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Students' Tendency To Assume Resemblances between a Function and Its Derivative.

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Title: Students' Tendency To Assume Resemblances between a Function and Its Derivative.
Language: English
Authors: Nemirovsky, Ricardo, Rubin, Andee, TERC Communications, Cambridge, MA.
Availability: TERC Communications, 2067 Massachusetts Avenue, Cambridge, MA 02140 ($5).
Peer Reviewed: N
Page Count: 42
Publication Date: 1992
Sponsoring Agency: National Science Foundation, Washington, DC.
Document Type: Reports - Research
Descriptors: Air Flow, Calculus, Cognitive Development, Cognitive Processes, Cognitive Style, College Mathematics, Computer Assisted Instruction, Concept Formation, Discovery Learning, Discovery Processes, Functions (Mathematics), Interviews, Learning Processes, Mathematics Education, Motion, Qualitative Research, Secondary Education
Abstract: This study was designed to determine students' abilities and difficulties in articulating the relationship between function and derivative. High-school students were presented 15 problems during two 75-minute interviews in which they were asked to construct functions experimentally in three different contexts: motion, fluids, and number-change. In each of the environments the students utilized tools, ranging from computer software to manipulative materials, that enabled them to generate functions. Analysis of the interviews indicated that students had the tendency to assume resemblances between the behavior or appearance of the function and its derivative in all three contexts. Three types of cues that activated resemblances in the predicted functions were identified: syntactic, semantic, and linguistic. Approaches that students used to move from the derivative to the function and vice-versa are described. A case study of one 17-minute episode of a student working with an airflow device describes the evolution of one such approach. The report concluded that the construction of such an approach was complex and that tools to explore the mathematical ideas helped frame the interviewer/student discourse through which the approach was developed. (MDH)
Entry Date: 1993
Accession Number: ED351193
Database: ERIC
FullText Text:
  Availability: 0
CustomLinks:
  – Url: https://eric.ed.gov/contentdelivery/servlet/ERICServlet?accno=ED351193
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  Data: Students' Tendency To Assume Resemblances between a Function and Its Derivative.
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  Data: <searchLink fieldCode="AR" term="%22Nemirovsky%2C+Ricardo%22">Nemirovsky, Ricardo</searchLink><br /><searchLink fieldCode="AR" term="%22Rubin%2C+Andee%22">Rubin, Andee</searchLink><br /><searchLink fieldCode="AR" term="%22TERC+Communications%2C+Cambridge%2C+MA%2E%22">TERC Communications, Cambridge, MA.</searchLink>
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  Label: Availability
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  Data: TERC Communications, 2067 Massachusetts Avenue, Cambridge, MA 02140 ($5).
– Name: PeerReviewed
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  Data: N
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  Data: 42
– Name: DatePubCY
  Label: Publication Date
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  Data: 1992
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  Label: Sponsoring Agency
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  Data: National Science Foundation, Washington, DC.
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  Data: Reports - Research
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  Data: <searchLink fieldCode="DE" term="%22Air+Flow%22">Air Flow</searchLink><br /><searchLink fieldCode="DE" term="%22Calculus%22">Calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Development%22">Cognitive Development</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Processes%22">Cognitive Processes</searchLink><br /><searchLink fieldCode="DE" term="%22Cognitive+Style%22">Cognitive Style</searchLink><br /><searchLink fieldCode="DE" term="%22College+Mathematics%22">College Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Assisted+Instruction%22">Computer Assisted Instruction</searchLink><br /><searchLink fieldCode="DE" term="%22Concept+Formation%22">Concept Formation</searchLink><br /><searchLink fieldCode="DE" term="%22Discovery+Learning%22">Discovery Learning</searchLink><br /><searchLink fieldCode="DE" term="%22Discovery+Processes%22">Discovery Processes</searchLink><br /><searchLink fieldCode="DE" term="%22Functions+%28Mathematics%29%22">Functions (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Interviews%22">Interviews</searchLink><br /><searchLink fieldCode="DE" term="%22Learning+Processes%22">Learning Processes</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+Education%22">Mathematics Education</searchLink><br /><searchLink fieldCode="DE" term="%22Motion%22">Motion</searchLink><br /><searchLink fieldCode="DE" term="%22Qualitative+Research%22">Qualitative Research</searchLink><br /><searchLink fieldCode="DE" term="%22Secondary+Education%22">Secondary Education</searchLink>
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  Data: This study was designed to determine students' abilities and difficulties in articulating the relationship between function and derivative. High-school students were presented 15 problems during two 75-minute interviews in which they were asked to construct functions experimentally in three different contexts: motion, fluids, and number-change. In each of the environments the students utilized tools, ranging from computer software to manipulative materials, that enabled them to generate functions. Analysis of the interviews indicated that students had the tendency to assume resemblances between the behavior or appearance of the function and its derivative in all three contexts. Three types of cues that activated resemblances in the predicted functions were identified: syntactic, semantic, and linguistic. Approaches that students used to move from the derivative to the function and vice-versa are described. A case study of one 17-minute episode of a student working with an airflow device describes the evolution of one such approach. The report concluded that the construction of such an approach was complex and that tools to explore the mathematical ideas helped frame the interviewer/student discourse through which the approach was developed. (MDH)
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  Data: 1993
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  Data: ED351193
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  BibEntity:
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 42
    Subjects:
      – SubjectFull: Air Flow
        Type: general
      – SubjectFull: Calculus
        Type: general
      – SubjectFull: Cognitive Development
        Type: general
      – SubjectFull: Cognitive Processes
        Type: general
      – SubjectFull: Cognitive Style
        Type: general
      – SubjectFull: College Mathematics
        Type: general
      – SubjectFull: Computer Assisted Instruction
        Type: general
      – SubjectFull: Concept Formation
        Type: general
      – SubjectFull: Discovery Learning
        Type: general
      – SubjectFull: Discovery Processes
        Type: general
      – SubjectFull: Functions (Mathematics)
        Type: general
      – SubjectFull: Interviews
        Type: general
      – SubjectFull: Learning Processes
        Type: general
      – SubjectFull: Mathematics Education
        Type: general
      – SubjectFull: Motion
        Type: general
      – SubjectFull: Qualitative Research
        Type: general
      – SubjectFull: Secondary Education
        Type: general
    Titles:
      – TitleFull: Students' Tendency To Assume Resemblances between a Function and Its Derivative.
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            NameFull: TERC Communications, Cambridge, MA.
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            NameFull: Nemirovsky, Ricardo
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              Type: published
              Y: 1992
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