Dependent Sample Assessment Plots Using granovaGG and R

9/4/2011 Update: granovaGG is now available directly from CRAN.

Just over one year ago, I wrote about creating Dependent Sample Assessment Plots (DSAP) Using granova and R. Since then, Brian Danielak has been developing a new, ggplot2-based version of granova named granovaGG, which is almost ready for release on CRAN. This article updates my earlier granova-based version, but leaves much of the article text unchanged.
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“It’s the model that matters!” — Eric Mazur

At the ICER 2011 keynote, Eric Mazur reported that when students see a demonstration and either do or do not engage in a discussion of the demonstration, they adjust their memory to fit their model1. In other words, they retain their prior (possibly non-canonical) mental model and mis-remember the facts of the event to fit that model, rather than updating their mental model to account for the new facts2.

In physics education, given the following modes of instruction

  • No demonstration
  • Demonstration to students
  • Student Prediction without discussion
  • Student-to-student Discussion (similar to peer instruction)

students do equally poorly on a standard instrument intended to assess students’ understanding of Newtonian mechanics.

So, if we assume that we can’t skip demonstration altogether, and if we can’t just demonstrate, and if demonstration followed by discussion all suffer this fate, then what can be done? Engage students directly.

It’s not the act of predicting or discussing a prediction that triggers changes in student mental models, but rather confrontation with confusing experiences: staking ones intellectual ground so that one knows what one believes, then being confronted by a confounding example, and finally needing to substantially defend and explain the new experience.

Confusion seems to be an essential part of the learning process, or at least the ability of students to reflect and express their confusion3. In a physics class where students were asked to report on what they were most confused about each week, those who expressed confusion did much better than students who claimed no confusion. Willingness to express confusion positively correlates with understanding4.

So, in a peer instruction environment, we teach by questioning, not by telling or showing. We facilitate students’ engagement with the material rather than their obedience while in our classroom.

There is work on students’ use of mechanistic reasoning (i.e., trying to articulate the underlying entities, entity properties, activities in which entities engage, and the mechanism by which those activities give rise the the phenomena of interest) in physics and math education by David Hammer (now at Tufts), Rosemary S. Russ5 (now at Northwestern), Andrew Elby, Ayush Gupta, and Brian Danielak that relates to this… how students express their understandings of and reasoning about mechanisms underlying physical phenomena.

In short, if we’re not changing students’ mental models, than any learning that may occur is shallow and fragile. Some modes of instruction have a better chance of engaging students and changing their models, but unfortunately not the most popular modes of instruction, currently.

  1. Mazur, E. (2011) International Computing Education Research Conference (ICER) Keynote. Providence, RI. Slides available from http://mazur.harvard.edu
  2. The keynote is also discussed by Mark Guzdial on his blog at http://computinged.wordpress.com/2011/08/17/eric-mazurs-keynote-at-icer-2011-observing-demos-hurts-learning-and-confusion-is-a-sign-of-understanding/
  3. see the Dunning–Kruger effect http://en.wikipedia.org/wiki/Dunning–Kruger_effect
  4. forthcoming from Mazur, E., et al
  5. Russ, R. S. (2005) A Framework for Recognizing Students’ Mechanistic Reasoning. A dissertation available from http://drum.lib.umd.edu/handle/1903/4146

Richard Feynman on Question Formulation

How we frame a question both constrains and frees our creativity1,2. The form of the question itself either encourages or precludes certain types of answers. Some forms of questions encourage shallow, quick answers while others encourage you to dig deeper into a topic.

In this video, Richard Feynman– lecturer and physicist– discusses why questions in an attempt to understand magnetic force.