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"Find the Area Enclosed By..." Parceling an Especially Robust Model of Reasoning among First-Year Students

Artigo2023

Igor' Kontorovich

Metadados apenas Página oficial: "Find the Area Enclosed By..." Parceling an Especially Robust Model of Reasoning among First-Year Students (abre em nova aba)

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Resumo

Mathematics education research has been aware that calculus students can draw on single definite integrals as a model to compute areas (SImA), without minding whether the function changes its sign in the assigned interval. In this study, I take conceptual and empirical steps to understand this phenomenon in more depth. Building on Fischbein's theory, I conceptualize area as a figural concept and associate its calculation with intra-mathematical modelling routes that pass through the network of figures and integrals. To characterize these routes, I analyzed video clips that students in a large first-year service course in mathematics submitted as part of their coursework. This led to the construction of an analytical cycle explicating the models that students generated when implementing SImA. To appreciate how widespread SImA can be, I use the responses of nearly twelve thousand students in final multiple-choice exams in the same course over a decade. This analysis found that nearly thirty percent of the students chose answers that are consistent with this model of reasoning; in some exams the SImA-options were selected more frequently than the correct answers. Drawing on these findings, I make several teaching-oriented comments about the relations between areas and definite integrals.

Dados da obra

Tipo
Artigo
Periódico
International Journal of Research in Undergraduate Mathematics Education
Ano
2023
Idioma
en
Palavras-chave
College Freshmen; Mathematics Education; Thinking Skills; Content Analysis; Calculus; Mathematical Concepts
Temas
Cálculo, Modelagem Matemática
ISSN
2198-9745
Acesso
Metadados apenas
Fontes
ERIC — Education Resources Information Center
Na Biblioteca desde
01/10/2026 · verificada em 03/10/2026

Como citar

ABNT
KONTOROVICH, Igor'. "Find the Area Enclosed By..." Parceling an Especially Robust Model of Reasoning among First-Year Students. International Journal of Research in Undergraduate Mathematics Education, 2023. Disponível em: http://dx.doi.org/10.1007/s40753-023-00213-3. Acesso em: 5 nov. 2026.

APA

Kontorovich, I. (2023). "Find the Area Enclosed By..." Parceling an Especially Robust Model of Reasoning among First-Year Students. International Journal of Research in Undergraduate Mathematics Education. http://dx.doi.org/10.1007/s40753-023-00213-3

BibTeX
@article{kontorovich2023,
  author = {Kontorovich, Igor'},
  title = {"Find the Area Enclosed By..." Parceling an Especially Robust Model of Reasoning among First-Year Students},
  year = {2023},
  journal = {International Journal of Research in Undergraduate Mathematics Education},
  url = {http://dx.doi.org/10.1007/s40753-023-00213-3},
  language = {en}
}
RIS
TY  - JOUR
AU  - Kontorovich, Igor'
TI  - "Find the Area Enclosed By..." Parceling an Especially Robust Model of Reasoning among First-Year Students
PY  - 2023
JO  - International Journal of Research in Undergraduate Mathematics Education
UR  - http://dx.doi.org/10.1007/s40753-023-00213-3
LA  - en
ER  -

Referência gerada automaticamente a partir dos metadados das fontes; confira com o documento original. Baixar BibTeX · Baixar RIS

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