The unfolding of third graders’ conceptualization of a function: a collective case study

Date

2019-12-01

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Journal ISSN

Volume Title

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Abstract

The goal of this study was to understand elementary students’ meaning-making process of early algebra representations in the context of number patterns about even and odd numbers within their natural classroom setting. A particular emphasis was placed on understanding the role of the function as a way to generalize a relationship between inputs and outputs where every input has exactly one output, i.e. an even number can be defined as f(n)= 2n for an integer n and an odd integer could be defined as f(n)= 2n+1 for an integer n. Through a collective case study of individual students in a third-grade classroom, I qualitatively analyzed and characterized individual noticing patterns when given a function rule table and moreover, concluded that third-graders are able to conceptualize a function rule in the context of generating even integers and were able to act upon a function rule when generating odd integers. The study suggests that the benefit of integrating function tables into the early elementary instruction will support formal functional understanding in later grades.

Description

Keywords

Elementary mathematics, Early algebra instruction, Mathematics education, Noticing

Graduation Month

December

Degree

Doctor of Philosophy

Department

Curriculum and Instruction Programs

Major Professor

Sherri L. Martinie

Date

2019

Type

Dissertation

Citation