
Covariational reasoning surfaced in the first chapters of the book, however, it needs more elaboration as it will dominate the case studies included in Part III. This chapter presents a current perspective on covariational reasoning and its fit to the proposed modeling discourse. It delves deeper into mathematical representations that can be used during modeling enterprises to reach this goal. Research proved that modeling supported by empirical-mathematical thinking is an effective way of organizing learning environments in the physics classroom. Observing lab processes and concluding general patterns reflects on physicists’ scientific inquiry methods. A mathematical structural domain consisting of algebraic functions is the leading mathematical apparatus used during physics labs quantitative analyses. Thus the techniques of blending scientific thought processes with algebraic apparatus called for more elaboration. This chapter attempts to demystify formulas algebraic structures and extract covariational sense that is stored in these structures. Initiated from contrasting functions and formulas, this chapter zooms deeper into the elementary blocks of these representations; parameters, and variables. An attempt to categorize physics formulas by their complexity of covariate entanglement will conclude this chapter.
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