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The method of presentation varies, but the pedagogic story is often historically driven. Algebra is old, calculus is newer, and topology is recent. Classical mechanics is old, thermodynamics is newer, and quantum mechanics is recent. When teaching, these subjects are taught by building on previous content -- calculus leverages algebra, thermodynamics leverages classical mechanics.
The Physics Derivation Graph can show the relevance to Physics of what math technique is being taught. The focus for students in mathematics classes is on the technique, e.g., "integrate both sides with respect to \(Y\)," and application is of secondary importance. Physics students are expected to know the mathematical techniques and teaching is focused on application. The Physics Derivation Graph can assist both scenarios. The student in a math class can see where the inference rules they learn are applied in Physics. The student in the Physics class can see which inference rules are required in their field.
For Physics teachers, the Physics Derivation Graph could address questions like
For Math teachers, the Physics Derivation Graph could address questions like
See Fundamental rules for physics mathematical derivations?
By measuring the frequency of a specific inference rule in the Physics Derivation Graph, the question "What is the relative importance of this math skill?" can be addressed.
In the Physics Derivation Graph, it is simple to count utilization of inference rules. Thus, we are able to measure the ratio of how often "multiply both sides by X" is used relative to "integrate both sides with respect to \(Y\)."