Is there an optimal approach to physics problem solving?

Not too long ago, while procrastinating physics competitions homework, I was browsing the vast corpus of academia in the hopes of finding a "royal road" to expert performance. I eventually arrived on a specific branch of academia known as PER or Physics Education Research. And after an afternoon or two of digging, I came to a daring conclusion: the "royal road" may not exist. Nevertheless, I firmly believe that pivotal discoveries from within the field can be utilized to pave a well-sounding "royal road".

A short history about the prescriptive model of problem solving

It was the spring of 1984 in California when the Prescriptive Model of Problem Solving came to light. The term was coined by Joan I. Heller, who at that time was a researcher at Berkeley's renowned SESAME group, and Frederick Reif--- Co-Founder of the SESAME group, and an accomplished physicist. Together, they published a seminal paper that revolutionized the way introductory undergraduate physics courses were taught, and this terrific model was at the heart of their paper.

It was evident at the time, given that many emerging papers within PER converged on a similar conclusion, that students often had troubles identifying properties and interactions of physical systems, contributing to low problem-solving adequacy. One such study demonstrated that students often fail to identify nontrivial forces, and consequently, fail to attribute their effect on the motion of a physical system. Others pointed out that some students struggled with misconceptions regarding basic physical phenomena, of those within Newtonian mechanics, these include friction and normal forces.

The Prescriptive Model of Problem Solving was the answer Heller and Reif proposed to help tackle students misconceptions, and more specifically, to promote the increase in their problem solving competency. Earlier research suggests that novices, or in this case students, should mimic the problem solving processes of experts, under the premise that these experts consistently demonstrate competent performance. However, as is often the case in practice, it is of ubiquitous challenge to rigorously maintain consistency at such level of expertise. Heller and Reif, then, proposed an alternative solution that has prominently shaped the basis of today’s pedagogical approach in physics education.

How does the prescriptive model of problem solving help with physics competitions?

The International Physics Olympiad, which held its first annual competition in 1967, was (and still is) widely regarded as the crème de la crème of physics problem solving contest at the secondary education level. Much of its theoretical and experimental examinations were imported from research at the frontiers of physics, although modified to be compatible with secondary level mathematics, this does not diminish its high degree of complexity. In fact, this reduction of mathematical technicalities, allows a unique challenge for students, whereby the exploitation of elegant and subtle properties of physical systems becomes a dominant predictor of success. In other words, the mastery of problem solving skills is a crucial aspect of physics problem solving.

Experts tend to spend more time constructing qualitative descriptions of a problem, ensuring a thorough analysis of all the physical properties involved, such that a proposed plan is conceived, before carrying out the technical (or mathematical) details of said plan. Novices, on the contrary, often exhibit pattern-based approach in physics problem solving, a tendency to match (arbitrary) superficial features of a problem to a set of formulas and performing trial-and-error based approach.

The prescriptive model of problem solving, however, closes this gap by assigning a four step protocol, that for this context I've decided to paraphrase as: identification, redescription, execution, and evaluation. To explain it lightly, identification explicitly asks the student to define the coordinate system and frame of reference, and identify systems most relevant to the problem. Redescription requires the student to construct appropriate force, motion diagrams, define system boundaries, and construct an appropriate physical model for the problem. The execution phase is straightforward: mathematical execution. So once the model for the problem has been set up, it is in the execution stage where the mathematical labor is done. The final stage is reserved for evaluating student's solution to the problem.

Conclusion: Could prescriptive problem solving be a royal road to the IPhO?

As of now, we have yet to see a concrete example of it. However, I'm happy to announce that I've been (consistently) implementing a modified version of these 4 heuristics on my studies. So far, I've spent about 60 hours practicing these heuristics on assorted problem sets. And I have indeed been noticing (rather satisfactory!) improvements. According to some of my previous posts here, my CPPS has moved from ~0.2 average to ~0.45 within just 60 hours of practice---that's more or less two months of consecutive two hours per day of self study.

I'll be back with an update a month from now!
February 9, 2026