NCTM Mathematics
Curriculum Standards for Every Picture Tells a Story (58)
Standard 1: Mathematics as Problem Solving
In grades 58, the mathematics curriculum should include numerous and
varied experiences with problem solving as a method of inquiry and application
so that students can:
1) use problemsolving approaches to investigate and understand mathematical
content;
2) formulate problems from situations within and outside mathematics;
3) develop and apply a variety of strategies to solve problems, with emphasis
on multistep and nonroutine problems;
4) verify and interpret results with respect to new problem situations;
5) acquire confidence in using mathematics meaningfully.
Standard 2: Mathematics as Communication
In grades 58, the mathematics curriculum should include opportunities
to communicate so that students can:
1) model situations using oral, written, concrete, pictorial, graphical,
and algebraic methods;
2) reflect on and clarify their own thinking about mathematical ideas
and situations;
3) develop common understandings of mathematical ideas, including the
role of definitions;
4) use the skills of reading, listening, and viewing to interpret and
evaluate mathematical ideas;
5) discuss mathematical ideas and make conjectures and convincing arguments;
6) appreciate the value of mathematical notation and its role in the development
of mathematical ideas.
Standard 3: Mathematics as Reasoning
In grades 58, reasoning shall permeate the mathematics curriculum so
that students can:
1) recognize and apply deductive and inductive reasoning;
2) understand and apply reasoning processes, with special attention to
spatial reasoning and reasoning with proportions and graphs;
3) make and evaluate mathematical conjectures and arguments;
4) validate their own thinking;
5) appreciate the pervasive use and power of reasoning as a part of mathematics.
Standard 8: Patterns and Functions
In grades 58, the mathematics curriculum should include explorations
of patterns and functions so that students can:
1) describe, extend, analyze, and create a wide variety of patterns;
2) describe and represent relationships with tables, graphs, and rules;
3) analyze functional relationships to explain how a change in one quantity
results in a change in another;
4) use patterns and functions to represent and solve problems.
