From Piaget’s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2014

AUTHORS

Ilana Arnon , Jim Cottrill , Ed Dubinsky , Asuman Oktaç , Solange Roa Fuentes , María Trigueros , Kirk Weller

ABSTRACT

The aim of this chapter is to explain where APOS Theory came from and when it originated. A discussion of the main components of APOS Theory—the mental stages or structures of Action, Process, Object, and Schema and the mental mechanisms of interiorization, coordination, reversal, encapsulation, and thematization—points to when they first came on the scene and how their meanings developed. The published research of those involved in the development of APOS Theory, which includes some early colleagues and students of Dubinsky as well as those who were members of the Research in Undergraduate Mathematics Education Community (RUMEC), is described. The descriptions in this chapter are very brief and will be expanded in later chapters. More... »

PAGES

5-15

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4614-7966-6_2

DOI

http://dx.doi.org/10.1007/978-1-4614-7966-6_2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1013421800


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "name": [
            "College of Education, Givat Washington Academic, Tel Aviv, Israel"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Arnon", 
        "givenName": "Ilana", 
        "id": "sg:person.013535443771.50", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013535443771.50"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Ohio Dominican University", 
          "id": "https://www.grid.ac/institutes/grid.423067.4", 
          "name": [
            "Department of Mathematics, Ohio Dominican University, Columbus, Ohio, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cottrill", 
        "givenName": "Jim", 
        "id": "sg:person.014172555236.68", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014172555236.68"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Miami", 
          "id": "https://www.grid.ac/institutes/grid.26790.3a", 
          "name": [
            "School of Education, University of Miami, Miami, Florida, 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"
      }, 
      {
        "affiliation": {
          "alternateName": "Instituto Polit\u00e9cnico Nacional", 
          "id": "https://www.grid.ac/institutes/grid.418275.d", 
          "name": [
            "Departamento de Matem\u00e1tica Educativa, Cinvestav-IPN, Mexico City, Mexico"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Okta\u00e7", 
        "givenName": "Asuman", 
        "id": "sg:person.014135507725.80", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014135507725.80"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Industrial University of Santander", 
          "id": "https://www.grid.ac/institutes/grid.411595.d", 
          "name": [
            "Escuela de Matem\u00e1ticas, Universidad Industrial de Santander, Bucaramanga, Colombia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Fuentes", 
        "givenName": "Solange Roa", 
        "id": "sg:person.014733070325.21", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014733070325.21"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico", 
          "id": "https://www.grid.ac/institutes/grid.454349.b", 
          "name": [
            "Departamento de Matem\u00e1ticas, Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico, Col. Tizap\u00e1n, San Angel, Mexico"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Trigueros", 
        "givenName": "Mar\u00eda", 
        "id": "sg:person.07736257147.62", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07736257147.62"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Ferris State University", 
          "id": "https://www.grid.ac/institutes/grid.255908.3", 
          "name": [
            "Department of Mathematics, Ferris State University, Big Rapids, Michigan, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Weller", 
        "givenName": "Kirk", 
        "id": "sg:person.011331220147.55", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011331220147.55"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/s0732-3123(97)90028-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000070728"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0732-3123(97)90029-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002829160"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10649-005-2531-z", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008344527", 
          "https://doi.org/10.1007/s10649-005-2531-z"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10649-005-2531-z", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008344527", 
          "https://doi.org/10.1007/s10649-005-2531-z"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/0020739830140305", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011947520"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00305619", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012824368", 
          "https://doi.org/10.1007/bf00305619"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00305619", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012824368", 
          "https://doi.org/10.1007/bf00305619"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1080/14926150902817381", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025981405", 
          "https://doi.org/10.1080/14926150902817381"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1026693753", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-017-2193-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026693753", 
          "https://doi.org/10.1007/978-94-017-2193-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-017-2193-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026693753", 
          "https://doi.org/10.1007/978-94-017-2193-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00302715", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028982638", 
          "https://doi.org/10.1007/bf00302715"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00302715", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028982638", 
          "https://doi.org/10.1007/bf00302715"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0732-3123(97)90015-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030212131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1159/000271225", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031445469"
        ], 
        "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://app.dimensions.ai/details/publication/pub.1037158969", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-3592-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037158969", 
          "https://doi.org/10.1007/978-1-4612-3592-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-3592-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037158969", 
          "https://doi.org/10.1007/978-1-4612-3592-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/0-306-47203-1_7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1037990507", 
          "https://doi.org/10.1007/0-306-47203-1_7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/10511979908965918", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038638039"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0732-3123(96)90015-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044235623"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.laa.2009.06.034", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044343493"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10649-005-0473-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046693607", 
          "https://doi.org/10.1007/s10649-005-0473-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10649-005-0473-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046693607", 
          "https://doi.org/10.1007/s10649-005-0473-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1017998922475", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050738006", 
          "https://doi.org/10.1023/a:1017998922475"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0732-3123(97)90012-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050870058"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1080/14926156.2011.570612", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051801976", 
          "https://doi.org/10.1080/14926156.2011.570612"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/2687114", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1070059805"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/749441", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1070668245"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/749505", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1070668277"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/749887", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1070668513"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/cbmath/006/01", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089185099"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/cbmath/008/05", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089185123"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/cbmath/012/05", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089185217"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/cbmath/016/05", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089185284"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/cbo9781139013536.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089380412"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2014", 
    "datePublishedReg": "2014-01-01", 
    "description": "The aim of this chapter is to explain where APOS Theory came from and when it originated. A discussion of the main components of APOS Theory\u2014the mental stages or structures of Action, Process, Object, and Schema and the mental mechanisms of interiorization, coordination, reversal, encapsulation, and thematization\u2014points to when they first came on the scene and how their meanings developed. The published research of those involved in the development of APOS Theory, which includes some early colleagues and students of Dubinsky as well as those who were members of the Research in Undergraduate Mathematics Education Community (RUMEC), is described. The descriptions in this chapter are very brief and will be expanded in later chapters.", 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-1-4614-7966-6_2", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-1-4614-7965-9", 
        "978-1-4614-7966-6"
      ], 
      "name": "APOS Theory", 
      "type": "Book"
    }, 
    "name": "From Piaget\u2019s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory", 
    "pagination": "5-15", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4614-7966-6_2"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "3ff059d67bdcf1362dd5e31a60b1f497380e7cd3fb1de7548fa7be2d29b3ef62"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1013421800"
        ]
      }
    ], 
    "publisher": {
      "location": "New York, NY", 
      "name": "Springer New York", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4614-7966-6_2", 
      "https://app.dimensions.ai/details/publication/pub.1013421800"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T18:09", 
    "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/v90/0000000001_0000000264/records_8681_00000251.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-1-4614-7966-6_2"
  }
]
 

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.10.1007/978-1-4614-7966-6_2'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4614-7966-6_2'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4614-7966-6_2'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4614-7966-6_2'


 

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

222 TRIPLES      22 PREDICATES      58 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4614-7966-6_2 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N1350d5fa7e404d56951e200bb07a4659
4 schema:citation sg:pub.10.1007/0-306-47203-1_7
5 sg:pub.10.1007/978-1-4612-3592-7
6 sg:pub.10.1007/978-94-010-9321-7
7 sg:pub.10.1007/978-94-017-2193-6
8 sg:pub.10.1007/bf00302715
9 sg:pub.10.1007/bf00305619
10 sg:pub.10.1007/s10649-005-0473-0
11 sg:pub.10.1007/s10649-005-2531-z
12 sg:pub.10.1023/a:1017998922475
13 sg:pub.10.1080/14926150902817381
14 sg:pub.10.1080/14926156.2011.570612
15 https://app.dimensions.ai/details/publication/pub.1026693753
16 https://app.dimensions.ai/details/publication/pub.1032615320
17 https://app.dimensions.ai/details/publication/pub.1037158969
18 https://doi.org/10.1016/j.laa.2009.06.034
19 https://doi.org/10.1016/s0732-3123(96)90015-2
20 https://doi.org/10.1016/s0732-3123(97)90012-2
21 https://doi.org/10.1016/s0732-3123(97)90015-8
22 https://doi.org/10.1016/s0732-3123(97)90028-6
23 https://doi.org/10.1016/s0732-3123(97)90029-8
24 https://doi.org/10.1017/cbo9781139013536.004
25 https://doi.org/10.1080/0020739830140305
26 https://doi.org/10.1080/10511979908965918
27 https://doi.org/10.1090/cbmath/006/01
28 https://doi.org/10.1090/cbmath/008/05
29 https://doi.org/10.1090/cbmath/012/05
30 https://doi.org/10.1090/cbmath/016/05
31 https://doi.org/10.1159/000271225
32 https://doi.org/10.2307/2687114
33 https://doi.org/10.2307/749441
34 https://doi.org/10.2307/749505
35 https://doi.org/10.2307/749887
36 schema:datePublished 2014
37 schema:datePublishedReg 2014-01-01
38 schema:description The aim of this chapter is to explain where APOS Theory came from and when it originated. A discussion of the main components of APOS Theory—the mental stages or structures of Action, Process, Object, and Schema and the mental mechanisms of interiorization, coordination, reversal, encapsulation, and thematization—points to when they first came on the scene and how their meanings developed. The published research of those involved in the development of APOS Theory, which includes some early colleagues and students of Dubinsky as well as those who were members of the Research in Undergraduate Mathematics Education Community (RUMEC), is described. The descriptions in this chapter are very brief and will be expanded in later chapters.
39 schema:genre chapter
40 schema:inLanguage en
41 schema:isAccessibleForFree false
42 schema:isPartOf Nde9f54f6fd8f497bbfa60840fbd75d98
43 schema:name From Piaget’s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory
44 schema:pagination 5-15
45 schema:productId N23539f37006f42efa662772700d46a15
46 Nbba7fa1108f74e63bdc13b383d22a82a
47 Nd64c5c7cde1747a7a82555cf19e28dbb
48 schema:publisher N7523fdf52a0e4251a4f44a4e14bedddc
49 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013421800
50 https://doi.org/10.1007/978-1-4614-7966-6_2
51 schema:sdDatePublished 2019-04-15T18:09
52 schema:sdLicense https://scigraph.springernature.com/explorer/license/
53 schema:sdPublisher N832d834d46024d85b6639988fefe1a52
54 schema:url http://link.springer.com/10.1007/978-1-4614-7966-6_2
55 sgo:license sg:explorer/license/
56 sgo:sdDataset chapters
57 rdf:type schema:Chapter
58 N1350d5fa7e404d56951e200bb07a4659 rdf:first sg:person.013535443771.50
59 rdf:rest N4dada52fe5124d7ead841b0e1ffa30a3
60 N23539f37006f42efa662772700d46a15 schema:name readcube_id
61 schema:value 3ff059d67bdcf1362dd5e31a60b1f497380e7cd3fb1de7548fa7be2d29b3ef62
62 rdf:type schema:PropertyValue
63 N33fd2200e4914aefaddbe5dc205b5482 rdf:first sg:person.014733070325.21
64 rdf:rest Nc254c0d857cf4bd09e7ecf8e7bbac044
65 N4dada52fe5124d7ead841b0e1ffa30a3 rdf:first sg:person.014172555236.68
66 rdf:rest N7878b59736de454fb1ffdffcb64ce828
67 N603fa2e6197240b48bb90f8039ebdfe4 rdf:first sg:person.011331220147.55
68 rdf:rest rdf:nil
69 N7523fdf52a0e4251a4f44a4e14bedddc schema:location New York, NY
70 schema:name Springer New York
71 rdf:type schema:Organisation
72 N7878b59736de454fb1ffdffcb64ce828 rdf:first sg:person.016413461715.34
73 rdf:rest N92c1be27898748e198a92e474c10e6b7
74 N832d834d46024d85b6639988fefe1a52 schema:name Springer Nature - SN SciGraph project
75 rdf:type schema:Organization
76 N8f35c57df76c4e7a8c8fc556bdd84754 schema:name College of Education, Givat Washington Academic, Tel Aviv, Israel
77 rdf:type schema:Organization
78 N92c1be27898748e198a92e474c10e6b7 rdf:first sg:person.014135507725.80
79 rdf:rest N33fd2200e4914aefaddbe5dc205b5482
80 Nbba7fa1108f74e63bdc13b383d22a82a schema:name dimensions_id
81 schema:value pub.1013421800
82 rdf:type schema:PropertyValue
83 Nc254c0d857cf4bd09e7ecf8e7bbac044 rdf:first sg:person.07736257147.62
84 rdf:rest N603fa2e6197240b48bb90f8039ebdfe4
85 Nd64c5c7cde1747a7a82555cf19e28dbb schema:name doi
86 schema:value 10.1007/978-1-4614-7966-6_2
87 rdf:type schema:PropertyValue
88 Nde9f54f6fd8f497bbfa60840fbd75d98 schema:isbn 978-1-4614-7965-9
89 978-1-4614-7966-6
90 schema:name APOS Theory
91 rdf:type schema:Book
92 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
93 schema:name Mathematical Sciences
94 rdf:type schema:DefinedTerm
95 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
96 schema:name Pure Mathematics
97 rdf:type schema:DefinedTerm
98 sg:person.011331220147.55 schema:affiliation https://www.grid.ac/institutes/grid.255908.3
99 schema:familyName Weller
100 schema:givenName Kirk
101 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011331220147.55
102 rdf:type schema:Person
103 sg:person.013535443771.50 schema:affiliation N8f35c57df76c4e7a8c8fc556bdd84754
104 schema:familyName Arnon
105 schema:givenName Ilana
106 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013535443771.50
107 rdf:type schema:Person
108 sg:person.014135507725.80 schema:affiliation https://www.grid.ac/institutes/grid.418275.d
109 schema:familyName Oktaç
110 schema:givenName Asuman
111 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014135507725.80
112 rdf:type schema:Person
113 sg:person.014172555236.68 schema:affiliation https://www.grid.ac/institutes/grid.423067.4
114 schema:familyName Cottrill
115 schema:givenName Jim
116 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014172555236.68
117 rdf:type schema:Person
118 sg:person.014733070325.21 schema:affiliation https://www.grid.ac/institutes/grid.411595.d
119 schema:familyName Fuentes
120 schema:givenName Solange Roa
121 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014733070325.21
122 rdf:type schema:Person
123 sg:person.016413461715.34 schema:affiliation https://www.grid.ac/institutes/grid.26790.3a
124 schema:familyName Dubinsky
125 schema:givenName Ed
126 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016413461715.34
127 rdf:type schema:Person
128 sg:person.07736257147.62 schema:affiliation https://www.grid.ac/institutes/grid.454349.b
129 schema:familyName Trigueros
130 schema:givenName María
131 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07736257147.62
132 rdf:type schema:Person
133 sg:pub.10.1007/0-306-47203-1_7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037990507
134 https://doi.org/10.1007/0-306-47203-1_7
135 rdf:type schema:CreativeWork
136 sg:pub.10.1007/978-1-4612-3592-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037158969
137 https://doi.org/10.1007/978-1-4612-3592-7
138 rdf:type schema:CreativeWork
139 sg:pub.10.1007/978-94-010-9321-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032615320
140 https://doi.org/10.1007/978-94-010-9321-7
141 rdf:type schema:CreativeWork
142 sg:pub.10.1007/978-94-017-2193-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026693753
143 https://doi.org/10.1007/978-94-017-2193-6
144 rdf:type schema:CreativeWork
145 sg:pub.10.1007/bf00302715 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028982638
146 https://doi.org/10.1007/bf00302715
147 rdf:type schema:CreativeWork
148 sg:pub.10.1007/bf00305619 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012824368
149 https://doi.org/10.1007/bf00305619
150 rdf:type schema:CreativeWork
151 sg:pub.10.1007/s10649-005-0473-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046693607
152 https://doi.org/10.1007/s10649-005-0473-0
153 rdf:type schema:CreativeWork
154 sg:pub.10.1007/s10649-005-2531-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1008344527
155 https://doi.org/10.1007/s10649-005-2531-z
156 rdf:type schema:CreativeWork
157 sg:pub.10.1023/a:1017998922475 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050738006
158 https://doi.org/10.1023/a:1017998922475
159 rdf:type schema:CreativeWork
160 sg:pub.10.1080/14926150902817381 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025981405
161 https://doi.org/10.1080/14926150902817381
162 rdf:type schema:CreativeWork
163 sg:pub.10.1080/14926156.2011.570612 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051801976
164 https://doi.org/10.1080/14926156.2011.570612
165 rdf:type schema:CreativeWork
166 https://app.dimensions.ai/details/publication/pub.1026693753 schema:CreativeWork
167 https://app.dimensions.ai/details/publication/pub.1032615320 schema:CreativeWork
168 https://app.dimensions.ai/details/publication/pub.1037158969 schema:CreativeWork
169 https://doi.org/10.1016/j.laa.2009.06.034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044343493
170 rdf:type schema:CreativeWork
171 https://doi.org/10.1016/s0732-3123(96)90015-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044235623
172 rdf:type schema:CreativeWork
173 https://doi.org/10.1016/s0732-3123(97)90012-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050870058
174 rdf:type schema:CreativeWork
175 https://doi.org/10.1016/s0732-3123(97)90015-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030212131
176 rdf:type schema:CreativeWork
177 https://doi.org/10.1016/s0732-3123(97)90028-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000070728
178 rdf:type schema:CreativeWork
179 https://doi.org/10.1016/s0732-3123(97)90029-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002829160
180 rdf:type schema:CreativeWork
181 https://doi.org/10.1017/cbo9781139013536.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089380412
182 rdf:type schema:CreativeWork
183 https://doi.org/10.1080/0020739830140305 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011947520
184 rdf:type schema:CreativeWork
185 https://doi.org/10.1080/10511979908965918 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038638039
186 rdf:type schema:CreativeWork
187 https://doi.org/10.1090/cbmath/006/01 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089185099
188 rdf:type schema:CreativeWork
189 https://doi.org/10.1090/cbmath/008/05 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089185123
190 rdf:type schema:CreativeWork
191 https://doi.org/10.1090/cbmath/012/05 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089185217
192 rdf:type schema:CreativeWork
193 https://doi.org/10.1090/cbmath/016/05 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089185284
194 rdf:type schema:CreativeWork
195 https://doi.org/10.1159/000271225 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031445469
196 rdf:type schema:CreativeWork
197 https://doi.org/10.2307/2687114 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070059805
198 rdf:type schema:CreativeWork
199 https://doi.org/10.2307/749441 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070668245
200 rdf:type schema:CreativeWork
201 https://doi.org/10.2307/749505 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070668277
202 rdf:type schema:CreativeWork
203 https://doi.org/10.2307/749887 schema:sameAs https://app.dimensions.ai/details/publication/pub.1070668513
204 rdf:type schema:CreativeWork
205 https://www.grid.ac/institutes/grid.255908.3 schema:alternateName Ferris State University
206 schema:name Department of Mathematics, Ferris State University, Big Rapids, Michigan, USA
207 rdf:type schema:Organization
208 https://www.grid.ac/institutes/grid.26790.3a schema:alternateName University of Miami
209 schema:name School of Education, University of Miami, Miami, Florida, USA
210 rdf:type schema:Organization
211 https://www.grid.ac/institutes/grid.411595.d schema:alternateName Industrial University of Santander
212 schema:name Escuela de Matemáticas, Universidad Industrial de Santander, Bucaramanga, Colombia
213 rdf:type schema:Organization
214 https://www.grid.ac/institutes/grid.418275.d schema:alternateName Instituto Politécnico Nacional
215 schema:name Departamento de Matemática Educativa, Cinvestav-IPN, Mexico City, Mexico
216 rdf:type schema:Organization
217 https://www.grid.ac/institutes/grid.423067.4 schema:alternateName Ohio Dominican University
218 schema:name Department of Mathematics, Ohio Dominican University, Columbus, Ohio, USA
219 rdf:type schema:Organization
220 https://www.grid.ac/institutes/grid.454349.b schema:alternateName Instituto Tecnológico Autónomo de México
221 schema:name Departamento de Matemáticas, Instituto Tecnológico Autónomo de México, Col. Tizapán, San Angel, Mexico
222 rdf:type schema:Organization
 




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


...