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The Role of k Versus n in Mathematical Induction

The Role of k Versus n in Mathematical Induction

A task for promoting students' distinction between the role of the variable k and the variable n in proof by Mathematical Induction.

Task for the role of k versus n in PMI
This task was designed using the following references:
Dawkins, P. C., & Roh, K. H. (2020a). Assessing the influence of syntax, semantics, and pragmatics in student interpretation of multiply quantified statements in mathematics. International Journal of Research in Undergraduate Mathematics Education, 6(1), 1-22.
Dawkins, P. C., & Roh, K. H. (2020b). Coordinating two meanings of variables in proofs that apply definitions repeatedly. In Karunakaran, S. S., Reed, Z., & Higgins, A. (Eds), Proceedings of the 23rd annual conference for Research in Undergraduate Mathematics Education, (pp. 87-95). Boston, MA.
Norton, A., Arnold, R., Kokushkin, V., & Tiraphatna, M. (2022). Addressing the Cognitive Gap in Mathematical Induction. International Journal of Research in Undergraduate Mathematics Education, 1-27.