Examining Interrelations Between Variation in Instructional Practices and Student Attitudes to Mathematics in Norwegian Lower Secondary Classrooms.

Author(s):

Ole Kristian Bergem(presenting / submitting)

Conference:

ECER 2014

Network:

03. Curriculum Innovation

Format:

Paper (Copy for Joint Session)

Session Information

03 SES 10 JS, Issues of Achievement and Curriculum in Mathematics Education

Paper Session, Joint Session NW 3 and NW 24

Time:

2014-09-04

15:30-17:00

Room:

B113 Sala de Aulas

Chair:

Ole Kristian Bergem

Contribution

In comprehensive meta-studies of educational research, a close relationship between affective factors, motivational factors and student proficiency in mathematics is reported (Marzano, 2003; Hattie, 2009). These findings are supported in large scale international studies like PISA and TIMSS (Mullis, Martin & Foy, 2008; OECD 2010). An urgent challenge within educational research is therefore to discover and examine key factors that seem to support student development of positive attitudes towards mathematics.

The main ambition of the current analysis is to investigate the relation between variation in instructional practices and student attitudes to mathematics in Norwegian lower secondary classrooms. The research question is:

How does instructional variation seem to influence student’s attitudes towards mathematics?

The analysis is based on data from the PISA+ Video Study and the TIMSS 2007 Study. In both these studies, which have quite different designs, data about classroom instruction in mathematics and student attitudes to mathematics were collected. PISA+ provides video data of mathematics lessons that through coding can be used to examine the degree of instructional variation, and interview data that gives information about students’ attitudes to mathematics. One important instrument in the TIMSS Study design is the Student Questionnaire. Some of the questions and propositions that are formulated in this Questionnaire afford information about students’ attitudes to mathematics and others provide data about various aspects and qualities of instruction, for example the frequency of certain activities taking place during mathematics lessons. Based on these data sources, the two constructs “student attitudes to mathematics” and “instructional variation” were developed and a positive correlation between the constructs was found. It should be mentioned that the values of the two TIMSS’ constructs are computed on the basis of only the Norwegian 8^th grade students’ answers.

One approach to research on motivational factors and achievement has been to study this theme in relation to aspects of teaching quality. Operationalizing teaching quality is challenging, and has been done in various ways in educational studies within mathematics, i.e. as “time on task” (Berliner, 1987), variation in content coverage (Rowan, Harrison &
Hayes 2003), the use of higher order questioning (Kilpatrick, Swafford & Findell, 2001; Ball, Thames & Phelps, 2009), the quality of instructional conversations (Cobb, Yackel & McClain, 2000; Sfard, 2000) or more generally by contrasting the use of reform based instructional methods to traditional or conventional teaching methods, i.e. “direct teaching”, review and practice of routine mathematical skills (Boaler, 2002).

An aspect of teaching quality that often is debated within mathematics education, and which is strongly recommended, is to vary the working methods applied in the classroom (Resnick & Harwell, 2000; Kilpatrick, Swafford & Findell, 2001; Boaler, 2002). From studies using student interviews it is often reported that many students themselves express that they would have preferred that the mathematics lessons were less monotonous and more varied (Boaler, 2002; Nardi & Steward, 2003; Lee & Johnston-Wilder, 2013). Nevertheless, few studies have tried to operationalize variation as an aspect of teaching quality and make inquiries into its effect on student attitudes. An important objective of the current study is to make a contribution in this respect.

Method

In the TIMSS 2007 Questionnaire the students answered a multitude of questions aiming to measure different background variables assumed to influence student achievement. These questions covered a range of different issues. In the current study two constructs are developed based on data from this Questionnaire. The first one is a modified version of a construct previously reported in the TIMSS 2007 study, named “Attitude Toward Mathematics” (ATM) (Mullis, Martin & Foy, 2008). The second construct was calculated based on individual student answers to a set of questions about classroom instruction. By recoding the students’ answers, a construct named “Instructional Variation in Mathematics” (IVM) has been developed. In the next step of analysis, the values of the two constructs were aggregated on the classroom level, to provide more precise and robust measures, and finally the correlation between the constructs were calculated by the use of SPSS. Another set of data is provided by the PISA+ Video Study. In this study, which was carried out in Norway in the period 2005 – 2008, 31mathematics lessons in 6 different classrooms were video filmed and 61 students were interviewed. The lessons were later analyzed on the basis of sets of theory based categories and codes developed by project members (Klette et al., 2005; Ødegaard, Arnesen & Bergem, 2006). Encoding of video captures was done through the use of Videograph, a software program developed in Germany (Rimmele, 2002). The coding was initially done in second intervals, but later this was transferred to minute intervals. One main category used in the subject specific analysis of the mathematics lessons was called "Teaching Activities". This category consisted of 8 separate codes of teaching activities, making it possible to discover different teaching patterns in the 6 classrooms. One interesting finding was that some teachers had a more varied repertoire of teaching activities than others. Based on this finding, the classrooms were clustered in two groups, constituting Group LV (Low Variation) and Group HV (High Variation). In the interviews, all the involved students were asked about their attitudes to mathematics. They were also prompted to give reasons for their attitudes to this subject. In the analysis of this paper, the students were grouped according to their positive /negative assertions on whether they liked mathematics.

Expected Outcomes

Based on the constructs developed form the TIMSS 2007 data, a significant positive correlation was found between ATM and IVM. Interpreting correlations between different constructs should always be done very cautiously, but it seems reasonable to argue that the correlation between these two constructs indicates that providing a greater variation in activities in the mathematics classroom influences students’ attitudes towards mathematics positively. Table 1: Correlation coefficients between ATM and IVM (classroom level) ATM IVM ATM 0,22** ** Correlation is significant at the 0.01 Level An interesting finding in the PISA+ Video Study was that 92 % of the students belonging to the Group HV classrooms expressed positive attitudes to mathematics in the interviews. Several of these students emphasized the important role played by the teacher for their own liking of the subject. When asked specifically why they liked mathematics, the students pointed to the teacher and the way he/she organized the activities in the classroom as a main reason for their positive attitudes. Only 45 % of the students in the Group LV classrooms expressed positive attitudes to mathematics. Many of the students that disliked mathematics (55 %) argued that the mathematics lessons were boring because “it’s just the same stuff over and over again”, clearly indicating a lack of variation in student activities in mathematics lessons. Table 2: Percentage of interviewed students in the PISA+ study who stated that they liked/disliked mathematics Group Like mathematics Do not like mathematics Number of students interviewed LV 45 % 55 % 23 HV 92 % 8 % 25 The analysis in this paper gives support to the notion that increased levels of instructional variation can positively stimulate student attitudes to mathematics.

References

Ball, D., Thames, M. H., & Phelps, G. (2009). Content knowledge for teaching. What makes it special? Journal of Teacher Education, 59(5), 389–407. Berliner, D. C. (1987). Simple views of effective teaching and a simple theory of classroom instruction. In D. C. Berliner & B. Rosenshine (Eds.), Talks to teachers (93-110). New York: Random House. Boaler, J. (2002). Experiencing School Mathematics. Traditional and Reform Approaches to Teaching and Their Impact on Student Learning. Mahwah, N.J.: Lawrence Erlbaum Ass. Cobb, P., Yackel, E. & McClain, K. (red.) (2000). Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design. Mahwah, NJ: Lawrence Erlbaum Associates. Hattie, J. (2009). Visible Learning. London: Routledge. Kilpatrick, J., Swafford, J. & Findell, B. (2001). Adding It Up: Helping Children Learn Mathematics. Washington DC: The National Academies Press. Klette, K.(et. al.) (2005). Categories for video analysis of classroom activities with a focus on the teacher. Oslo: University of Oslo. Lee, C. & Johnston-Wilder, S. (2013). Learning mathematics – letting the pupils have their say. Educational Studies in Mathematics, Vol. 83(2), (163-180). Marzano, RJ (2003). What works in school. Alexandria, VA: ASCD. Mullis, I. V. S., Martin, M. O. & Foy, P. (2008). TIMSS 2007 International Mathematics Report. Boston : TIMSS and PIRLS International Study Center. Nardi, E. & Steward, S. (2003). Is Mathematics T.I.R.E.D? A Profile of Quiet Disaffection in the Secondary Mathematics Classroom. British Educational Research Journal, Vol. 29(3), 345-367. OECD 2010: PISA 2009 Results: What Students Know and Can Do – Student Performance in Reading, Mathematics and Science. (Vol. 1). Paris: OECD. Resnick, L. B. & Harwell, M. (2000). Instructional Variation and Student Achievement in a Standards-Based Education District. CSE Technical Report 522. Center for the Study of Evaluation, University of California, Los Angeles. Rimmele, R. (2002). Videograph. Kiel: IPN, Universitetet i Kiel. Nettadresse: http://www.ipn.uni-kiel.de/projekte/video/en_vgfenster.htm. Rowan, B., Harrison, D. M., & Hayes, A. (2004). Using instructional logs to study mathematics curriculum and teaching in the early grades. The Elementary School Journal, 105(1), 103-127. Sfard, A. (2000). Symbolizing mathematical reality into being. I P. Cobb, E. Yackel, & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms: Perspectives on discourse, tools, and instructional design. Mahwah, NJ: Lawrence Erlbaum Associates. Ødegaard, M., Arnesen, N. E. & Bergem, O. K. (2006). Categories for Video Analysis of Mathematics Classroom Activities. Oslo: University of Oslo.

Author Information

Ole Kristian Bergem (presenting / submitting)

University of Oslo, Norway

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