The Rule of Four, Executive Function and Neural Exercises

Russell Jay Hendel

Deborah Hughes-Hallet has made many significant contributions to Calculus pedagogy. Among the tools she has introduced is the rule of four, which requires successful pedagogy to simultaneously address four approaches to each course concept, verbal, graphical, algebraic and numeric. We explore examples of this rule of X approach in other disciplines: i) Literary analysis is enhanced through the rule of two, a simultaneous approach of grammar and literary analysis; ii) Actuarial mathematics requires a rule of six, a simultaneous approach of verbal, graphical, algebraic, calculator, modules, and English conventions; (iii) Masters of Tic-Tac-Toe and Chess use a rule of two, simultaneously approaching the game positionally and combinatorically. We offer a unified and deep analysis of the rule of X approach by relating it to executive function, the area of the brain responsible for organizing and synthesizing multiple brain areas. We conclude the paper with an illustration of classroom activities that strengthen executive function and improve pedagogy. Our results are content independent, depending exclusively on paths of information flow, and consequently, our analysis is cybernetic in flavor [1].

[1] American Society of Cybernetics, www.asc-cybernetics.org/

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