


Elementary Mathematics Curriculum. Process Standards.
The task: To rank five process standards in education of mathematics:
problem solving, reasoning, communication,
connections, and representations without external evaluator.
See also:
Elementary Mathematics Curriculum,
Boulder Valley School District,
Adopted by Board of Education 06/10/2008 and National Council of Teachers of Mathematics
(2000). Principles and Standards for School Mathematics. Reston, VA: Author.
A short description of the problem
The Process Standards of the National Council of Teachers of Mathematics are a
key component to the BVSD mathematics curriculum. They indicate the ways in
which students should acquire and use their content knowledge. The five process
standards in mathematics are problem solving, reasoning, communication,
connections, and representations. These processes are an integral part of all
mathematics learning and teaching. A mathematical learning experience focused
on the five process standards prepares students with the processes necessary
for continued learning in future mathematical courses and careers. Therefore
every process standards should be an integral part of the learning and
assessment of every essential learning result and performance indicator.
The five Process Standards (definition):
 1. Communication
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• Organize and consolidate their
mathematical thinking through
communication

• Communicate their mathematical thinking
coherently and clearly to peers, teachers, and
others

• Analyze and evaluate the mathematical
thinking and strategies of others

• Use the language of mathematics to express
mathematical ideas precisely
 2. Representations
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• Create and use representations to organize,
record, and communicate mathematical ideas

• Select, apply, and translate among
mathematical representations to solve
problems

• Use representations to model and interpret
physical, social, and mathematical
phenomena
 3. Reasoning
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• Recognize reasoning and proof and
fundamental aspects of math

• Make and investigate mathematical
conjectures

• Develop and evaluate mathematical
arguments

• Select and use various types of reasoning and
methods of proof
 4. Connections
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• Recognize and use connections among
mathematical ideas

• Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole

• Recognize and apply mathematics in
contexts outside of mathematics
 5. Problem Solving
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• Build new mathematical knowledge through
problem solving

• Solve problems that arise in mathematics and
in other contexts

• Apply and adapt a variety of appropriate
strategies to solve problems

• Monitor and reflect on the process of
mathematical problem solving

Calculate fixed point of the consensus function of the whole group.
Process subgroup  choosing the criteria first (one step).
Change the initial weights of the processes.
