Skip to main content
SpringerLink
Log in

Comparative studies of mathematics teachers’ observable learning objectives: validating low inference codes

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

Videotape is an increasingly used tool in cross-national studies of mathematics teaching. However, the means by which videotaped lessons are coded and analysed remains an underdeveloped area with scholars adopting substantially different approaches to the task. In this paper we present an approach based on generic descriptors of mathematics learning objectives. Exploiting live observations in five European countries, the descriptors were developed in a bottom-up recursive manner for application to videotaped lessons from four of these countries, Belgium (Flanders), England, Hungary and Spain. The analyses showed not only that the descriptors were consistently operationalised but also that they facilitated the identification of both similarities and differences in the ways in which teachers conceptualise and present mathematics that resonated with the available literature. In so doing we make both methodological and theoretical contributions to comparative mathematics research in general and debates concerning the national mathematics teaching script in particular.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. Throughout our study we have regarded Flanders, one of the two autonomous regions of Belgium, as a country in the manner of the third international mathematics and science study (TIMSS) and its repeats.

  2. In addition to an acknowledgement of a mandated national curriculum, English teachers are invited to work within a voluntary framework in which the number, and particular content, of lessons within a topic are specified.

  3. This paper focuses on the one section of the schedule for no other reason than lack of space.

  4. The project team videotaped five lessons during the Spanish observation week and 16 during the formal round of topic-based data collection.

References

  • Alsina, C., & Richard, P. (2001). Reference levels in school mathematics education in Europe: National presentation Spain. Paper presented to the Committee on Mathematics Education, European Mathematical Society.

  • An, S., Kulm, G., & Wu, J. (2004). The pedagogical content knowledge of middle school mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172.

    Article  Google Scholar 

  • Andrews, P. (2003). Opportunities to learn in the Budapest mathematics classroom. International Journal of Science and Mathematics Education, 1(2), 201–225.

    Article  Google Scholar 

  • Andrews, P. (2007a). Negotiating meaning in cross-national studies of mathematics teaching: kissing frogs to find princes. Comparative Education, 43(4), 489–509.

    Article  Google Scholar 

  • Andrews, P. (2007b). The curricular importance of mathematics: a comparison of English and Hungarian teachers’ espoused beliefs. Journal of Curriculum Studies, 39(3), 317–338. doi:10.1080/00220270600773082.

    Article  Google Scholar 

  • Baroody, A. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. Baroody, & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 1–33). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Blanco, L. 2003. The mathematical education of primary teachers in Spain. International Journal of Mathematics Teaching and Learning. Retrieved September 14, 2008, from: http://www.cimt.plymouth.ac.uk/journal/blanco1.pdf

  • Cai, J., & Wang, T. (2006). U.S. and Chinese teachers’ conceptions and constructions of representations: a case of teaching ratio concept. International Journal of Mathematics and Science Education, 4(1), 145–186. doi:10.1007/s10763-005-9006-7.

    Article  Google Scholar 

  • Carrillo, J., & Climent, N. (2005). The mathematics education traditions of Europe (METE) project: the teaching of polygons in primary schools. Paper presented at the biennial conference of the European Association for Research on Learning and Instruction, Nicosia, Cyprus.

  • Clarke, D. (2002). The learner’s perspective study: methodology as the enactment of a theory of practice. Paper presented at the annual meeting of the American Educational Research Association, New Orleans.

  • Clarke, D., Emanuelsson, J., Jablonka, E., & Mok, I. (2006). Making connections: comparing mathematics classrooms around the world. Rotterdam: Sense.

    Google Scholar 

  • Clarke, D., Keitel, C., & Shimizu, Y. (2006). Mathematics classrooms in twelve countries: the insider’s perspective. Rotterdam: Sense.

    Google Scholar 

  • Cogan, L. S., & Schmidt, W. H. (1999). An examination of instructional practices in six countries. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International comparisons in mathematics education (pp. 68–85). London: Falmer.

    Google Scholar 

  • Depaepe, F., De Corte, E., Op’t Eynde, P., & Verschaffel, L. (2005). Teaching percentages in the primary school: a four country comparative study. In L. Verschaffel, E. De Corte, G. Kanselaar, & M. Valcke (Eds.), Powerful environments for promoting deep conceptual and strategic learning (pp. 147–171). Leuven: Leuven University Press.

    Google Scholar 

  • De Bock, D., Verschaffel, L., Janssens, D., Van Dooren, W., & Claes, K. (2003). Do realistic contexts and graphical representations always have a beneficial impact on students’ performance? Negative evidence from a study on modelling non-linear geometry problems. Learning and Instruction, 13(4), 441–463. doi:10.1016/S0959-4752(02)00040-3.

    Article  Google Scholar 

  • Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: the state of the art. Lewes: Falmer.

    Google Scholar 

  • Givvin, K., Hiebert, J., Jacobs, J., Hollingworth, H., & Gallimore, R. (2005). Are there national patterns of teaching? Evidence from the TIMSS 1999 video study. Comparative Education Review, 49(3), 311–343. doi:10.1086/430260.

    Article  Google Scholar 

  • Graham, T., Rowlands, S., Jennings, S., & English, J. (1999). Towards whole-class interactive teaching. Teaching Mathematics and its Applications, 18(2), 50–60.

    Article  Google Scholar 

  • Haggarty, L., & Pepin, B. (2002). An investigation of mathematics textbooks and their use in English, French and German classrooms: who gets an opportunity to learn what. British Educational Research Journal, 28(4), 567–590. doi:10.1080/0141192022000005832.

    Article  Google Scholar 

  • Hatano, G., & Inagaki, K. (1986). Two courses of expertise. In H. Stevenson, H. Azuma, & K. Hakuta (Eds.), Child Development and Education in Japan (pp. 262–272). New York: Freeman.

    Google Scholar 

  • Hiebert, J., & Lefevre, P. (1986). Conceptual knowledge and procedural knowledge in mathematics: an introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: the case of mathematics (pp. 1–27). Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Hiebert, J., & Wearne, D. (1993). Instructional tasks, classroom discourse, and students’ learning in second-grade arithmetic. American Educational Research Journal, 30(2), 393–425.

    Google Scholar 

  • Hiebert, J., Gallimore, R., Garnier, H., Bogard Givvin, K., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries: results from the TIMSS 1999 video study. Washington: National Center for Educational Statistics.

    Google Scholar 

  • Hofstede, G. (1986). Cultural differences in teaching and learning. International Journal of Intercultural Relations, 10(3), 301–320. doi:10.1016/0147-1767(86)90015-5.

    Article  Google Scholar 

  • Hufton, N., & Elliott, J. (2000). Motivation to learn: the pedagogical nexus in the Russian school: some implications for transnational research and policy borrowing. Educational Studies, 26(1), 115–136. doi:10.1080/03055690097772.

    Article  Google Scholar 

  • Jennings, S., & Dunne, R. (1996). A critical appraisal of the National Curriculum by comparison with the French experience. Teaching Mathematics and its Applications, 15(2), 49–55.

    Article  Google Scholar 

  • Kaiser, G., Hino, K., & Knipping, C. (2006). Proposal for a framework to analyse mathematics education traditions in eastern and western traditions. In F. Leung, K.-D. Graf, & F. Lopez-Real (Eds.), Mathematics education in different cultural traditions: a comparative study of East Asia and the West (pp. 319–351). New York: Springer.

    Chapter  Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: helping children learn mathematics. Washington, DC: The National Academies.

    Google Scholar 

  • Knipping, C. (2003). Learning from comparing: a review and reflection on qualitative oriented comparisons of teaching and learning mathematics in different countries. ZDM. Zentralblatt für Didaktik der Mathematik, 35(6), 282–293. ZDM. doi:doi:10.1007/BF02656692.

    Article  Google Scholar 

  • Landis, J., & Koch, G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159–174. doi:10.2307/2529310.

    Article  Google Scholar 

  • LeTendre, G., Baker, D., Akiba, M., Goesling, B., & Wiseman, A. (2001). Teachers’ work: Institutional isomorphism and cultural variation in the U.S. Germany, and Japan. Educational Researcher, 30(6), 3–15. doi:10.3102/0013189X030006003.

    Article  Google Scholar 

  • Leung, F. (1995). The mathematics classroom in Beijing, Hong Kong and London. Educational Studies in Mathematics, 29(3), 297–325. doi:10.1007/BF01273909.

    Article  Google Scholar 

  • Lin, F. -L. (1988). Societal differences and their influence on children’s mathematical understanding. Educational Studies in Mathematics, 19(4), 471–497. doi:10.1007/BF00578695.

    Article  Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • Office for Standards in Education (Ofsted) (2008). Mathematics: understanding the score. London: Ofsted.

    Google Scholar 

  • Organisation for Economic Cooperation and Development (OECD) (2007). Education at a glance: OECD indicators 2007. Paris: OECD.

    Google Scholar 

  • Osborn, M. (2004). New methodologies for comparative research? Establishing ‘constants’ and ‘contexts’ in educational experience. Oxford Review of Education, 30(2), 265–285. doi:10.1080/0305498042000215566.

    Article  Google Scholar 

  • Sayers, J., & Andrews, P.(2005). The mathematics education traditions of Europe (METE) project: the teaching of linear equations. Paper presented at the biennial conference of the European Association for Research on Learning and Instruction. Nicosia, Cyprus.

  • Schmidt, W., Jorde, D., Cogan, L., Barrier, E., Gonzalo, I., Moser, U., et al. (1996). Characterizing pedagogical flow: an investigation of mathematics and science teaching in six countries. Dordrecht: Kluwer.

    Google Scholar 

  • Sharpe, K. (1997). The Protestant ethic and the spirit of Catholicism: ideological and institutional constraints on system change in English and French primary schooling. Comparative Education, 33(3), 329–348. doi:10.1080/03050069728406.

    Article  Google Scholar 

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

    Google Scholar 

  • Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: an analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33(2), 455–488.

    Google Scholar 

  • Stigler, J., & Perry, M. (1990). Mathematics learning in Japanese, Chinese and American classrooms. In J. Stigler, R. Shweder, & G. Herdt (Eds.), Cultural Psychology: essays on comparative human development (pp. 328–353). Cambridge: Cambridge University Press.

    Google Scholar 

  • Stigler, J., Gonzales, P., Kawanaka, T., Knoll, S., & Serrano, A. (1999). The TIMSS video study: Methods and findings from an exploratory research project on eighth grade mathematics instruction in Germany, Japan and the United States. Washington: National Center for Education Statistics.

    Google Scholar 

  • Stigler, J., Gallimore, R., & Hiebert, J. (2000). Using video surveys to compare classrooms and teaching across cultures: examples and lessons from the TIMSS video studies. Educational Psychologist, 35(2), 87–100. doi:10.1207/S15326985EP3502_3.

    Article  Google Scholar 

  • Sutherland, R. (2000). A comparative study of algebra curricula: report prepared for the Qualifications and Curriculum Authority. Bristol: University of Bristol, Graduate School of Education.

    Google Scholar 

  • Szalontai, T. (2000). Some facts and tendencies in Hungarian mathematics teaching. International Journal of Mathematics Teaching and Learning. Retrieved September 14, 2008, from: http://www.cimt.plymouth.ac.uk/journal/tshungmt.pdf

  • Szeredi, E., & Török, J.(2005). Teaching polygons in the secondary school: a four country comparative study. Paper presented to the biennial conference of the European Association for Research into Learning and Instruction, Nicosia, Cyprus.

  • Thompson, A. (1984). The relationship of teachers’ conceptions of mathematics and mathematics teaching instructional practice. Educational Studies in Mathematics, 15(2), 105–127. doi:10.1007/BF00305892.

    Article  Google Scholar 

  • Tweed, R., & Lehman, D. (2002). Learning considered within a cultural context: Confucian and Socratic approaches. The American Psychologist, 57(2), 89–99. doi:10.1037/0003-066X.57.2.89.

    Article  Google Scholar 

  • Ulewicz, M., & Beatty, A. (2001). The power of video technology in international comparative research in education. Washington: National Academy.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M. (1994). Improvement of (didactical) assessment by improvement of problems: an attempt with respect to percentage. Educational Studies in Mathematics, 27(4), 341–372.

    Article  Google Scholar 

  • Van Dooren, W., De Bock, D., Depaepe, F., Janssens, D., & Verschaffel, L. (2003). The illusion of linearity: expanding the evidence towards probabilistic reasoning. Educational Studies in Mathematics, 53(2), 113–138. doi:10.1023/A:1025516816886.

    Article  Google Scholar 

  • Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems. Learning and Instruction, 4(4), 273–294. doi:10.1016/0959-4752(94)90002-7.

    Article  Google Scholar 

  • Wilson, L., Andrew, C., & Sourikova, S. (2001). Shape and structure in primary mathematics lessons: a comparative study in the North-east of England and St Petersburg, Russia—some implications for the daily mathematics lesson. British Educational Research Journal, 27(1), 30–58. doi:10.1080/01411920125004.

    Article  Google Scholar 

  • Yoshida, H., Verschaffel, L., & De Corte, E. (1997). Realistic considerations in solving problematic word problems: Do Japanese and Belgian children have the same difficulties. Learning and Instruction, 7(4), 329–338. doi:10.1016/S0959-4752(97)00007-8.

    Article  Google Scholar 

Download references

Acknowledgements

The mathematics education traditions of Europe (METE) project team gratefully acknowledges the financial support of the European Union, Socrates Action 6.1 programme, project code 2002-5048.

The METE project team were Erik De Corte, Fien Depaepe, Peter Op’t Eynde and Lieven Verschaffel, The Catholic University of Leuven, Belgium; Paul Andrews, Gillian Hatch (sadly deceased) and Judy Sayers, Cambridge, Manchester Metropolitan and Northampton Universities respectively, England; George Malaty and Tuomas Sorvali, University of Joensuu, Finland; Kati Fried, Sári Pálfalvi, Éva Szeredi and Judit Török, Eötvös Loránd University, Budapest, Hungary; and José Carrillo, Nuria Climent and Cinta Muñoz, University of Huelva, Spain.

Author information

Authors and Affiliations

  1. Faculty of Education, University of Cambridge, 184 Hills Road, Cambridge, CB2 8PQ, UK

    Paul Andrews

Authors
  1. Paul Andrews
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul Andrews.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andrews, P. Comparative studies of mathematics teachers’ observable learning objectives: validating low inference codes. Educ Stud Math 71, 97–122 (2009). https://doi.org/10.1007/s10649-008-9165-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10649-008-9165-x

Keywords

Search

Navigation