<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" 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" xml:lang="ru"><front><journal-meta><journal-id journal-id-type="publisher-id">ellibs</journal-id><journal-title-group><journal-title xml:lang="ru">Электронные библиотеки</journal-title><trans-title-group xml:lang="en"><trans-title>Russian Digital Libraries Journal</trans-title></trans-title-group></journal-title-group><issn pub-type="epub">1562-5419</issn><publisher><publisher-name>Казанский (Приволжский) федеральный университет</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26907/1562-5419-2019-22-5-287-295</article-id><article-id custom-type="elpub" pub-id-type="custom">ellibs-116</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>Статьи</subject></subj-group></article-categories><title-group><article-title>From mistakes, we learn: teachers` positional framing toward errors in mathematical classrooms</article-title><trans-title-group xml:lang="en"><trans-title>From mistakes, we learn: teachers` positional framing toward errors in mathematical classrooms</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Alvidrez</surname><given-names>M.</given-names></name></name-alternatives><email xlink:type="simple">mouratt@utep.edu</email></contrib></contrib-group><pub-date pub-type="collection"><year>2019</year></pub-date><pub-date pub-type="epub"><day>28</day><month>10</month><year>2019</year></pub-date><volume>22</volume><issue>5</issue><fpage>287</fpage><lpage>295</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Alvidrez M., 2019</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="ru">Alvidrez M.</copyright-holder><copyright-holder xml:lang="en">Alvidrez M.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://ellibs.elpub.ru/jour/article/view/116">https://ellibs.elpub.ru/jour/article/view/116</self-uri><trans-abstract xml:lang="en"><p>The productive status of errors is discussed in Mexico and the US mathematics education reforms. However, teachers’ positionings toward mistakes may or may not converge with this productive status. For that reason, reflecting on teachers’ positioning during the teaching and learning process is crucial (Stooksberry et al., 2009). This study examines teachers’ positional framing during teacher and students’ moment-to-moment interaction in the context of errors occurring in the classroom. Findings reveled two opposite error frames that teachers used to address errors in their classrooms. One of these frames provided student support for using errors as tools for their learning. On the contrary, the other provided an idea of student incapacity to cope with errors.
</p></trans-abstract><kwd-group xml:lang="en"><kwd>disposition</kwd><kwd>positioning</kwd><kwd>errors</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Ayres P.L. Systematic mathematical errors and cognitive load. Contemporary Educational Psychology, 2001, 26(2), P. 227–248.</mixed-citation><mixed-citation xml:lang="en">Ayres P.L. Systematic mathematical errors and cognitive load. Contemporary Educational Psychology, 2001, 26(2), P. 227–248.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Beyers J. Student dispositions with respect to mathematics: What current literature says. Motivation and disposition: Pathways to learning mathematics, 2011, P. 69–79.</mixed-citation><mixed-citation xml:lang="en">Beyers J. Student dispositions with respect to mathematics: What current literature says. Motivation and disposition: Pathways to learning mathematics, 2011, P. 69–79.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Booth J.L., Lange K.E., Koedinger K.R., and Newton K.J. Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 2013, 25, P. 24–34.</mixed-citation><mixed-citation xml:lang="en">Booth J.L., Lange K.E., Koedinger K.R., and Newton K.J. Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 2013, 25, P. 24–34.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Borasi R. Exploring mathematics through the analysis of errors. For the Learning of Mathematics, 1987, 7(3), P. 2–8.</mixed-citation><mixed-citation xml:lang="en">Borasi R. Exploring mathematics through the analysis of errors. For the Learning of Mathematics, 1987, 7(3), P. 2–8.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Borasi R. Capitalizing on errors as “springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education, 1994, P. 166–208.</mixed-citation><mixed-citation xml:lang="en">Borasi R. Capitalizing on errors as “springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education, 1994, P. 166–208.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Brousseau G. Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990, 2006, Vol. 19. Springer Science &amp; Business Media.</mixed-citation><mixed-citation xml:lang="en">Brousseau G. Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990, 2006, Vol. 19. Springer Science &amp; Business Media.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Creswell J.W., Plano Clark V.L., Gutmann M.L., and Hanson W.E. Advanced mixed methods research designs. Handbook of mixed methods in social and behavioral research, 2003, 209, P. 240.</mixed-citation><mixed-citation xml:lang="en">Creswell J.W., Plano Clark V.L., Gutmann M.L., and Hanson W.E. Advanced mixed methods research designs. Handbook of mixed methods in social and behavioral research, 2003, 209, P. 240.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Del Puerto S.M., Minnaard C., and Seminara S.A. Análisis de los errores: una valiosa fuente de información acerca del aprendizaje de las Matemáticas. Revista Iberoamericana de Educación, 2006, 4, P. 38.</mixed-citation><mixed-citation xml:lang="en">Del Puerto S.M., Minnaard C., and Seminara S.A. Análisis de los errores: una valiosa fuente de información acerca del aprendizaje de las Matemáticas. Revista Iberoamericana de Educación, 2006, 4, P. 38.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Gojak L.M. The power of a good mistake. NCTM Summing Up, 2013, http://www. nctm. org/about/content. aspx.</mixed-citation><mixed-citation xml:lang="en">Gojak L.M. The power of a good mistake. NCTM Summing Up, 2013, http://www. nctm. org/about/content. aspx.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Greeno J.G. A theory bite on contextualizing, framing, and positioning: A companion to Son and Goldstone. Cognition and Instruction, 2009, 27(3), P. 269–275.</mixed-citation><mixed-citation xml:lang="en">Greeno J.G. A theory bite on contextualizing, framing, and positioning: A companion to Son and Goldstone. Cognition and Instruction, 2009, 27(3), P. 269–275.</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Hammer D., Elby A., Scherr R.E., and Redish E.F. Resources, framing, and transfer. Transfer of learning from a modern multidisciplinary perspective, 2005, 89.</mixed-citation><mixed-citation xml:lang="en">Hammer D., Elby A., Scherr R.E., and Redish E.F. Resources, framing, and transfer. Transfer of learning from a modern multidisciplinary perspective, 2005, 89.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Harré R. The discursive turn in social psychology. The handbook of discourse analysis, 2001, P. 688–706.</mixed-citation><mixed-citation xml:lang="en">Harré R. The discursive turn in social psychology. The handbook of discourse analysis, 2001, P. 688–706.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Harré R. and Slocum N. Disputes as complex social events on the uses of positioning theory. Common Knowledge, 2003, 9(1), P. 100–118.</mixed-citation><mixed-citation xml:lang="en">Harré R. and Slocum N. Disputes as complex social events on the uses of positioning theory. Common Knowledge, 2003, 9(1), P. 100–118.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">Morse J.M. Approaches to qualitative-quantitative methodological triangulation. Nursing Research, 1991, 40(2), P. 120–123.</mixed-citation><mixed-citation xml:lang="en">Morse J.M. Approaches to qualitative-quantitative methodological triangulation. Nursing Research, 1991, 40(2), P. 120–123.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Santagata R. and Bray W. Professional development processes that promote teacher change: the case of a video-based program focused on leveraging students’ mathematical errors. Professional Development in Education, 2016, 42(4), P. 547–568.</mixed-citation><mixed-citation xml:lang="en">Santagata R. and Bray W. Professional development processes that promote teacher change: the case of a video-based program focused on leveraging students’ mathematical errors. Professional Development in Education, 2016, 42(4), P. 547–568.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Schleppenbach M., Flevares L.M., Sims L.M., and Perry M. Teachers’ responses to student mistakes in Chinese and US mathematics classrooms. The Elementary School Journal, 2007, 108(2), P. 131–147.</mixed-citation><mixed-citation xml:lang="en">Schleppenbach M., Flevares L.M., Sims L.M., and Perry M. Teachers’ responses to student mistakes in Chinese and US mathematics classrooms. The Elementary School Journal, 2007, 108(2), P. 131–147.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Steuer G., Rosentritt-Brunn G., and Dresel M. Dealing with errors in mathematics classrooms: Structure and relevance of perceived error climate. Contemporary Educational Psychology, 2013, 38(3), P. 196–210.</mixed-citation><mixed-citation xml:lang="en">Steuer G., Rosentritt-Brunn G., and Dresel M. Dealing with errors in mathematics classrooms: Structure and relevance of perceived error climate. Contemporary Educational Psychology, 2013, 38(3), P. 196–210.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Stooksberry L.M., Schussler D.L., and Bercaw L.A. Conceptualizing dispositions: Intellectual, cultural, and moral domains of teaching. Teachers and Teaching: theory and practice, 2009, 15(6), 719–736.</mixed-citation><mixed-citation xml:lang="en">Stooksberry L.M., Schussler D.L., and Bercaw L.A. Conceptualizing dispositions: Intellectual, cultural, and moral domains of teaching. Teachers and Teaching: theory and practice, 2009, 15(6), 719–736.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Tulis M. Error management behavior in classrooms: Teachers' responses to student mistakes. Teaching and Teacher Education, 2013, 33, P. 56–68.</mixed-citation><mixed-citation xml:lang="en">Tulis M. Error management behavior in classrooms: Teachers' responses to student mistakes. Teaching and Teacher Education, 2013, 33, P. 56–68.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Zimmerman B.J., Moylan A., Hudesman J., White N., and Flugman B. Enhancing self-reflection and mathematics achievement of at-risk urban technical college students. Psychological Test and Assessment Modeling, 2011, 53(1), P. 141–160.</mixed-citation><mixed-citation xml:lang="en">Zimmerman B.J., Moylan A., Hudesman J., White N., and Flugman B. Enhancing self-reflection and mathematics achievement of at-risk urban technical college students. Psychological Test and Assessment Modeling, 2011, 53(1), P. 141–160.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
