By high school, students' mathematical sensitivity should be sharpened. Students start perceiving logical subtleties and appreciate the need for sound mathematical arguments before making conclusions. As students progress in the study of mathematics, they develop greater skills:
learn to distinguish between inductive and deductive reasoning
understand the meaning of logical implication
test general assertions
realize that one counterexample is enough to show that a general assertion is false
understand conceptually that although a general assertion is true in a few cases, it is not true in all cases
distinguish between something being proven and a mere plausibility argument
and identify logical errors in chains of reasoning
Content standards were designed to encourage the highest achievement of every student, by defining the knowledge, concepts, and skills that students should acquire at each grade level.
Click the link to view academic content standards for Mathematics, adopted by the California State Board of Education:
