1. Dimensions for Analyzing Teaching
2. Work plan and calendar
3. Mathematics code development team
4. Progress Report

To compare and describe lessons videotaped in different countries, we have constructed a common framework. Our framework consists of six dimensions that represent different aspects of classroom lessons. Our hypothesis is that every lesson can be marked to show changes across the lesson within each dimension. Cultural patterns can be defined in terms of regular changes within each dimension AND in terms of the way the changes in one or more dimensions relate to changes (or the absence of changes) in the other dimensions. This can be visualized by imagining each dimension as a line segment (see the picture), with the length representing the total time of the lesson, and the segment marked when changes occur. Then the line segments can be overlaid to see how changes in one dimension match changes in other dimensions.

Visual Metaphor for Analytic Framework

(click image for larger version)

PURPOSE

What is the teacher's purpose for each segment of the lesson. The purpose will sometimes, but not always, be labeled with a culturally specific term. Cultural "insiders" are usually in the best position to infer the purpose. This dimension is highly inferential and cannot be transformed directly into codes, but it can provide a context, for that part of the lesson, within which to interpret coding results.

Are there specialized routines or action patterns that are likely to be seen at this point in the lesson. Entries in this dimension are intended to capture those classroom routines that have evolved within a country's teaching system to accomplish particular purposes (e.g., oral exams in the Czech Republic, checking homework in the U.S., working through in Switzerland). It is not uncommon for these routines to have special labels. Empty cells in this dimension are likely; they indicate that there are no special routines, commonly recognized within the country, for handling that part of the lesson. Entries in this dimension do not translate directly into codes, but they can be "unpacked" and represented in the remaining dimensions with descriptors that can be translated into codes.

Where are the classroom participants located and what are they doing. Observable descriptions of the teacher and the students are provided in this dimension. Descriptions include where the students and teachers are located during that segment of the lesson (e.g., at the chalkboard, circulating around the room, at their seats) and what they are doing (e.g., asking questions, working in groups). Descriptors in this dimension will translate into codes in a relatively straightforward way.

What is the nature of the verbal interaction during the lesson. Classroom talk will be coded at several levels of specificity. Descriptors will be pitched at a level that help to mark shifts in the general nature of verbal interaction during the lesson. These descriptors might address one or more of the follow features:

The relative amount of speech by teacher and students
The pace of the interaction
The openness of the question/answer conversation
The degree of evaluation present in the conversation
In what sense is the conversation about mathematics
How errors are treated
How much mathematical precision is expected in students' expressions

What is the nature of the mathematical content in the lesson. We developed a list of descriptors that comprise this complex dimension. The entries in the list are expressed at a level that, on the one hand, can be used to help "unpack" culturally specific constructs within the country models (identified in earlier dimensions), and, on the other hand, suggest types of codes that will need to be carefully defined. Our current list includes the following:

A. Tasks (The smallest unit)

1. Individual tasks

The mathematical or cognitive processes prompted by tasks
The detail with which tasks are worked out
The language (e.g., precision) used to deal with tasks
Student solution methods: how they are solicited and treated by the teacher

2. Relationships between tasks (Relationships can be described by identifying the ways in which tasks differ: in situation, topic, representation [e.g., tables, graphs, equations], type of solution method expected, numbers/algebraic expressions])

B. Topics (A larger unit)

The mathematical topic(s) covered during the lesson
The level of the topic(s), relative to an international norm
The way in which topics are introduced (e.g., how extensively they are developed)
How topics are represented (materials, tools, visual aids, etc.)
How topics are connected to: past content, real life, history of mathematics

C. Emphasis: In a global, impressionistic sense, there seem to be differences in where and how emphases are placed during the lesson. For example, some lessons, or parts of lessons, seem to emphasize understanding of ideas whereas others focus on the proficiency of skills.

Climate is a dimension that we agree is potentially significant but difficult to define operationally. The classroom atmosphere can be relatively serious, or more relaxed; the pace can be fast or slow; the students can be relatively quiet, or relatively talkative; mistakes can be more or less acceptable. Global ratings might be possible, but impressions seem to be influenced directly by familiarity with the country's educational practices. Some indicators, such as time-on-task and discipline actions, might approximate climate but could be misleading as well. We could re-define this dimension to focus more on observable management or organization features, but these would not capture the impressions of many during the field-test discussions--that the lessons differed in "climate." Additional work is needed before this dimension can be used for code development.

Examine contents of field test tapes, both mathematics and science. Describe similarities and differences within and between cultures. Construct potential coding categories by collecting and organizing impressions of country consultants regarding significant features of teaching. Use tapes to make final decisions regarding videography procedures.

Report of Field Test is being prepared by Takako Kawanaka.

Using field test tapes and knowledge of the Country Associates, develop a hypothetical model, or ethnography, of eighth-grade mathematics teaching in each country.

The cultural models of eighth-grade mathematics teaching will be used to (1) identify, capture, and preserve the unique cultural categories and features of teaching within each country; (2) provide a starting point for developing discrete codes that will be used across all countries (the models serve as each country’s statement about specific features that should be coded); (3) serve as hypotheses about the design of instruction within each country that can be tested later by analysis of specific quantitative codes; and, (4) conserve the contexts to which the quantified data can be related and thus interpreted properly.

To increase comparability, each country’s model will be built upon a tentative set of descriptive dimensions. The dimensions serve to organize and describe the specific features of the teaching models. The six dimensions form an emergent and revisable framework: purpose, classroom routines, actions of participants, classroom talk, content, and climate.

Models will be presented to educational experts within each country and revised based on feedback.

This phase is intended to deal with the problem of conducting comparative analyses across the countries on specific quantitative codes and at the same time preserving culturally unique meanings of each coded category.

Using feedback from country experts, and comparisons of the initial descriptions of each model, refine and elaborate the basic dimensions (and add others if needed) to ensure that all important elements within each country's model are adequately represented.

This is an intermediate step between the general ethnographic descriptions of each country's teaching model, and the more specific quantitative indicators which will be coded for each lesson and subjected to blind reliability checks. During this step commonalties across countries will be identified, and differences will be specified. This step will pinpoint what must be represented in the many specific codes that are to be developed in Phase 4. It begins the process of constructing a cross cultural inventory of the features of teaching that must be represented in the quantitative codes, showing how those codes are related according to the basic dimensions, and identifying where the specific codes connect back to the broader ethnographic context of the teaching models.

Develop discrete codes elated according to the basic dimensions, and identifying where the specific codes connect back to the broader ethnographic context of the teaching models.

Develop discrete codes that can be used reliably across all mathematics lessons in all countries. Use the dimensions that comprise the model framework as guides for selecting culturally meaningfully and universally applicable codes.

Transform the appropriate entries in the dimensions into codes through a recurring cycle of: specifying further the definitions of each dimension, proposing codes that capture each aspect of the definitions, trying out the codes on the incoming tapes, revising the code definitions based on information gained during the trials.

Re-check codes for appropriate meaning within the contexts of the country models; consult with country experts as needed.

Train coders to reliably code tapes. Conduct full tests of inter-coder reliability for all codes not tested in Phase 4. Refine codes where needed to achieve satisfactory reliability.

Ronald Gallimore is Co-Director of the Mathematics Coding Development Team and Associate Director of the Video Study. He is Professor (Psychology), Departments of Psychiatry & Biobehavioral Sciences & Education, UCLA. 1993 Grawemeyer Award (Tharp & Gallimore, Rousing Minds to Life: Teaching, Learning and Schooling in Social Context. Cambridge University Press). Current projects include Spencer & OERI funded longitudinal study of school restructuring and teaching improvement; and NICHD funded longitudinal and cultural studies of immigrant Latino family adaptation to, and support of, children's school performance.

Karen Givvin is the Code Developer representing the Netherlands. She was, however, born and attended school in the Los Angeles area. (Her parents immigrated from the Netherlands after they married.) Karen’s undergraduate degree is in Psychology from UCLA and she holds a Master's in Educational Psychology from California State University, Northridge. Karen earned her Ph.D. a little over a year ago from UCLA's School of Education. She has a particular interest in motivation across domains (e.g., school and sport).

James Hiebert is Co-Director of the Mathematics Coding Development Team. He is H. Rodney Sharp Professor of Mathematics Education at the University of Delaware, editor of several books on mathematics learning, and coauthor of Making Sense: Teaching and Learning Mathematics with Understanding (Heinemann, 1997) and The Teaching Gap (with Jim Stigler, Free Press, Summer 1999). He served as consultant on the TIMSS 1995 Video Study of Mathematics Teaching. NSF funded research projects have focused on elementary school students' mathematics learning.

Jennifer Jacobs is the Code Developer representing the United States. Jennifer was born and attended school in Baltimore, Maryland. She attended college at the University of Michigan, where she was a double major in Psychology and Japanese. Jennifer’s Master’s degree and Ph.D. are in Developmental Psychology from UCLA. Her dissertation, completed this year, focused on American and Japanese teachers’ beliefs about mathematics instruction.

Nicole Kersting is the Code Developer representing Switzerland. Nicole was born and attended school in Germany; she has also lived in Italy. She holds a Master’s degree in Literature and Linguistics from Friedrich-Wilhelm University of Bonn in Germany. Nicole worked for the past several years on the TIMSS 1995 Video Study as the German coder and data analyst. She has also taught German and Italian at several community colleges in the Los Angeles area.

Svetlana Trubacova is the Code Developer representing the Czech Republic. She was born and attended school in a small town called Sala in the Slovak Republic. Svetlana went to Charles University in Prague, Czech Republic, where she completed her Master’s degree in Education, with a specialization in teaching Math and Physics at the high school level. Her Master’s thesis was a text for university students to learn about a type of geometrical transformation - Inverse on a Circle. Svetlana has experience teaching math and physics in the Czech Republic, the Slovak Republic, and the United States.