#ModChem Day 5

Modeler's Log, Day 5--

At the end of our first week of the chemistry modeling workshop, we have learned a ton about teaching, learning, chemistry content, and ourselves as educators. Though we didn't read an article for today to discuss, our session began with a very poignant discussion nonetheless.

With regard to my Day 4 summary, our instructor noted that my recap of the day had conflated the mechanics of a thermometer, barometer, and manometer. Upon pointing out my error and talking through it briefly, I realized that what I had written did not, in fact, reflect what I thought but rather what I had observed in class. A demonstration of expansion was done with water and ethanol in test tubes the day before, where each was heated in a water bath and the liquid expanded up a glass tube. During class, we concluded that the liquid expanded due to a transfer of energy from heating, but we noticed that when the instructor sealed the stoppers on the test tubes (thus applying some pressure to the inside of the tube) the liquid also traveled up the glass tube. Mixing these two ideas together led to the confusion that a thermometer worked because of gas pressure and not thermal expansion.

The discussion was very important, because it elucidated that our instructor even runs into the same conflation of ideas with her own high school students after doing this unit and was unable to identify the etiology of the misunderstanding. After seeing that we participants could fall victim to the same misunderstanding, and through a discussion of what happened that led to that misunderstanding, we identified that there was a sequence which may be at fault. We learned thermal expansion in liquids, equated that to thermometers, defined and discussed gas pressure, and moved right on to working with barometers and manometers in one continuous quick sequence. These measuring tools can all appear very similar at a superficial glance and without a dedicated treatment to their subtle differences, including the openness or closedness of the system, it is easy to mismatch how each works. We finished the discussion with a clarification of the way that each measuring device works and brainstormed ways to ensure that students leave this unit with the proper understanding of how each works.

It's critically important that teachers be aware (and clairvoyant, if possible) of the misunderstandings and pitfalls that exist for students when learning certain ideas in the content. This is an element of what is known as pedagogical content knowledge, and sets mere content experts apart from master teachers of a content area. This was a prime example of an area that requires special attention to detail to ensure that students construct the correct model for how each, a thermometer, barometer, and manometer, works.

We moved into a review of the relationships we learned through experimentation the day prior, between gas pressure, gas volume, gas temperature, and number of particles of a gas. We took our developed model of the relationships between these quantities and deployed it on some hypothetical problems on a homework worksheet. Each pair of students attended to one of the homework problems and whiteboarded their solution to present to the class. The catch to this whiteboarding session was that we were to participate in the "Mistake Game" as we constructed our whiteboards. This is where you intentionally embed a mistake into your board but present it as if it is correct. The other students in the class must try to decode the mistake you made. I personally like to call this game, "What's Up With That Whiteboard," after the popular SNL skit. All the participants did a great job feigning ignorance during the whiteboard session with their mistakes while others were quite the sleuths in elucidating the mistakes.

Our whiteboard session, and pretty much the remainder of the day, consisted of two other major ideas: Socratic dialogue and a cognitive approach to solving P, V, T, & n problems (without formulas.) The former of these two ideas is essential to the modeling instructional methodology, while the latter is specific to the pedagogical content knowledge of chemistry.

Socratic dialogue is a method of discourse-based instruction that has its roots in philosophy. It is attributed to Socrates, who is noted for teaching through dialogue with individuals in his time and area. Socrates' dialogues are famous works studied in universities and philosophy courses around the world. Modern day Socratic dialogue, or Socratic discourse, can be applied in any content area by any teacher, but serves a main role in the discourse of modeling instructors' classrooms. To get a sense of Socratic dialogue in a philosophical sense, you can check out this inquiry into the nature of authenticity. Every participant in a modeling workshop needs to be keen at crafting questions that are differentiated enough to target specific misunderstandings at a variety of different levels in the scheme of a learning progression for every student in a way that appeals to their their experiences as well. Our instructor is masterful at Socratic dialogue and questioning technique. She has demonstrated some top-rate approaches to questioning and dialogue; in week 2, the participants will be on the hot seat to practice their question and play the role of teacher with the rest of the participants during a whiteboarding session. Many have expressed concern with their ability to execute a successful Socratic dialogue in the modeling methodology in their own classroom, but it is really a matter of practice and it comes naturally with time to everyone who attempts it.

The other idea that came up during whiteboarding was our problem-solving methodology for attacking the P, V, T, & n problems without equations/formulas. This was done using a special table, deemed an "IFE table" for PVTn problems. Though the table has algorithmic appearance, it is not an algorithm (an "if I see this, then I do this" step-wise approach to problem-solving.) This table is a cognitive approach to approaching gas law problems based on proportional reasoning and keeping students focused on the relationships between the variables, which arose from our lab data in the experiments, rather than merely "plugging" numbers into an equation. Here is an example:

A 475 cm3 sample of gas at standard temperature and pressure is allowed to expand until it occupies a volume of 600 cm3.  What temperature would be needed to return the gas to standard pressure? Draw particle diagrams to represent the situation and solve.

The table is difficult to describe in words, but I will say that IFE stands for "initial, final, effect" and requires students to consider the initial and final conditions, which is common with the formula-based approach, but also the fraction by which each quantity changes. This step differs from other equation-based methods to solving gas law problems, because the students focus on the relationships and the fact that the proportional effect must be the same for each quantity. Like I said, because it is not an algorithm, it is challenging to merely "name the steps" of this strategy as it is with conventional algorithms; however, I will say that one cannot use this method to solve problems without having to think through the problem and really understand the relationships between the variables. It was a very different approach to solving gas law problems and I really found value in it because of its cognitive approach to proportional reasoning. My own personal philosophy on problem-solving strategies is anti-algorithm and pro-cognitive whenever possible, so this method will find a welcoming home in my classroom!

The conclusion of the whiteboarding session ended unit two for us, but the day did not end without a short introductory discussion of unit three: "an honest conversation about energy." Unit three will examine energy storage and transfer more quantitatively, but its approach to handling energy, like most other things in modeling instruction, is heavily influenced by cognitive science. The major contributions of Greg Swackhamer, with his article on a cognitive approach to teaching energy, are a driving force behind the treatment of energy in physics and chemistry modeling instruction. We are reading the entire article by Swackhamer to discuss next week.

Overall, the first week was tremendous and such a positive experience. The next two weeks hold many more things for us to learn, but if these first days are any indication, the remaining days will also be awesome!

So that you might have a taste of where this is all going, I leave you with the following question to consider:

What is energy and how would you explain it to someone?