This is a work in progress, and I encourage feedback. The current version of the poster source code will be at GitHub. Here’s the current PDF (lab-whiteboarding-defend-the-model-beamer-poster-18×24-2013-14-2.pdf) if you don’t have LaTeX.

The idea for the poster comes from Frank Noschese, but blame me for the implementation. As a poster it’s not great yet. The example is just there with no prompts for how to use it. A graph would be helpful. These I’ll add later if the basic idea is sound. It could also do with a different example.

I’ll post images of the various incarnations below.

1st attempt

Update 2013-06-16: Based on feedback from Josh Gates, I’ve changed the last conceptual tool.

2nd attempt

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I have a question, though, it may be due to my ignorance with modeling. Is this defense supposed to be done without the aid of computer/graphing calculator? If so, could you explain why? If not, how do you see this prompting students to utilize various mathematical relationships? If as you wrote in the referenced exchange, the default analysis is linear, would there be room in the modeling framework for quick lab-type events for graphical analysis to constantly present data to push for an almost intuitive analysis of data points, i.e., start recognizing a subtle curve? (Or is it already built-in and I’m off base?)

I did omit most of the context for this. When students perform a laboratory experiment in Modeling Instruction, they “whiteboard” their results, which entails summarizing their results and presenting and defending them in front of a class of their peers. If you visit the link from Frank Noschese’s photoblog, you can see an example of a student who applies a linear model to something that may not be linear. The poster is my first attempt at nailing down a protocol for helping students to think about their choice of best-fit equation for their data. I’d love to hear your thoughts about whether or not the protocol would accomplish that. Certaintly, the poster could also make this process clearer! On my todo list is to add an example plot showing the data and best-fit equation.

I don’t envision this poster prompting students to know about certain types of mathematical relationships. In Modeling Instruction, we embed this teaching in the context of experiments and design experiments to require the use of varied mathematical models. So yes, there is room for using lab and lab-type events to find instances where data deviates from linearity. I also keep a few posters in my classroom of just this sort. See https://fockphysics.wordpress.com/2012/04/20/basic-classes-of-mathematical-models/ and https://fockphysics.wordpress.com/2012/04/07/graphical-methods-summary/ , for instance. Until I clean up my blog to show an image preview, just click on the PDF links to see the 18″x24″ posters.

The question students invariable have trouble with is, “How far away from a best-fit line does a data point need to be before I start questioning my model?”, so I definitely think the uncertainty part needs work. They are happy to throw away one or two data points as a fluke without trying to repeat those data points. That may be reasonable (though still intellectually lazy) if the best-fit equation is what we expect from other of the conceptual tools in the poster, but the goal is that student-colleagues can help decide that the experiment does not quite meet muster and that the experiment should be repeated/replicated. Then, as students internalize this type of thinking, they will hopefully start to ask it of themselves and use it to guide their own thinking. The problem is that even though students know other mathematical models, they still “default” to linear.

Does this answer your questions? Also, what kinds of quick lab-type activities do you envision?

I like the questions (and the other posters you linked). I’m hoping to use similar questions in my Chemistry classes in those quick labs, though, mine are much simpler: How good is your point? & How far off the line are you? The quick labs are, for example, mix this white powder (baking soda) with this clear liquid (vinegar). Each lab group’s data would be collected and the class data is plugged into a graphing calculator (or excel or whatever) and a line of best fit is made. This particular example would be a linear, mass to mass, relationship, but hopefully might invite a ‘prove it’ challenge (in which case you could do sodium carbonate, washing soda, and vinegar or hydrochloric acid; or any stoichiometry lab) and/or a question about the amounts mattering (limiting reagents), etc. In any case, along with the basic questions, the graph and slope of the line, should become tangible. Back to the original example, you could compare the mass of white powder to the mass of gas (lost mass after the reaction) and determine an experimental relationship from the slope, grams of gas lost per 1 g of solid used. Then, provide the equation for the reaction, determine the formula masses (44g of gas produced per 84g of solid used), and graph the new line comparing data with what should have been, allowing another round of discussion of ‘How good..’ and ‘How far….’ The goal is two-fold, get them graphing and used to graphing and analyzing their results; and two, allow questions and discussion and extension which should make it more like a guided inquiry experience. (Trying to explain this to you makes me realize, I should take the time to write this out as a blog post, too, because I think I’m leaving stuff out.) Ultimately, the relationships will have to change from y=mx+b to 1/x or log x, and so on. So, yes, I think you answered my questions, though I have a couple of more. When they graph, is it just their personal data or class data? (Thinking, from what you wrote the answer is ‘personal,’ which means my question is why not use class data?) And, is the whiteboard just what they put together as a highlight reel of results that is presented to the class or is it presenting the analysis process (i.e., no lab notebook, just a whiteboard)?

I hope I answered yours, probably with more information than you needed.

The data they graph depends on the experiment, but is usually (for me, at least) collected by a group of 2-4. I have used both individual and class data before too. Yes, the whiteboard is a highlight reel, but it also helps keep the lab group in sync, as each student keeps a lab notebook. Thanks for your thoughts!