Linear Modeling: Which Do You Prefer?

In our most recent fellow’s prompt, we asked the fellows to compare Lego Prices and Are People Waiting to Get Married?. Our discussion highlighted values and unique perspectives, helping us to develop common ideas around what makes a good Desmos activity. Many of the fellows highlighted elements of the Desmos guide for building activities as they compared the activities, while others focused on the objective and how their students would relate to each context.

Incorporates a Variety of Nouns and Verbs

  • Heather Kohn, Linda Saeta, and Paul Jorgens noticed that both activities incorporate a variety of nouns and verbs. Over the course of each activity students are asked to predict, sketch, build a model, use an equation or graph to answer questions about the context, interpret parameters, and to reflect on their thinking.

Create Problematic Activities

  • Bob Lochel acknowledges that both activities allow students to connect representations effectively, but thinks that Lego Prices does a better job of developing need to connect the data and graph to an algebraic expression. Using the computation layer then personalizes the experience for students, builds informal practice, and allows students to take ownership of next steps.
  • Nathan Kraft also comments on the way that Lego Prices connects student thinking throughout the activity with a central problem, and notices the absence of this in Are People Waiting to Get Married?. “We really did something with those initial guesses [in Lego Prices] thanks to the computation layer. With Marriage, we’re asked to guess a median age in 2010, but then that never really comes up again, unless the student remembered this question from slide 1 and feels like checking the graphs. As I was going through the activity, I wasn’t sure what the focus was (slope? intercepts? systems? linear vs. non-linear?)”
  • Anna Scholl and Paul Jorgens also note the lack of a clear problem in Are People Waiting to Get Married?, with Paul offering some ideas for how to improve the frame for the activity. “I don’t feel connected to the prediction in the opening screen. Maybe I need to be asked how old I think I will be when I get married. Maybe we can see a median of our class data and then look at some trends of real data. Perhaps a better opening question might be to ask about the speculate on the typical age for someone to get married.” Thanks Paul!
  • Michael Fenton offers his perspective on how Lego Prices does a better job with creating problematic activities.

Create Cognitive Conflict

Though Lego Prices may do a better job of framing a central problem, we still have lots of love for Are People Waiting to Get Married?, which ends with this particularly compelling screen.

  • Nick Corley and Linda Saeta notice that extrapolation on the last screen of Are People Waiting to Get Married? drives home lots of cognitive conflict.
  • Dan Anderson notes that “I liked how the Marriage activity talked about the danger of extrapolation while the Lego activity extrapolation NAILED the prediction for the Death Star. Both are valuable lessons. The Lego extrapolation is nice because it works, and the Marriage extrapolation is nice because it doesn’t work.”

Instructional Goals

  • Anna Scholl points to the differences in prequisite knowledge for both activities, and that they each seem to have different instructional goals. Knowing the standards for the courses that you teach as well as how those standards progress throughout courses can help in determining such subtleties.
  • Heather Kohn reminds us that choosing between these activities depends on what we want students to do mathematically. In Lego Prices students will build a model with draggable points. They’ll use an automatically generated graph and equation to answer questions about the context. Are People Waiting to Get Married? asks students to build a model by hand, and use that model to answer questions. Both models are linear, but the skill involved is quite different.
  • Nick Corley, Linda Saeta, and Dan Anderson find that Lego Prices might be suitable for students in middle school both due to the y-intercept being zero and the model being built by a draggable line.

What do you consider when choosing activities? Let us know on Twitter @desmos.