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Title:           Exploring the role of assumptions in mathematical modeling teacher training using Fermi problems
Subject:         ZDM – Mathematics Education, https://doi.org/10.1007/s11858-025-01677-0
Author:          Lluís Albarracín 
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     Item: 
      Title: Exploring the role of assumptions in mathematical modeling teacher training using Fermi problems
      Children: 
       Item: 
        Title: Abstract
       Item: 
        Title: 1 Introduction
       Item: 
        Title: 2 Background, theoretical foundation and research questions
        Children: 
         Item: 
          Title: 2.1 Mathematical modeling
         Item: 
          Title: 2.2 Research on assumptions in educational research on mathematical modeling
         Item: 
          Title: 2.3 Fermi problems as mathematical modeling activities
         Item: 
          Title: 2.4 Fermi problems activity templates
         Item: 
          Title: 2.5 Theoretical framework and research question
       Item: 
        Title: 3 Methodology
        Children: 
         Item: 
          Title: 3.1 Settings of the study, participants, design and data collected
         Item: 
          Title: 3.2 Analysis
          Children: 
           Item: 
            Title: 3.2.1 The complexity of the solution
           Item: 
            Title: 3.2.2 The quality of assumptions
           Item: 
            Title: 3.2.3 The FPAT activities
           Item: 
            Title: 3.2.4 Examples of data and analysis
       Item: 
        Title: 4 Results
        Children: 
         Item: 
          Title: 4.1 The complexity of the solutions
         Item: 
          Title: 4.2 The quality of the assumptions made
         Item: 
          Title: 4.3 Activities proposed in the FPATs
       Item: 
        Title: 5 Discussion and conclusions
       Item: 
        Title: References
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                  <pdfaSchema:namespaceURI>http://prismstandard.org/namespaces/basic/2.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>prism</pdfaSchema:prefix>
                  <pdfaSchema:schema>Prism Schema</pdfaSchema:schema>
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                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>This element provides the url for an article or unit of content. The attribute platform is optionally allowed for situations in which multiple URLs must be specified. PRISM recommends that a subset of the PCV platform values, namely “mobile” and “web”, be used in conjunction with this element. NOTE: PRISM recommends against the use of the #other value allowed in the PRISM Platform controlled vocabulary. In lieu of using #other please reach out to the PRISM group at prism-wg@yahoogroups.com to request addition of your term to the Platform Controlled Vocabulary.</pdfaProperty:description>
                           <pdfaProperty:name>url</pdfaProperty:name>
                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The Digital Object Identifier for the article.&#xA;The DOI may also be used as the dc:identifier. If used as a dc:identifier, the URI form should be captured, and the bare identifier should also be captured using prism:doi. If an alternate unique identifier is used as the required dc:identifier, then the DOI should be specified as a bare identifier within prism:doi only. If the URL associated with a DOI is to be specified, then prism:url may be used in conjunction with prism:doi in order to provide the service endpoint (i.e. the URL). </pdfaProperty:description>
                           <pdfaProperty:name>doi</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>ISSN for an electronic version of the issue in which the resource occurs. Permits publishers to include a second ISSN, identifying an electronic version of the issue in which the resource occurs (therefore e(lectronic)Issn. If used, prism:eIssn MUST contain the ISSN of the electronic version.</pdfaProperty:description>
                           <pdfaProperty:name>issn</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Volume number</pdfaProperty:description>
                           <pdfaProperty:name>volume</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Issue number</pdfaProperty:description>
                           <pdfaProperty:name>number</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Starting page</pdfaProperty:description>
                           <pdfaProperty:name>startingPage</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Ending page</pdfaProperty:description>
                           <pdfaProperty:name>endingPage</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>The aggregation type specifies the unit of aggregation for a content collection. Comment PRISM recommends that the PRISM Aggregation Type Controlled Vocabulary be used to provide values for this element. Note: PRISM recommends against the use of the #other value currently allowed in this controlled vocabulary. In lieu of using #other please reach out to the PRISM group at info@prismstandard.org to request addition of your term to the Aggregation Type Controlled Vocabulary. </pdfaProperty:description>
                           <pdfaProperty:name>aggregationType</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Title of the magazine, or other publication, in which a resource was/will be published. Typically this will be used to provide the name of the magazine an article appeared in as metadata for the article, along with information such as the article title, the publisher, volume, number, and cover date. Note: Publication name can be used to differentiate between a print magazine and the online version if the names are different such as “magazine” and “magazine.com.”</pdfaProperty:description>
                           <pdfaProperty:name>publicationName</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Copyright</pdfaProperty:description>
                           <pdfaProperty:name>copyright</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
                        </rdf:li>
                     </rdf:Seq>
                  </pdfaSchema:property>
               </rdf:li>
               <rdf:li rdf:parseType="Resource">
                  <pdfaSchema:namespaceURI>http://ns.adobe.com/pdf/1.3/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>pdf</pdfaSchema:prefix>
                  <pdfaSchema:schema>Adobe PDF Schema</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>A name object indicating whether the document has been modified to include trapping information</pdfaProperty:description>
                           <pdfaProperty:name>Trapped</pdfaProperty:name>
                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                  <pdfaSchema:schema>XMP Media Management Schema</pdfaSchema:schema>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>UUID based identifier for specific incarnation of a document</pdfaProperty:description>
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                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>The common identifier for all versions and renditions of a document.</pdfaProperty:description>
                           <pdfaProperty:name>DocumentID</pdfaProperty:name>
                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>The common identifier for all versions and renditions of a document.</pdfaProperty:description>
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                           <pdfaProperty:valueType>URI</pdfaProperty:valueType>
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                           <pdfaProperty:description>A reference to the original document from which this one is derived. It is a minimal reference; missing components can be assumed to be unchanged. For example, a new version might only need to specify the instance ID and version number of the previous version, or a rendition might only need to specify the instance ID and rendition class of the original.</pdfaProperty:description>
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                           <pdfaProperty:valueType>ResourceRef</pdfaProperty:valueType>
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                        <rdf:li rdf:parseType="Resource">
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                           <pdfaType:type>Part</pdfaType:type>
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                  <pdfaSchema:prefix>pdfaid</pdfaSchema:prefix>
                  <pdfaSchema:schema>PDF/A ID Schema</pdfaSchema:schema>
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                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Part of PDF/A standard</pdfaProperty:description>
                           <pdfaProperty:name>part</pdfaProperty:name>
                           <pdfaProperty:valueType>Integer</pdfaProperty:valueType>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Amendment of PDF/A standard</pdfaProperty:description>
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                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>Conformance level of PDF/A standard</pdfaProperty:description>
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                           <pdfaProperty:valueType>Text</pdfaProperty:valueType>
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               </rdf:li>
               <rdf:li rdf:parseType="Resource">
                  <pdfaSchema:schema>Springer Nature ORCID Schema</pdfaSchema:schema>
                  <pdfaSchema:namespaceURI>http://springernature.com/ns/xmpExtensions/2.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>sn</pdfaSchema:prefix>
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                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Author information: contains the name of each author and his/her ORCiD (ORCiD: Open Researcher and Contributor ID). An ORCiD is a persistent identifier (a non-proprietary alphanumeric code) to uniquely identify scientific and other academic authors.</pdfaProperty:description>
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                           <pdfaType:prefix>author</pdfaType:prefix>
                           <pdfaType:description>Specifies the types of author information: name and ORCID of an author.</pdfaType:description>
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                                    <pdfaField:name>name</pdfaField:name>
                                    <pdfaField:valueType>Text</pdfaField:valueType>
                                    <pdfaField:description>Gives the name of an author.</pdfaField:description>
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                                    <pdfaField:valueType>URI</pdfaField:valueType>
                                    <pdfaField:description>Gives the ORCID of an author.</pdfaField:description>
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                  <pdfaSchema:prefix>xmpTPg</pdfaSchema:prefix>
                  <pdfaSchema:schema>XMP Paged-Text</pdfaSchema:schema>
                  <pdfaSchema:property>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>XMP08 Spec: An ordered array of plate names that are needed to print the document (including any in contained documents).</pdfaProperty:description>
                           <pdfaProperty:name>PlateNames</pdfaProperty:name>
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                           <pdfaProperty:category>internal</pdfaProperty:category>
                           <pdfaProperty:description>A structure containing the characteristics of a font used in a document</pdfaProperty:description>
                           <pdfaProperty:name>Fonts</pdfaProperty:name>
                           <pdfaProperty:valueType>Bag Font</pdfaProperty:valueType>
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                  <pdfaSchema:valueType>
                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaType:description>A structure containing the characteristics of a font used in a document.</pdfaType:description>
                           <pdfaType:namespaceURI>http://ns.adobe.com/xap/1.0/sType/Font#</pdfaType:namespaceURI>
                           <pdfaType:prefix>stFnt</pdfaType:prefix>
                           <pdfaType:type>Font</pdfaType:type>
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                  <pdfaSchema:namespaceURI>http://www.niso.org/schemas/jav/1.0/</pdfaSchema:namespaceURI>
                  <pdfaSchema:prefix>jav</pdfaSchema:prefix>
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                     <rdf:Seq>
                        <rdf:li rdf:parseType="Resource">
                           <pdfaProperty:category>external</pdfaProperty:category>
                           <pdfaProperty:description>Values for Journal Article Version are one of the following:&#xA;AO = Author’s Original&#xA;SMUR = Submitted Manuscript Under Review&#xA;AM = Accepted Manuscript&#xA;P = Proof&#xA;VoR = Version of Record&#xA;CVoR = Corrected Version of Record&#xA;EVoR = Enhanced Version of Record</pdfaProperty:description>
                           <pdfaProperty:name>journal_article_version</pdfaProperty:name>
                           <pdfaProperty:valueType>Closed Choice of Text</pdfaProperty:valueType>
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