A framework for analyzing the collaborative construction of arguments and its interplay with agency

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem...

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Vydáno v:	Educational studies in mathematics Ročník 80; číslo 3; s. 369 - 387
Hlavní autoři:	Mueller, Mary, Yankelewitz, Dina, Maher, Carolyn
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Dordrecht Springer 01.07.2012 Springer Netherlands
Témata:	After School Programs Analysis Buildings Clothing industry Collaboration Collaborative learning Communities Cooperation Education Grade 6 Influences Learning Learning Processes Mathematical Logic Mathematics Mathematics Activities Mathematics Education Mathematics teachers Problem Solving Reasoning School Activities Secondary School Mathematics Student diversity Teachers Thinking Skills Urban Areas France Mathematical arguments Problem solving Discourse Reasoning and proof Agency Collaboration
ISSN:	0013-1954, 1573-0816
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Abstract	In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and discuss their influence on the building of mathematical arguments and student agency. The framework is exemplified using data from a study of the development of mathematical reasoning in an urban sixth-grade informal after-school program.
AbstractList	In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and discuss their influence on the building of mathematical arguments and student agency. The framework is exemplified using data from a study of the development of mathematical reasoning in an urban sixth-grade informal after-school program. In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and discuss their influence on the building of mathematical arguments and student agency. The framework is exemplified using data from a study of the development of mathematical reasoning in an urban sixth-grade informal after-school program. Keywords Collaboration * Mathematical arguments * Problem solving * Reasoning and proof * Agency * Discourse
Audience	Grade 6 Secondary Education Academic
Author	Mueller, Mary Maher, Carolyn Yankelewitz, Dina
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Keywords	Mathematical arguments Problem solving Discourse Reasoning and proof Agency Collaboration
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References	YackelECobbPSociomathematical norms, argumentation, and autonomy in mathematicsJournal for Research in Mathematics Education199627445847710.2307/749877 GresalfiMMartinTHandVGreenoJConstructing competence: An analysis of student participation in the activity systems of mathematics classroomsEducational Studies in Mathematics200970497010.1007/s10649-008-9141-5 DavisBListening for differences: An evolving conception of mathematics teachingThe Journal of Mathematical Behavior1997283355376 FormanEAKilpatrickJMartinWGSchifterDA sociocultural approach to mathematics reform: Speaking, inscribing, and doing mathematics within communities of practiceA research companion to principles and standards for school mathematics2003RestonNational Council of Teachers of Mathematics333352 CobbPStephanMMcClainKGravemeijerKParticipating in classroom mathematical practicesJournal of the Learning Sciences20011011316410.1207/S15327809JLS10-1-2_6 MercerNWegerifRDawesLChildren's talk and the development of reasoning in the classroomBritish Educational Research Journal19992519510510.1080/0141192990250107 AlrøHSkovsmoseODialogue and learning in mathematics education2003DordrechtKluwer Academic Publishers GoosMLearning mathematics in a classroom community of inquiryJournal for Research in Mathematics Education200435425829110.2307/30034810 DavisBSimmtEUnderstanding learning systems: Mathematics education and complexity scienceJournal for Research in Mathematics Education200334213716710.2307/30034903 PowellABFranciscoJMMaherCAAn evolving analytical model for understanding the development of mathematical thinking using videotape dataThe Journal of Mathematical Behavior200322440543510.1016/j.jmathb.2003.09.002 Maher, C. A. (2002). How students structure heir own investigations and educate us: What we have learned from a fourteen-year study. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the twenty-sixth annual meeting of the International Group for the Psychology of Mathematics Education (PME26) (Vol. 1, pp. 31-46). Norwich, England: School of Education and Professional Development, University of East Anglia. BauersfeldHCobbPBauersfeldH“Language games” in the mathematics classroom: Their function and their effectsThe emergence of mathematical meaning: Interaction in classroom cultures1995HillsdaleLawrence Erlbaum Associates1724 CobbPGresalfiMHodgeLLAn interpretive scheme for analyzing the identities that students develop in mathematics classroomsJournal for Research in Mathematics Education20094014068 GeeJSocial linguistics and literacies: Ideology in discourses1996LondonTaylor and Francis BoalerJGreenoJGBoalerJIdentity, agency and knowing in mathematics worldsMultiple perspectives on mathematics teaching and learning2000StamfordAblex4582 HoweCJTolmieAThurstonAToppingKChristieDLivingstonKJessimanEDonaldsonCGroup work in elementary science: Towards organizational principles for supporting pupil learningLearning and Instruction20071754956310.1016/j.learninstruc.2007.09.004 Maher, C. A., Martino, A. M., & Davis, R. B. (1994). Children's different ways of thinking about fractions. Proceedings of Psychology of Mathematics Education XVIII. Lisbon, Portugal. MercerNDawesLWegerifaRSamsaCReasoning as a scientist: Ways of helping children to use language to learn scienceBritish Educational Research Journal200430335937710.1080/01411920410001689689 Alston, A., Davis, R. B., Maher, C. A., & Martino A. (1994). Children's use of alternative structures. Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education PME, (Vol. 2, pp. 208–214). Lisbon, Portugal. MercerNTalk and the development of reasoning and understandingHuman Development2008519010010.1159/000113158 Powell, A. B., & Maher, C. A. (2002). Inquiry into the interlocution of students engaged with mathematics: Appreciating links between research and practice. In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Wiegel, R. L. Bryant, & K. Nooney (Eds.), Proceedings of the twenty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Vol. 1 (pp. 317–329). Athens, Georgia. StaplesMSupporting whole-class collaborative inquiry in a secondary mathematics classroomCognition & Instruction200725226410.1080/07370000701301125 MartinLTowersJPirieSCollective mathematical understanding as improvisationMathematical Thinking and Learning20068214918310.1207/s15327833mtl0802_3 AmitMFriedMNAuthority and authority relations in mathematics education: A view from an 8th grade classroomEducational Studies in Mathematics20055814516810.1007/s10649-005-3618-2 MaherCAMuellerMFPaulisMUsing an informal learning environment to promote mathematical reasoning among middle-school studentsMathematics Bulletin2011496472 MoschkovichJExamining mathematical discourse practicesFor the Learning of Mathematics20072712430 DavisBTeaching mathematics: Toward a sound alternative1996New YorkGarland PickeringAThe mangle of practice: Time, agency, and science1995ChicagoUniversity of Chicago Press Mueller, M. (2007). A study of the development of reasoning in sixth grade students. Unpublished doctoral dissertation. Rutgers, The State University of New Jersey, New Brunswick. University. PowellABSocially emergent cognition: Particular outcome of student to-student discursive interaction during mathematical problem solvingHorizontes20062413342 CobbPContexts, goals, beliefs, and learning mathematicsFor the Learning of Mathematics19866229 LampertMCobbPKilpatrickJMartinWGSchifterDCommunication and languageA research companion to principles and standards for school mathematics2003RestonNCTM237249 National Council of Teachers of MathematicsPrinciples and standards for school mathematics20003RestonNCTM Wagner, D. (2004). Critical awareness of voice in mathematics classroom discourse: learning the steps in the “dance of agency”. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. IV (pp. 401–408). Bergen, Norway. 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References_xml	– reference: AmitMFriedMNAuthority and authority relations in mathematics education: A view from an 8th grade classroomEducational Studies in Mathematics20055814516810.1007/s10649-005-3618-2 – reference: AlrøHSkovsmoseODialogue and learning in mathematics education2003DordrechtKluwer Academic Publishers – reference: DavisBListening for differences: An evolving conception of mathematics teachingThe Journal of Mathematical Behavior1997283355376 – reference: MartinLTowersJPirieSCollective mathematical understanding as improvisationMathematical Thinking and Learning20068214918310.1207/s15327833mtl0802_3 – reference: GoosMLearning mathematics in a classroom community of inquiryJournal for Research in Mathematics Education200435425829110.2307/30034810 – reference: Alston, A., Davis, R. B., Maher, C. A., & Martino A. (1994). Children's use of alternative structures. Proceedings of the Eighteenth International Conference for the Psychology of Mathematics Education PME, (Vol. 2, pp. 208–214). Lisbon, Portugal. – reference: BauersfeldHCobbPBauersfeldH“Language games” in the mathematics classroom: Their function and their effectsThe emergence of mathematical meaning: Interaction in classroom cultures1995HillsdaleLawrence Erlbaum Associates1724 – reference: MaherCAMuellerMFPaulisMUsing an informal learning environment to promote mathematical reasoning among middle-school studentsMathematics Bulletin2011496472 – reference: Powell, A. B., & Maher, C. A. (2002). Inquiry into the interlocution of students engaged with mathematics: Appreciating links between research and practice. In D. S. Mewborn, P. Sztajn, D. Y. White, H. G. Wiegel, R. L. Bryant, & K. Nooney (Eds.), Proceedings of the twenty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Vol. 1 (pp. 317–329). Athens, Georgia. – reference: Maher, C. A., Martino, A. M., & Davis, R. B. (1994). Children's different ways of thinking about fractions. Proceedings of Psychology of Mathematics Education XVIII. Lisbon, Portugal. – reference: MoschkovichJExamining mathematical discourse practicesFor the Learning of Mathematics20072712430 – reference: CobbPGresalfiMHodgeLLAn interpretive scheme for analyzing the identities that students develop in mathematics classroomsJournal for Research in Mathematics Education20094014068 – reference: CobbPContexts, goals, beliefs, and learning mathematicsFor the Learning of Mathematics19866229 – reference: LampertMCobbPKilpatrickJMartinWGSchifterDCommunication and languageA research companion to principles and standards for school mathematics2003RestonNCTM237249 – reference: BoalerJGreenoJGBoalerJIdentity, agency and knowing in mathematics worldsMultiple perspectives on mathematics teaching and learning2000StamfordAblex4582 – reference: GresalfiMMartinTHandVGreenoJConstructing competence: An analysis of student participation in the activity systems of mathematics classroomsEducational Studies in Mathematics200970497010.1007/s10649-008-9141-5 – reference: CobbPStephanMMcClainKGravemeijerKParticipating in classroom mathematical practicesJournal of the Learning Sciences20011011316410.1207/S15327809JLS10-1-2_6 – reference: National Council of Teachers of MathematicsPrinciples and standards for school mathematics20003RestonNCTM – reference: GeeJSocial linguistics and literacies: Ideology in discourses1996LondonTaylor and Francis – reference: PowellABSocially emergent cognition: Particular outcome of student to-student discursive interaction during mathematical problem solvingHorizontes20062413342 – reference: DavisBSimmtEUnderstanding learning systems: Mathematics education and complexity scienceJournal for Research in Mathematics Education200334213716710.2307/30034903 – reference: Mueller, M. (2007). A study of the development of reasoning in sixth grade students. Unpublished doctoral dissertation. Rutgers, The State University of New Jersey, New Brunswick. University. – reference: HoweCJTolmieAThurstonAToppingKChristieDLivingstonKJessimanEDonaldsonCGroup work in elementary science: Towards organizational principles for supporting pupil learningLearning and Instruction20071754956310.1016/j.learninstruc.2007.09.004 – reference: DavisBTeaching mathematics: Toward a sound alternative1996New YorkGarland – reference: MercerNDawesLWegerifaRSamsaCReasoning as a scientist: Ways of helping children to use language to learn scienceBritish Educational Research Journal200430335937710.1080/01411920410001689689 – reference: Wagner, D. (2004). Critical awareness of voice in mathematics classroom discourse: learning the steps in the “dance of agency”. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. IV (pp. 401–408). 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A. (2002). How students structure heir own investigations and educate us: What we have learned from a fourteen-year study. In A. D. Cockburn & E. Nardi (Eds.), Proceedings of the twenty-sixth annual meeting of the International Group for the Psychology of Mathematics Education (PME26) (Vol. 1, pp. 31-46). 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Snippet	In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes...
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SubjectTerms	After School Programs Analysis Buildings Clothing industry Collaboration Collaborative learning Communities Cooperation Education Grade 6 Influences Learning Learning Processes Mathematical Logic Mathematics Mathematics Activities Mathematics Education Mathematics teachers Problem Solving Reasoning School Activities Secondary School Mathematics Student diversity Teachers Thinking Skills Urban Areas
Title	A framework for analyzing the collaborative construction of arguments and its interplay with agency
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