We present a replication study of one of the most renowned seminal works in the field of mathematics education, i.e., the Fischbein et al. (1985) study on implicit models of multiplication and division in solving word problems. The original instrument was administered to a sample of 902 grade 7 students, proposing some methodological variations. The discussion focuses on four items involving partitive division of integer numbers, and results are compared to the original study: the main results of the original study are confirmed, but we contribute further with considerations on the statistical significance of differences observed in item difficulty. Finally, through our new methodological approach, we broaden the results of the original study by analysing students’ behaviour on the basis of their general arithmetical problem-solving ability. Students with medium-level ability are more influenced by the primitive model than those with lower ability.

Primitive Model of Partitive Division: A Replication of the Fischbein et al. Study / Chiara Giberti; Andrea Maffia. - In: IMPLEMENTATION AND REPLICATION STUDIES IN MATHEMATICS EDUCATION. - ISSN 2667-0127. - ELETTRONICO. - 2:2(2022), pp. 149-173. [10.1163/26670127-bja10007]

Primitive Model of Partitive Division: A Replication of the Fischbein et al. Study

Andrea Maffia
2022

Abstract

We present a replication study of one of the most renowned seminal works in the field of mathematics education, i.e., the Fischbein et al. (1985) study on implicit models of multiplication and division in solving word problems. The original instrument was administered to a sample of 902 grade 7 students, proposing some methodological variations. The discussion focuses on four items involving partitive division of integer numbers, and results are compared to the original study: the main results of the original study are confirmed, but we contribute further with considerations on the statistical significance of differences observed in item difficulty. Finally, through our new methodological approach, we broaden the results of the original study by analysing students’ behaviour on the basis of their general arithmetical problem-solving ability. Students with medium-level ability are more influenced by the primitive model than those with lower ability.
2022
Primitive Model of Partitive Division: A Replication of the Fischbein et al. Study / Chiara Giberti; Andrea Maffia. - In: IMPLEMENTATION AND REPLICATION STUDIES IN MATHEMATICS EDUCATION. - ISSN 2667-0127. - ELETTRONICO. - 2:2(2022), pp. 149-173. [10.1163/26670127-bja10007]
Chiara Giberti; Andrea Maffia
File in questo prodotto:
File Dimensione Formato  
PaperGibertiMaffia_Revised_final.pdf

accesso aperto

Tipo: Postprint
Licenza: Licenza per accesso libero gratuito
Dimensione 618.06 kB
Formato Adobe PDF
618.06 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/901508
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact