Good News!
It’s March and I have finally finished my review season. In this document, I will report on my findings and draw a decisive conclusion from them.
1.1. Introduction
Throughout this review spree, I focused mainly on addressing the fundamentals. I realized, after a couple of days researching PER in December, that physics problem solving is primarily about constructing an appropriate model and finding relevant solutions for that model; not just blind algebra. I also read that experts tend to spend a disproportionate amount of time doing qualitative analysis before touching the mathematics when solving problems; different from a novice. Departing from these, I modified existing problem solving frameworks to satisfy my needs, and incorporated my CPPS rating system as a quantifiable metric of performance on them. I will list some relevant variables associated with these findings in a table below.
1.2. Findings
| Phase | Date | CPPS | Notes |
|---|---|---|---|
| Pre-Review | June-Aug 2025 Sept-Dec 2025 |
0.279 ~0.350 |
Calibrated with OSK, framework not yet developed Still no framework usage. |
| Mid Review | January February March (as of 4 March) |
[<1/1] 0.41 [3/1] 0.63 [NA/1] 0.65 [8/1] 0.70 [13/1]0.55 [20/1] 0.40 [23/1] 0.43 [1/2] 0.46 [5/2] 0.33 [9/2] 0.85 [15/2] 0.51 [16/2] 0.84 [17/2] 0.93 [17/2] 0.88 [25/2] 0.90 [27/2] 0.67 [1/3] 0.55 [4/3] 0.81 |
January: Framework established, beginning of practice. It took about 60-75 minutes to apply the framework per question. Elo at the beginning: 0.350 Elo at the end: 0.526 February: Framework readapted, incorporated kalda style. Adapted for olympiads. Took about 30-40 minutes per question with framework. Elo at the beginning: 0.526 Elo at the end: 0.707 March: framework has not been adjusted since February. Took about 20-30 minutes per question. |
| Post Review | March (post 4th) | 0.68 within 0.02 margin of error |
1.3. Discussions
I’d also like to mention the things that ended up working out for me. Since January, I’ve learned to consider defining the system of interest such that conservation laws apply. However, recent chapters taught me to also consider appropriate subsystem(s) on which the construction phase may be easier and appropriate to carry out. In addition, it may be noted that some problems benefit from not including everything as part of a single system, so careful attention is appropriate. I have also found well drawn diagrams, especially those that explicitly show the geometrical relationships of the relevant stuff (e.g. vectors, objects, axes, etc.), to be really helpful.
As a natural extension, time-sequenced diagrams often offer insights to how the system (or subsystem) behaves over time, and may lead to symmetry or conservations that can simplify the process further. It may also be appropriate to mention boundary conditions, steady state, phase diagrams, and adiabatic invariants here. Being able to recognize, differentiate, and appropriately use them to model a case is of significant advantage.
I have also found that treating objects as continuum of differential elements often offer unparalleled insight, especially in approaching nontrivial and novel cases. However, one must verify that the proposed mechanisms governing these differential elements do not violate what had been established earlier (e.g. not violating the symmetry, conservation laws [if appropriate], geometric constraint, etc.). For the evaluation section, I’ve noticed that even briefly (or moderately) considering the proposed model, contrasting it with “real life” or a less idealized version, can help catch errors. It is also of commendable interest to verify the models (e.g. limiting cases, symmetry, special conditions, etc.).
Despite the laughable absurdity of the problem solving framework upon its conception, it surprisingly yields satisfactory results. A jump from 0.350 CPPS rating to 0.680 (with a margin error of 0.02) is a 94% improvement over ~18 sessions, an average of ~5% per session improvement rate. Total time spent during the review phase was 101 hours, an average of ~1% improvement per hour. Compared to an analysis for an answer to some question from May 2025, my latest answer is evaluated to be 700% more than that. I declare this pilot project a success.