Comparison of Instructional Practices in Norwegian and Finnish-Swedish Mathematics Classrooms: Representation of content

Author(s):

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

Conference:

ECER 2017

Network:

27. Didactics - Learning and Teaching

Format:

Paper

Session Information

27 SES 06 A 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

Mathematical content requires representation in a rich and meaningful way in order for young students to be able to achieve mathematical competence, which is important for understanding and participating in public debate, and developing technology and solutions for emerging issues related to environment, poverty and health (Kilpatrick et al., 2001; UNESCO, 2012). Research has shown that teachers’ instructional practices make a difference to students’ learning (Hattie, 2012; Seidel & Shavelson, 2007) and that instruction shapes what students learn (Boaler, 2000, p. 172).

The present study examines teachers’ representation of mathematical content in Norwegian (Oslo area) and Finnish-Swedish (Helsinki area) 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. The analytical framework applied consists of parts of an observation manual (PLATO, see methods section), called Representation and use of content, which is divided into four sub-elements: Connections to prior academic knowledge, Purpose,Quality of instructional explanations, and Conceptual richness of instructional explanations. ‘Connections to prior academic knowledge’ captures to what degree teachers elicit and connect prior knowledge to new content, which is considered important for developing conceptual understanding (Greeno, 2006; Hiebert & Grouws, 2007). The element ‘Purpose’ encompasses to what degree learning goals are made explicit. Research suggests children benefit when purposes and goals of their work are clearly articulated and the relationship between what they learn and broader goals are clear (Borko & Livingston, 1989). ‘Quality of instructional explanations’ of content involves making students pay attention to similarities and differences of concepts and procedures (Zaslavsky & Sullivan, 2011) and whether teacher pays attention to normal misconceptions, focus on students’ thinking and address emerging misunderstandings (Ball & Hill, 2009). ‘Conceptual richness of instructional explanations’ captures to what degree deeper conceptual understanding is provided in explanations, in relation to procedural attention. This entails whether content is represented in a context relevant for students, facilitating later refinement of content into generalized strategies (Anthony & Walshaw, 2009) and makes mathematics meaningful for students (Cobb & Yackel, 1998). Still, researchers stress that conceptual understanding and learning procedures ought to be developed in conjunction (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

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 formats and patterns observed during our video material students are parts of a complex lesson and planning cycle. It is unrealistic to expect teachers to make consistent reference to for example ‘Purpose’ through a whole lesson, thus all classrooms were observed during three-four sequential lessons to allow a more contextual description of the instruction. The participants of this study consist of teachers and students from eight classrooms in Norway and eight classrooms in Finland where the mathematical content dealt with during the lesson is numbers, algebra or geometry. These classrooms were chosen because the teachers taught similar content in both contexts and they represent schools located in both inside and outside city schools in Oslo and Helsinki, as well as socioeconomically different areas. The data was collected during the school years 2014-2016. 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. The lessons were coded in 15 minute segments for instructional patterns on a 1-4 scale of one of the four PLATO domains, Representation and use of content.

Expected Outcomes

Findings suggest that there are patterns of variation and similarity in how Oslo and Helsinki teachers represent content, as it is defined in this study. While teachers in both contexts pay mostly attention to procedures rather than conceptual understanding when providing explanations, Helsinki teachers more often scored at the high end of quality of instructional explanation, indicating addressing student misconceptions, and provided different examples to a greater extent than Oslo teachers. The Helsinki teachers more often referred to previous mathematical knowledge, generally occurring during homework check and when introducing new content. In both contexts learning goals were frequently framed as activities. Somewhat more often Helsinki teachers referred to explicit learning goals, usually in settings of mathematics relevant for upcoming tests. Where Oslo teachers spent the majority of segments in whole class instruction format, the learning in Helsinki classrooms was more individualized and the majority of the segments were individual seatwork. Representation of content was thus executed during different instructional formats. Another key finding is that it was the same teachers scoring consistently scoring high in both contexts. The findings of this study renews debate on discussing whether the instructional practices in classrooms corresponds to the need of mathematical competence and especially development of conceptual understanding as stated by research (Kilpatrick et al., 2001) and implied by the national curriculums in the two countries (Kunnskapsdepartementet, 2013; Opetushallitus, 2014). As there is a recognized need to develop students’ mathematical competence nationally as well as internationally, this study is highly relevant for teachers and teacher educators in both contexts as well as internationally.

References

Ball, D. L., & Hill, H. (2009). Measuring Teacher Quality in Practice. In D. H. Gitomer (Ed.), Measurement Issues and Assessment for Teaching Quality (pp. 80-98). Los Angeles: Sage Publications. 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 Borko, H., & Livingston, C. (1989). Cognition and Improvisation: Differences in Mathematics Instruction by Expert and Novice Teachers. American Educational Research Journal, 26(4), 473-498. doi:10.3102/00028312026004473 Cobb, P., & Yackel, E. (1998). A constructivist perspective on the culture of the mathematics classroom. In F. Seeger, J. Voigt, & U. Waschescio (Eds.), The Culture of the Mathematics Classroom (pp. 158-190). Cambridge: Cambridge University Press. Cohen, J. (2015). Challenges in Identifying High-Leverage Practices. Teach. Coll. Rec., 117(7). Greeno, J. (2006). Theoretical and Practical Advances Through Research on Learning. In J. L. Green, G. Camilli, P. B. Elmore, A. Skukauskaitė, & E. Grace (Eds.), Handbook of Complementary Methods in Education Research: Routledge. Grossman, P. (2015). Protocol for Language Arts Teaching Observations (PLATO 5.0). Palo Alto: Stanford University. Hattie, J. (2012). Visible learning for teachers : maximizing impact on learning. London: Routledge. Hiebert, J., & Grouws, A. D. (2007). The effects of classroom mathematics teaching on studnets' learning Second handbook of research on mathematics teaching and learning (pp. 371-404). Charlotte, N.C: Information Age. 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. 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 Star, J. R. (2005). Reconceptualizing Procedural Knowledge. Journal for Research in Mathematics Education, 36(5), 404-411. UNESCO. (2012). Challenges in basic mathematics education: United Nations Educational, Scientific and Cultural Organization.

Author Information

Jennifer Luoto (presenting / submitting)

University of Oslo

Department of Teacher Education and School Research

Oslo

Kirsti Klette

University of Oslo, Norway

Marte Blikstad-Balas

University of Oslo

Dept of Teacher Education and School Research