I've asked around because this question was quite interesting, not that I know much about it. However, according to Bayaga, mnemonic is not a model and that it is simply to help learners remember the trigonometric basic functions. At best refer to it as a "rule".  Does this makes sense? I can introduce you to him.

No doubt it (SOHCAHTOA) is a 'rule' for writing and computing the sine, cosine & tangent ratios.  This mnemonic will have to be revised when it comes the other three trig ratios. Thus the mnemonic 'models' only three ratios. The user/learner will have to adapt it in order to write down or to computer the other trig ratios. My point is that mnemonics have limits in terms of what they can 'model' or be a 'model of' and a 'model for.' The user must be adept at knowing the limits of the particular mnemonic. Do you agree?

Hi Mohammad,

As Verbra pointed out citing Bayaga, a mnemonic can hardly be considered a model.The trigonometric circle and analytical definition or the trig functions is a model. The way we may understand the trig ratios in rectangle triangles is also a model.

A model is an abstract construction that can be used to understand and explain a family of complex phenomena because it has a behavior that has similarities with the studied systems in his components and relations. (See for example Balacheff, N. or Saboya, M. for a model of control; Jeannotte, D. for a model of math reasoning, Kieran, C. for a model of algebraic activity, etc) .Your explanation in fact seems to prove that the sohcah.. is not a model because it does not help understand nor explains something.

For that matter, remembering the names of the planets with a phrase or repeating PEMDAS while calculating are not models either.

But maybe what  interests you is semiology, symbols and the meaning we can give to them (socially or individually, like a key or a password)?  I would try to investigate the semantic field of the idea of "model" as you say there is a myriad of definitions, and classify them according to what you want to investigate precisely.

As salaam ...

Hi

I tend to agree with the above views. A model should explain or describe (in this case mathematically or structurally) certain elements of another (more complex, bigger etc) system. I think mnemonics only help us remember procedures to follow, they don't really help us understand the concepts at hand? Interesting question!

Okay, the above comments are quite useful in clarifying differences between mnemonics and 'models.' Thank you.

What I pick up so far is that models are comprehensive, reified abstractions that encode interrelated ideas or 'complex phenomena' as Christian noted. On their own 'models' can never 'explain.' I hesitate to give models the agency of 'explaining.'  It is only when a model 'sits in the middle' and forms the basis of classroom discussions or conversations,  between a teacher and learners, say,  that I think there can be the emergence of 'understanding' or an explaining of the 'model.' This brings me to the notion of a 'boundary object', which I think is a more suitable interpretation of a mnemonic...