One of the common refrains in maths, physics and engineering education is to “show your working” and “check your working”. In physics and engineering, “check the units” is also commonly heard.
If you have a calculation to do, show the algebraic steps, then substitute in the numbers as part of the working, showing partial results along the way.
As I slowly start to sketch out examples of how we can use one piece generative document workflows to both create educational materials, and, by sharing the tools of production with learners in the guise now of a mechanical tutor, support self-checking, worked equations, and checking your working, both seem to provide good examples of how to demonstrate this sort of practice.
handcalcs python package provides a simple but effective way to to write simple mathematical expressions and then automate the production of a simple worked example.
In phyics and engineering settings, dimensional analysis can provide a powerful shortcut to checking that a derived equation produces a thing of the correct dimension: was it V=IR, or V=I/R? A quick dimensional analysis, if you know your SI units, can help check.
There are several packages out there that provide units of measurements that can be used to type numerical values with particular units. The
forallpeople package is onesuch, and also happens to play nicely with
Another handy benefit of a good units of measurement package, for production as well as student self-checking, is the mechanical support for expressing the units in appropriate form, given the magnitude of an expressed quantity:
Current SubjectMatterNotebooks example: https://opencomputinglab.github.io/SubjectMatterNotebooks/maths/worked-equations.html