Relationships between students' fractional knowledge and equation writing

Amy J. Hackenberg, Mi Lee

Research output: Contribution to journalArticlepeer-review

39 Scopus citations

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
DOIs
StatePublished - 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

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