Development of the process conception of function View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1992-06

AUTHORS

Daniel Breidenbach, Ed Dubinsky, Julie Hawks, Devilyna Nichols

ABSTRACT

Our goal in this paper is to make two points. First, college students, even those who have taken a fair number of mathematics courses, do not have much of an understanding of the function concept; and second, an epistemological theory we have been developing points to an instructional treatment, using computers, that results in substantial improvements for many students. They seem to develop a process conception of function and are able to use it to do mathematics. After an introductory section we outline, in Section 2, our theoretical epistemology in general and indicate how it applies to the function concept in particular. In Sections 3, 4, and 5 we provide specific details on this study and describe the development of the function concept that appeared to take place in the students that we are considering. In Section 6 we interpret the results and draw some conclusions. More... »

PAGES

247-285

References to SciGraph publications

  • 1976. Piaget’s Theory in PIAGET AND HIS SCHOOL
  • 1991. Constructive Aspects of Reflective Abstraction in Advanced Mathematics in EPISTEMOLOGICAL FOUNDATIONS OF MATHEMATICAL EXPERIENCE
  • 1977. Epistemology and Psychology of Functions in NONE
  • Journal

    TITLE

    Educational Studies in Mathematics

    ISSUE

    3

    VOLUME

    23

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02309532

    DOI

    http://dx.doi.org/10.1007/bf02309532

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1021341987


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/1302", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Curriculum and Pedagogy", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/13", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Education", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "familyName": "Breidenbach", 
            "givenName": "Daniel", 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Purdue University", 
              "id": "https://www.grid.ac/institutes/grid.169077.e", 
              "name": [
                "Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Dubinsky", 
            "givenName": "Ed", 
            "id": "sg:person.016413461715.34", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016413461715.34"
            ], 
            "type": "Person"
          }, 
          {
            "familyName": "Hawks", 
            "givenName": "Julie", 
            "type": "Person"
          }, 
          {
            "familyName": "Nichols", 
            "givenName": "Devilyna", 
            "id": "sg:person.07625672501.18", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07625672501.18"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-3-642-46323-5_2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1007869091", 
              "https://doi.org/10.1007/978-3-642-46323-5_2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-1-4612-3178-3_9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015598624", 
              "https://doi.org/10.1007/978-1-4612-3178-3_9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://app.dimensions.ai/details/publication/pub.1032615320", 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-010-9321-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032615320", 
              "https://doi.org/10.1007/978-94-010-9321-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-94-010-9321-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032615320", 
              "https://doi.org/10.1007/978-94-010-9321-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/749068", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070668017"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/749441", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070668245"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3102/00346543060001001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070970129"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3102/00346543060001001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1070970129"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1109/9780470546550.ch1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1086102122"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1992-06", 
        "datePublishedReg": "1992-06-01", 
        "description": "Our goal in this paper is to make two points. First, college students, even those who have taken a fair number of mathematics courses, do not have much of an understanding of the function concept; and second, an epistemological theory we have been developing points to an instructional treatment, using computers, that results in substantial improvements for many students. They seem to develop a process conception of function and are able to use it to do mathematics. After an introductory section we outline, in Section 2, our theoretical epistemology in general and indicate how it applies to the function concept in particular. In Sections 3, 4, and 5 we provide specific details on this study and describe the development of the function concept that appeared to take place in the students that we are considering. In Section 6 we interpret the results and draw some conclusions.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/bf02309532", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136108", 
            "issn": [
              "0013-1954", 
              "1573-0816"
            ], 
            "name": "Educational Studies in Mathematics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "23"
          }
        ], 
        "name": "Development of the process conception of function", 
        "pagination": "247-285", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "65af02fa6dd3c92d7186b2f7379eab710973526822b06f91fddf9a3156e7cfeb"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf02309532"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1021341987"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf02309532", 
          "https://app.dimensions.ai/details/publication/pub.1021341987"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T12:54", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000364_0000000364/records_72866_00000000.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1007/BF02309532"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02309532'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02309532'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02309532'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02309532'


     

    This table displays all metadata directly associated to this object as RDF triples.

    103 TRIPLES      21 PREDICATES      35 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf02309532 schema:about anzsrc-for:13
    2 anzsrc-for:1302
    3 schema:author Nf279937cb73b4567ab511b9b2a32269f
    4 schema:citation sg:pub.10.1007/978-1-4612-3178-3_9
    5 sg:pub.10.1007/978-3-642-46323-5_2
    6 sg:pub.10.1007/978-94-010-9321-7
    7 https://app.dimensions.ai/details/publication/pub.1032615320
    8 https://doi.org/10.1109/9780470546550.ch1
    9 https://doi.org/10.2307/749068
    10 https://doi.org/10.2307/749441
    11 https://doi.org/10.3102/00346543060001001
    12 schema:datePublished 1992-06
    13 schema:datePublishedReg 1992-06-01
    14 schema:description Our goal in this paper is to make two points. First, college students, even those who have taken a fair number of mathematics courses, do not have much of an understanding of the function concept; and second, an epistemological theory we have been developing points to an instructional treatment, using computers, that results in substantial improvements for many students. They seem to develop a process conception of function and are able to use it to do mathematics. After an introductory section we outline, in Section 2, our theoretical epistemology in general and indicate how it applies to the function concept in particular. In Sections 3, 4, and 5 we provide specific details on this study and describe the development of the function concept that appeared to take place in the students that we are considering. In Section 6 we interpret the results and draw some conclusions.
    15 schema:genre research_article
    16 schema:inLanguage en
    17 schema:isAccessibleForFree false
    18 schema:isPartOf N469d642689094acbaf41ef23854ee5b3
    19 Nf509e40e47374f3abe3c080fec292a26
    20 sg:journal.1136108
    21 schema:name Development of the process conception of function
    22 schema:pagination 247-285
    23 schema:productId N40e94440ad5f421e8429678f0e67b574
    24 N67398821959041c89e377e7a5d1c995d
    25 N674b0af4e7bd4d7abde3966c5f38ff8e
    26 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021341987
    27 https://doi.org/10.1007/bf02309532
    28 schema:sdDatePublished 2019-04-11T12:54
    29 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    30 schema:sdPublisher N2e118b7b7688461f8c3d92724ad01a24
    31 schema:url http://link.springer.com/10.1007/BF02309532
    32 sgo:license sg:explorer/license/
    33 sgo:sdDataset articles
    34 rdf:type schema:ScholarlyArticle
    35 N1d5f34d1e68e4929bbd2eea5a71bac7d schema:familyName Breidenbach
    36 schema:givenName Daniel
    37 rdf:type schema:Person
    38 N2e118b7b7688461f8c3d92724ad01a24 schema:name Springer Nature - SN SciGraph project
    39 rdf:type schema:Organization
    40 N345c41d6ffe04a719e1612a0eb9654de rdf:first sg:person.016413461715.34
    41 rdf:rest N5cfbc261b45545448e3829183a29111a
    42 N40e94440ad5f421e8429678f0e67b574 schema:name doi
    43 schema:value 10.1007/bf02309532
    44 rdf:type schema:PropertyValue
    45 N469d642689094acbaf41ef23854ee5b3 schema:issueNumber 3
    46 rdf:type schema:PublicationIssue
    47 N5cfbc261b45545448e3829183a29111a rdf:first N9c330acfbfc246fcbc426edc2f608197
    48 rdf:rest Nc8a2db976f954222b12f0314ab99781a
    49 N67398821959041c89e377e7a5d1c995d schema:name dimensions_id
    50 schema:value pub.1021341987
    51 rdf:type schema:PropertyValue
    52 N674b0af4e7bd4d7abde3966c5f38ff8e schema:name readcube_id
    53 schema:value 65af02fa6dd3c92d7186b2f7379eab710973526822b06f91fddf9a3156e7cfeb
    54 rdf:type schema:PropertyValue
    55 N9c330acfbfc246fcbc426edc2f608197 schema:familyName Hawks
    56 schema:givenName Julie
    57 rdf:type schema:Person
    58 Nc8a2db976f954222b12f0314ab99781a rdf:first sg:person.07625672501.18
    59 rdf:rest rdf:nil
    60 Nf279937cb73b4567ab511b9b2a32269f rdf:first N1d5f34d1e68e4929bbd2eea5a71bac7d
    61 rdf:rest N345c41d6ffe04a719e1612a0eb9654de
    62 Nf509e40e47374f3abe3c080fec292a26 schema:volumeNumber 23
    63 rdf:type schema:PublicationVolume
    64 anzsrc-for:13 schema:inDefinedTermSet anzsrc-for:
    65 schema:name Education
    66 rdf:type schema:DefinedTerm
    67 anzsrc-for:1302 schema:inDefinedTermSet anzsrc-for:
    68 schema:name Curriculum and Pedagogy
    69 rdf:type schema:DefinedTerm
    70 sg:journal.1136108 schema:issn 0013-1954
    71 1573-0816
    72 schema:name Educational Studies in Mathematics
    73 rdf:type schema:Periodical
    74 sg:person.016413461715.34 schema:affiliation https://www.grid.ac/institutes/grid.169077.e
    75 schema:familyName Dubinsky
    76 schema:givenName Ed
    77 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016413461715.34
    78 rdf:type schema:Person
    79 sg:person.07625672501.18 schema:familyName Nichols
    80 schema:givenName Devilyna
    81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07625672501.18
    82 rdf:type schema:Person
    83 sg:pub.10.1007/978-1-4612-3178-3_9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1015598624
    84 https://doi.org/10.1007/978-1-4612-3178-3_9
    85 rdf:type schema:CreativeWork
    86 sg:pub.10.1007/978-3-642-46323-5_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007869091
    87 https://doi.org/10.1007/978-3-642-46323-5_2
    88 rdf:type schema:CreativeWork
    89 sg:pub.10.1007/978-94-010-9321-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032615320
    90 https://doi.org/10.1007/978-94-010-9321-7
    91 rdf:type schema:CreativeWork
    92 https://app.dimensions.ai/details/publication/pub.1032615320 schema:CreativeWork
    93 https://doi.org/10.1109/9780470546550.ch1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1086102122
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.2307/749068 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070668017
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.2307/749441 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070668245
    98 rdf:type schema:CreativeWork
    99 https://doi.org/10.3102/00346543060001001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070970129
    100 rdf:type schema:CreativeWork
    101 https://www.grid.ac/institutes/grid.169077.e schema:alternateName Purdue University
    102 schema:name Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA
    103 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...