Task Design for Differentiated Instruction in Mixed-ability Mathematics Classrooms: Manifestations of Contradictions in a Professional Learning Community
Keywords:
Differentiated instruction, Content focus, Challenging problems, In-service teachers, Professional learning communityAbstract
The aim of this study is to investigate task design for differentiated instruction in mathematics in professional learning communities. Based on the cultural-historical activity theory, we conceptualize a professional learning community as an activity system and use the analytical construct of contradictions to give an account of structures that bring forward the teachers’ work. Eight Swedish upper secondary teachers, engaged in designing tasks for differentiated instruction in mixed-ability mathematics classrooms, are studied. The analysis outlines three contradictions, manifested as three dilemmas, and shows how the teachers, by noticing a dilemma and making it an explicit object of inquiry, came to address a diversity of issues related to differentiated instruction in mathematics. For example, the teachers addressed students’ different learning needs, problem-solving activities for a mixed-ability classroom, and design of tasks that are challenging for all students. With input from our findings on the three dilemmas, we then discuss the design of a task analysis guide as a means for facilitating the development of a professional learning community that is inquiry-oriented with a strong content focus on designing tasks for differentiated instruction in mixed-ability mathematics classrooms.
References
Anthony, G., & Hunter, R. (2017). Grouping practices in New Zealand mathematics classrooms: Where are we at and where should we be? New Zealand Journal of Educational Studies, 52(1), 73–92. https://doi.org/10.1007/s40841-016-0054-z
Bauersfeld, H. (1998). Interaction, construction, and knowledge: Alternative perspectives for mathematics education. In D. Grouws, T. Cooney, & D. Jones (Eds.), Perspectives on research on effective mathematics teaching (pp. 27–46). National Council of Teachers of Mathematics.
Brodie K. (2020). Professional learning communities in mathematics education. In S. Lerman (Ed.) Encyclopedia of Mathematics Education. Springer. https://doi.org/10.1007/978-3-030-15789-0_130
Benölken, R. (2015). “Mathe für kleine Asse” – An enrichment project at the university of Münster. In F. M. Singer, F. Toader, & C. Voica (Eds.), Proceedings of the Ninth Mathematical Creativity and Giftedness International Conference (pp. 140–145). Sinaia, Romania: The International Group for Mathematical Creativity and Giftedness.
Bobis, J., Russo, J., Downton, A., Feng, M., Livy, S., McCormick, M., & Sullivan, P. (2021). Instructional moves that increase chances of engaging all students in learning mathematics. Mathematics, 9(6). https://doi.org/10.3390/math9060582
Daniels, H. (2004). Cultural historical activity theory and professional learning. International Journal of Disability, Development and Education, 51(2), 185–200.
Darling-Hammond, L., Hyler, M. E., & Gardner, M. (2017). Effective teacher professional development. Learning Policy Institute.
Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181–199. http://doi.org/10.3102/0013189X08331140
Dogan, S., Pringle, R., & Mesa, J. (2016). The impacts of professional learning communities on science teachers’ knowledge, practice and student learning: a review. Professional Development in Education, 42(4), 569–588. https://doi.org/10.1080/19415257.2015.1065899
Gaitas, S., & Alves Martins, M. (2017). Teacher perceived difficulty in implementing differentiated instructional strategies in primary school. International Journal of Inclusive Education, 21(5), 544–556. doi:10.1080/13603116.2016.1223180
Engeström, Y. (1987). Learning by Expanding. Orienta Konsultot Oy.
Engeström, Y. (1999). Activity theory and individual and social transformation. In Y. Engeström, R. Miettinen, & R.-L. Punamäki (Eds.), Perspectives on activity theory.Cambridge University Press.
Engeström, Y. (2001). Expansive learning at work: Toward an activity theoretical reconceptualization. Journal of Education and Work, 14(1), 133-156.
Engeström, Y., & Sannino, A. (2011). Discursive manifestations of contradictions in organizational change efforts. A methodological framework. Journal of Organizational Change Management, 24(3), 368–387. https://doi.org/10.1108/09534811111132758
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Information Age.
Hsu, E., Kysh, J., & Resek, D. (2007). Using rich problems for differentiated instruction. New England Mathematics Journal, 39, 6–13. http://bilbowdish.ipage.com/atmne/journal.html
Hunter, J., Hunter, R., & Anthony, G. (2019). Shifting towards equity: Challenging teacher views about student capability in mathematics. Mathematics Education Research Journal. https://link.springer.com/article/10.1007/s13394-019-00293-y
Jaworski, B. (2008). Building and sustaining inquiry communities in mathematics teaching development: Teachers and didactitians in collaboration. In K. Krainer & T. Wood (Eds.), International handbook of mathematics teacher education: Participants in mathematics teacher education (Vol. 3, pp. 309–330). Sense Publishers. https://doi.org/10.1163/9789087905491_015
Jäder, J., Lithner, J., Sidenvall, J. (2019). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology, 51, 1–17. https://doi.org/10.1080/0020739X.2019.1656826
Jonsson, B., Norqvist, M., Liljekvist, Y., & Lithner, J. (2014). Learning mathematics through algorithmic and creative reasoning. The Journal of Mathematical Behavior, 36, 20–32. https://doi.org/10.1016/j.jmathb.2014.08.003
Le Fevre, D., Timperley, H., & Ell, F. (2016). Curriculum and pedagogy: the future of teacher professional learning and the development of adaptive expertise. In D. Wyse, L. Hayward & J. Pandya (Eds.). The SAGE Handbook of curriculum, Pedagogy and Assessment (Vol. 2, pp. 309–324). SAGE Publications. https://doi.org/10.4135/9781473921405.n20
Leikin, R., & Stanger, O. (2011). Teachers’ images of gifted students and the roles assigned to them in heterogeneous mathematics classes. In B. Sriraman & K. Lee W. (Eds.), The elements of creativity and giftedness in mathematics (pp. 103-118). Sense Publisher. http://doi.org/10.1007/978-94-6091-439-3_7
Marks, R. (2014). Educational triage and ability-grouping in primary mathematics: a case-study of the impacts on low-attaining pupils. Research in Mathematics Education, 16(1), 38–53. https://doi.org/10.1080/14794802.2013.874095
Mattsson, L. (2018). Särskilt matematikbegåvade elever [Mathematically gifted students]. In O. Helenius & M. Johansson (Eds.), Att bli lärare i matematik [To become a teacher in mathematics] (pp. 174–199). Liber AB.
Mellroth, E. (2018). Harnessing teachers’ perspectives: Recognizing mathematically highly able pupils and orchestrating teaching for them in diverse classroom. Doctoral thesis. Karlstad, Sweden: Karlstad University Studies.
Mellroth, E. (2021). Teachers’ views on teaching highly able pupils in a heterogeneous mathematics classroom. Scandinavian Journal of Educational Research 65, 481–499. https://doi.org/10.1080/00313831.2020.1716065
Mellroth, E., van Bommel, J., & Liljekvist, Y. (2019). Elementary teachers on orchestrating teaching for mathematically highly able pupils. The Mathematics Enthusiast 16(1-3), 127-153.
Mhlolo, M. K. (2017). Regular classroom teachers’ recognition and support of the creative potential of mildly gifted mathematics learners. ZDM, 49(1), 81–94. http://doi.org/10.1007/s11858-016-0824-6
Nordgren, K., Kristiansson, M., Liljekvist, Y, & Bergh, D. (2019). Lärares planering och efterarbete av lektioner – Infrastrukturer för kollegialt samarbete och forskningssamverkan [Teachers’ planning and finishing of lessons: Infrastructures for teachers collaboration and research collaboration]. Karlstad University Studies.
Österholm, M., Bergqvist, T., Liljekvist, Y., & van Bommel, J. (2016). Utvärdering av Matematiklyftets resultat: slutrapport [Evaluation of the Boost for mathematics: Final report]. Umeå university.
Plauborg, H. (2009). Opportunities and limitations of learning within teachers’ collaboration in teams: Perspectives from action learning. Action Learning: Research and Practice, 6, 25–34. https://doi.org/10.1080/14767330902731293
Russo, J., Bobis, J., Downton, A., Hughes, S., Livy, S., McCormick, M., & Sullivan, P. (2020). Elementary teachers’ beliefs on the role of struggle in the mathematics classroom. The Journal of Mathematical Behavior, 58, 100774.
Shayshon, B., Gal, H., Tesler, B., & Ko, E. (2014). Teaching mathematically talented students: A cross-cultural study about their teachers’ views. Educational Studies in Mathematics, 87(3), 409-438. http://doi.org/10.1007/s10649-014-9568-9
Sheffield, L. J. (2003). Extending the challenge in mathematics: Developing mathematical promise in K-8 students. Corwin Press.
Slavit, D., Kennedy, A., Lean, Z., Nelson, T., & Deuel, A. (2011). Support for professional collaboration in middle school mathematics: A complex web. Teacher Education Quarterly, 38, 113–131.
Stoll, L., Bolam, R., McMahon, A., Wallace, M., & Thomas, S. (2006). Professional learning communities: A review of the literature. Journal of Educational Change, 7(4), 221–258.
Sullivan, P., Borcek, C., Walker, N., & Rennie, M. (2016). Exploring a structure for mathematics lessons that initiate learning by activating cognition on challenging tasks. The Journal of Mathematical Behavior, 41, 159-170. https://doi.org/10.1016/j.jmathb.2015.12.002
Sullivan, P., Knott, L., Yang, Y., Askew, M., Brown, L., Bussi, M. G. B., … Gimenez, J. (2015). The relationship between task design, anticipated pedagogies, and student learning. In A. Watson & M. Ohtani (Eds.), Task design in mathematics education (pp. 83–114). Springer. https://doi.org/10.1007/978-3-319-09629-2_3
Suprayogi, M. N., Valcke, M., & Godwin, R. (2017). Teachers and their implementation of differentiated instruction in the classroom. Teaching and Teacher Education, 67, 291–301. https://doi.org/10.1016/j.tate.2017.06.020
Szabo, A. (2017). Matematikundervisning för begåvade elever: En forskningsöversikt [Mathematics instruction for gifted students: A review of research]. Nordic Studies in Mathematics Education, 22(1), 21–44.
Taflin, E. (2007). Matematikproblem i skolan: För att skapa tillfällen till lärande. [Mathematical problems in school: To create opportunities for learning]. Doctoral thesis, Umeå, Sweden: Umeå University.
Tomlinson, C. A. (2016). The differentiated classroom: Responding to the needs of all learners. Pearson education.
Tomlinson, C. A., Brighton, C., Hertberg, H., Callahan, C. M., Moon, T. R., Brimijoin, K., Conover, L.A., & Reynolds, T. (2003). Differentiating instruction in response to student readiness, interest, and learning profile in academically diverse classrooms: A review of literature. Journal for the Education of the Gifted, 27(2–3), 119-145. https://doi.org/10.1177/016235320302700203
Trust, T. (2017). Using cultural historical activity theory to examine how teachers seek and share knowledge in a peer-to-peer professional development network. Australasian Journal of Educational Technology, 33(1), 98–113. https://doi.org/10.14742/ajet.2593
Vangrieken, K., Dochy, F., Raes, E., & Kyndt, E. (2015). Teacher collaboration: A systematic review. Educational Research Review, 15(1), 17e40. http://dx.doi.org/ 10.1016/j.edurev.2015.04.002.
Wegerif, R., & Mercer, N. (1997). A dialogical framework for researching peer talk. In R. Wegerif & P. Scrimshaw (Eds.), Computers and talk in the primary classroom (pp. 49–65). Multilingual Matters.
Vygotsky, L. S. (1987). Thinking and speech. In R. W. Rieber, & A. S. Carton (Eds.), The collected works of L. S. Vygotsky: Problems of general psychology (Vol. 1) (pp. 39–285). Plenum.