Teachers’ beliefs and instructional quality of Languaging in primary school mathematics

Eunji Kim; Päivi Perkkilä; Jorma Joutsenlahti

doi:10.31129/LUMAT.13.1.2752

Authors

Eunji Kim Tampere University, Finland https://orcid.org/0000-0002-1064-4972
Päivi Perkkilä University of Turku, Finland https://orcid.org/0000-0001-7680-6420
Jorma Joutsenlahti Tampere University, Finland https://orcid.org/0000-0002-6043-5255

DOI:

https://doi.org/10.31129/LUMAT.13.1.2752

Keywords:

Languaging, teachers' beliefs, instructional quality, mathematics education, primary school

Abstract

Despite its inclusion in the Finnish national curriculum, the Languaging approach— teaching mathematics through diverse tools and interactive activities—remains challenging to implement in practice. Teachers’ beliefs shaped by prior schooling and the decontextualization of Languaging in local curricula can hinder interpretation and enactment. This study examined primary teachers’ beliefs development, their interpreted curricula around Languaging, and the enacted curricula as evidenced in classroom instructional quality. Using a qualitative multiple-case design, we purposively sampled six teachers who actively integrate Languaging; data collection included surveys, interviews, classroom observations with field notes. Qualitative data were analyzed thematically within and across cases; quantitative rubric scores (1–4) were summarized with medians. Findings indicate that teachers’ beliefs are shaped by personal learning histories and evolve through reflective engagement with Languaging. The interpreted curricula commonly emphasized foundational knowledge and skills, as well as the relevance of mathematics in daily life. The enacted curricula showed high and stable performance in functional learning environment, purposeful material use, and teacher-led multiple representations, alongside lower and more variable performance in student-generated representations, sustained conceptual press, and differentiation. The discussion identifies implications for teachers, teacher educators, local curriculum developers, and policymakers.

References

Artemenko, C., Masson, N., Georges, C., Nuerk, H.-C., & Cipora, K. (2021). Not all elementary school teachers are scared of math. Journal of Numerical Cognition, 7(3), 275–294. https://doi.org/10.5964/jnc.6063 DOI: https://doi.org/10.5964/jnc.6063

Bekdemir, M. (2010). The pre-service teachers’ mathematics anxiety related to depth of negative experiences in mathematics classroom while they were students. Educational Studies in Mathematics, 75(3), 311–328. https://doi.org/10.1007/s10649-010-9260-7 DOI: https://doi.org/10.1007/s10649-010-9260-7

Cai, J., & Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: Conceptualization and initial findings of a problem‑posing project. ZDM Mathematics Education, 53(6), 1403–1416. https://doi.org/10.1007/s11858-021-01252-3 DOI: https://doi.org/10.1007/s11858-021-01252-3

Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education (5th ed.). Routledge. https://doi.org/10.4324/9780203224342 DOI: https://doi.org/10.4324/9780203224342

Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Sage.

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics Teaching: The State of the Art (pp. 249–254). Falmer Press.

Finnish National Agency for Education (EDUFI). (2016). National core curriculum for basic education 2014 (Publication 2016:5). https://www.ellibslibrary.com/book/9789521362590

Finnish National Agency for Education (EDUFI). (2021). Teachers and principals in Finland 2019 [Brochure]. Finnish National Agency for Education. https://www.oph.fi/sites/default/files/documents/teachers_and_principals_in_finland_2019.pdf

Hannula, M. S. (2020). Affect in mathematics education. In S. Lerman (Ed.), Encyclopedia of mathematics education (2nd ed., pp. 32–36). Springer. https://doi.org/10.1007/978-3-030-15789-0_174 DOI: https://doi.org/10.1007/978-3-030-15789-0_174

Hart, L. C. (2004). Beliefs and perspectives of first-year, alternative preparation, elementary teachers in urban classrooms. School Science and Mathematics, 104(2), 79–88. https://doi.org/10.1111/j.1949-8594.2004.tb17985.x DOI: https://doi.org/10.1111/j.1949-8594.2004.tb17985.x

Hemmi, K., Krzywacki, H., & Koljonen, T. (2018). Investigating Finnish teacher guides as a resource for mathematics teaching. Scandinavian Journal of Educational Research, 62(6), 911–928. https://doi.org/10.1080/00313831.2017.1307278 DOI: https://doi.org/10.1080/00313831.2017.1307278

Joutsenlahti, J., & Kulju, P. (2015). Kielentäminen matematiikan ja äidinkielen opetuksen kehittämisessä. https://trepo.tuni.fi/handle/10024/98022

Joutsenlahti, J., & Perkkilä, P. (2024). Mastery of the concept of percentage and its representations in Finnish comprehensive school grades 7–9. Education Sciences, 14(10), 1043. https://doi.org/10.3390/educsci14101043 DOI: https://doi.org/10.3390/educsci14101043

Joutsenlahti, J., & Rättyä, K. (2015). Kielentämisen käsite ainedidaktisissa tutkimuksissa. Suomen Ainedidaktinen Tutkimusseura, 8, 45–62.

Kalantzis, M., Cope, B., Chan, E., & Dalley-Trim, L. (2012). Literacies. Cambridge University Press. DOI: https://doi.org/10.1017/CBO9781139196581

Kim, E. (2024, October 31). Languaging effects on pre-service class teachers’ mathematical beliefs and attitudes [Conference presentation]. Matematiikan ja luonnontieteiden opetuksen tutkimuspäivät 2024, University of Eastern Finland, Joensuu, Finland.

Kim, E., Mallat, E., & Joutsenlahti, J. (2023). A systematic review of primary school class teachers views of mathematics teaching and learning. LUMAT: International Journal on Math, Science and Technology Education, 11(2). https://doi.org/10.31129/LUMAT.11.2.2055 DOI: https://doi.org/10.31129/LUMAT.11.2.2055

Klette, K. (2023). Classroom observation as a means of understanding teaching quality: Towards a shared language of teaching? Journal of Curriculum Studies, 55(1), 49–62. https://doi.org/10.1080/00220272.2023.2172360 DOI: https://doi.org/10.1080/00220272.2023.2172360

Krzywacki, H., Pehkonen, L., & Laine, A. (2016). Promoting mathematical thinking in Finnish mathematics education. In H. Niemi, A. Toom, & A. Kallioniemi (Eds), Miracle of Education (pp. 109–123). SensePublishers. https://doi.org/10.1007/978-94-6300-776-4_8 DOI: https://doi.org/10.1007/978-94-6300-776-4_8

Kuhs, T., & Ball, D. L. (1986). Approaches to teaching mathematics: Mapping the domains of knowledge, skills, and dispositions. National Center for Research on Teacher Education, Michigan State University.

Kupari, P. (2007). The significance of reading, communication and dialogue in learning mathematics. In L. P & A. I (Eds.), Finnish reading literacy: When quality and equity meet (pp. 215–228). Institute for Educational Research, University of Jyväskylä.

Lehtonen, D. (2022). ‘Now I get it!’ Developing a real-world design solution for understanding equation-solving concepts [Doctoral dissertation, Tampere University]. Trepo. https://urn.fi/URN:ISBN:978-952-03-2250-2

Liljedahl, P., & Andrà, C. (2020). Emotions and learning. In C. Andrà, D. Brunetto, & F. Martignone (Eds.), Theorizing and measuring affect in mathematics teaching and learning (pp. 3–10). Springer International Publishing. https://doi.org/10.1007/978-3-030-50526-4_1 DOI: https://doi.org/10.1007/978-3-030-50526-4_1

Luoto, J. M., Klette, K., & Blikstad-Balas, M. (2022). Patterns of instruction in Finnish and Norwegian lower secondary mathematics classrooms. Research in Comparative and International Education, 17(3), 399–423. https://doi.org/10.1177/17454999221077848 DOI: https://doi.org/10.1177/17454999221077848

Ministry of Education and Culture. (2023). Results from PISA 2022. https://okm.fi/en/pisa-2022-en

Olsson, J., & Granberg, C. (2024). Teacher-student interaction supporting students’ creative mathematical reasoning during problem solving using Scratch. Mathematical Thinking and Learning, 26(3), 278–305. https://doi.org/10.1080/10986065.2022.2105567 DOI: https://doi.org/10.1080/10986065.2022.2105567

Palsa, L., & Mertala, P. (2022). Disciplinary contextualisation of transversal competence in Finnish local curricula: The case of multiliteracy, mathematics, and social studies. Education Inquiry, 13(2), 226–247. https://doi.org/10.1080/20004508.2020.1855827 DOI: https://doi.org/10.1080/20004508.2020.1855827

Pehkonen, E. (1993). What are Finnish teacher educators’ conceptions about the teaching of problem solving in mathematics? European Journal of Teacher Education, 16(3), 237–256. https://doi.org/10.1080/0261976930160306 DOI: https://doi.org/10.1080/0261976930160306

Pehkonen, E., & Törner, G. (1995). Mathematical belief systems and their meaning for the teaching and learning of mathematics. In G. Törner (Ed.), Current state of research on mathematical beliefs: Proceedings of the MAVI Workshop (October 4–5, 1995, Duisburg, Germany) (pp. 1–14). University of Duisburg.

Perkkilä, P. (2003). Primary school teachers’ mathematics beliefs and teaching practices. In M. A. Mariotti (Ed.), Proceedings of CERME 3: Third Conference of the European Society for Research in Mathematics Education (28 February–3 March 2003, Bellaria, Italy).

Perkkilä, P., & Joutsenlahti, J. (2021). Academic literacy supporting sustainability for mathematics education—A case: Collaborative working as a meaning making for ‘2/3’? In E. Jeronen (Ed.), Transitioning to Quality Education (Vol. 41, pp. 163–188). MDPI. https://doi.org/10.3390/books978-3-03897-893-0-8 DOI: https://doi.org/10.3390/books978-3-03897-893-0-8

Piaget, J. (1952). The origins of intelligence in children. (M. Cook, Trans.). W. W. Norton & Company. https://doi.org/10.1037/11494-000 DOI: https://doi.org/10.1037/11494-000

Pikk, K., Leijen, Ä., Radišić, J., & Uibu, K. (2025). Exploring the relationship between teachers’ beliefs on the nature and learning of mathematics and self-efficacy in teaching mathematics at the primary school level. LUMAT: International Journal on Math, Science and Technology Education, 13(1), Article 3. https://doi.org/10.31129/LUMAT.13.1.2504 DOI: https://doi.org/10.31129/LUMAT.13.1.2504

Purnomo, Y. W., Suryadi, D., & Darwis, S. (2016). Examining pre-service elementary school teacher beliefs and instructional practices in mathematics class. International Electronic Journal of Elementary Education, 8(4), 629–642.

Rinneheimo, K.-M., & Suhonen, S. (2022). Languaging and conceptual understanding in engineering mathematics. LUMAT: International Journal on Math, Science and Technology Education, 10(2). https://doi.org/10.31129/LUMAT.10.2.1729 DOI: https://doi.org/10.31129/LUMAT.10.2.1729

Russo, J., Bobis, J., Sullivan, P., Downton, A., Livy, S., McCormick, M., & Hughes, S. (2020). Exploring the relationship between teacher enjoyment of mathematics, their attitudes towards student struggle and instructional time amongst early years primary teachers. Teaching and Teacher Education, 88, Article 102983. https://doi.org/10.1016/j.tate.2019.102983 DOI: https://doi.org/10.1016/j.tate.2019.102983

Sahlberg, P., & Walker, T. D. (2021). In teachers we trust: The Finnish way to world-class schools. W.W. Norton & Company.

Sánchez Mendías, J., Segovia Alex, I., & Miñán Espigares, A. (2020). Anxiety and self-confidence toward mathematics in preservice primary education teachers. Electronic Journal of Research in Educational Psychology, 18(51), 127–152.

Schaeffer, M. W., Rozek, C. S., Maloney, E. A., Berkowitz, T., Levine, S. C., & Beilock, S. L. (2021). Elementary school teachers’ math anxiety and students’ math learning: A large-scale replication. Developmental Science, 24(4), e13080. https://doi.org/10.1111/desc.13080 DOI: https://doi.org/10.1111/desc.13080

Schlesinger, L., Jentsch, A., Kaiser, G., König, J., & Blömeke, S. (2018). Subject-specific characteristics of instructional quality in mathematics education. ZDM Mathematics Education, 50(3), 475–490. https://doi.org/10.1007/s11858-018-0917-5 DOI: https://doi.org/10.1007/s11858-018-0917-5

Stewart, M. (2021). Understanding learning. In L. Hunt & D. Chalmers (Eds.), University Teaching in Focus (2nd edn, pp. 3–28). Routledge. https://doi.org/10.4324/9781003008330-2 DOI: https://doi.org/10.4324/9781003008330-2

Teig, N., Nilsen, T., & Yang Hansen, K. (Eds.). (2024). Effective and equitable teacher practice in mathematics and science education: A Nordic perspective across time and groups of students (Vol. 14). Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-49580-9 DOI: https://doi.org/10.1007/978-3-031-49580-9

Thompson, A. G. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 127–146). Macmillan Publishing.

Ukkola, A., Suomilammi, M., Silverström, C., Metsämuuronen, J., & Marjanen, J. (2025). Matematiikan ja äidinkielen taidot kuudennen luokan lopussa (1). Finnish Education Evaluation Centre (FINEEC). https://www.karvi.fi/sites/default/files/sites/default/files/documents/KARVI_0125.pdf

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press.

Yin, R. K. (2018). Case study research and applications: Design and methods (6th ed.). Sage.