Investigating secondary students’ generalization, graphing, and construction of figural patterns for making sense of quadratic functions

Research output: Contribution to journalArticleResearchpeer-review

Abstract

An important aim in school mathematics is to help students experience algebra's power to express generality. Researchers have been investigating figural growing pattern generalization as an early route to developing students’ understanding of functional relationships. More recently studies have been considering ‘open’ or ‘free’ tasks involving figural growing pattern construction. This study explored twelve Years 7–12 Australian students’ intuitions and connection of meanings for quadratic functions through growing pattern generalization, graphing, and construction activities during individual task-based interviews. The students who evidenced complementary correspondence and covariation views when generalizing appeared to handle pattern construction activities in productive ways, regardless of their prior formal study of quadratic functions. Areas of difficulty with graphing growing patterns and potential benefits of pattern construction tasks for exploring quadratic equations and for formative assessment are discussed.

Original languageEnglish
Article number100689
Number of pages17
JournalJournal of Mathematical Behavior
Volume54
DOIs
Publication statusPublished - 1 Jun 2019

Keywords

  • Figural growing pattern construction
  • Figural growing pattern generalization
  • Multiple-representational activities
  • Quadratic functional relationships
  • Secondary mathematics

Cite this

@article{479febf2e3d2484595caad806e4a05ab,
title = "Investigating secondary students’ generalization, graphing, and construction of figural patterns for making sense of quadratic functions",
abstract = "An important aim in school mathematics is to help students experience algebra's power to express generality. Researchers have been investigating figural growing pattern generalization as an early route to developing students’ understanding of functional relationships. More recently studies have been considering ‘open’ or ‘free’ tasks involving figural growing pattern construction. This study explored twelve Years 7–12 Australian students’ intuitions and connection of meanings for quadratic functions through growing pattern generalization, graphing, and construction activities during individual task-based interviews. The students who evidenced complementary correspondence and covariation views when generalizing appeared to handle pattern construction activities in productive ways, regardless of their prior formal study of quadratic functions. Areas of difficulty with graphing growing patterns and potential benefits of pattern construction tasks for exploring quadratic equations and for formative assessment are discussed.",
keywords = "Figural growing pattern construction, Figural growing pattern generalization, Multiple-representational activities, Quadratic functional relationships, Secondary mathematics",
author = "Wilkie, {Karina J.}",
year = "2019",
month = "6",
day = "1",
doi = "10.1016/j.jmathb.2019.01.005",
language = "English",
volume = "54",
journal = "Journal of Mathematical Behavior",
issn = "0732-3123",
publisher = "Elsevier",

}

TY - JOUR

T1 - Investigating secondary students’ generalization, graphing, and construction of figural patterns for making sense of quadratic functions

AU - Wilkie, Karina J.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - An important aim in school mathematics is to help students experience algebra's power to express generality. Researchers have been investigating figural growing pattern generalization as an early route to developing students’ understanding of functional relationships. More recently studies have been considering ‘open’ or ‘free’ tasks involving figural growing pattern construction. This study explored twelve Years 7–12 Australian students’ intuitions and connection of meanings for quadratic functions through growing pattern generalization, graphing, and construction activities during individual task-based interviews. The students who evidenced complementary correspondence and covariation views when generalizing appeared to handle pattern construction activities in productive ways, regardless of their prior formal study of quadratic functions. Areas of difficulty with graphing growing patterns and potential benefits of pattern construction tasks for exploring quadratic equations and for formative assessment are discussed.

AB - An important aim in school mathematics is to help students experience algebra's power to express generality. Researchers have been investigating figural growing pattern generalization as an early route to developing students’ understanding of functional relationships. More recently studies have been considering ‘open’ or ‘free’ tasks involving figural growing pattern construction. This study explored twelve Years 7–12 Australian students’ intuitions and connection of meanings for quadratic functions through growing pattern generalization, graphing, and construction activities during individual task-based interviews. The students who evidenced complementary correspondence and covariation views when generalizing appeared to handle pattern construction activities in productive ways, regardless of their prior formal study of quadratic functions. Areas of difficulty with graphing growing patterns and potential benefits of pattern construction tasks for exploring quadratic equations and for formative assessment are discussed.

KW - Figural growing pattern construction

KW - Figural growing pattern generalization

KW - Multiple-representational activities

KW - Quadratic functional relationships

KW - Secondary mathematics

UR - http://www.scopus.com/inward/record.url?scp=85061553099&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2019.01.005

DO - 10.1016/j.jmathb.2019.01.005

M3 - Article

VL - 54

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

M1 - 100689

ER -