Critical thinking is something we all say we want to impart to our students but something for which we frequently see very little explicit classroom modeling. This is one of the reasons the LCTTA (Learning Critical Thinking Through Astronomy) Project was started. This post will provide a very explicit way to introduce one aspect of critical thinking, namely reading for depth, into an introductory calculus-based physics course. Obviously the course doesn’t have to be calculus-based, but that the context in which I currently work.
According to Arnold Arons, we must explicitly model what we want students to learn. If we want students to read our textbooks in anything other than a superficial way, we must show them precisely how to do that. We most often assume that students, especially college students, enter our classrooms already knowing to do this. My experience has been that the students I serve do not understand how to do this, or at least if they do they don’t do it for some reason. I feel it is the former rather than the latter. So, here’s what I do.
I use the critical framework developed by Linda Elder and Richard Paul of the Foundation for Critical Thinking. This framework is based on the Elements of Thought, eight components into which everything from specific concepts to very broad concepts can be mapped. This mapping process operationally defines (again, in the spirit of Arnold Arons and Percy Bridgman) what we mean by reading for depth or reading for understanding, the assumption being that if one can perform this mapping then one understand the thing being mapped. I provide all of my students with a copy of this booklet explaining both the Elements of Thought and the accompanying Intellectual Standards. Incidentally, the latter are a good place for formulating standards for standards-based grading.
I also provide them with a copy of this chapter of a 1965 introductory calculus-based physics textbook by Arnold Arons, which, in my opinion, is a model of clarity. Although this is chapter 36 of the book, I have used it as an introduction to special relativity for several years. Arons hits the history that led Einstein to articulate what we usually think of as the embodiment of special relativity with an emphasis on the Michelson-Morley experiment. Beyond that, Arons takes a deliberate and very measured approach to build up to the concepts of time dilation, length contraction, and Lorentz transformation. The chapter goes beyond that but that’s as far as we go.
So yesterday in class, students took a few minute to read section 36.1 and I asked them in their groups (four groups of three) to address the element of “question at hand” by making a list of every question that came to mind as they read through the section. The results were, expectedly, quite varied and this is what I hoped for. This gave us a reason to discuss what constitutes a “good” question in science. One student had “Does time exist?” on his list along with other rather philosophical questions. I then led them to, hopefully, see that in science we need questions which are more easily approached, especially by students. This led them to refine their list by eliminating questions that were mostly philosophical, leaving them with more concrete questions. So I assigned section 36.2 for them to read outside of class and this morning, I asked them to once again put their questions on whiteboards, do a mock poster session in which they look at all the whiteboards, question the authors (questioning about questions!), offer constructive criticisms, and refine their lists. They eventually saw much commonality in their questions. Then, I asked them to address the element of “purpose” by articulating the purpose of section 36.2. There was wide variation, but I asked them to look for any commonality, and they found it. They all realized that they has all mentioned “simultaneity” in their articulation. I asked them to condense their articulations down to one sentence, and then finally to one word. That word just happened to be “simultaneity.” So then I asked them what the author’s purpose for this section is, and they all clearly agreed that it was to introduce the notion of simultaneity.
What I didn’t expect, and had not noticed before in similar activities, was that having them write broadly at first, then narrow down to one sentence, and finally narrow down to one word allowed them to quite literally see the author’s intended purpose appear right off the printed page into their minds. I always told students that they should think this way, but the explicit action of writing it all down proved beneficial. Even more amazing was that this happened despite two or three of the students admitting they didn’t know what “simultaneity” even means. Then, and only then, did the focus turned to actually defining that term after they realized that it was THE most important word in this section. Of course, they knew more about what simultaneity is than they originally thought. Once they saw that, as one student read a dictionary definition out loud, the entire section made sense to them by their own admission. This more than backed up my statement to them at the beginning of the class that Arons’ writing is almost always exceptionally clear. Oh, and all of this happened in a standards fifty minute class period.
This is precisely how reading for understanding is supposed to work. This was for only one of the eight elements of thought, and only for one section of one chapter. Tomorrow, we will address another one and will also introduce the elements’ accompanying intellectual standards, specifically the standards of “clarity.” My experience has been that students complain most about textbooks’ clarity. They tell us, “I read the chapter but didn’t understand what the author was saying.” The Elder/Paul framework directly addresses this issue.
So, the operational definition (again channeling Arons) of “reading for understanding” as my students now see it is to “map the passage (paragraph, section, chapter, book,…) into the elements of thought while using the intellectual standards for metacognitive assessment” and suddenly (okay, not so suddenly because this is an iterative process) physics begins to make sense. I also offered this as an attempt at an operational definition of “learning” in that learning is the outcome of going through this process. The entire class bought it. One student even stated that this was difficult for him, but also that he wished he had known about this framework before now. I can ask for more than that.