Mathematical
Teaching Practices |
Cognitive Development
•
Use of manipulative materials
• Cooperative
group work
• Discussion of mathematics
• Questioning and making conjectures
•
Justification of thinking
• Writing about
mathematics
• Problem-solving approach to
instruction
• Content integration
•
Use of calculators and computers
• Being
a facilitator of learning
• Assessing learning
as an integral part of instruction |
Traditional Delivery
•
Rote practice
• Rote memorization of rules
and formulas
• Single answers and single
methods to find answers
• Use of drill worksheets
• Repetitive written practice
• Teaching
by telling
• Teaching computation out of
context
• Stressing memorization
•
Testing for grades only
• Being the dispenser
of knowledge |
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Numbers/Operations/Computation
(Standard A) |
Cognitive Development
• Developing
number and operation sense
• Understanding
the meaning of key concepts such as place value, fractions,
decimals, ratios, proportions, and percents
•
Various estimation strategies
• Thinking
strategies for basic facts
• Using calculators
for complex calculations |
Traditional
• Early use of symbolic
notation
• Complex and tedious paper-pencil
computations
• Memorizing rules and procedures
without understanding |
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Geometry/Measurement
(Standard A) |
Cognitive Development
• Developing
spatial sense
• Actual measuring and the
concepts related to units of measure
• Using
geometry in problem solving |
Traditional
• Memorizing facts
and relationships
• Memorizing equivalencies
between units of measure
• Memorizing geometric
formulas |
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|
Statistics/Probability
(Standard A) |
Cognitive Development
• Collection
and organization of data
• Using statistical
methods to describe, analyze, evaluate and make decisions |
Traditional
• Memorizing formulas |
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Pattern/Functions/Algebra
(Standard A) |
Cognitive Development
• Pattern
recognition and description
• Identifying
and using functional relationships
• Developing
and using tables, graphs, and rules to describe situations
• Using variables to express relationships |
Traditional
• Manipulating symbols
• Memorizing procedures and drilling |
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|
Mathematics
as Problem Solving (Standard B) |
Cognitive Development
• Word
problems with a variety of structures and solution
paths
• Everyday problems and applications
• Problem-solving strategies practiced
•
Open-ended problems and extended problem-solving projects
scored with a rubric
• Investigating and
formulating questions from problem situations |
Traditional
• Use of cue words
to determine operation to be used
• Practicing
routine, one-step problems
• Practicing
problems categorized by types |
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Mathematics
as Communication (Standard C) |
Cognitive Development
• Discuss
mathematics to explain strategy and solution
•
Reading mathematics proof
• Writing problems
and solutions with mathematics
• Listening
and debating mathematical ideas |
Traditional
• Doing fill-in-the
blank worksheets
• Answering questions that
need only yes or no responses
• Answering
questions that need only numerical responses |
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Mathematics
as Reasoning (Standard D) |
Cognitive Development
•
Drawing logical conclusions
• Justifying
answers and solution processes
• Reasoning
inductively and deductively
• Using multiple
assessment techniques, including written, oral and
demonstration formats |
Traditional
• Relying on authorities
(teacher, answer key) |
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Evaluation |
Cognitive Development
• Having
assessment be an integral part of teaching
•
Focusing on a broad range of mathematical tasks and
taking a holistic view of mathematics
•
Developing problem situations that require applications
of a number of mathematical ideas
• Using
multiple assessment techniques, including written,
oral and demonstration formats |
Traditional
• Having assessment
be simply counting correct answers on tests for the
sole purpose of assigning grades
• Focusing
on a large number of specific and isolated skills
• Using exercises or word problems requiring
only one or two skills
• Using only written
tests |