Habits of Scientific Thinking
A few years ago, I had the pleasure of visiting the math department at the Park School of Baltimore. At the time, Park was in its first year of developing a truly innovative math curriculum, focused around 14 Mathematical Habits of Mind. Here is an example of a few of the habits:
- Guess: to guess a solution and see how it works with the posed problem, then refine your thinking based on what you have learned.
- Seek proof: to desire that a statement be proved to you or by you; to engage in dialouge aimed at clarifying an argument; to establish a deductive proof; to use indirect reasoning or a counter example as a way of constructing an argument.
- Take things apart: to break a large or complex problem into smaller chunks or cases, achieve some understanding of these parts or cases, and rebuild the original problem. To foucs one one part of a problem (or definition or concept) in order to understand the larger problem.
From this, Park then developed three levels of problems for each habit:
- Teach the habit. These problems explicitly instruct the student on the habit by taking them through it. The focus in on getting the student to recognize when to use a particular habit to solve a problem.
- Suggest the habit. These are problems that refer to the habit, but don’t walk the student through how to apply it.
- Tacitly require the habit. At the highest level, these are problems that no mention of the habit is required, but using the habit is necessary for the solution.
From here, the Park School faculty decided upon a content base for the first two years of its high school math curriculum (SAT math), and then went about writing a text that taught this content using the mathematical habits I mentioned above.
From everything I could tell from my one day visit, this was an extraordinary collaboration. The math department worked beautifully together to develop this curriculum on the fly, and everyone was deeply engaged in this endeavor.
Recently, I’ve been thinking about this again, and wondering if it might be possible to develop a similar set of habits of scientific thinking. One habit I might propose is
Estimate: use basic numeric sense, unit analysis, explicit assumptions and mathematical reasoning to develop an reasonable estimate to a particular question, and then be able to examine the plausibility of that estimate based its inputs.
Ok, so clearly these habits will need considerable editing and revision.
And one tacit type of problem that would test this habit would be those Fermi Questions that I love so much, but never seem to fit in the official physics curriculum.
Ultimately, I could envision my curriculum being based on three different pillars: Physics content, Scientific Habits, and Metacognitive Skills (obviously not weighted equally).
What habits of scientific thinking can you think of? Could we create a virtual collaboration akin to what I saw at the Park School?