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Standard VIII

Ways of Thinking Mathematically
Accomplished mathematics teachers develop students’ abilities to reason and think mathematically—to investigate and explore patterns, to discover structures and establish relationships, to formulate and solve problems, to justify and communicate their conclusions, and to question and extend those conclusions.

Reflection on the Standard
More than just a dull, dry collection of disparate procedures and rules, mathematics is a coherent and dynamic problem solving juggernaut. While a fair amount of structure and practice are essential to the learning of mathematics, so too are discovery and wonderment. By challenging students with substantial and sophisticated problems, and by requiring them to communicate their thought processes and results in a clear and coherent fashion, the effective mathematics teacher instills in his or her students not only competence in the procedures of mathematics, but also an appreciation for its power and possibilities.

Evidence, Examples, and Artifacts
Sample artifacts are being collected and will appear at a later date.

Dr. Michael P. Ida
Kalani High School
4680 Kalanianaole Hwy.
Honolulu, HI 96821
(808) 377-7744

Hawaii Public Schools

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