Conceptual Understanding in Introductory Physics I: Models, Testability, and Falsifiability

This post begins a series that was inspired by Grant Wiggins’ post on conceptual understanding in mathematics. Wiggins presents a list of thirteen questions aimed mainly at high school students “who have passed all traditional math courses through algebra and geometry.” These questions reminded of a list of about twenty similar questions I have been compiling (mostly from scratch) over the past year or so aimed at undergraduate students who have completed introductory physics, particularly introductory calculus-based physics. Many of these questions can be traced back to my experience with Matter & Interactions and even further back to my discovery of Arnold Arons body of work in 1997. More recently, some of the questions can be traced to my discovery of the critical thinking framework developed by Richard Paul and Linda Elder. At least two of the questions were borrowed directly from a talk Gordon Emslie gave at AAPTWM12 in Ontario, CA. He said he likes to pose these questions to first year graduate students to check their understanding of certain things, and is frequently amused at the results.

In this series, I will present the questions one at a time with one questions per post. I will not, however, include answers to any of the questions because I don’t want students to find the answers, at least not here. That means I won’t divulge whether a posted answer is correct or not. Please keep that in mind if you comment on these posts (and I certainly welcome all comments). The questions cover the first two semesters of introductory calculus-based physics. In the spirit of Arons, some of the questions may have no definitive answers and are intended to just get the student to think and to convey reasoning in writing; metacognition is missing from introductory physics. In my mind, Paul Hewitt defines what most of us mean, or intend to mean, by “conceptual” in that Hewitt-type questions often don’t require direct calculation. Some of my questions may indeed deviate from that idealization but could easily be recast to fit Hewitt’s style. I must also caution readers that many of these questions come directly from my experience with Matter & Interactions, having used it since 1999 when it was still very much in its formative stages. Finally, I have also derived inspiration from topics that I feel are treated inadequately, if at all, in introductory textbooks. We should not fear going outside the boundaries of textbooks, even Matter & Interactions, to give introductory students a good foundation in physics. After all, textbooks are merely one of many resources, and no course should be built only around a textbook.

My experience has been that many colleagues will find some of these questions irrelevant to introductory physics. I encourage those people to think more deeply about what introductory should include. Some colleagues may argue that some of the questions reflect topics too deep or too complicated for introductory students. My response to that is to think about how we want students to perform as upper level physics majors or as physics graduate students. Think of the complaints voiced at meetings about this issue, and think about what students really know versus what paper documentation indicates they may know. I want introductory physics to be something more than a passive activity, and I want my students to outperform your students (in the friendliest sort of way, of course). Generally, these questions do stem from certain personal biases I have toward science, physics, and instruction and I hope that my biases don’t ruin the scope of these posts.

Finally, my thanks to Grant Wiggins for inspiring me to post this series.

So, without any further ado, here is the first question.

In one sentence, explain what scientists mean when we use the word “model.” In a second sentence, explain what scientists mean when we say a model is testable. In a third sentence, explain what scientists mean when we say a model is falsifiable.

Go!