Students’ distributive reasoning with fractions and unknowns

Amy J. Hackenberg, Mi Lee

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students’ fractional knowledge and algebraic reasoning are explored.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalEducational Studies in Mathematics
DOIs
StateAccepted/In press - May 24 2016

Fingerprint

Reasoning
Unknown
Multiplicative
student
Unit
Sharing
interview
Fractional
Composite
Concepts
lack
school
Relationships
Awareness

Keywords

  • Algebraic reasoning
  • Distributive partitioning scheme
  • Distributive property
  • Distributive reasoning
  • Fractional knowledge
  • Multiplicative concepts
  • Unknowns

ASJC Scopus subject areas

  • Mathematics(all)
  • Social Sciences(all)

Cite this

Students’ distributive reasoning with fractions and unknowns. / Hackenberg, Amy J.; Lee, Mi.

In: Educational Studies in Mathematics , 24.05.2016, p. 1-19.

Research output: Contribution to journalArticle

@article{55b19627fef14f03902a72fed2d3f177,
title = "Students’ distributive reasoning with fractions and unknowns",
abstract = "To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students’ fractional knowledge and algebraic reasoning are explored.",
keywords = "Algebraic reasoning, Distributive partitioning scheme, Distributive property, Distributive reasoning, Fractional knowledge, Multiplicative concepts, Unknowns",
author = "Hackenberg, {Amy J.} and Mi Lee",
year = "2016",
month = "5",
day = "24",
doi = "10.1007/s10649-016-9704-9",
language = "English (US)",
pages = "1--19",
journal = "Educational Studies in Mathematics",
issn = "0013-1954",
publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Students’ distributive reasoning with fractions and unknowns

AU - Hackenberg, Amy J.

AU - Lee, Mi

PY - 2016/5/24

Y1 - 2016/5/24

N2 - To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students’ fractional knowledge and algebraic reasoning are explored.

AB - To understand relationships between students’ quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite units (units of units). Students participated in two 45-min semi-structured interviews and completed a written fraction assessment. This paper reports on how 12 students operating with the second and third multiplicative concepts demonstrated distributive reasoning in equal sharing problems and in taking fractions of unknowns. Students operating with the second multiplicative concept who demonstrated distributive reasoning appeared to lack awareness of the results of their reasoning, while students operating with the third multiplicative concept demonstrated this awareness and the construction of more advanced distributive reasoning when they worked with unknowns. Implications for relationships between students’ fractional knowledge and algebraic reasoning are explored.

KW - Algebraic reasoning

KW - Distributive partitioning scheme

KW - Distributive property

KW - Distributive reasoning

KW - Fractional knowledge

KW - Multiplicative concepts

KW - Unknowns

UR - http://www.scopus.com/inward/record.url?scp=84969969877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84969969877&partnerID=8YFLogxK

U2 - 10.1007/s10649-016-9704-9

DO - 10.1007/s10649-016-9704-9

M3 - Article

AN - SCOPUS:84969969877

SP - 1

EP - 19

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

SN - 0013-1954

ER -