As our Gas Laws unit was coming to an end, it was time to create the test. As I thought of potential test questions that were both challenging and in alignment with the learning objectives we had previously identified for the unit, I was reminded of a multiple-choice question I had been shown in an old Modeling InstructionTM resource.
Which of the following samples of gas will have the greatest pressure if they all have the same volume?
A. 10 moles at 80 0C B. 10 moles at 70 0C C. 5 moles at 81 0C D. 2 moles at 82 0C
I loved this question because it required a particle-level understanding of pressure. Since we continuously try to connect the macro level with the particulate level, it served as a useful conceptual question. More specifically, there is no memorized equation/formula that could potentially mask understanding and no mnemonic device to rely on. Instead, it just requires a moment in which you must stop and think about how the two variables, moles and temperature, relate to pressure. In other words, the only thing students need to do is ask themselves, “which of these answers would produce the most amount of collisions1 with the inner walls of the container?”
To be honest, I was pretty confident in my students’ ability to answer this question correctly. After all, the idea of pressure came up frequently throughout the unit which meant we had multiple opportunities to explain why pressure would increase or decrease from a particle-level perspective. Within these opportunities, feedback was provided with the hope that it would be used to improve future explanations and overall understanding. In fact, I saw the majority of students citing the concept of particle-wall collisions much more frequently after they were given time to acknowledge previous feedback.
However, as I was grading the tests, I started to notice something—many students were choosing answers that I had previously thought would have been easily dismissed. After I was done grading the tests, I decided to look at the data.
Which of the following samples of gas will have the greatest pressure if they all have the same volume?
A. 10 moles at 80 0C B. 10 moles at 70 0C C. 5 moles at 81 0C D. 2 moles at 82 0C
Out of 160 students:
16% (26) chose B—10 moles at 70 0C
17% (27) chose D—2 moles at 82 0C
How was it possible that 1/3 of my students got this question wrong?! After reflecting on this for a bit, here is what I think happened and how it reflects a recurring issue especially in science education.
Answer—10 moles at 70 0C
Of all the answers available, I thought this one was going to be the easiest to dismiss. After all, if answers A and B both had the same number of moles but one was at a lower temperature, how could the answer with a lower temperature possibly cause a greater frequency of collisions? It wasn’t until I started to look at some of the tests that I noticed some of the “work” students were doing on the side. Students were literally plugging in temperature values from answers A and B to a memorized equation (Gay-Lussac’s Law or the Combined Gas Law) which lead through a line of reasoning that appeared to go something like this:
The bigger the bottom number (temp) the smaller the answer will be. Therefore, the smaller of these two temperatures will result in the greater pressure.
Forget the fact that it’s a complete misuse of Gay-Lussac’s Law or the Combined Gas Law. Forget the fact that the mathematical reasoning they were trying to use doesn’t even make sense. My biggest concern here was that the moment they saw some numbers, they instantly resorted to an equation, which was completely misused.
In case you’re wondering, nobody tried using the Ideal Gas Law.
To be clear, it’s not that I’m necessarily against using an equation to prove an answer to a conceptual question that could have easily been solved for after a moment of thinking about it. What is most interesting to me is the number of students that were SO RELIANT and SO CONFIDENT in their memorized formulas, that using them completely blocked out the thought process that would have allowed them to see the obvious contradiction in their answer.
So, what about the students that chose the other answer?
Answer—2 moles at 82 0C
I think the thought process that would lead someone to choose this answer is much easier to explain. Students knew about the directly proportional relationship between pressure and temperature. They reasoned that the higher the temperature, the more collisions. Therefore, they chose the answer with the highest temperature.
Though these students showed no evidence of plugging values into memorized formulas, I consider their error in reasoning to fall within the same category as the other group. Instead of resorting to a memorized formula, they instantly resorted to a memorized procedural relationship: As temperature increases, pressure increases. In doing so, it completely blocked out any consideration of the effect that the number of moles present in each sample would have or even the small discrepancy between temperature values among the answers available. Not only that, like the students from the other group, they misused the concept of Gay-Lussac’s Law by forgetting the fact that it’s only true when both volume and moles are held constant.
The two groups of students that I identified are made up of students with reasoning skills all over the spectrum and earned grades on this test anywhere from an A to a D. To make it even weirder, this specific test had the highest performance of any test we have had throughout the year with an average of 82.5%.
So Why Am I Even Bringing This Up?
Regardless of the topic being taught, we can all think of situations or concepts that students typically resort to a more procedural way of thinking. Though the reason so many students approach many chemistry concepts this way is a topic that has been extensively researched,2-4 I still find myself continuously “battling” with students to overcome the attraction to constantly approaching problems with an algorithmic or procedural mindset. Not only does this happen with students, but with colleagues as well—though it’s a bit more refined conversation.
Just to clarify, I did use a question from a Modeling InstructionTM resource as the basis of this post. I have been trained in Modeling InstructionTM but I am unable to use a full-blown version of the provided curriculum in my current teaching assignment. I do try to use many of the practices of Modeling InstructionTM but I neglected to use the PVnT tables that Modelers often use in the gas law unit. After seeing the above results, I am anxious to incorporate the PVnT tables into my gas law unit next year and compare the results for this question to what I saw this year.
What are some strategies you use to not only promote a conceptual understanding but also teach students when algorithms are beneficial and when it’s potentially inappropriate to use them? How do you convince your students and colleagues that just because students may arrive at the correct answer, that doesn’t mean they understand what’s going on. In other words, why is it so difficult to convince people that quantitative correctness doesn’t automatically suggest understanding? If you have any thoughts or recommendations on the matter, I would love to hear them. Though this was just one example, it’s one of many that occur throughout the year and I want to do anything I can to promote thinking skills and overall reasoning ability.
1Since pressure is not universally defined this way, I just wanted to provide a bit of clarity here. In Modeling InstructionTM, the concept of pressure is explained using a model that primarily focuses on the frequency of collisions between particles and inner walls of the container. The more collisions, the more pressure and vice versa. For example, we can account for the increase in pressure when the temperature of a system is raised since the particles have a higher average kinetic energy which leads to an increase in the frequency of collisions between the particles and the inner walls of the container that hold them. You can learn more about Modeling InstructionTM at http://modelinginstruction.org (accessed 3/20/17).
2 Cracolice, Mark, John Deming, and Brian Ehlert. “Concept Learning versus Problem Solving: A Cognitive Difference.” Journal of Chemical Education 85-6 (2008):873-878
3 Gallet, Christian. “Problem-Solving Teaching in the Chemistry Laboratory: Leaving the Cooks…” Journal of Chemical Education 75-1 (1998): 72-77
4 de Vos, Wobbe, Berry van Berkel, and Adri Verdonk. “A Coherent Conceptual Structure of the Chemistry Curriculum.” Journal of Chemical Education 71-9 (1994): 743-746