<?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>1607-4041</journal-id>
<journal-title><![CDATA[Revista electrónica de investigación educativa]]></journal-title>
<abbrev-journal-title><![CDATA[REDIE]]></abbrev-journal-title>
<issn>1607-4041</issn>
<publisher>
<publisher-name><![CDATA[Universidad Autónoma de Baja California, Instituto de Investigación y Desarrollo Educativo]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1607-40412017000100110</article-id>
<article-id pub-id-type="doi">10.24320/redie.2017.19.1.971</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Tareas con diversas soluciones: estructura conceptual en profesores de matemáticas]]></article-title>
<article-title xml:lang="en"><![CDATA[Multiple-Solutions Tasks: Mathematics Teachers&#8217; Conceptual Structure]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Barrera-Mora]]></surname>
<given-names><![CDATA[Fernando]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Reyes-Rodríguez]]></surname>
<given-names><![CDATA[Aarón Víctor]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Autónoma del Estado de Hidalgo  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2017</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2017</year>
</pub-date>
<volume>19</volume>
<numero>1</numero>
<fpage>110</fpage>
<lpage>122</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1607-40412017000100110&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1607-40412017000100110&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1607-40412017000100110&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En el artículo se analizan las diferentes soluciones que un grupo de 15 profesores de matemáticas propuso para resolver un problema rutinario de aritmética, con el objetivo de identificar qué elementos específicos puede aportar el uso de tareas con múltiples soluciones para la formación y actualización docente. La posición teórica que sustenta este trabajo tiene como elemento fundamental la identificación y discusión de rutas de solución para fortalecer el conocimiento matemático y didáctico de los profesores, y favorecer el desarrollo de una postura crítica respecto a su práctica profesional.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract This paper analyzes the different solutions proposed by a group of 15 mathematics teachers to a routine arithmetic problem, with the aim of identifying the contribution provided by multiple-solution tasks in the training and continuing education of teachers. The theoretical background of this work is based on the identification and discussion of solution routes to strengthen teachers&#8217; knowledge of mathematics and didactics, in addition to promoting a critical approach to their professional practice.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Procesos de aprendizaje]]></kwd>
<kwd lng="es"><![CDATA[resolución de problemas]]></kwd>
<kwd lng="es"><![CDATA[formación de profesores]]></kwd>
<kwd lng="en"><![CDATA[Learning processes]]></kwd>
<kwd lng="en"><![CDATA[problem solving]]></kwd>
<kwd lng="en"><![CDATA[teacher education]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Multiple solutions to problems in mathematics teaching: Do teachers really value them?]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bingolbali]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Australian Journal of Teacher Education]]></source>
<year>2011</year>
<volume>36</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>18-31</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Problem solving in chinese mathematics education: research and practice]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cai]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Nie]]></surname>
<given-names><![CDATA[B.]]></given-names>
</name>
</person-group>
<source><![CDATA[ZDM Mathematics Education]]></source>
<year>2007</year>
<volume>39</volume>
<page-range>459-73</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[A cognitive analysis of problems of comprehension in learning of mathematics]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Duval]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2006</year>
<volume>61</volume>
<page-range>103-31</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fennema]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Romberg]]></surname>
<given-names><![CDATA[T. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics classroom that promote understanding]]></source>
<year>1999</year>
<publisher-loc><![CDATA[Mahwah, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Lawrence Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Gu]]></surname>
<given-names><![CDATA[L]]></given-names>
</name>
<name>
<surname><![CDATA[Huang]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Marton]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Teaching with variation: a Chinese way of promoting effective mathematics learning]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Fan]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Wong]]></surname>
<given-names><![CDATA[N.-Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Cai]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[How chinese learn mathematics: Perspectives from insiders]]></source>
<year>2004</year>
<page-range>309-47</page-range><publisher-loc><![CDATA[NJ ]]></publisher-loc>
<publisher-name><![CDATA[World Scientific]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Interesting and difficult mathematical problems: changing teachers&#8217; views by employing multiple-solution tasks]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Guberman]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Mathematics Teachers Education]]></source>
<year>2013</year>
<volume>16</volume>
<page-range>33-56</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Mathematical tasks and students cognition: Classroom-based factor that support and inhibit high level mathematical thinking and reasoning]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Henningsen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Stein]]></surname>
<given-names><![CDATA[M. K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>1997</year>
<volume>28</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>524-49</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Hiebert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Carpenter]]></surname>
<given-names><![CDATA[T. P.]]></given-names>
</name>
<name>
<surname><![CDATA[Fennema]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Fuson]]></surname>
<given-names><![CDATA[K. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Wearne]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Murray]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Olivier]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Human]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Making sense: teaching and learning mathematics with understanding]]></source>
<year>1997</year>
<publisher-loc><![CDATA[Portsmouth, NH ]]></publisher-loc>
<publisher-name><![CDATA[Heinemann]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kieran]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The false dichotomy in mathematics education between conceptual understanding and procedural skills: An example from algebra]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Leatham]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
</person-group>
<source><![CDATA[Vital directions in mathematics education research]]></source>
<year>2013</year>
<page-range>153-71</page-range><publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lamon]]></surname>
<given-names><![CDATA[S. J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Mahwah, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Lawrence Erlbaum Associates]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks]]></source>
<year>2007</year>
<conf-name><![CDATA[ FifthConference of the European Society for Research in Mathematics Education]]></conf-name>
<conf-loc> </conf-loc>
<page-range>2330-9</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning through teaching through the lens of multiple solution tasks]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Zaskis]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Learning through teaching mathematics: development of teachers&#8217; knowledge and expertise in practice]]></source>
<year>2010</year>
<page-range>69-85</page-range><publisher-loc><![CDATA[Dordrecht, Holanda ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Multiple-solution tasks: from a teacher education course to teacher practice]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[ZDM Mathematics Education]]></source>
<year>2011</year>
<volume>43</volume>
<page-range>993-1006</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Challenging mathematics with multiple solution tasks and mathematical investigations in geometry]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Silver]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Li]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Transforming mathematics instruction: Multiple approaches and practices]]></source>
<year>2014</year>
<page-range>59-80</page-range><publisher-loc><![CDATA[Cham, Alemania ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Lev]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Multiple solution tasks as a magnifying glass for observation of mathematical creativity]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Woo]]></surname>
<given-names><![CDATA[J. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Lew]]></surname>
<given-names><![CDATA[H. C.]]></given-names>
</name>
<name>
<surname><![CDATA[Park]]></surname>
<given-names><![CDATA[K. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Seo]]></surname>
<given-names><![CDATA[D. Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education]]></source>
<year>2007</year>
<volume>3</volume>
<page-range>161-8</page-range><publisher-loc><![CDATA[Seúl ]]></publisher-loc>
<publisher-name><![CDATA[PME]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Levav-Waynberg]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2007</year>
<volume>66</volume>
<page-range>349-71</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Solution spaces of multiple-solution connecting tasks as a mirror of the development of mathematics teachers&#8217; knowledge]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Leikin]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Levav-Waynberg]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Canadian Journal of Science, Mathematics and Technology Education]]></source>
<year>2008</year>
<volume>8</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>233-51</page-range></nlm-citation>
</ref>
<ref id="B18">
<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>2010</year>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Routledge]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<collab>National Council of Teachers of Mathematics</collab>
<source><![CDATA[Principles and standards for school mathematics]]></source>
<year>2000</year>
<publisher-loc><![CDATA[Reston, VA ]]></publisher-loc>
<publisher-name><![CDATA[Autor]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Polya]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
</person-group>
<source><![CDATA[How to solve it: A new aspect of mathematical method]]></source>
<year>1945</year>
<publisher-loc><![CDATA[NJ ]]></publisher-loc>
<publisher-name><![CDATA[Princeton University Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Romberg]]></surname>
<given-names><![CDATA[T. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Classroom instruction that fosters mathematical thinking and problem solving: Connections between theory and practice]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Schoenfeld]]></surname>
<given-names><![CDATA[A. H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical thinking and problem solving]]></source>
<year>1994</year>
<page-range>287-304</page-range><publisher-loc><![CDATA[Hillsdale, NJ ]]></publisher-loc>
<publisher-name><![CDATA[Lawrence Erlbaum]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rubio]]></surname>
<given-names><![CDATA[C. J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Problemas para la 20a. Olimpiada Mexicana de Matemática en San Luis Potosí]]></source>
<year>2006</year>
<publisher-loc><![CDATA[Mérida ]]></publisher-loc>
<publisher-name><![CDATA[Universidad Autónoma de Yucatán]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[An exploration of strategies used by students to solve problems with multiple ways of solution]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Santos-Trigo]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Mathematical Behavior]]></source>
<year>1996</year>
<volume>15</volume>
<page-range>263-84</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[La transferencia del conocimiento y la formulación o rediseño de problemas en el aprendizaje de las matemáticas]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Santos-Trigo]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Revista Mexicana de Investigación Educativa]]></source>
<year>1997</year>
<volume>2</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>11-30</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Santos-Trigo]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[La resolución de problemas matemáticos: fundamentos cognitivos]]></source>
<year>2007</year>
<publisher-loc><![CDATA[México ]]></publisher-loc>
<publisher-name><![CDATA[Trillas]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Innovación e investigación en educación matemática]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Santos-Trigo]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Innovación Educativa]]></source>
<year>2009</year>
<volume>9</volume>
<numero>46</numero>
<issue>46</issue>
<page-range>5-13</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schoenfeld]]></surname>
<given-names><![CDATA[A. H.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical problem solving]]></source>
<year>1985</year>
<publisher-loc><![CDATA[Orlando, FL ]]></publisher-loc>
<publisher-name><![CDATA[Academic Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schoenfeld]]></surname>
<given-names><![CDATA[A. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Grouws]]></surname>
<given-names><![CDATA[D. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Handbook of research on mathematics teaching and learning]]></source>
<year>1992</year>
<page-range>334-71</page-range><publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[Macmillan]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shimada]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Becker]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[The open ended approach: A new proposal for teaching mathematics]]></source>
<year>1997</year>
<publisher-loc><![CDATA[Reston, VA ]]></publisher-loc>
<publisher-name><![CDATA[NCTM]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Conocimiento y enseñanza: fundamentos de la nueva reforma]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Shulman]]></surname>
<given-names><![CDATA[L. S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Profesorado. Revista de currículum y formación del profesorado]]></source>
<year>2005</year>
<volume>9</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>1-30</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Fostering creativity through instruction rich in mathematical problem solving and problem posing]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Silver]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[ZDM Mathematics Education]]></source>
<year>1997</year>
<volume>29</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>75-80</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Moving from rhetoric to praxis: Issues faced by teachers in having students consider multiple solutions for problems in the mathematics classroom]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Silver]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Ghousseini]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Gosen]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Charalambous]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Font Strawhum]]></surname>
<given-names><![CDATA[B. T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal of Mathematical Behavior]]></source>
<year>2005</year>
<volume>24</volume>
<page-range>287-301</page-range></nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Silver]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Kenney]]></surname>
<given-names><![CDATA[P. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Sources of assessment information for instructional guidance in mathematics]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Romberg]]></surname>
<given-names><![CDATA[T. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Reform in school mathematics and authentic assessment]]></source>
<year>1995</year>
<page-range>38-68</page-range><publisher-loc><![CDATA[Albany ]]></publisher-loc>
<publisher-name><![CDATA[State University of New York]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Learning mathematics and learning to teach: Learning cycles in mathematics teacher education]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Simon]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1994</year>
<volume>26</volume>
<page-range>71-94</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Towards a constructivist perspective: An intervention study of mathematics teacher development]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Simon]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Schifter]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>1991</year>
<volume>22</volume>
<page-range>309-31</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Explicating the role of mathematical tasks in conceptual learning: an elaboration of the hypothetical learning trajectory]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Simon]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Tzur]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Thinking and Learning]]></source>
<year>2004</year>
<volume>6</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>91-104</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[The science of patterns]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Steen]]></surname>
<given-names><![CDATA[L. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Science]]></source>
<year>1988</year>
<volume>240</volume>
<page-range>611-6</page-range></nlm-citation>
</ref>
<ref id="B38">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Mathematical tasks as a framework for reflection: From research to practice]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stein]]></surname>
<given-names><![CDATA[M. K.]]></given-names>
</name>
<name>
<surname><![CDATA[Smith]]></surname>
<given-names><![CDATA[M. S.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematics Teaching in the Middle School]]></source>
<year>1998</year>
<volume>3</volume>
<page-range>268-75</page-range></nlm-citation>
</ref>
<ref id="B39">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Stigler]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Hiebert]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[The teaching gap: Best ideas from the world&#8217;s teachers for improving education in the classroom]]></source>
<year>1999</year>
<publisher-loc><![CDATA[Nueva York ]]></publisher-loc>
<publisher-name><![CDATA[The Free Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B40">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Multiple solution methods and multiple outcomes- is it a task for kindergarten children?]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tsamir]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Tirosh]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Tabach]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Levenson]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Educational Studies in Mathematics]]></source>
<year>2010</year>
<volume>73</volume>
<page-range>217-31</page-range></nlm-citation>
</ref>
<ref id="B41">
<nlm-citation citation-type="journal">
<article-title xml:lang=""><![CDATA[Sociomathematical norms, argumentation, and autonomy in mathematics]]></article-title>
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yackel]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Cobb]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Journal for Research in Mathematics Education]]></source>
<year>1996</year>
<volume>27</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>458-77</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
