Sharpening Math Skills

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


  • Algebra I
  • Geometry
  • Algebra II
  • Trigonometry
  • Mathematical Analysis
  • Linear Algebra
  • Probability & Statistics
  • Calculus

State Standards

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:

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