In this blogpost, I continue to write about my thinking going into the 2018 Physics Education Research Conference.
I’ll start by saying this. It can be hard to have it both ways: I want my students to have a degree of epistemic agency in the construction of their own personally-meaningful, scientific knowledge. And I want my students to develop robust understandings of established scientific concepts as a body of knowledge. Trying to do so is fraught with uncertainty.
One of the things that has helped to navigate these uncertainties over the years is the following way of thinking about the content I aim to teach: I try to decide in advance what understandings (of a scientific concept) function as necessary “anchors”, for which I must carefully plan for, and which understandings (of a scientific concept) I can leave as open territory for sense-making [Foot note]
In my previous post, I wrote about an example in which students were learning about Newton’s 2nd Law. In the sequence of learning, students were carefully guided through an understanding of contact forces as arising from tangible mechanisms. To me, this was a necessary anchor, because I felt it would be crucial for students’ understanding that they have a sense for what is (and what is not) meant by force, and also how one goes about identifying its occurrences in actual situations. The next anchor point I wanted us to get to was an understanding that constant force causes constant acceleration; and, furthermore, I wanted this understanding to be anchored to actual observations that would help students answer questions like, “How do I know? Why do I believe?”
I could go into more detail concerning other necessary anchor points, but the point is that I try to carve out the aspects of an understanding which are “must haves” for my students as we learn about a topic or concept. I carefully prepare, plan, and scaffold for these as anchors for students in the body of scientific knowledge.
The second part is to then build pedagogical space for others aspects of the content that will remain more open–that is, I expect there to be territory in landscape of understanding (that needs exploring) but does not need to be explored in a particular way that I prescribe in advance. Rather, it is more important that students meaningfully explore the territory around and in between the anchors I help us to forge.
In my previous post about N2nd Law, the open territory my students explored around these anchors concerned questions like, “Why does constant force produce constant acceleration?” This particular year, students explored this space in a particular way that involved thinking about the details of what happens to the degree of compression between two objects as they press into each other and they get away. It is often tempting the following year to try to make this conversation happen again, but I am learning that this is not the goal. Sure, knowing that this conversation can happen, should leave me better prepared to notice it as a possibility, but it need not become a new “anchor point” that I prescribe. Instead, to keep the space alive as a open territory for sense-making is to help students explore that space (meaningfully in a broad sense), and that will vary from year to year.
Other semesters this conversation has gone in different directions–for example one year my students explored the space by more carefully thinking about friction vs. non-friction. Students introduced the idea of a “lurch” –what happens when you push an object against some rough surface and it doesn’t go until it suddenly does; and how with the hover pucks and low-friction carts there is no “lurch”. The hover pucks and carts just start going. The lack of a lurch was how students made sense of why a constant force produces constant acceleration.
While different educators are likely to disagree about what exactly should be the anchors and what exactly should be the open territory, the practice of carving out the two is I think critical for navigating the tensions described above.
It helps to perhaps give a second example:
For uniform circular motion, a standard way that physicists understand the sensation of an outward force is to say “there is no outward force. The so-called centrifugal is a fictional force resulting from a non-inertial reference frame.” Over the years, I have decided that this is not an anchor for me. The main anchor for me is, “only an inward force is needed to maintain circular motion,” but I try to leave open questions like “why is only an inward force needed? and “What is the outward force we seem to feel?” open While I carefully scaffold students’ understanding of the anchor, the lesson is structured in a way that encourages students to meaningful explore the territory around that anchor. Various ways that my students have made sense of the outward force include “The outward force is the Newton’s 3rd law pair to the necessary inward force (in other words a force by the object moving in the circle),” and and that maybe “the outward sensation is the result of torque on an extended body, like the ones that results in tipping over.”
So what’s the point? I think one of the main points here is that careful instructional planning is required for both the meaningful establishing of anchors and the exploration of open territory. I know that this should not not surprising to anyone who aims to teach this way–thinking about improvisational acting / music or even wandering in the woods / city benefit immensely from careful planning and knowledge of anchor points that provide structure, but also allowing space and time for exploring the territory around these anchor points. Said another way, filling your travel schedule completely full both day and night does not readily allow for opportunistic explorations–all you can to is keep onto the prescribe path. As a teacher, what I have found is that this way of thinking about concepts (i.e., anchors and territories) provides me with tools for planning and carrying out instruction in ways that lessens some of the tension between discovery and coverage.
Foot Note: I sort of steal this language from this paper, and while I think my sentiment here shares some overlap with the meanings developed in this paper, I know that it is not a one-to-one correspondence.