### 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 language | English (US) |
---|---|

Pages (from-to) | 196-243 |

Number of pages | 48 |

Journal | Journal for Research in Mathematics Education |

Volume | 46 |

Issue number | 2 |

State | Published - Mar 1 2015 |

### Fingerprint

### 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

*Journal for Research in Mathematics Education*,

*46*(2), 196-243.

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

Research output: Contribution to journal › Article

*Journal for Research in Mathematics Education*, vol. 46, no. 2, pp. 196-243.

}

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 -