom like they sank (we did see some of that). Or, maybe you had an idea about how mass and volume determine if something sinks or floats. Did you come up with one of these?

If you are like the majority of eighth graders, you probably came up with something like the graph on the left. Even if you didn’t, you can probably still interpret it – heavy things sink, light things float. The graph on the right – the correct one – is more difficult to understand. It requires you to think about the relative amounts of mass and volume. As the volume increases, proportionally more mass is needed to make something sink. Even if you had memorized the density formula (density = mass / volume), would you have been able to apply it to this graph?

We – the folks currently or formerly at UC Berkeley (Jonathan Vitale, Lauren Applebaum, and Marcia Linn) – love this kind of graphing problem because it really tests how integrated a student’s knowledge is. You can’t memorize an answer to this – you really need to fit all the pieces together in real time. Beyond assessment, we wondered whether constructing this graph could help students actually learn about density and buoyancy. As we know, generation tasks have a very strong track record in the learning sciences.

But, there’s more to generation than simply making something. Generation is really about representing your ideas. Once ideas are committed to a concrete representation – such as a graph – efforts to revise the artifact become opportunities to revise the underlying ideas. In our study, in a treatment condition, we started students off with the problem you tackled above. We then used automated guidance and an interactive simulation to help them refine their graphs and ideas. Here’s a screenshot of the graph and simulation:

After plotting the initially requested points and a divider line, students had the opportunity to test any point in the graph space with the simulation on the right. In this case the student is testing a point labelled as “float”, but which actually sinks. Students also received messages such as, “Try adding more points to your graph and running the simulation. Do all heavy objects sink?”

We compared this treatment condition (called *generate*), to a more typical graph construction condition (*analyze*) in which students were given a table of data to plot and then asked to analyze the resulting graph. The students had access to similar guidance and the simulation, although they were less inclined to use it because they quickly arrived at a correct graph. The results suggest that by orienting the task towards the students’ ideas, the *generate* condition promoted more robust learning than the *analyze *condition. Read the paper to find out more about how we assessed student learning and tracked progress through videotaped interviews and log-data analysis.