Relationships between students' fractional knowledge and equation writing

Amy J. Hackenberg, Mi Lee

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students participated in two 45-minute interviews and completed a written fractions assessment. Students operating with the second multiplicative concept had not constructed fractional numbers, but students operating with the third multiplicative concept had; students operating with the second multiplicative concept represented multiplicatively related unknowns in qualitatively different ways than students operating with the third multiplicative concept. A facilitative link is proposed between the construction of fractional numbers and how students represent multiplicatively related unknowns.

Original languageEnglish (US)
Pages (from-to)196-243
Number of pages48
JournalJournal for Research in Mathematics Education
Volume46
Issue number2
StatePublished - Mar 1 2015

Fingerprint

Fractional
Multiplicative
student
Unknown
Relationships
Knowledge
Concepts
Reasoning
Composite
interview
Unit
secondary school

Keywords

  • Algebraic reasoning
  • Fractional knowledge
  • Iterative fraction scheme
  • Middle school students
  • Multiplicative concept
  • Quantitative reasoning
  • Unknowns

ASJC Scopus subject areas

  • Education
  • Mathematics (miscellaneous)

Cite this

Relationships between students' fractional knowledge and equation writing. / Hackenberg, Amy J.; Lee, Mi.

In: Journal for Research in Mathematics Education, Vol. 46, No. 2, 01.03.2015, p. 196-243.

Research output: Contribution to journalArticle

@article{3f032970b3d34fe3a087fc41574a193c,
title = "Relationships between students' fractional knowledge and equation writing",
abstract = "To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students participated in two 45-minute interviews and completed a written fractions assessment. Students operating with the second multiplicative concept had not constructed fractional numbers, but students operating with the third multiplicative concept had; students operating with the second multiplicative concept represented multiplicatively related unknowns in qualitatively different ways than students operating with the third multiplicative concept. A facilitative link is proposed between the construction of fractional numbers and how students represent multiplicatively related unknowns.",
keywords = "Algebraic reasoning, Fractional knowledge, Iterative fraction scheme, Middle school students, Multiplicative concept, Quantitative reasoning, Unknowns",
author = "Hackenberg, {Amy J.} and Mi Lee",
year = "2015",
month = "3",
day = "1",
language = "English (US)",
volume = "46",
pages = "196--243",
journal = "Journal for Research in Mathematics Education",
issn = "0021-8251",
publisher = "National Council of Teachers of Mathematics",
number = "2",

}

TY - JOUR

T1 - Relationships between students' fractional knowledge and equation writing

AU - Hackenberg, Amy J.

AU - Lee, Mi

PY - 2015/3/1

Y1 - 2015/3/1

N2 - To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students participated in two 45-minute interviews and completed a written fractions assessment. Students operating with the second multiplicative concept had not constructed fractional numbers, but students operating with the third multiplicative concept had; students operating with the second multiplicative concept represented multiplicatively related unknowns in qualitatively different ways than students operating with the third multiplicative concept. A facilitative link is proposed between the construction of fractional numbers and how students represent multiplicatively related unknowns.

AB - To understand relationships between students' fractional knowledge and algebraic reasoning in the domain of equation writing, an interview study was conducted with 12 secondary school students, 6 students operating with each of 2 different multiplicative concepts. These concepts are based on how students coordinate composite units. Students participated in two 45-minute interviews and completed a written fractions assessment. Students operating with the second multiplicative concept had not constructed fractional numbers, but students operating with the third multiplicative concept had; students operating with the second multiplicative concept represented multiplicatively related unknowns in qualitatively different ways than students operating with the third multiplicative concept. A facilitative link is proposed between the construction of fractional numbers and how students represent multiplicatively related unknowns.

KW - Algebraic reasoning

KW - Fractional knowledge

KW - Iterative fraction scheme

KW - Middle school students

KW - Multiplicative concept

KW - Quantitative reasoning

KW - Unknowns

UR - http://www.scopus.com/inward/record.url?scp=84927133061&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927133061&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84927133061

VL - 46

SP - 196

EP - 243

JO - Journal for Research in Mathematics Education

JF - Journal for Research in Mathematics Education

SN - 0021-8251

IS - 2

ER -