One of the reasons why I dislike teaching “algebra-based” physics in a fast pace manner is that for many students algebra is barely in their grasp. This becomes most apparent when we first starting learning about how to solve problems related to Newton’s 2nd Law.

For example, today students were solving a problem, where a 4 kg is being pushed with a 30N. The coefficients of static and kinetic friction are 0.5 and 0.3 respectively. The question is, does the block move, and if so, with what acceleration?

Students all correctly identify that the maximum static friction force is 20N (based on normal force being equal to weight), and so 30N is enough to be in the kinetic regime. They can then calculate the kinetic friction force as 12N. Many of these students can readily say that 18N is the net force acting on the object. Then most can at this point say that a = Fnet / m = 4.5 m/s/s.

Students’ productive and natural problem-solving approach does not look like what we teach them do:

F_net = ma

F – f_k = ma

F – u F_n = ma

F – u mg = ma

a = 1/m (F-umg)

Students of course just simply do this in “chunks”, calculating pieces along the way, comparing values, doing arithmetic calculations. The formal approaches codify these chunks into the algebra and string them together. Logically that’s true, btu students do not experience it that way.

I think that teaching the formal approaches has the promise of being generally powerful (that’s the allure to teach it this way), but in reality it mostly disenfranchises students from their natural problem-solving skills, their ability to apply insight into problems, and to make sense of what they are doing.

What compounds the negative effects of teaching abstract algebra approaches is that it has quite varied effects.

- I do have some strong algebra students and sense-makers who can apply the formal approaches and make sense of them as they do.
- I also have some good “algorithm” followers who can apply formal approaches, but are not making sense of them. They follow the script.
- I also have strong sense-makers who will approach problem from their own intuitive approach, basically ignoring the approaches you are trying to teach them.
- I also have students who cannot follow the algorithms, and feeling disenfranchised from anything resembling sense-making, they cobble together strange algebra.

Having one or two of these different types seems manageable to me, but having all four I find hard to navigate.