Connections between empirical and structural reasoning in technology-aided generalization activities

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.

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Work Title Connections between empirical and structural reasoning in technology-aided generalization activities
Access
Open Access
Creators
  1. Xiangquan Yao
  2. John Elia
Keyword
  1. empirical reasoning, structural reasoning, mathematical generalization
License CC BY 4.0 (Attribution)
Work Type Article
Publisher
  1. Modestum Publishing Ltd
Publication Date March 7, 2021
Publisher Identifier (DOI)
  1. 10.29333/iejme/9770
Source
  1. International Electronic Journal of Mathematics Education
Deposited July 01, 2022

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  • Added Creator John Elia
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    Keyword
    • empirical reasoning, structural reasoning, mathematical generalization
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