Networking frameworks: a method for analyzing the complexities of classroom cultures focusing on justifying

Anthony, G., Kaur, B., Ohtani, M., & Clarke, D. (2013). The learner’s perspective study: Attending to student voice. In Student voice in mathematics classrooms around the world (pp. 1-11). Brill Sense. Askew, M. (1997). Effective teachers of numeracy. King’s College London. Australian Curriculum, A.a. R. A. A. (2017). Bildungspläne baden-württemberg. Baden-Württemberg, M. f. K. J. u. S. (2016). Bildungspläne baden-württemberg. Ball, D. (1993). With an eye on the mathematical horizon: Dilemmas of teaching elementary school mathematics. Elementary School Journal, 93(4), 373–397 http://stats.lib.pdx.edu/proxy.php?url=http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ461722&site=ehost-live Ball, D. L., & Bass, H. (2003). Making mathematics reasonable in school. A research companion to principles and standards for school mathematics (pg. 27–44). NCTM. Bikner-Ahsbahs, A., & Prediger, S. (2006). Diversity of theories in mathematics education—how can we deal with it? Zentralblatt für Didaktik der Mathematik, 38(1), 52–57. Bikner-Ahsbahs, A., & Prediger, S. (2010). Networking of theories—an approach for exploiting the diversity of theoretical approaches. In B. Sriraman, & L. English (Eds.), Theories of mathematics education (pp. 483–506). Berlin, Heidelberg: Springer. Bikner-Ahsbahs, A., & Prediger, S. (2014). Networking of theories as a research practice in mathematics education. Springer. Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of railside school. Teachers College Record, 110(3), 608–645. Brodie, K. (2010). Learning mathematical reasoning in a collaborative whole-class discussion. In K. Brodie (Ed.), Teaching mathematical reasoning in secondary school classrooms (pp. 57–72). Boston: Springer. [Record #1578 is using a reference type undefined in this output style.] Brown, R., & Renshaw, P. (2000). Collective argumentation: A sociocultural approach to reframing classroom teaching and learning. In H., Teoksessa Cowie & G. van der Aalswoort (Eds.), Social interaction in learning and instruction. The meaning of discourse for the construction of knowledge. Amsterdam: Bergamon Press. Cai, J., Kaiser, G., Perry, G., & Wong, N.-Y. (2009). Effective mathematics teaching from teachers’ perspectives: National and cross national studies. Rotterdam: Sense Publlishing. Cengiz, N., Kline, K., & Grant, T. J. (2011). Extending students’ mathematical thinking during whole-group discussions. Journal of Mathematics Teacher Education, 14(5), 355–374. Chapin, S. H., O’Connor, C., & Anderson, N. C. (2013). Classroom discussions in math. Math Solutions. Charalambous, C. Y., & Hill, H. C. (2012). Teacher knowledge, curriculum materials, and quality of instruction: Unpacking a complex relationship. Journal of Curriculum Studies, 44(4), 443–466. Charalambous, C. Y., & Praetorius, A.-K. (2018). Studying mathematics instruction through different lenses: Setting the ground for understanding instructional quality more comprehensively. ZDM-Mathematics Education, 50(3), 355–366. Chi, M. T., & Wylie, R. (2014). The icap framework: Linking cognitive engagement to active learning outcomes. Educational psychologist, 49(4), 219–243. Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational psychologist, 31(3-4), 175–190. Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational evaluation and policy analysis, 25(2), 119–142. Conner, A., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401–429. da Ponte, J. P., & Quaresma, M. (2016). Teachers’ professional practice conducting mathematical discussions. Educational Studies in mathematics, 93(1), 51–66. De Villiers, M. D. (1990). The role and function of proof in mathematics. Pythagoras, 24, 17–24. Department for Education (2014) The national curriculum in England: Complete framework for key stages 1 to 4. Available at: https://www.gov.uk/government/publications/national-curriculum-in-england-framework-for-key-stages-1-to-4 Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers, grades 6-10. Heinemann. Ellis, A. B. (2007). A taxonomy for categorizing generalizations--generalizing actions and reflection generalizations. Journal of the Learning Sciences, 16(2), 221–262. http://stats.lib.pdx.edu/proxy.php?url=http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ772330&site=ehost-live. https://doi.org/10.1080/10508400701193705 Fernandez, C., Yoshida, M., & Stigler, J. W. (1992). Learning mathematics from classroom instruction: On relating lessons to pupils’ interpretations. The Journal of the Learning Sciences, 2(4), 333–365. Franke, M. L., Kazemi, E., & Battey, D. (2007). Mathematics teaching and classroom practice. Second handbook of research on mathematics teaching and learning, 1(1), 225–256. Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60(4), 380–392. Frey, N., & Fisher, D. (2010). Identifying instructional moves during guided learning. The Reading Teacher, 64(2), 84–95. Hawkins, D. (2002). I, thou, and it. In The informed vision: Essays on learning and human nature (pp. 51–64). New York: Algora Publishing. Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 524–549. Herbel-Eisenmann, B. A., & Otten, S. (2011). Mapping mathematics in classroom discourse. Journal for Research in Mathematics Education, 42(5), 451–485. Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for research in mathematics education, 81–116. Jacobs, V., & Spangler, D. (2017). Research on core practices in k–12 mathematics teaching. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 766–792). National Council of Teachers of Mathematics. Jaffe, A. (1997). Proof and the evolution of mathematics. Synthese, 111(2), 133–146. Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. Lampert, M. (2001). Teaching problems and the problems of teaching. Yale University. Lampert, M., Franke, M. L., Kazemi, E., Ghousseini, H., Turrou, A. C., Beasley, H., … Crowe, K. (2013). Keeping it complex using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), 226–243. Leinhardt, G., & Steele, M. (2005). Seeing the complexity of standing to the side: Instructional dialogues. Cognition and Instruction, 23, 87–163. Lozano, M.-D. (2017). Investigating task design, classroom culture and mathematics learning: An enactivist approach. ZDM-Mathematics Education, 49(6), 895–907. Mata-Pereira, J., & da Ponte, J.-P. (2017). Enhancing students’ mathematical reasoning in the classroom: Teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186. Melhuish, K., & Thanheiser, E. (2017). Using formative evaluation to support teachers in increasing student reasoning. In L. West & M. Boston (Eds.), Annual perspectives in mathematics education 2017: Reflective and collaborative processes to improve mathematics teaching (pp. 183–200). National Council of Teachers of Mathematics. Melhuish, K., Thanheiser, E., & Fagan, J. (2019). The student discourse observation tool: Supporting teachers in noticing justifying and generalizing. Mathematics Teacher Educator, 7(2), 57–74. Melhuish, K., Thanheiser, E., & Guyot, L. (2018). Elementary school teachers’ noticing of essential mathematical reasoning forms: Justification and generalization. Journal of Mathematics Teacher Education, 1–33. Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(5), 584–635. Nasir, N. i. S., & Cobb, P. (2006). Improving access to mathematics: Diversity and equity in the classroom. ERIC: Multicultural education series. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. National Council of Teachers of Mathematics. (2018). Catalyzing change in high school mathematics. National Council of Teachers of Mathematics. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors. National Research Council (Ed.). (2001). Adding it up: Helping children learn mathematics. National Academy Press. Ozgur, Z., Reiten, L., & Ellis, A. B. (2015). On framing teacher moves for supporting student reasoning. North American Chapter of the International Group for the Psychology of Mathematics Education. Praetorius, A.-K., & Charalambous, C. Y. (2018). Classroom observation frameworks for studying instructional quality: Looking back and looking forward. ZDM-Mathematics Education, 50(3), 535–553. Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches: First steps towards a conceptual framework. ZDM-Mathematics Education, 40(2), 165–178. Reid, D. A. (2002). Conjectures and refutations in grade 5 mathematics. Journal for research in mathematics education, 5–29. Remillard, J. (1996). Curriculum materials in mathematics education reform. PME CONFERENCE. Rezat, S., & Sträßer, R. (2012). From the didactical triangle to the socio-didactical tetrahedron: Artifacts as fundamental constituents of the didactical situation. ZDM-Mathematics Education, 44(5), 641–651. Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of naomi. Journal of mathematics teacher education, 8(3), 255–281. Sahin, A., & Kulm, G. (2008). Sixth grade mathematics teachers’ intentions and use of probing, guiding, and factual questions. Journal of mathematics teacher education, 11(3), 221–241. Schoenfeld, A. H. (2011). Toward professional development for teachers grounded in a theory of decision making. ZDM-Mathematics Education, 43(4), 457–469. Schoenfeld, A. H. (2012). Problematizing the didactic triangle. ZDM-Mathematics Education, 44(5), 587–599. Schoenfeld, A. H. (2018). Video analyses for research and professional development: The teaching for robust understanding (tru) framework. Zentralblatt fuer Didaktik der Mathematick, 50(3), 491–506. Sfard, A. (2012). Introduction: Developing mathematical discourse—some insights from communicational research. International Journal of Educational Research, 51-52, 1–9. Simon, M. A., & Blume, G. W. (1996). Justification in the mathematics classroom: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 15(1), 3–31. Sleep, L. (2012). The work of steering instruction toward the mathematical point: A decomposition of teaching practice. American Educational Research Journal, 49(5), 935–970. Smith, E. (1998). Social constructivism, individual constructivism and the role of computers in mathematics education. The Journal of Mathematical Behavior, 17(4), 411–425. Smith, M., & Stein, M. K. (1998). Selecting and creating mathematical tasks: From research to practice. Mathematics Teaching in the Middle School, 3(5), 344–350. Sowder, L., & Harel, G. (1998). Types of students’ justifications. The Mathematics Teacher, 91(8), 670–675. Staples, M. (2007). Supporting whole-class collaborative inquiry in a secondary mathematics classroom. Cognition and Instruction, 25(2-3), 161–217. Staples, M., Bartlo, J., & Thanheiser, E. (2012). Justification as a teaching and learning practice: Its (potential) multifacted role in middle grades mathematics classrooms. Journal of Mathematical Behavior, 31(4), 447–462. http://stats.lib.pdx.edu/proxy.php?url=http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ983356&site=ehost-live. https://doi.org/10.1016/j.jmathb.2012.07.001 Staples, M., & Newton, J. (2016). Teachers’ contextualization of argumentation in the mathematics classroom. Theory into Practice, 55(4), 294–301. Stein, M. K., Crowley, K., & Resnick, L. (2016). Education policy and the learning sciences: The case for a new alliance. Reflections on the Learning Sciences, 210–233. Stein, M. K., Engle, R. A., Smith, M., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical thinking and learning, 10(4), 313–340. Stein, M. K., & Smith, M. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics teaching in the middle school, 3(4), 268–275. Stein, M. K., & Smith, M. (2011). 5 practices for orchestrating productive mathematics discussions. National Council of Teachers of Mathematics. Stigler, J. W., & Hiebert, J. (1999). The teaching gap. The Free Press. Stigler, J. W., & Perry, M. (1988). Mathematics learning in Japanese, Chinese, and American classrooms. New Directions for Child and Adolescent Development, 1988(41), 27–54. Stylianides, A. J. (2007). Proof and proving in school mathematics. Journal for Research in Mathematics Education, 38(3), 289–321 http://stats.lib.pdx.edu/proxy.php?url=http://search.ebscohost.com/login.aspx?direct=true&db=eric&AN=EJ765496&site=ehost-livehttp://my.nctm.org/eresources/article_summary.asp?URI=JRME2007-05-289a&from=B Tabach, M., Rasmussen, C., Dreyfus, T., & Apkarian, N. (2020). Towards an argumentative grammar for networking: A case of coordinating two approaches. Educational Studies in Mathematics, 103(2), 139–155. Teachers Development Group. (2013). How math teaching matters. Best Practices Notebook. Turner, E., Dominguez, H., Maldonado, L., & Empson, S. (2013). English learners’ participation in mathematical discussion: Shifting positionings and dynamic identities. Journal for Research in Mathematics Education, 44(1), 199–234. Walshaw, M., & Anthony, G. (2008). The teacher’s role in classroom discourse: A review of recent research into mathematics classrooms. Review of educational research, 78(3), 516–551. Williams, S. R. (1993). Mathematics and being in the world: Toward an interpretive framework. For the Learning of Mathematics, 13(2), 2–7. Wood, T. (1999). Creating a context for argument in mathematics class. Journal for research in mathematics education, 171–191.