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Dimensions
for Analyzing Teaching
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
What is the teacher's purpose for
each segment of the lesson? The purpose will sometimes, but not always,
is 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. Classroom Routines 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. Actions of Participants 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. Classroom Talk 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:
Content 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
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)
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 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.
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