The purpose of this paper is to propose an empirically grounded and relatively well-specified framework for analysing creative problem solving reasoning and rote algorithmic reasoning. This is motivated by i) the persistent focus by students and by mathematics teachers, textbooks, and tests on rote learnt algorithms, ii) this algorithmic focus as a main cause behind learning difficulties, and iii) the lack of frameworks that can further help us to understand, analyse, and communicate the relevant phenomena.