Choice: Dan Schwartz’s Vision

When people find out that I teach high school physics or maths, the response is usually, “Oh, I was terrible at that.” There are two levels at which to analyze that statement. On the face, it’s a sort of mutual apology: “I’m sorry I didn’t learn the area of knowledge you care about” followed by my “I’m sorry that physics teachers like me are bad at their jobs.”

At a deeper level, one needs to recognize that most people don’t feel shame at their mathematical shortcomings; instead, they consider failure at mathematics to be an inevitable part of the educational process. In this light, the casual dinner party comment, “Oh, I was terrible at maths,” must be interpreted as “Oh, I was terrible at maths, but my life is alright, therefore maths isn’t important.”

I’ve seen this attitude, in varying shades of forthrightness, from community and business leaders, from education administrators, from fellow teachers and — of course — from parents. I’m sympathetic — it’s a rare day that I calculate an integral or use trigonometry explicitly — but there is a lot of value in learning mathematics (which I outline in this video).

This brings us to the point I’d like to make in this post: in math, physics, and most other subjects, the true goal of education is substantially different from the goals perceived by society. We don’t learn math so we can “solve for x” in a hundred different ways any more than we learn history so we can recount the denouement of the Vietnam War.

Stanford professor Dan Schwartz advocates a new approach to education, and particularly assessment, based not on knowledge or shallow domain-specific skills, but on the choices we make. After all,

It is our choices, Harry, that show what we truly are, far more than our abilities.
– Albus Dumbledore in JK Rowling’s Harry Potter and the Chamber of Secrets

I think Professor Schwartz does his thesis a disservice by identifying choice as the theme, as his programme seems more concerned with a holistic, process-based approach to assessment (which thus informs learning). I’ll try to identify the major salient points of his approach:

1. Assessment in the current education system, even at its best, is obsessed with knowledge. However, the end-goals of education are about much, much more than knowledge.
2. With new technologies, we have the ability to create activities that produce an “assessment of processes”.
3. These new assessments will allow us to (finally?) evaluate the effectiveness of instructional techniques and strategies, which will simplify the identification of best practices.

This should jive pretty well with the emerging trends (a) toward technology-based education systems (MOOCs, animations, etc), and (b) toward data-driven schools and data-mining, more generally.

Back to choice. Professor Schwartz correctly sees that the subplot in all this drama is the question of what the students are actually doing as they learn, and how they’ll take their learning into the world when they leave the classroom. Student autonomy seems to be increasingly important for educating participants in global democracies, in addition to the myriad of educational benefits that are experienced when students feel free to learn in a comfortable fashion.

However, there is a contradiction inherent in this argument: if a student is making poor choices, does the school not have a responsibility to correct those inappropriate actions? For example, if a student is writing with poor technique, one would expect a teacher to insist s/he correct her/his approach. On the other hand, if that same student organizes a Marxist student club, should the school intervene? And to what extent should teachers intervene: is classical or operant conditioning appropriate as a discipline-building strategy in a high school classroom?

Scientific Reasoning in Physics

For many students, high school or university science courses are their last formal contact with the lofty ideals and approaches of organized science. Educators have traditionally done a poor job equipping such students with the vaunted skills of scientific reasoning. In this post, I’ll explore why, and look at how we might improve our teaching.

The 1977 paper of Fuller, Karplus & Lawson [FKL] was the first in the modern era to combine the concerns of developmental psychology and tertiary-level physics education. FKL identifies three ways “patterns of reasoning” that are more prevalent among physicists:

1. identifying and focusing on the most important variables
2. using propositional logic
3. using proportions

These are not unique to physics: my mother could see a broken window and know to look for the baseball, spot holes in my alibis and, deduce that cooking six-sevenths of a baked omelet that normally requires a dozen eggs means you scale it back to about ten. However, FKL argue, their consistent use is a hallmark of both scientific reasoning and progression to Piaget’s formal operational stage of development. The argument further suggests that physicist-style reasoning is uncommon because formal operation is uncommon (FKL suggest a third of American adults do not employ formal operation patterns), poorly promoted in the public sphere, and more cognitively difficult than concrete operation. Consider the comparison below (from FKL): where do high school students fit?

Stephens & Clement (2010) identifies three patterns of thought associated with the analysis of models in physics. They note that, in group settings, students might either generate or run with  (ie: follow on from another student) the approach. Their patterns of thought are:

1. Using analogies
2. Considering extreme cases
3. Thought experiments (gedankenexperiment)

In the American Next Generation Science Standards [NGSS], scientific skills and practices — essentially an expanded vision of Fuller’s view of scientific reasoning — comprises the first of three dimensions, along with “cross-cutting concepts” and the actual content. The “practices” are such statements as:

Apply scientific reasoning to show why the data or evidence is adequate for the explanation or conclusion (for gr. 6-8, p. 27)

Clearly, scientific reasoning is important. But it’s also difficult to teach. Steinberg, Cormier & Fernandez (2009) [SCF] taught a summer enrichment course in astrophysics for New York high school students. Their approach — presenting physical models, providing no direct answers, etc — provided only modest returns. Book-end tasks asking students to motivate heliocentrism (or geocentrism) saw a dramatic increase in the number of geocentrists (42%in the exit task!) with only anecdotal improvements in reasoning. A second end-task saw that 95% chose “I don’t know” about the existence of black holes, indicating that this inquiry-heavy approach might have swung the pendulum so far as to push most students to adopt a highly positivistic view of science.

At the undergraduate level, Moore & Rubbo (2012) note that non-STEM majors performed worse on Lawson’s Classroom Test of Formal Reasoning [LCTFR (also LCTSR)] than STEM students (54% vs 75%). Worse, although the non-STEM students made significant gains on content-based tests (38% to 41%), the post-course gains on the LCTFR were marginal (6%). In a class with explicit instruction on scientific reasoning, LCTFR gains were more substantial (68%). Small sample sizes, particularly for the last (N=14), means that this conclusion should be considered only a suggestion.

Otero & Gray (2007) note a much smaller effect: in a larger study (N=189) of the PET/PSET curriculum, the students achieved an 8.8% increase on the CLASS assessment.

In addition to the LCTFR (Arizona) and the CLASS (Colorado), there are at least three other recent tools for analyzing student understandings of scientific processes. The MPEX was developed by a team from Maryland and adopted by SCF, above. EBAPS, from Berkeley, has questions that apply to students who do not have experience as physics students. VASS (Arizona) aims to determine views about physics, rather than focusing on reasoning skills.

Another approach to determining students’ thinking is to observe gestures. Stephens & Clement (2007) have been working on this. Among my ESOL students, I’ve seen abundant use of gestures, not only shape-, movement-, and force-indicating, but also gestures to represent the universe and direct representations of abstract concepts such as magnetic fields.