“Are you going to make us memorize proofs* for the exam?” A student of mine asked me this dreaded question during the first week of class. His partner replied, “In my last physics class, we had to do that a lot. It was so hard. Please don’t make us do that.”
This conversation concerned me for a number of reasons. Both of these students took their first semester physics class at another institution, and during the first week in my class, they are still feeling out my approach to teaching physics. They were excited to hear that I won’t make them memorize anything, but didn’t seem to understand that won’t make the exams any easier.
I wasn’t in the other classes that these students took, but I’m fairly certain that the goal of that exam question was not that the students memorize the derivation. What we have here is a disconnect between the goals the instructor has for the class and how those goals are communicated. The professor wants the students to apply a fundamental concept (Newton’s Second Law, for example) to a new system (say a mass on a spring), and build a mathematical model for how the position of the spring will change over time. But the student thinks he has been asked to regurgitate how we get from F=ma to an equation for position, without a real understanding of the modelling process.
The issue here is that the professor did not clearly communicate what he expected the students to be learning – the students thought they needed to have this factual knowledge (i.e. memorize the derivation), the professor thought that he was teaching them a technique used by physicists to derive new mathematical models. The students in this scenario walk away with an understanding of physics that couldn’t be more different from an expert’s understanding of physics, or more at odds with the learning objectives of most physics professors.
Experts and novices approach problems in very different ways (see the NRC reference below for details). Although most experts have vast amounts of factual knowledge, this is not what differentiates an expert from a novice. The biggest difference is how they organize and access this information. Most chemists have not memorized the periodic table, but they know how to use the periodic table as a tool to help them locate information about any given element quickly and efficiently. A savant may know more integrals than someone with a PhD in physics, but that doesn’t mean they can solve advanced problems.
The trick to being a good teacher is not just know your content (we all know the content) but how to teach students to access and synthesize ideas in meaningful ways. This is the difference between being an expert in “content knowledge” and being an expert in “pedagogical content knowledge.” (There’s your jargon for the day.) Most college professors are really good at their content, but need to work on their PCK. This is not a fault, it’s just the system isn’t designed to train them (you) to be teachers. The PCK is what we need to get past teaching and assessing facts.
The question remains, how can we teach students how to think like experts? The NRC publication, How People Learn, recognizes this as one of the key findings of educational research: “To develop competence in an area of inquiry, students must: (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a framework, and (c) organize knowledge retrieval and application.” (p. 16). Science instruction at the college level too often focuses on (a) and (b), but does not spend much time on (c). Ok, so how do we teach our students to develop expertise?
One solution to this conundrum is to de-emphasize facts in our courses. We need to reign in the curriculum, and not feel like we are required to teach every topic in the massive introductory textbooks. One study showed that students only record about 11% of critical ideas presented during class in their notes. Other studies repeatedly demonstrate that students retain very little factual knowledge after the semester ends. If they aren’t retaining it, then we aren’t really loosing much by not covering every topic in the book. This allows us to spend more time talking about the process of doing science. We can take a step back from the content to teach students scientific inquiry skills such as mathematical modeling, problem solving, computational skills, pattern recognition, graphical analysis, etc. These skills are just as important, and more memorable, than the factual knowledge students think we want them to memorize. I don’t think I have to convince you that these skills are important. Most science professors would agree, but we have to make it abundantly clear to students that we value these skills over the facts. That’s where the communication about goals and expectations is vitally important. The students won’t figure out how to be an expert on their own. We have to give them opportunities to apply these thinking skills, and be up front about what the goals of these activities are.
Getting back to the anecdote at the top, the thing that really motivates students is assessments. We need to do a better job of making sure that our assessment match the goals that we have for the class. If the exams continue to be based on factual recall, then that’s how the students will study. If the exams require more problems with higher levels of reasoning, then students will have to study these skills to be successful. Many physics allow their students to use a notecard or equation sheet. This goes a long way in emphasizing that memorizing the equations is not the goal of the assessment. Assessments other than exams, such as presentations, debates, or written papers, can also help to emphasize scientific thinking skills.
*He means derivations, not proofs. This is physics, not math.
For more information
National Research Council (NRC). (2000.) Chapter 2: How Experts Differ from Novices. How People Learn. National Academies Press: Washington, DC. https://www.nap.edu/read/9853/chapter/5
Michael C. Friedman. Notes on Note-Taking: Review of Research and Insights for Students and Instructors. Harvard University. http://hilt.harvard.edu/files/hilt/files/notetaking_0.pdf
Halpern & Hakel. (2003). Applying the Science of Learning to the University and Beyond. Change, July/August 2003. http://www.chabotcollege.edu/SLOAC/more%20reading/HalpernHake%20science%20of%20learning.pdf