Teaching mathematics with high cognitive activation: instructional formats and connection-making interactions in high-level Nordic lessons

Authors

Jóhann Örn Sigurjónsson

Abstract

Cognitive activation is a dimension of teaching quality which considers to what extent the teacher addresses the educational goal of student understanding, such as through successful implementation of demanding tasks. This study aimed to enrich empirical understandings of instructional formats and teacher-student interactions in cognitively activating lessons. Eight lessons were purposefully selected from a Nordic video database containing 125 lessons. The interactions in the lessons were analysed using reflexive thematic analysis and instructional formats using content analysis. Whole-class discussions and group work were the dominant formats. Four types of connection-making interactions were observed, connecting both within mathematics and to non-mathematical experience.

References

Baumert, J. & Kunter, M. (2013). The effect of content knowledge and pedagogical content knowledge on instructional quality and student achievement. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 175-205). Springer. https://doi.org/10.1007/978-1-4614-5149-5_9

Baumert, J., Kunter, M., Blum, W., Klusmann, U., Krauss, S. & Neubrand, M. (2013). Professional competence of teachers, cognitively activating instruction, and the development of students' mathematical literacy (COACTIV): a research program. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 1-21). Springer. https://doi.org/10.1007/978-1-4614-5149-5_1

Bergem, O. K., Nilsen, T. & Scherer, R. (2016). Undervisningskvalitet i matematikk. In O. K. Bergem, H. Kaarstein & T. Nilsen (Eds.), Vi kan lykkes i realfag: resultater og analyser fra TIMSS 2015. Universitetsforlaget. https://doi.org/10.18261/97882150279999-2016

Bergem, O. K. & Pepin, B. (2013). Developing mathematical proficiency and democratic agency through participation - an analysis of teacher-student dialogues in a Norwegian 9th grade classroom. In B. Kaur, G. Anthony, M. Ohtani, & D. Clarke (Eds.), Student voice in mathematics classrooms around the world (pp. 143-160). Sense. https://doi.org/10.1007/978-94-6209-350-8_9

Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J. et al. (2014). Developing mathematical competence: from the intended to the enacted curriculum. The Journal of Mathematical Behavior, 33, 72-87. https://doi.org/10.1016/j.jmathb.2013.10.001

Braun, V. & Clarke, V. (2013). Successful qualitative research. Sage.

Braun, V. & Clarke, V. (2022). Thematic analysis: a practical guide. Sage. https://doi.org/10.53841/bpsqmip.2022.1.33.46

Brenner, M. E., Mayer, R. E., Moseley, B., Brar, T., Durán, R. et al. (1997). Learning by understanding: the role of multiple representations in learning algebra. American Educational Research Journal, 34 (4), 663-689. https://doi.org/10.3102/00028312034004663

Cantley, I., Prendergast, M. & Schlindwein, F. (2017). Collaborative cognitive-activation strategies as an emancipatory force in promoting girls' interest in and enjoyment of mathematics: a cross-national case study. International Journal of Educational Research, 81, 38-51. https://doi.org/10.1016/j.ijer.2016.11.004

Clarke, D. (2006). Deconstructing dichotomies: arguing for a more inclusive approach. In D. Clarke, J. Emanuelsson, E. Jablonka, & I. A. C. Mok (Eds.), Making connections: comparing mathematics classrooms around the world (pp. 215-236). Sense. https://doi.org/10.1163/9789087901639_012

Croninger, R. G., Valli, L. & Chambliss, M. J. (2012). Researching quality in teaching: enduring and emerging challenges. Teachers College Record, 114 (4), 1-15. Diederich, J. & Tenorth, H. E. (1997). Theorie der Schule. Ein Studienbuch zu Geschichte, Funktionen und Gestaltung. Cornelsen. https://doi.org/10.1177/016146811211400404

Ekatushabe, M., Nsanganwimana, F., Muwonge, C. M. & Ssenyonga, J. (2021). The relationship between cognitive activation, self-efficacy, achievement emotions and (meta)cognitive learning strategies among Ugandan biology learners. African Journal of Research in Mathematics, Science and Technology Education, 25 (3), 1-12. https://doi.org/10.1080/18117295.2021.2018867

Franke, M. L., Kazemi, E. & Battey, D. (2007). Mathematics teaching and classroom practice. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning, Vol. 1 (pp. 225-256). Information Age.

Fries, L., Son, J. Y., Givvin, K. B. & Stigler, J. W. (2021). Practicing connections: a framework to guide instructional design for developing understanding in complex domains. Educational Psychology Review, 33 (2), 739-762. https://doi.org/10.1007/s10648-020-09561-x

Glasersfeld, E. von. (1995). A constructivist approach to teaching. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 21-34). Taylor & Francis. https://doi.org/10.4324/9780203052600-1

Grossman, P. (2019). Protocol for language arts teaching observations (PLATO 5.0). Stanford University.

Grossman, P., Loeb, S., Cohen, J., & Wyckoff, J. (2013). Measure for measure: The relationship between measures of instructional practice in middle school English language arts and teachers' value-added scores. American Journal of Education, 119 (3), 445-470. https://doi.org/10.1086/669901

Gunnarsdóttir, G. H. & Pálsdóttir, G. (2015). Instructional practices in mathematics classrooms. In K. Krainer & N. Vondrová (Eds.), Proceedings of the ninth congress of the European society for Research in Mathematics Education (pp. 3036-3042). ERME.

Hatano, G. & Inagaki, K. (1986). Two courses of expertise. In H. W. Stevenson, H. Azuma & K. Hakuta (Eds.), Child development and education in Japan (pp. 262-272). Freeman.

Helmke, A. (2015). Unterrichtsqualität und Lehrerprofessionalität. Diagnose, Evaluation und Verbesserung des Unterrichts. Kallmeyer.

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, Vol. 1 (pp. 371-404). Information Age.

Hsieh, H.-F. & Shannon, S. E. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15 (9), 1277-1288. https://doi.org/10.1177/1049732305276687

Klette, K. (2022). Quality in Nordic teaching (NCoE) common QUINT dataset 2022 (Version 1). Zenodo. https://doi.org/10.5281/zenodo.6381818

Klieme, E., Lipowsky, F., Rakoczy, K. & Ratzka, N. (2006). Qualitätsdimensionen und Wirksamkeit von Mathematikunterricht. Theoretische Grundlagen und ausgewählte Ergebnisse des Projekts "Pythagoras" [Quality dimensions and effectiveness of mathematics lessons. Theoretical foundations and selected results of the "Pythagoras" project]. In M. Prenzel & L. Allolio-Näcke (Eds.), Untersuchungen zur Bildungsqualität von Schule. Abschlussbericht des DFG-Schwerpunktprogramms (pp. 127-146). Waxmann.

Klieme, E., Schümer, G. & Knoll, S. (2001). Mathematikunterricht in der Sekundarstufe I: "Aufgabenkultur" und Unterrichtsgestaltung im internationalen Vergleich [Mathematics instruction at lower secondary level: "Task culture" and quality of instruction in international comparison]. In E. Klieme & J. Baumert (Eds.), TIMSS - Impulse für Schule und Unterricht: Forschungsbefunde, Reforminitiativen, Praxisberichte und Video-Dokumente (pp. 43-57). BMBF.

Krauss, S., Bruckmaier, G., Lindl, A., Hilbert, S., Binder, K. et al. (2020). Competence as a continuum in the COACTIV study: the "cascade model." ZDM, 52 (2), 311-327. https://doi.org/10.1007/s11858-020-01151-z

Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T. & Hachfeld, A. (2013). Professional competence of teachers: effects on instructional quality and student development. Journal of Educational Psychology, 105 (3), 805-820. https://doi.org/10.1037/a0032583

Kunter, M. & Voss, T. (2013). The model of instructional quality in COACTIV: a multicriteria analysis. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers (pp. 97-124). Springer. https://doi.org/10.1007/978-1-4614-5149-5_6

Leung, D. Y. & Chung, B. P. M. (2019). Content analysis: using critical realism to extend its utility. In P. Liamputtong (Ed.), Handbook of research methods in health social sciences (pp. 827-841). Springer. https://doi.org/10.1007/978-981-10-5251-4_102

Lipowsky, F., Rakoczy, K., Pauli, C., Drollinger-Vetter, B., Klieme, E. & Reusser, K. (2009). Quality of geometry instruction and its short-term impact on students' understanding of the Pythagorean theorem. Learning and Instruction, 19 (6), 527-537. https://doi.org/10.1016/j.learninstruc.2008.11.001

Mok, I. A. C. & Lopez-Real, F. (2006). A tale of two cities: a comparison of six teachers in Hong Kong and Shanghai. In D. Clarke, C. Keitel & Y. Shimizu (Eds.), Making connections: comparing mathematics classrooms around the world (pp. 237-246). Sense. https://doi.org/10.1163/9789087901622_017

Pianta, R. C. & Hamre, B. K. (2009). Conceptualization, measurement, and improvement of classroom processes: standardized observation can leverage capacity. Educational Researcher, 38 (2), 109-119. https://doi.org/10.3102/0013189X09332374

Pianta, R. C., La Paro, K. M. & Hamre, B. K. (2008). Classroom assessment scoring system (CLASS) manual, pre-K. Paul H. Brookes.

Praetorius, A.-K. & Charalambous, C. Y. (2018). Classroom observation frameworks for studying instructional quality: looking back and looking forward. ZDM, 50 (3), 535-553. https://doi.org/10.1007/s11858-018-0946-0

Praetorius, A.-K., Klieme, E., Herbert, B. & Pinger, P. (2018). Generic dimensions of teaching quality: the German framework of Three Basic Dimensions. ZDM, 50 (3), 407-426. https://doi.org/10.1007/s11858-018-0918-4

Savola, L. (2010). Comparison of the classroom practices of Finnish and Icelandic mathematics teachers. Journal of Mathematics Education at Teachers College, 1 (2), 43-55.

Schoenfeld, A. H. (2017). Teaching for robust understanding of essential mathematics. In T. McDougal (Ed.), Essential mathematics for the next generation: what and how students should learn (pp. 104-129). Tokyo Gakugei University Press.

Sigurjónsson, J. Ö. (2023). Quality in Icelandic mathematics teaching [PhD thesis] University of Iceland. https://hdl.handle.net/20.500.11815/3843

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77 (4), 20-26.

Skovsmose, O. (2001). Landscapes of investigation. ZDM, 33 (4), 123-132. https://doi.org/10.1007/BF02652747

Smith, M. S. & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussion. NCTM.

Star, J. R., Newton, K., Pollack, C., Kokka, K., Rittle-Johnson, B. & Durkin, K. (2015). Student, teacher, and instructional characteristics related to students' gains in flexibility. Contemporary Educational Psychology, 41, 198-208. https://doi.org/10.1016/j.cedpsych.2015.03.001

Stovner, R. B. & Klette, K. (2022). Teacher feedback on procedural skills, conceptual understanding, and mathematical practices: a video study in lower secondary mathematics classrooms. Teaching and Teacher Education,110, 103593. https://doi.org/10.1016/j.tate.2021.103593

Teig, N., Scherer, R. & Nilsen, T. (2019). I know I can, but do I have the time? The role of teachers' self-efficacy and perceived time constraints in implementing cognitive-activation strategies in science. Frontiers in Psychology, 10, 1-17. https://doi.org/10.3389/fpsyg.2019.01697

Tengberg, M., Bommel, J. van, Nilsberth, M., Walkert, M. & Nissen, A. (2021). The quality of instruction in Swedish lower secondary language arts and mathematics. Scandinavian Journal of Educational Research, 66 (5) 1-18. https://doi.org/10.1080/00313831.2021.1910564

Vieluf, S. & Klieme, E. (2023). Teaching effectiveness revisited through the lens of practice theories. In A.-K. Praetorius & C. Y. Charalambous (Eds.), Theorizing teaching (pp. 57-95). Springer. https://doi.org/10.1007/978-3-031-25613-4_3

Weingartner, E. (2021). Cognitive activation potential of E&S tasks at commercial vocational schools in German speaking Switzerland. In M. Blikstad-Balas, K. Klette, & M. Tengberg (Eds.), Ways of analyzing teaching quality: potentials and pitfalls (pp. 204-228). Scandinavian University Press. https://doi.org/10.18261/9788215045054-2021-07

Willig, G. (2013). Introducing qualitative research in psychology (3rd ed.). Open University Press.

Þórðardóttir, Þ. & Hermannsson, U. (2012). Úttekt á stærðfræðikennslu á unglingastigi grunnskóla [A report on mathematics teaching in lower secondary schools]. Ministry of Education, Science, and Culture.

Downloads

Published

2024-06-01

How to Cite

Sigurjónsson, J. Örn. (2024). Teaching mathematics with high cognitive activation: instructional formats and connection-making interactions in high-level Nordic lessons. NOMAD Nordic Studies in Mathematics Education, 29(2). Retrieved from https://tidsskrift.dk/NOMAD/article/view/146422