From the National Council of Teachers of Mathematics’ Standards

Changes in Content and Emphases in Grades 9-12

ALGEBRA

• The use of real-world problems to motivate and apply theory
• The use of computer utilities to develop conceptual understanding
• Computer-based methods such as successive approximations and
• graphing utilities for solving equations and inequalities
• The structure of number systems
• Matrices and their applications

GEOMETRY

• Integration across topics at all grade levels
• Coordinate and transformation approaches
• The development of short sequences of theorems
• Deductive arguments expressed orally and in sentence or paragraph form
• Computer-based explorations of 2-D and 3-D figures
• Three-dimensional geometry
• Real-world applications and modeling

TRIGONOMETRY

• The use of appropriate scientific calculators
• Realistic applications and modeling
• Connections among the right triangle ratios, trigonometric functions, and circular functions
• The use of graphing utilities for solving equations and inequalities

FUNCTIONS

• Integration across topics at all grade levels
• The connections among a problem situation, its model as a function in symbolic form, and the graph of that function
• Function equations expressed in standardized form as checks on the reasonableness of graphs produced by graphing utilities
• Functions constructed as models of real-world problems

STATISTICS

• Probability

DISCRETE MATH

ALGEBRA

• Word problems by type, such as coin, digit, and work
• The simplification of radical expressions
• The use of factoring to solve equations and to simplify rational expressions
• Operations with rational expressions
• Paper-and-pencil graphing of equations by point plotting
• Logarithm calculations using tables and interpolation
• The solution of systems of equations using determinants
• Conic sections

GEOMETRY

• Euclidean geometry as a complete axiomatic system
• Proofs of incidence and ‘between-ness’ theorems
• Geometry from a synthetic viewpoint
• Two-column proofs
• Inscribed and circumscribed polygons
• Theorems for circles involving segment ratios
• Analytic geometry as a separate course

TRIGONOMETRY

• The verification of complex identities
• Numerical applications of sum, difference, double-angle, and half-angle identities
• Calculations using tables and interpolation
• Paper-and-pencil solutions of trigonometric equations

FUNCTIONS

• Paper-and pencil evaluation of functions
• The graphing of functions by hand using tables of values
• Formulas given as models of real-world problems
• The expression of function equations in standardized form in order to graph them
• Treatment as a separate course

Changes in Instructional Practice in Grades 9-12 Math

Increased Attention to:

• The active involvement of students in constructing and applying mathematical ideas
• Problem solving as a means as well as a goal of instruction
• Questioning techniques that promote student interaction
• The use of a variety of instructional formats (small groups, individual explorations, peer instruction, class discussions, project work)
• The use of calculators and computers as tools for learning and doing mathematics
• Student communication of mathematical ideas orally and in writing
• The establishment and application of the interrelatedness of mathematical topics
• The systematic maintenance of student learnings and embedding review in the context of new topics and problem situations
• The assessment of learning as an integral part of instruction

Decreased Attention to:

• Teacher and text as exclusive sources of knowledge
• Rote memorization of facts and procedures
• Extended periods of individual seatwork practicing routine tasks
• Instruction by teacher exposition
• Paper-and-pencil manipulative skill work
• The relegation of testing to an adjunct role with the sole purpose of assigning grades