Comparing Instrucional Practices In Norwegian And Finnish-Swedish Mathematics Classrooms

Author(s):

Jennifer Luoto(presenting / submitting)Kirsti Klette Marte Blikstad-Balas

Conference:

ECER 2017

Network:

24. Mathematics Education Research

Format:

Paper (Copy for Joint Session)

Session Information

24 SES 06 JS, Cultural Approach in Mathematics Education

Joint Paper Session NW 24 and NW 27

Time:

2017-08-23

15:30-17:00

Room:

K6.04

Chair:

Florence Ligozat

Contribution

Objectives and theoretical frameworks

Mathematics proficiency is considered a prerequisite for all students to become full participants in a knowledge-based society (Organisation For Economic & Development, 2016). Research has shown that teachers’ instructional practices make a difference to students’ learning in general (Hattie, 2012; Seidel & Shavelson, 2007), and for developing students’ mathematical proficiency (Kilpatrick et al., 2001).

In order to understand and gain knowledge about what mathematical proficiencies and learning goals teachers emphasize during their instruction, the present study examines instructional practices and how new content is introduced in Norwegian and Finnish-Swedish 7^th and 8^th grade classrooms. This is the same age group of 13-year olds, since Norwegian students start school at the age of 6 and Finnish students at the age of 7. Instructional practices where teaching a concept only means pointing out definitions and rules, followed by the teacher stating procedures, provokes some students to view mathematics as an unrelated set of rules and procedures (Kaasila, 2009). While for others, this kind of procedure may be preferable. How teachers introduce content depends on what kind of content is at focus, as some content may allow a different approach than other (Hill & Grossman, 2013). Therefore this study compares the introduction of new content in both national contexts, namely algebra and geometry. Algebra related content is introduced in three different Finnish-Swedish and three Norwegian classrooms, while geometry-related content is introduced in one Finnish-Swedish and two Norwegian classrooms (N= 9).

The theoretical framework applied is Kilpatrick et al. (2001) five strands of mathematical proficiency, in order to operationalize what mathematical proficiencies teachers prioritize their students to acquire and develop when they introduce new content. The five strands are; Conceptual understanding, meaning comprehension of mathematical concepts, operations and relations; Procedural fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately; Strategic competence – ability to formulate, represent, and solve mathematical problems; Adoptive reasoning – capacity for logical thought, reflection, explanation, and justification; Productive disposition – habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy. Albeit some disagreement in the field of mathematical education research on how to define mathematical proficiencies and which are of greater importance, researchers highlight the need to develop strands of proficiency in conjunction, especially conceptual understanding and procedural fluency (Baroody, Feil, & Johnson, 2007; Star, 2005). This is also in line with the standards set in the national curriculums in Norway (Kunnskapsdepartementet, 2013) and in Finland (Opetushallitus, 2014).

Method

Methods Video recordings have proven to be a powerful tool for educational research in classrooms as it generates detailed insight of social interactions in real time (Knoblauch, Hubert, Schnettler, & Bernt, 2012). However, issues such as contextualization are important to address when using videos, especially when comparing different context (Blikstad-Balas, 2016). The instructional practices teachers apply when introducing new mathematical content to their students is one part of a complex lesson and planning cycle. All classrooms were observed during four sequential lessons to allow a more contextual description of the introduction event. Thus, the events of introducing new content are not looked at as isolated features but as intertwined with many other lesson components. The participants of this study consist of teachers and students from five classrooms in Norway and four classrooms in Finland where the teacher introduces new mathematical content in algebra or geometry. These classrooms were chosen because the teachers introduced similar new content in both contexts for the students and they represent schools located in both rural and urban areas, as well as socioeconomically different areas. The new content concerns different computations within algebra as well as how to calculate areal of polygons. The data was collected during the school year 2014/2015. The video design relied on two cameras in each classroom, one capturing the entire classroom and one focusing on the teacher. This study utilizes elements from the standardized and theory-based observation protocol PLATO (Grossman, 2015), designed to code language arts instruction and modified for reliable scoring in math teaching (Cohen, 2015), to analyze teacher instruction and emphasis on mathematical proficiencies. The cross cultural and comparative nature of the study enhances understanding of one’s own practices by contrasting with another context, and hence facilitates new perspectives.

Expected Outcomes

Initial findings of this study suggest there is a greater variation of instructional practices overall in the Norwegian classrooms than in the Finnish-Swedish classrooms. While introducing new content, Norwegian teachers spent more time instructing during whole class sessions than the teachers in the Finnish-Swedish classrooms. Whereas the focus of instruction in the Finnish classrooms concentrated mostly on procedural fluency, learning of rules and practicing procedures, the instruction in the Norwegian classrooms were also focusing on conceptual understanding during the introduction events. There were exceptions in both contexts. For example, one teacher in a Finnish-Swedish classroom spent a long time trying to develop students’ conceptual understanding and adaptive reasoning when introducing areal calculations of polygons. These initial findings suggest that in both contexts there is variance in how teachers introduce new content and what mathematical proficiencies they emphasize. However, there is an initial pattern starting to form suggesting conceptual understanding is given less priority in the Finnish-Swedish classrooms than in Norwegian classrooms, which can be seen in relation to previous research showing gaps in Finnish students conceptual understanding of mathematics (Hannula, Pehkonen, Maijala, & Soro, 2006). These findings are also interesting in relation to studies like Haapasalo (2003) and Simola (2005) which suggests that the explanations for Finnish students’ success in PISA may lie outside mathematics teaching. The initial findings of this study renews debate on discussing whether the instructional practices in classrooms corresponds to the need of mathematical proficiency as stated by research (Kilpatrick et al., 2001), the OECD (Organisation For Economic & Development, 2016) and implied by the national curriculums in the two countries (Kunnskapsdepartementet, 2013; Opetushallitus, 2014). As there is a recognized need to develop students’ mathematical proficiencies nationally and internationally, this study is highly relevant for teachers and teacher educators in both contexts as well as internationally.

References

Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An Alternative Reconceptualization of Procedural and Conceptual Knowledge. Journal for Research in Mathematics Education, 38(2), 115-131. Blikstad-Balas, M. (2016). Key challenges of using video when investigating social practices in education: contextualization, magnification, and representation. International Journal of Research & Method in Education, 1-13. doi:10.1080/1743727X.2016.1181162 Cohen, J. (2015). Challenges in Identifying High-Leverage Practices. Teach. Coll. Rec., 117(7). Grossman, P. (2015). Protocol for Language Arts Teaching Observations (PLATO 5.0). Palo Alto: Stanford University. Haapasalo, L. (2003). The conflict between conceptual and procedural knowledge: Should we need to understand in order to be able to do, or vice versa?2017. Retrieved from Hannula, M. S., Pehkonen, E., Maijala, H., & Soro, R. (2006). Levels of students' understanding on infinity. Teaching Mathematics and Computer Science, 4(2), 317-337. doi:10.5485/TMCS.2006.0129 Hattie, J. (2012). Visible learning for teachers : maximizing impact on learning. London: Routledge. Hill, H., & Grossman, P. (2013). Learning from Teacher Observations: Challenges and Opportunities Posed by New Teacher Evaluation Systems. Harvard Educational Review, 83(2), 371-384,401. Kaasila, R. P., Erkki. (2009). Effective mathematics teaching in Finland through the eyes of elementary student teachers. In J. K. Cai, Gabriel; Perry, Bob; Wong, Ngai-Ying (Ed.), Effective Mathematics Teaching from Teachers' Perspectives (pp. 203-216). Rotterdam: Sense Publishers. Kilpatrick, J., Swafford, J., Findell, B., Mathematics Learning Study, C., National Research Council Center for Education, D. o. b., & social sciences, e. (2001). Adding it up : helping children learn mathematics. Washington, DC: National Academy Press. Knoblauch, Hubert, Schnettler, & Bernt. (2012). Videography: analysing video data as a ‘focused’ ethnographic and hermeneutical exercise. Qualitative Research, 12(3), 334-356. doi:10.1177/1468794111436147 Kunnskapsdepartementet. (2013). Læreplan i matematikk fellesfag. https://www.udir.no/kl06/MAT1-04. Opetushallitus. (2014). Grunderna för läroplanen för den grundläggande utbildningen 2014. http://www.oph.fi/lp2016/grunderna_for_laroplanen. Organisation For Economic, C.-O., & Development. (2016). PISA 2015 Results (Volume I): Excellence and Equity in Education: Paris: OECD Publishing. Seidel, T., & Shavelson, R. J. (2007). Teaching Effectiveness Research in the Past Decade: The Role of Theory and Research Design in Disentangling Meta-Analysis Results. Review of Educational Research, 77(4), 454-499. doi:10.3102/0034654307310317 Simola, H. (2005). The Finnish miracle of PISA: historical and sociological remarks on teaching and teacher education. Comparative Education, 41(4), 455-470. doi:10.1080/03050060500317810 Star, J. R. (2005). Reconceptualizing Procedural Knowledge. Journal for Research in Mathematics Education, 36(5), 404-411.

Author Information

Jennifer Luoto (presenting / submitting)

University of Oslo, Norway

Kirsti Klette

University of Oslo, Norway

Marte Blikstad-Balas

University of Oslo, Norway

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