National Council of Teachers of Mathematics  Curriculum Standards Go back to Lesson. STANDARD 1: MATHEMATICS AS PROBLEM SOLVING In grades 9-12, the mathematics curriculum should include the refinement and extensions of methods of mahtematical problem solving so that all students can- use, with increasing confidence, problem-solving approaches to investigate and understand mathematical content;  apply integrated mathematical problem-solving strategies to solve problems from within and outside mathematics; recognize and formulate problems from situations within and outside mathematics; apply the process of mathematical modeling to real-world problem stiuations.. STANDARD 3: MATHEMATICS AS REASONING In grades 9-12, the mathematics curriculum should include numerous and varied experiences that reinforce and extend logical reasoning skills so that all students can- make and test conjectures; formulate counterexamples; follow logical arguments judge the validity of arguments; construct simple valid arguments.  STANDARD 10: STATISTICS  In grades 9-12, the mathematics curriculum should include the continued studey of data anlysis and statistics so that all students can-  construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations.