본문 바로가기
KERD
논문KCI 등재

Intervening in Mathematics Group Work in the Middle Grades

0

조회

0

다운로드

1

인용

0

참고문헌

키워드

초록

Over the last three decades, there has been an increasingly strong emphasis on group-centered approaches to mathematics teaching. One primary responsibility for teachers who use group-centered instruction is to “check in”, or intervene, with groups to monitor group learning and provide mathematical support when necessary. While prior research has contributed valuable insight for successful teacher interventions in mathematics group work, there is a need for more fine-grained analyses of interactions between teachers and students. In this study, we co-conducted research with an exemplary middle grade teacher (Ms. Green) to learn about fine-grained details of her intervention practices, hoping to generate knowledge about successful teacher interventions that can be expanded, replicated, and/or contradicted in other contexts. Analyzing Ms. Green’s practices as an exemplary case, we found that she used exceptionally short interventions (35 seconds on average), provided space for student dialogue, and applied four distinct strategies to support groups to make mathematical progress: (1) observing/listening before speaking; (2) using a combination of social and analytic scaffolds; (3) redirecting students to task instructions; (4) abruptly walking away. These findings imply that successful interventions may be characterized by brevity, shared dialogue between the teacher and students, and distinct (and sometimes unnatural) teaching moves.

Abstract

Over the last three decades, there has been an increasingly strong emphasis on group-centered approaches to mathematics teaching. One primary responsibility for teachers who use group-centered instruction is to “check in”, or intervene, with groups to monitor group learning and provide mathematical support when necessary. While prior research has contributed valuable insight for successful teacher interventions in mathematics group work, there is a need for more fine-grained analyses of interactions between teachers and students. In this study, we co-conducted research with an exemplary middle grade teacher (Ms. Green) to learn about fine-grained details of her intervention practices, hoping to generate knowledge about successful teacher interventions that can be expanded, replicated, and/or contradicted in other contexts. Analyzing Ms. Green’s practices as an exemplary case, we found that she used exceptionally short interventions (35 seconds on average), provided space for student dialogue, and applied four distinct strategies to support groups to make mathematical progress: (1) observing/listening before speaking; (2) using a combination of social and analytic scaffolds; (3) redirecting students to task instructions; (4) abruptly walking away. These findings imply that successful interventions may be characterized by brevity, shared dialogue between the teacher and students, and distinct (and sometimes unnatural) teaching moves.

참고문헌 (31)

  1. Juliet A. Baxter, "Social and analytic scaffolding in middle school mathematics: managing the dilemma of telling", Journal of Mathematics Teacher Education, 13(1), pp.7~26 (2009), Springer Science and Business Media LLC[DOI]
  2. Boaler, J., "Mathematical mindsets: Unleashing students’ potential through creative math, inspiring messages and innovative teaching" (2015), John Wiley & Sons
  3. Tye G. Campbell, "Professional noticing of coordinated mathematical thinking", British Educational Research Journal, 48(3), pp.488~503 (2022), Wiley[DOI]
  4. Tye G. Campbell, "Exploring In-The-Moment Teaching Moves that Support Sociomathematical and General Social Norms in Dialogic Instruction", International Journal of Science and Mathematics Education, 21(1), pp.1~23 (2021), Springer Science and Business Media LLC[DOI]
  5. Rijkje Dekker, "Teacher Interventions Aimed at Mathematical Level Raising During Collaborative Learning", Educational Studies in Mathematics, 56(1), pp.39~65 (2004), Springer Science and Business Media LLC[DOI]
  6. Meixia Ding, "Teacher Interventions in Cooperative-Learning Mathematics Classes", The Journal of Educational Research, 100(3), pp.162~175 (2007), Informa UK Limited[DOI]
  7. Joy Egbert, "A Study of Flow Theory in the Foreign Language Classroom", The Canadian Modern Language Review, 60(5), pp.549~586 (2004), University of Toronto Press Inc. (UTPress)[DOI]
  8. Megan L. Franke, "Student Engagement with Others’ Mathematical Ideas", The Elementary School Journal, 116(1), pp.126~148 (2015), University of Chicago Press[DOI]
  9. Robyn M. Gillies, "Promoting academically productive student dialogue during collaborative learning", International Journal of Educational Research, 97, pp.200~209 (2019), Elsevier BV[DOI]
  10. R. Hofmann, "Teacher interventions in small group work in secondary mathematics and science lessons", Language and Education, 30(5), pp.400~416 (2015), Informa UK Limited[DOI]
  11. Hunter, R., "Facilitating communities of mathematical inquiry", Navigating currents and charting directions:Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, 1, pp.31~39 (2008), Mathematics Education Research Group of Australasia
  12. Jackson, K., "Investigating how setting up cognitively demanding tasks is related to opportunities to learn in middle-grades mathematics classrooms", Research Presession of the National Council of Teachers of Mathematics Annual Meeting (2011)
  13. Victoria R. Jacobs, "Professional Noticing of Children's Mathematical Thinking", Journal for Research in Mathematics Education, 41(2), pp.169~202 (2010), National Council of Teachers of Mathematics[DOI]
  14. Jacobs, V. R., "Responding to children’s mathematical thinking in the moment : an emerging framework of teaching moves", ZDM, 48(1-2), pp.185~197 (2016)[DOI]
  15. Donna Kotsopoulos, "The Case of Mitchell's Cube: Interactive and Reflexive Positioning During Collaborative Learning in Mathematics", Mind, Culture, and Activity, 21(1), pp.34~52 (2013), Informa UK Limited[DOI]
  16. Jennifer M. Langer-Osuna, "The Social Construction of Authority Among Peers and Its Implications for Collaborative Mathematics Problem Solving", Mathematical Thinking and Learning, 18(2), pp.107~124 (2016), Informa UK Limited[DOI]
  17. Jennifer M. Langer-Osuna, "Authority, Identity, and Collaborative Mathematics", Journal for Research in Mathematics Education, 48(3), pp.237~247 (2017), National Council of Teachers of Mathematics[DOI]
  18. Liljedahl, P., "Building thinking classrooms in mathematics, Grades K-12: 14teaching practices for enhancing learning", pp.14~ (2020), Corwin
  19. Neil Mercer, "Children's Talk and the Development of Reasoning in the Classroom", British Educational Research Journal, 25(1), pp.95~111 (1999), Wiley[DOI]
  20. Merriam, S. B., "Qualitative research and case study applications in education" (1998), Jossey-Bass
  21. Munter, C., "Dialogic and direct instruction: Two distinct models of mathematics instruction and the debate(s) surrounding them", Teachers College Record, 117(11), pp.1~32 (2015)[DOI]
  22. National Council of Teachers of Mathematics, "Principles and standards for school mathematics" (2000), National Council of Teachers of Mathematics
  23. National Council of Teachers of Mathematics, "Principles to actions: Ensuring mathematics success for all" (2014), National Council of Teachers of Mathematics
  24. Nowell, L. S., "Thematic analysis : Striving to meet the trustworthiness criteria", International Journal of Qualitative Methods, 16(1), pp.1~13 (2017)[DOI]
  25. Catherine O’Connor, "Supporting teachers in taking up productive talk moves: The long road to professional learning at scale", International Journal of Educational Research, 97, pp.166~175 (2019), Elsevier BV[DOI]
  26. "The Ontario curriculum Grades 1–8mathematics" (2020)[URL]
  27. Byungeun Pak, "Examining How Teacher Identities Explain Their Interactions with Students in Small Groups", 수학교육연구, 25(2), pp.117~133 (2022), 한국수학교육학회[DOI]
  28. Mary Kay Stein, "Orchestrating Productive Mathematical Discussions: Five Practices for Helping Teachers Move Beyond Show and Tell", Mathematical Thinking and Learning, 10(4), pp.313~340 (2008), Informa UK Limited[DOI]
  29. Van de Walle, J. A., "Elementary and middle school mathematics: Teaching developmentally" (2013), Pearson
  30. Noreen M. Webb, "Teacher practices that promote productive dialogue and learning in mathematics classrooms", International Journal of Educational Research, 97, pp.176~186 (2019), Elsevier BV[DOI]
  31. 여승현, "Development of Mathematical Task Analytic Framework: Proactive and Reactive Features", 수학교육연구, 25(4), pp.285~309 (2022), 한국수학교육학회[DOI]

관련 논문AI추천

이 간행물의 다른 논문 (3건)