Connections between Empirical and Structural Reasoning in Technology-Aided Generalization Activities
Xiangquan Yao 1 * , John Elia 1
More Detail
1 Department of Curriculum and Instruction, The Pennsylvania State University, University Park, PA 16802, USA* Corresponding Author


Mathematical generalization can take on different forms and be built upon different types of reasoning. Having utilized data from a series of task-based interviews, this study examined connections between empirical and structural reasoning as preservice mathematics teachers solved problems designed to engage them in constructing and generalizing mathematical ideas aided by digital tools. The study revealed closer connections between naïve empiricism and result pattern generalization, between naïve empiricism and recognizing a structure in thought, between reasoning by generic example and process pattern generalization, and between reasoning by generic example and reasoning in terms of general structures. Results from this study imply that the ability to generalize based on perception and numerical pattern does not necessarily lead learners to generalize based on mathematical structure.


This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, 2021, Volume 16, Issue 2, Article No: em0628

Publication date: 07 Mar 2021

Article Views: 1531

Article Downloads: 1023

Open Access Disclosures References How to cite this article