Page 142 - Standards for K-12 Engineering Education

Standards for K-12 Engineering Education?

APPENDIX B 127

Table 5: Curriculum Standards in School Mathematics

Mathematics as problem-solving
Grades The study of mathematics should emphasize problem solving so that students can:
K–4 • Use problem-solving approaches to investigate and understand mathematical content;
• Formulate problems from everyday and mathematical situations;
• Develop and apply strategies to solve a wide variety of problems;
• Verify and interpret results with respect to the original problem;
• Acquire confidence in using mathematics meaningfully.
Grades The mathematics curriculum should include numerous and varied experiences with problem solving as a
5–8 method of inquiry and application so that students can:
• Use problem-solving approaches to investigate and understand mathematical content;
• Formulate problems from situations within and outside mathematics;
• Develop and apply a variety of strategies to solve problems, with emphasis on multistep and
non-routine problems.
• Verify and interpret results with respect to the original problem situation;
• Generalize solutions and strategies to new problem situations;
• Acquire confidence in using mathematics meaningfully.
Grades The mathematics curriculum should include the refinement and extension of methods of mathematical
9–12 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 situations.
Mathematical connections
Grades The study of mathematics should include opportunities to make connections so that students can:
K–4 • Link conceptual and procedural knowledge;
• Relate various representations of concepts or procedures to one another;
• Recognize relationships among different topics in mathematics;
• Use mathematics in other curriculum areas;
• Use mathematics in their daily lives.
Grades The mathematics curriculum should include the investigation of mathematical connections so that
5–8 students can:
• See mathematics as an integrated whole;
• Explore problems and describe results using graphical, numerical, physical, algebraic, and
verbal mathematical models or representations;
• Use a mathematical idea to further their understanding of other mathematical ideas;
• Apply mathematical thinking and modeling to solve problems that arise in other disciplines;
such as art, music, psychology, science, and business;
• Value the role of mathematics in our culture and society.
Grades The mathematics curriculum should include investigation of the connections and interplay among various
9–12 mathematical topics and their applications so that all students can:
• Recognize equivalent representations of the same concept;
• Relate procedures in one representation to procedures in an equivalent representations;
• Use and value the connections among mathematical topics;
• Use and value the connections between mathematics and other disciplines.

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