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:

1. 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.
2. Suggest the habit. These are problems that refer to the habit, but don’t walk the student through how to apply it.
3. 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?

1. March 10, 2011 11:05 pm

Off the top of my head, habits of scientific thinking:
Record data.
Verify/check/doubt/be skeptical.

• March 11, 2011 11:38 am

I like these, and they overlap nicely with some of the Park school habits. The last one really is just like “test plausibility”

March 11, 2011 8:35 am

I really like your idea of the three pillar approach, especially the addition of the metacognition. Metacognition is something I know I do not do enough of in my classes with my students or with my colleagues during professional development. I’ve been thinking about the idea of scientific habits a bunch lately. Right now I am looking into evaluating my students based on: content, scientific processes (skills) and Habits of Work. The content would change with each unit, but the scientific process skills would be continually assessed through the year. There would obviously need to be a thoughtful integrated approach to when and where certain processes were taught, assessed and re-assessed. I listed my somewhat refined list of scientific processes below. I’d love any comments, additions, suggestions.

1. Designing Testable Experiments
a. Develops testable hypothesis
b. Distinguish between control and experimental groups
c. Determines adequate levels of treatment
d. Categorize appropriate controlled and experimental variables
e. Develops appropriate procedure for conducting experiment
2. Collecting, Analyzing, and Interpreting Data
a. Data collected in organized data table
b. Appropriate statistical tests performed
c. Patterns in data are identified and described
3. Constructing and Critiquing Arguments
a. Uses data to draw conclusions
b. Evaluate sources of error (procedure/model)
c. Makes appropriate suggestion for further study
4. Researching and Interpreting Scientific Texts
a. Uses a variety of sources
b.

5. Communication Using Various Media
a.

• March 11, 2011 11:08 am

“Develops testable hypothesis” is not the first step—it comes about halfway through a scientific investigation. The first step is something like “observes phenomenon” and the second “builds plausible models”. Only after you have multiple plausible models is it possible to develop a hypothesis, which must be the prediction from a model that distinguishes between models.

March 11, 2011 12:58 pm

I agree, in hindsight a sequential numbering system is probably not the best list format. I did not intend for it to be a sequential list. I probably should have used A, B, C, D etc…

• March 11, 2011 11:39 am

THis is a good list, but I’m wondering if it’s possible to boil these down to simpler, single word verbs—observe, analyze data, etc.

3. March 11, 2011 10:31 am

I love the way you tell your thinking journey. I am curious as to what, then, do you think develops in the “sweet spot” where content habits and cognition overlap? Is that internalization? mastery? passion? proficiency? learning outcomes accomplished – so success for teacher and student?

And, I am also wondering, who drives towards the center? Is there a point at which or practices that use the momentum in learning to really create co-ownership towards that sweet spot?

• March 11, 2011 12:01 pm

This is such a good question, and when I combine it with the following quote I read on Study Hacks (another truly awesome blog):

From: on the possibility of conformity in a non conformist career, Cal Newport wrote:

I think it helps not to see it as delaying gratification, but instead as an approach to work where you are constantly seeing how interesting you can make what you’re doing. As you get more and more expertise, the scale of this interestingness grows, but the general enjoyment remains constant.

I think the three pillars I mentioned in this post are the start of me trying to find the solution to the problem of helping students to find interest in what they’re doing, and using this interest to drive them to real accomplishment. By teaching metacogntive skills like growth mindset, resilience and the value of sleep, I’m working to help students to develop the tools to evaluate their own thinking, and give them the stamina they need to overcome obstacles and even see those obstacles as opportunities for growth. The habits pillar should be helping students to begin to see a field as an expert does—thinking like a scientist, or historian, which should help them to better understand the joy a physicist finds in describing so many phenomena with so few ideas, and all of this should help to motivate students to learn the content, and most importantly, keep learning once the course is over.

In fact, I think this might be the very solution to the ballet question I also wrote about last night. I also didn’t fully realize that when I made this a Venn diagram, I should think carefully about the meaning of the overlaps—it’s a great question to ponder. Unfortunately, I have a pile of grading that needs to get done, so I’ll add this to my ever growing pile of blog drafts (32 posts currently).

4. March 23, 2011 6:22 pm

Shameless plug, but I’ve been thinking about this for a long time from a math perspective. Here’s my list: http://mathteacherorstudent.blogspot.com/2010/09/habits-of-mind.html

• March 23, 2011 10:37 pm

Thanks! These are great.