Physics is a notoriously difficult subject. The math is complicated, the principles are subtle and even when students pass the final exam, they still frequently fail simple conceptual questions designed to test whether they really understood anything.
Given this difficulty, it makes sense that we should strive for more effective ways to teach and learn physics. Jennifer Docktor and José Mestre provide an elegant summary of the relevant research on evidence-based instructional practices in their book, The Science of Learning Physics [1].
Why is Physics So Hard to Learn?
While learning the math underpinning physics isn’t easy, Docktor and Mestre argue that conceptual reasoning is what students struggle to master.
We are born into a physical world; thus nature has endowed us with intuitions for dealing with physical objects. Unfortunately, these intuitions don’t align with the deeper laws of physics discovered by scientists.
Most people reason like Aristotle—we think objects stop moving when we stop applying force, that the force on a ball thrown directly up changes continuously, or that when two objects collide, the bigger one exerts a greater force on the smaller one. Instead, we’d like them to reason like Newton (and eventually Einstein)—objects in motion stay in motion without an external force, the force on a ball thrown up is constant (it’s just gravity), and every action causes an equal and opposite reaction.
A semester of college physics isn’t enough to overcome this failure to reason properly about physics. Instead, Docktor and Mestre argue for a knowledge-in-pieces view of building knowledge of physics. In this account, students don’t overcome their misconceptions simply by being taught the correct solution. Instead they acquire an accurate understanding piecemeal, sometimes exhibiting correct reasoning and other times falling back on naive intuitions.
Developing conceptual reasoning is different from merely being able to solve textbook problems, as it’s possible to memorize how to solve a problem without understanding why the process works.
How Do Physicists Think About Physics?
Physics classes aim to produce more expert-like reasoning about physical problems. To that end, psychologists have devoted considerable time to studying expert-novice differences in many fields, including physics.
These studies take a snapshot comparing the reasoning patterns exhibited by domain experts (in this case, physicists) and novices (usually people who have taken an undergraduate class or two).
Some of the common findings from this line of research include:
- Experts see principles, while novices see surface features. Asked to categorize physics problems, experts organize them based on the fundamental principle involved. Novices, in contrast, focus on surface features, like whether the problem involves a ramp or a pulley.
- Experts reason forward, while novices reason backward. Experts start from the “givens” of a problem and pick the right formulas to apply to get the intermediate quantities needed to solve a problem. Novices, in contrast, start with the goal and try to find equations to solve for the goal, working backward. This latter approach is more mentally demanding, which is one reason physics problems are so hard for beginners.
- Experts spend more time studying a problem, while novices rush to calculations right away. While experts generally solve problems faster than novices, proportionally, they spend more time trying to understand the problem before doing any computations. Novices, lacking the ability to categorize the problem by general principles, tend to rush to crunching numbers, hoping it will lead to a solution.
One way to understand these differences is that experts have sophisticated schemas, or organizing patterns, that cause them to perceive problems in terms of the principle underlying their solution. Novices, who lack these patterns, tend to “plug-and-chug” numbers into available formulas or use direct analogy to remembered problems of the same type.
Can the Deep Ideas of Physics Be Taught Better?
Docktor and Mestre are optimistic that there are better ways of teaching physics than the typical approach, in which a professor lectures to an audience, perhaps occasionally showing an example or derivation, and assigns homework problem sets.
One strategy that the authors believe shows promise is in making explicit the reasoning process that goes into solving a physics problem. Instructors, whose schemas make the next “correct” move in a physics problem obvious (to them), tend to focus on demonstrating the underlying math, rather than why a particular equation needs to be used.
If teachers can instead model the entire problem-solving process—not just the algebraic steps, but the conceptual reasoning that allows them to decide whether a problem is one of conservation of momentum or energy—students will hopefully clue in on the expert mode of reasoning sooner than might be expected by simply doing hundreds of problems.
Once multiple principles have been introduced, it may be wise to focus on teaching and practicing how to categorize problems. Since this is such an essential feature of expert problem-solving, physics students would do better if they spent more time practicing how to distinguish problem types, not merely solving them.
The authors also strongly advocate for active learning. Active learning involves the student in constructing knowledge, not merely passively receiving it. Active approaches typically advocate for problem-solving, hands-on experimentation and exploration, and frequent testing and feedback in the learning process.
Some strategies for implementing active learning that receive some evidence in support include:
- Frequent testing and retrieval practice. Students tend to prefer reading their notes, but they learn more from attempting to solve problems.
- Interleaving examples with testing. This can help offset some of the cognitive load problems of pure problem-solving while still encouraging active practice among students.
- Desirable difficulties [2]. Spacing, retrieval, and interleaving different examples side-by-side have all been shown to enhance learning, even though students tend not to realize their effectiveness.
- Flipped classrooms. Instead of an in-person lecture and take-home problem sets, video lectures are given for homework, and students work on their problem sets in the classroom, where peers and teachers can offer feedback and help.
- Clicker questions and pair-and-share. Interrupting the flow of the lecture for brief quizzes both encourages learning and informs teachers of when their explanations aren’t hitting the mark.
- Self-explanations. Students who try to explain worked examples or their own solutions understand the problems better than those who don’t.
Some Final Thoughts
Overall, I enjoyed this book, and given its slim size, I highly recommend it to anyone who has to teach or learn physics. I suspect many of the same ideas would apply to any STEM-based subject, although certainly, the challenges of learning organic chemistry or molecular biology differ somewhat from classical mechanics.
My only concern with the book was that it largely sidestepped controversies over the empirical status of educational theories. In a prominent paper [3], Lin Zhang, John Sweller, Paul Kirschner, and William Cobern argue that the support for problem-based, inquiry and other pedagogical innovations has been overstated. They argue that many of the experiments that support reform approaches have altered many aspects of instruction at once. In contrast, carefully controlled studies aimed at assessing the efficacy of individual components of those instructional strategies have often not supported their use.
For instance, problem-based learning is a popular approach to active learning, arguing that students should be taught less and spend more time actively solving problems. However, Sweller’s research [4] has found that novices learn faster and perform better after studying examples than solving the problems for themselves. Similarly, inquiry-based approaches, which model the learning process on how expert physicists do science, may be less effective than direct instruction [5].
My takeaway from the ongoing controversies is that active learning should not be confused with unguided learning. It’s important for students to think actively, try to understand deep concepts and see the broader context in which textbook problems are situated. But, it also seems clear that student activities cannot be a substitute for thorough and explicit teaching.
For a physics student, it seems clear that ample practice and examples are important. But we should also be focused on understanding why certain problems are solved the way they are—not just mindlessly inserting equations but stepping back to ask which principles are at work (and hopefully getting feedback from peers or teachers) to see if our intuitions are correct.