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Reflection
Tasks
Discourse
Student Learning
Teaching Decisions
Mathematics
Reflection
Reflection is a process of analyzing
our actions and our decisions in light of their impact on student
learning. Through this process, teachers examine relationships between
what they and their students are doing and what students are learning.
Effective reflection includes developing insight, making connections
between classroom actions and student learning, and arriving at
appropriate suggestions for change and improvement. To focus attention
on specific components or domains of teaching, Reflections categorizes
this analysis into five domains.
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Tasks
Tasks are the exercises, problems, activities, and investigations
in which students engage. Tasks provide the context for students’
mathematical development. Reflection should consider the appropriateness
of the tasks, their sequencing, variety, and responsiveness to students’
interests and learning styles.
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Discourse
Classroom discourse refers to the written and oral ways of representing,
thinking, communicating, agreeing, and disagreeing that teachers
and students use to engage in those tasks. It also refers to the
ways in which teachers orchestrate and promote discourse and to
the interplay of intellectual, social, and physical characteristics
that shape the ways of knowing and working that are expected in
the classroom. Reflection should consider the questions the teacher
asks; the responses given by students; the clarity and accuracy
of instructions, directions, answers, explanations, and clarifications;
as well as the range and effectiveness of mathematical approaches,
use of tools and materials, and other instructional strategies.
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Student Learning
Student learning refers to the strategies, techniques, and tools
that are used and the evidence that is gathered to assess and monitor
– both formally and informally – students’ mathematical
development. Reflection should consider the variety and appropriateness
of the techniques and strategies used, the quality of the evidence
collected, and the ways that this evidence is used to diagnose and
provide feedback.
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Teaching
Decisions
Teachers make a multitude of decisions, both consciously and unconsciously,
to support instruction. These include decisions about classroom
organization and management; grouping practices; dealing with mistakes
and misconceptions; transitions between lesson parts; and when to
clarify, explain, question, or let a student struggle. Reflection
should consider the various decisions that are made and the justifications
and implications of these decisions.
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Mathematics
Mathematics refers to the skills, concepts,
understandings, and applications that students are expected to learn
and to be able to use. It also refers to the connections between
and among mathematical ideas and representations of these ideas.
Reflection should consider the significance of the mathematics,
how clearly it is presented, and the depth of knowledge that teachers
need in order to provide effective instruction and that students
demonstrate.
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