About us | Lectures | Papers | Seminar | Examples | Programs | Download | Links | Contact

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.

Excerpt from: L. Čaklović, Selfduality in Group Decision.

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 View preferences.
• 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 View preferences.
• 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 View preferences.
• 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 View preferences.
• 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 View preferences.
• 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.