<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2448-8089</journal-id>
<journal-title><![CDATA[Educación matemática]]></journal-title>
<abbrev-journal-title><![CDATA[Educ. mat.]]></abbrev-journal-title>
<issn>2448-8089</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Investigación y Divulgación de la Educación Matemática A.C.; Universidad de Guadalajara]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2448-80892022000200101</article-id>
<article-id pub-id-type="doi">10.24844/em3402.04</article-id>
<title-group>
<article-title xml:lang="pt"><![CDATA[Ações do professor e desenvolvimento do raciocínio matemático durante a discussão coletiva de uma tarefa]]></article-title>
<article-title xml:lang="en"><![CDATA[Teachers&#8217; actions and mathematical reasoning development during the collective discussion of a task]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Brocardo]]></surname>
<given-names><![CDATA[Joana]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Delgado]]></surname>
<given-names><![CDATA[Catarina]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mendes]]></surname>
<given-names><![CDATA[Fátima]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ponte]]></surname>
<given-names><![CDATA[João Pedro da]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Politécnico de Setúbal Escola Superior de Educação Departamento de Ciências e Tecnologias]]></institution>
<addr-line><![CDATA[Setúbal ]]></addr-line>
<country>Portugal</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Instituto Politécnico de Setúbal Escola Superior de Educação Departamento de Ciências Sociais e Pedagogia]]></institution>
<addr-line><![CDATA[Setúbal ]]></addr-line>
<country>Portugal</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Instituto Politécnico de Setúbal Escola Superior de Educação Departamento de Ciências e Tecnologias]]></institution>
<addr-line><![CDATA[Setúbal ]]></addr-line>
<country>Portugal</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidade de Lisboa Instituto de Educação ]]></institution>
<addr-line><![CDATA[Lisboa ]]></addr-line>
<country>Portugal</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>00</month>
<year>2022</year>
</pub-date>
<volume>34</volume>
<numero>2</numero>
<fpage>101</fpage>
<lpage>133</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2448-80892022000200101&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2448-80892022000200101&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2448-80892022000200101&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo: Este artigo procura caracterizar as ações do professor em discussões coletivas que promovem o desenvolvimento do raciocínio matemático e identificar eventuais relações entre essas ações e os processos de raciocínio matemático. A par destes objetivos, pretende propor um modelo que integre características específicas destas ações e evidencie as que se relacionam com os processos de raciocínio matemático. A metodologia é interpretativa e os dados são recolhidos a partir da gravação, em vídeo, do momento de discussão coletiva de uma tarefa, numa aula de uma professora do 5.º ano de escolaridade. A análise dos dados permitiu especificar seis tipos de ações do professor associadas ao momento de trabalho na sala de aula (Convidar, Apoiar, Guiar, Desafiar, Informar e Sugerir), bem como as potencialidades de cada um deles no desenvolvimento de processos de raciocínio matemático dos alunos. Permitiu, ainda, evidenciar a inter-relação entre alguns destes tipos de ações tendo em vista esse desenvolvimento.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: This article seeks to characterize the teacher&#8217;s actions of in whole-class discussions, which promote the development of mathematical reasoning, and to identify possible relationships between these actions and mathematical reasoning processes. In addition to these aims, it intends to propose a model that integrates specific characteristics of these actions and shows those related to mathematical reasoning processes. The methodology is interpretive and the data are collected from the recording, on video, of the moment of whole-class discussion of a task, in a class of a grade 5 teacher. Data analysis allowed to specify six types of teacher actions associated with the moment of work in the classroom (Invite, Support, Guide, Challenge, Inform and Suggest), as well as the potential of each of them in the development of students&#8217; mathematical reasoning processes. It also allowed to evidence the interrelation between some of these types of actions in view of such development.]]></p></abstract>
<kwd-group>
<kwd lng="pt"><![CDATA[Ações do professor]]></kwd>
<kwd lng="pt"><![CDATA[processos de raciocínio matemático]]></kwd>
<kwd lng="pt"><![CDATA[discussões coletivas]]></kwd>
<kwd lng="pt"><![CDATA[tarefas matemáticas]]></kwd>
<kwd lng="en"><![CDATA[Teacher actions]]></kwd>
<kwd lng="en"><![CDATA[mathematical reasoning processes]]></kwd>
<kwd lng="en"><![CDATA[whole-class discussions]]></kwd>
<kwd lng="en"><![CDATA[mathematical tasks]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Bass]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Making mathematics reasonable in school]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Kilpatrick]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Martin]]></surname>
<given-names><![CDATA[W. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Schifter]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[A research companion to principles and standards for school Mathematics]]></source>
<year>2003</year>
<page-range>27-44</page-range><publisher-name><![CDATA[NCTM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Battista]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Reasoning and sense making in the mathematics classroom Grades: 3-5]]></source>
<year>2017</year>
<publisher-name><![CDATA[NCTM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Boaler]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The road to reasoning]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Brodie]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching mathematical reasoning in secondary school classrooms]]></source>
<year>2010</year>
<page-range>v-vii</page-range><publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Brodie]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching mathematical reasoning in secondary school classrooms]]></source>
<year>2010</year>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cengiz]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Kline]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Grant]]></surname>
<given-names><![CDATA[T. J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Extending students&#8217; mathematical thinking during whole-group discussions]]></article-title>
<source><![CDATA[Journal of Mathematics Teacher Education]]></source>
<year>2011</year>
<numero>14</numero>
<issue>14</issue>
<page-range>355-74</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ellis]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Özgür]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Reiten]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teacher moves for supporting student reasoning]]></article-title>
<source><![CDATA[Mathematics Education Research Journal]]></source>
<year>2018</year>
<numero>5</numero>
<issue>5</issue>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Erickson]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Qualitative methods in research on teaching]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Wittrockk]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of research on teaching]]></source>
<year>1986</year>
<edition>3rd</edition>
<page-range>119-61</page-range><publisher-name><![CDATA[MacMillan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fraivillig]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Murphy]]></surname>
<given-names><![CDATA[L. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Fuson]]></surname>
<given-names><![CDATA[K. C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Advancing children&#8217;s mathematical thinking in everyday mathematics classrooms]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>1999</year>
<volume>30</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>148-70</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jeannotte]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Kieran]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A conceptual model of mathematical reasoning for school mathematics]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2017</year>
<volume>96</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>1-16</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lampert]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching problems and the problems of teaching]]></source>
<year>2001</year>
<publisher-name><![CDATA[Yale University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lannin]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ellis]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Elliot]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Developing essential understanding of mathematical reasoning: Pre-K-Grade 8]]></source>
<year>2011</year>
<publisher-name><![CDATA[NCTM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lithner]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Principles for designing mathematical tasks that enhance imitative and creative reasoning]]></article-title>
<source><![CDATA[ZDM]]></source>
<year>2017</year>
<volume>49</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>937-49</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mata-Pereira]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ponte]]></surname>
<given-names><![CDATA[J. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Enhancing students&#8217; mathematical reasoning in the classroom: teacher actions facilitating generalization and justification]]></article-title>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2017</year>
<volume>96</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>169-86</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mata-Pereira]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ponte]]></surname>
<given-names><![CDATA[J. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Promover o raciocínio matemático dos alunos: Uma investigação baseada em design]]></article-title>
<source><![CDATA[Bolema]]></source>
<year>2018</year>
<volume>32</volume>
<numero>62</numero>
<issue>62</issue>
<page-range>781-801</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Mata-Pereira]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Ponte]]></surname>
<given-names><![CDATA[J. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teacher&#8217;s actions to promote students&#8217; justifications]]></article-title>
<source><![CDATA[Acta Scientiae]]></source>
<year>2018</year>
<volume>20</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>487-505</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<collab>NCTM</collab>
<source><![CDATA[Princípios e normas para a matemática escolar]]></source>
<year>2007</year>
<publisher-name><![CDATA[APM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="book">
<collab>NCTM</collab>
<source><![CDATA[Princípios para a ação: Assegurar a todos o sucesso em matemática]]></source>
<year>2017</year>
<publisher-name><![CDATA[APM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Oliveira]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[O raciocínio matemático à luz de uma epistemologia soft]]></article-title>
<source><![CDATA[Educação e Matemática]]></source>
<year>2008</year>
<numero>100</numero>
<issue>100</issue>
<page-range>3-9</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ponte]]></surname>
<given-names><![CDATA[J. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Mata-Pereira]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Quaresma]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Ações do professor na condução de discussões matemáticas]]></article-title>
<source><![CDATA[Quadrante]]></source>
<year>2013</year>
<volume>XXII</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>55-81</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rivera]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Becker]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Algebraic reasoning through patterns]]></article-title>
<source><![CDATA[Mathematics Teacher in the Middle School]]></source>
<year>2009</year>
<volume>15</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>213-21</page-range></nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stein]]></surname>
<given-names><![CDATA[M. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Engle]]></surname>
<given-names><![CDATA[R. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Smith]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Hughes]]></surname>
<given-names><![CDATA[E. K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell]]></article-title>
<source><![CDATA[Mathematical Thinking and Learning]]></source>
<year>2008</year>
<volume>10</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>313-40</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stylianides]]></surname>
<given-names><![CDATA[G. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Stylianides]]></surname>
<given-names><![CDATA[A. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Shilling-Traina]]></surname>
<given-names><![CDATA[L. N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Prospective teachers&#8217; challenges in teaching reasoning-and-proof]]></article-title>
<source><![CDATA[International Journal of Science and Mathematics Education]]></source>
<year>2013</year>
<volume>11</volume>
<numero>6</numero>
<issue>6</issue>
<page-range>1463-90</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wood]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Creating a context for argument in mathematics class]]></article-title>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>1999</year>
<volume>30</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>171-91</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
