## 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) |
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Pages (from-to) | 196-243 |

Number of pages | 48 |

Journal | Journal for Research in Mathematics Education |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2015 |

## Keywords

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

## ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Education