Download Recommendations for Teaching Mathematics

Recommendations for Teaching Mathematics
Increase Decrease Teaching Practices
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
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
Rote practice
Mathematics as Problem Solving
Word problems with a variety of structures and solution
paths
Everyday problems and applications
Problem-solving strategies
Open-ended problems and extended problem solving projects
Investigating and formulating questions from problem
situations Use of cue words to determine operation to be used
Practicing routine, one-step problems
Practicing problems categorized by types
Mathematics as Communication
Discussing mathematics
Reading mathematics
Writing mathematics
Listening to mathematical ideas Doing fill-in-the blank worksheets
Answering questions that need only yes or no responses
Answering questions that need only numerical responses
Mathematics as Reasoning
Drawing logical conclusions
Justifying answers and solution processes
Reasoning inductively and deductively Relying on authorities (teacher, answer key)
Mathematical Connections
Connecting mathematics to other subjects and to the real world
Connecting topics within mathematics
Applying mathematics Learning isolated topics
Developing skills out of context
Numbers/Operations/Computation
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 calculation Early use of symbolic notation
Complex and tedious paper and pencil computations
Memorizing rules and procedures without understanding
Geometry/Measurement
Developing spatial sense
Actual measuring and the concepts related to units of measure
Using geometry in problem solving Memorizing facts and relationships
Memorizing equivalencies between units of measure
Memorizing geometric formulas
Statistics/Probability
Collection and organization of data
Using statistical methods to describe, analyze, evaluate, and make decisions
formulas
Memorizing
Patterns/Functions/Algebra
Pattern recognition and description
Identifying and using functional relationships
Developing and using tables, graphs, and rules to describe situations
Using variables to express relationships Manipulating symbols
Memorizing procedures and drilling
Evaluation
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
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
"Evidence from many sources shows that the least effective mode for mathematics learning is the
one that prevails in most of America's classrooms: lecturing and listening . . . Students simply do
not retain for long what they learn by imitiation from lectures, worksheets, or routine homework . .
. Research on learning shows that students actually construct their own understanding based on
new experiences . . . Mathematics becomes useful to a student only when it has been developed
through a personal intellectual engagement that creates new understanding. Much of the failure
in school mathematics is due to a tradition of teaching that is inappropriate to the way most
students learn."
--Everybody Counts: A Report to the Nation on the Future of Mathematics Education. National
Research Council. Washington, D.C.: National Academy Press, 1989.
RECOMMENDATIONS FROM:
National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for
School Mathematics. Commission on Standards for School Mathematics, Reston, VA.
SUGGESTED READINGS:
Cooney, Thomas J. (ed.). (1990) Teaching and Learning Mathematics in the 1990's. Reston, VA:
National Council of Teachers of Mathematics.
Post, Thomas R. (ed.). (1988). Teaching Mathematics in Grades K-8: Research Based Methods.
Boston: Allyn & Bacon.
Trafton, Paul R. (ed.). (1989). New Directions for Elementary School Mathematics. Reston, VA:
National Council of Teachers of Mathematics.
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