<?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>2215-3470</journal-id>
<journal-title><![CDATA[Uniciencia]]></journal-title>
<abbrev-journal-title><![CDATA[Uniciencia]]></abbrev-journal-title>
<issn>2215-3470</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional, Costa Rica]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2215-34702021000100090</article-id>
<article-id pub-id-type="doi">10.15359/ru.35-1.6</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Conocimiento de profesores de matemáticas en formación sobre los productos notables]]></article-title>
<article-title xml:lang="en"><![CDATA[Knowledge of prospective mathematics teachers on notable products]]></article-title>
<article-title xml:lang="pt"><![CDATA[Conhecimento dos professores de matemáticas em formação sobre os produtos notáveis]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Graciano-Barragan]]></surname>
<given-names><![CDATA[Judith]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Escuela Secundaria General 46 &#8220;Ignacio Zaragoza&#8221; Secretaría de Educación Pública ]]></institution>
<addr-line><![CDATA[Jalisco ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma de Querétaro Facultad de Ingeniería ]]></institution>
<addr-line><![CDATA[ Santiago de Querétaro]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2021</year>
</pub-date>
<volume>35</volume>
<numero>1</numero>
<fpage>90</fpage>
<lpage>107</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S2215-34702021000100090&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S2215-34702021000100090&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S2215-34702021000100090&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen La presente investigación indaga sobre el conocimiento de futuros profesores de matemáticas en relación con los productos notables. El estudio de corte cualitativo y descriptivo se desarrolla con estudiantes universitarios que cursan un programa de formación de profesores de matemáticas para el nivel bachillerato. Se utilizaron criterios de análisis relativos al Conocimiento Matemático para la Enseñanza como elementos teóricos que permitieron, a partir de la aplicación de un cuestionario, analizar los conocimientos manifestados por los profesores en formación. Se proporciona evidencia de la actividad matemática que realizan los estudiantes para profesor, al resolver tareas que involucran a los productos notables y su enseñanza. Los resultados informan de las inconsistencias en los conocimientos de los futuros docentes y sobre las fortalezas que manifiestan en los subdominios del Conocimiento Matemático para la Enseñanza, lo que permite establecer áreas de desarrollo en su formación.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This paper studies preservice math teachers' knowledge regarding notable products. The qualitative and descriptive study is conducted with university students in a program for high school mathematics teachers. The theoretical elements used were analysis criteria related to Mathematical Knowledge for Teaching. This theoretical foundation allowed the analysis of the preservice teachers' knowledge through a questionnaire. The paper presents evidence of the mathematical activity of preservice teachers when solving tasks and lessons involving notable products. Results report the inconsistencies in preservice teachers' knowledge and the strengths that they manifest in the subdomains of Mathematical Knowledge for Teaching. These results suggest areas of development necessary for teacher training.]]></p></abstract>
<abstract abstract-type="short" xml:lang="pt"><p><![CDATA[Resumo Esta pesquisa investiga o conhecimento de futuros professores de matemática em relação a produtos notáveis. O estudo qualitativo e descritivo é realizado com estudantes universitários que cursam um programa de formação de professores de matemática para o nível de bacharelado. Foram utilizados critérios de análise relacionados ao Conhecimento Matemático para o Ensino como elementos teóricos que permitiram, a partir da aplicação de um questionário, analisar o conhecimento manifestado pelos professores em formação. É fornecida evidência da atividade matemática que os alunos para professor realizam ao resolver tarefas que envolvem produtos notáveis e seu ensino. Os resultados informam as inconsistências no conhecimento de futuros professores e sobre as fortalezas que manifestam nos subdomínios do Conhecimento Matemático para o Ensino, o que permite estabelecer áreas de desenvolvimento em sua formação.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[conocimiento matemático para la enseñanza]]></kwd>
<kwd lng="es"><![CDATA[formación de profesores]]></kwd>
<kwd lng="es"><![CDATA[producto notable]]></kwd>
<kwd lng="es"><![CDATA[educación matemática]]></kwd>
<kwd lng="es"><![CDATA[futuros docentes]]></kwd>
<kwd lng="es"><![CDATA[conocimiento matemático]]></kwd>
<kwd lng="en"><![CDATA[mathematical knowledge for teaching]]></kwd>
<kwd lng="en"><![CDATA[mathematics education]]></kwd>
<kwd lng="en"><![CDATA[teacher training]]></kwd>
<kwd lng="en"><![CDATA[notable product]]></kwd>
<kwd lng="en"><![CDATA[preservice teachers]]></kwd>
<kwd lng="en"><![CDATA[knowledge of mathematics]]></kwd>
<kwd lng="pt"><![CDATA[conhecimento matemático para o ensino]]></kwd>
<kwd lng="pt"><![CDATA[formação de professores]]></kwd>
<kwd lng="pt"><![CDATA[produto notável]]></kwd>
<kwd lng="pt"><![CDATA[educação matemática]]></kwd>
<kwd lng="pt"><![CDATA[futuros professores]]></kwd>
<kwd lng="pt"><![CDATA[conhecimentos de matemática]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Lubienski]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Research on Teaching mathematics: The unsolve problema of teachers&#8217; mathematical knowledge]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Richarson]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
</person-group>
<source><![CDATA[Hanbook of research on teaching]]></source>
<year>2001</year>
<volume>4</volume>
<page-range>433-56</page-range><publisher-loc><![CDATA[New York, USA ]]></publisher-loc>
<publisher-name><![CDATA[Macmilian]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Thames]]></surname>
<given-names><![CDATA[M. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Phelps]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Content knowledge for teaching. What makes it special?]]></article-title>
<source><![CDATA[Journal of Teacher Education]]></source>
<year>2008</year>
<volume>59</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>389-407</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chang]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Tsai]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An alternative Approach for the Learning of (a+b)2= a2+2ab+b2.]]></article-title>
<source><![CDATA[The 3er East Asia Regional Conference in Mathematics Education]]></source>
<year>2005</year>
</nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Creswell]]></surname>
<given-names><![CDATA[J. W.]]></given-names>
</name>
</person-group>
<source><![CDATA[Research Design: qualitative, quantitative, and mixed methods approaches]]></source>
<year>2009</year>
<edition>3.ª ed.</edition>
<publisher-loc><![CDATA[Londres ]]></publisher-loc>
<publisher-name><![CDATA[Sage]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Dolores]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[La formación de profesores de matemáticas en México desde el currículum oficial]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Dolores]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[García]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Sosa]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Matemática educativa: la formación de profesores]]></source>
<year>2013</year>
<page-range>13-25</page-range><publisher-loc><![CDATA[Guerrero, México ]]></publisher-loc>
<publisher-name><![CDATA[Díaz de Santos Ediciones, S. A.]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godino]]></surname>
<given-names><![CDATA[J. D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Categorías de análisis de los conocimientos del profesor de matemáticas]]></article-title>
<source><![CDATA[Revista Iberoamericana de Educación Matemática]]></source>
<year>2009</year>
<numero>20</numero>
<issue>20</issue>
<page-range>13-31</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gómez-Chacón]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Tendencias y retos en formación de profesores en Matemáticas. Vivir el presente y crear futuro en la cooperación Europa-Latinoamérica]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Gómez-Chacón]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Planchart]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Educación matemática y formación de profesores]]></source>
<year>2005</year>
<page-range>15-32</page-range><publisher-loc><![CDATA[Bilbao, España ]]></publisher-loc>
<publisher-name><![CDATA[Universidad de Deusto]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Graciano]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Aké]]></surname>
<given-names><![CDATA[L. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conocimiento común y especializado de productos notables de los futuros profesores de matemáticas]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Serna]]></surname>
<given-names><![CDATA[Luis Arturo]]></given-names>
</name>
</person-group>
<source><![CDATA[Acta latinoamericana de matemática educativa]]></source>
<year>2017</year>
<page-range>1320-9</page-range><publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Comité Latinoamericano de Matemática Educativa]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Graciano]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Aké]]></surname>
<given-names><![CDATA[L. P.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Conocimiento matemático para la enseñanza de productos notables: un estudio de tres casos]]></article-title>
<source><![CDATA[Revista Electrónica Investigación e Innovación en Matemática Educativa]]></source>
<year>2019</year>
<volume>4</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>192-201</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Schilling]]></surname>
<given-names><![CDATA[S. G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Unpacking Pedagogical Content Knowledge Conceptualizing and Measuring Teachers&#8217; Topic-Specific Knowledge of Students]]></article-title>
<source><![CDATA[Journal of Research in Mathematics Education]]></source>
<year>2008</year>
<volume>39</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>372-400</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hill]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Rowan]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Ball]]></surname>
<given-names><![CDATA[D. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effects of Teachers' Mathematical Knowledge for Teaching on Student Achievement]]></article-title>
<source><![CDATA[American educational research journal]]></source>
<year>2005</year>
<volume>42</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>371-406</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[León]]></surname>
<given-names><![CDATA[O. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Montero]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<source><![CDATA[Métodos de investigación en psicología y educación]]></source>
<year>2003</year>
<edition>3ª ed.</edition>
<publisher-loc><![CDATA[Madrid ]]></publisher-loc>
<publisher-name><![CDATA[McGraw-Hill]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[López]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Productos notables, factorización y ecuaciones de segundo grado con una incógnita, una propuesta didáctica para el bachillerato del colegio de ciencias y humanidades]]></source>
<year>2008</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Facultad de Estudios Superiores Acatlán, Universidad Nacional Autónoma de México]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ma]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Knowing and teaching elementary mathematics: teachers&#8217; understanding of fundamental mathematics in China and the United States]]></source>
<year>1999</year>
<publisher-loc><![CDATA[Mahwah, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Navarrete-Cazales]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Formación de profesores en las Escuelas Normales de México. Siglo XX.]]></article-title>
<source><![CDATA[Revista historia de la educación latinoamericana]]></source>
<year>2015</year>
<volume>17</volume>
<numero>25</numero>
<issue>25</issue>
<page-range>17-34</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sosa]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<source><![CDATA[Conocimiento matemático para la enseñanza en bachillerato: un estudio de dos casos]]></source>
<year>2011</year>
<publisher-loc><![CDATA[España ]]></publisher-loc>
<publisher-name><![CDATA[Facultad de Educación, Universidad de Huelva]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tzur]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Profound awareness of the learning paradox (PALP)]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Jaworski]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
<name>
<surname><![CDATA[Wood]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[The Mathematics Teacher Educator as a Developing Professional]]></source>
<year>2018</year>
<page-range>137-56</page-range><publisher-loc><![CDATA[Rotterdam, The Netherlands ]]></publisher-loc>
<publisher-name><![CDATA[Sense Publishers]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vega]]></surname>
<given-names><![CDATA[D. C.]]></given-names>
</name>
</person-group>
<source><![CDATA[Perfiles de alumnos de educación secundaria relacionados con el sentido estructural manifestado en experiencias con expresiones algebraicas]]></source>
<year>2013</year>
<publisher-name><![CDATA[Facultad de Educación, Universidad de Granada]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Vega-Gil]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Los sistemas educativos europeos y la formación de profesores. Los casos de Francia, Reino Unido, España y Finlandia]]></article-title>
<source><![CDATA[Revista de Educación]]></source>
<year>2005</year>
<numero>336</numero>
<issue>336</issue>
<page-range>169-87</page-range></nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Wu]]></surname>
<given-names><![CDATA[H. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The content knowledge mathematics teachers need]]></article-title>
<source><![CDATA[Mathematics Matters in Education]]></source>
<year>2018</year>
<page-range>pp. 43-91</page-range><publisher-loc><![CDATA[Springer ]]></publisher-loc>
<publisher-name><![CDATA[Cham]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
