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«by Lasse Tuomas Savola Dissertation committee: Professor Bruce Vogeli, Sponsor Professor Herbert Ginsburg Professor Robert McClintock Professor O. ...»

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VIDEO-BASED ANALYSIS OF MATHEMATICS CLASSROOM PRACTICE:

EXAMPLES FROM FINLAND AND ICELAND

by

Lasse Tuomas Savola

Dissertation committee:

Professor Bruce Vogeli, Sponsor

Professor Herbert Ginsburg

Professor Robert McClintock

Professor O. Roger Anderson

Professor Patrick Gallagher

Submitted in partial fulfillment of the requirements for the

Degree of Doctor of Philosophy under the Executive Committee of The Graduate School of Arts and Sciences Columbia University 2008 © 2008

LASSE TUOMAS SAVOLA

ALL RIGHTS RESERVED

ABSTRACT

VIDEO-BASED ANALYSIS OF MATHEMATICS CLASSROOM PRACTICE:

EXAMPLES FROM FINLAND AND ICELAND

Lasse Tuomas Savola The method of video analysis can be effective in pedagogical research. With insightful coding schemes, video analysis can generate valuable evidence in the study of the implemented curriculum. The purpose of this study is to explore the power and flexibility of video analysis as an observational tool in classroom research. Furthermore, this dissertation suggests ways in which an individual with limited resources can conduct meaningful video-based classroom research.

Through a review of literature spanning over a century, a historical perspective of video analysis in pedagogical research is outlined. Special attention is paid to video-based studies within the sociocultural, cognitive, and constructivist frameworks.

With recent international studies providing much of the orientation, a method of lesson structure analysis is introduced. The method offers a means of investigating the different forms of classroom interaction teachers use to achieve their pedagogical goals. The method involves two coding passes. The first pass is inspired by the TIMSS 1999 Video Study and is used to distinguish the main pedagogical functions of lesson segments. The second coding pass, which uses ideas from the Learner’s Perspective Study in addition to TIMSS, focuses on the forms of classroom participation. The coding categories are sample-sensitive.

Videos from Finnish and Icelandic mathematics classrooms are analyzed to demonstrate the coding method for lesson structure. These countries were chosen in part because of their performance in the PISA studies. Finnish students have excelled in all three PISA studies, while Iceland is the only country where girls have significantly outperformed boys in mathematics. The recordings—two lessons from ten randomly chosen mathematics teachers of 14 and 15-year-olds in each country—were collected in the spring of 2007.

Based on this sample, there are differences in how Finnish and Icelandic mathematics lessons are structured. The Finnish lessons in the sample follow the popular Review-Lesson-Practice-script. Approximately half of the recorded Icelandic lessons exhibit versions of the Independent learningpedagogical strategy. Public instructional discourse can be missing entirely from these lessons, and, instead, the teacher tutors the students one-on-one.

This is in contrast with the Finnish lessons where teacher-lead activities,

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Figure 4.7: Forms of Introducing New Content: Finland and Iceland* 169 Figure 4.

8: Forms of Practicing/Applying: Finland and Iceland* 170

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I would first like to thank my advisor, Bruce Vogeli, for his valuable assistance and encouragement during this project and beyond. I always walk out of your office with a lucid idea of what to do next. I would also like to express deep gratitude to the members of my dissertation committee, Herbert Ginsburg and Robbie McClintock, as well the examiners, O. Roger Anderson and Patrick Gallagher, for their contributions.

I could not have carried out this project without the hard work of the following individuals to whom I am forever indebted: Auður Anna Jónsdóttir, who assisted me in collecting the data in Iceland; Adam Wheeler and Margret Óskarsdóttir, who spent untold hours of their time translating the Icelandic lessons into English; Svandis Jónsdóttir and Chien Tai Shill, who translated the many forms and letters; Michael George, the second coder; and Soo Kim, whose help with the lesson diagrams is much, much appreciated.

Thanks are given anonymously to all the teachers, students, and principals in the twenty schools that participated in the study. Thank you also to all the parents who let their children take part in it.

Erkki Pehkonen (University of Helsinki), Pekka Kupari (Institute for Educational Research, University of Jyväskylä), Eva Jablonka (Luleå University of Technology), and Ólöf Björg SteinÞórsdóttir (University of North Carolina at

–  –  –

me understand how research should be conducted.

Andrew Porter (University of Pennsylvania), Jane Monroe (Teachers College, Columbia University), Mikko Sani (Tiirismaan Lukio), Lari Härkönen (Karttulan Lukio) and Päivi Portaankorva-Koivisto (University of Tampere) also helped along the way. Thank you!

I spent about nine months in Iceland during this endeavor. What an intriguing and beautiful country! Many people there facilitated my research. Inga Dóra Sigfúsdóttir and her wonderful family as well as Ásrún Matthíasdóttir and Jón Sigurðsson took me into their homes and showed me what Icelandic hospitality can mean. Others at Reykjavik University include Elín Þorgeirsdóttir, Jón Sigfússon, Álfgeir Kristjánsson, Viðar Halldorssón, Bryndis Björk Ásgeirsdóttir, Einar Steingrímsson, Pawel Bartoszek, Ellert Harðarson, and Arnar Egilsson, all of whom made my life in Iceland easier. Takk fyrir hjálpina!





Almar Halldórsson and Ragnar Ólafsson at Námsmatsstofnun in Reykjavik also supported my work. I would also like to thank Guðný Gunnarsdóttir, Kristin Bjarnadóttir, Jónína Vala Kristinsdóttir, Guðbjörg Pálsdóttir, and Svanhildur Kaaber at Kennaraháskóli Íslands for their assistance and encouragement.

The City of Reykjavik provided financial support. I am honored to be acknowledged by this fine city.

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worth it. In June 2006 I attended the summer seminar of the Finnish Graduate School of Mathematics, Physics, and Chemistry Education. There I received a spark for video-based classroom research from Knut Neumann. In June 2007 I spent a week at the Nordic Graduate School in Mathematics Education (NoGSME) summer school in Laugarvatn, Iceland. I am grateful to Barbro Grevholm and all of the faculty and students who made it such a fantastic and helpful experience.

My dear friends Soo Kim, Maukka Palmio, Tanja Lahtinen, Cooper Long, and Bo Kellam, all of whom have been in my corner for many years, as well as my colleagues at FIT, deserve my gratitude for their continued support. I feel fortunate to know such fine people.

Finally, this dissertation is dedicated to my parents, Leena-Maija Sani and Markku Savola, who have, literally, been there for me from the beginning.

Thanks also to Jussi, Paula, Kirsti, Risto, and the rest of my family. Kiitos!

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Video analysis is a powerful observational tool that can help deepen our understanding of classroom practices. As the technology needed to conduct video-based pedagogical research has become increasingly available, video analysis has secured a prominent place in the “toolboxes” of educational researchers studying the complex phenomena that take place in classrooms.

While video analysis is not suitable for every pedagogical study, it can be effective in a wide variety of research settings. This dissertation project explores some of the ways in which video can be used to make sense of classroom practices as well as the kinds of challenges the modern videographer 1 faces throughout the research process. With recent major international studies providing much of the orientation, an adaptive method of lesson structure analysis is introduced. Videos from Finnish and Icelandic mathematics

                                                       

The term “videographer” is used throughout the report to refer not only to the person collecting 1

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classrooms are analyzed using this method. Although this project focuses on research in mathematics education, much of what is discussed in this report can be applied to video-based classroom studies in general.

Classrooms are complex, dynamic settings. Therefore classroom video footage is always multilayered and rich, filled with nuances and subtleties.

Deciding which aspects of the behavior stream (Barker, 1963) to investigate is a crucial task. Indeed, it is possible to scrutinize classroom video footage with respect to countless research variables. In addition to the variables of interest, the dimensions of variation within those variables can be freely defined. There are thus virtually limitless ways to make meaning from video recordings. There are no predetermined boundaries for the use of video in pedagogical research. There are no standards either, although some have called for them (Derry, 2007).

The use of video in classroom research is not limited to certain types of studies or theoretical frameworks. Video recordings can effectively be used in quantitative, qualitative, or mixed-method studies; comparative or noncomparative studies; bottom-up (from observations) or top-down (from theory) studies; and experimental or non-experimental studies. Less than 40 years in, the mutual history of video technology and pedagogical research is impregnated with ingenious exemplars that apply various types of methodologies and theoretical perspectives. This manuscript provides examples on how data drawn from classroom videos can provide evidence in studies that are grounded in, for

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The use of video in classroom research is not without its problems and limitations. Beyond the typical financial and logistical issues, using video analysis in a pedagogical research project presents some unique challenges.

These challenges can be classified under two categories: data collection issues and those concerning the analysis of the data (Barron, 2007). Overall, however, the benefits of video analysis seem to outweigh the associated problems.

Video analysis technology—cameras, microphones, computer hardware, and software—has become increasingly affordable and user-friendly in recent years. The technological developments have been welcomed by pedagogical researchers wanting to incorporate video-based data collection methods into their projects. Information about these developments as well as commentary on modern video equipment and classroom filming techniques are included in this report. The concept of a neutral recording of a lesson is introduced.

Lesson structure analysis is an important part of many video-based pedagogical studies. Examples of different coding schemes for lesson structure can be found in large-scale classroom studies such as the International Association for the Evaluation of Educational Achievement [IEA]-sponsored 1995 Trends in International Mathematics and Science Study [TIMSS] (Stigler, Gonzales, Kawanaka, Knoll, & Serrano, 1999), the TIMSS 1999 Video Study (Hiebert et al., 2003), as well as the Learner’s Perspective Study [LPS] (Clarke,

–  –  –

One of the contributions of this project is an adaptive method of lesson structure analysis. The two-pass coding scheme, which combines a predetermined set of categories with an adaptive one, is derived from the TIMSS and LPS studies. With this method, the structures of any set of videoed mathematics lessons can be investigated. The method yields quantitative data that can prove valuable especially when combined with other research methods.

The first coding pass concerns the pedagogical functions of lesson elements. It uses a set of predetermined categories similar to those of the Purposevariable from the TIMSS 1999 Video Study. In contrast, the second pass-variable is based on the forms of social participation in the classroom. Its coding categories stem from asking “Who is doing what?” and “How are the participants interacting?” These categories vary from sample to sample according to the actions of the teachers and the students. The interaction of the two dimensions—function (first pass) and form (second pass)—is of particular interest as the main idea behind the method is to investigate the different forms of classroom interaction teachers employ in attaining their pedagogical goals.

Videos from Finnish and Icelandic mathematics classrooms are used to demonstrate the coding method for lesson structure. These countries were chosen for the study in part because of their performance in the Program for International Student Assessment [PISA] studies. Finland has come out on top in overall results in all three PISA studies, conducted in 2000, 2003, and 2006, while

–  –  –

boys in mathematics (OECD, 2004, 2007b). The recordings—two lessons from ten randomly chosen mathematics teachers of 14 and 15-year-olds in each country— were collected during the spring of 2007.

Although the terms “a typical teacher” and “a typical lesson” are difficult, if not impossible, to define for any educational community, comparisons of teaching patterns can still be made between Finnish and Icelandic mathematics teachers. Based on the sample, there are differences in the ways in which mathematics teachers in these countries conduct their classes. The Finnish mathematics lessons in the sample exemplify the Review-Lesson-Practice [RLP]lesson script and are fairly uniform in their functional structure. In contrast, Icelandic mathematics teachers seem to have adopted two distinct pedagogical philosophies: approximately half of the recorded lessons follow the RLP-pattern, while the others are conducted according to versions of Independent learning, a constructivist pedagogical strategy that promotes learner autonomy (see, e.g., Harvey & Chickie-Wolfe, 2007).



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