What Counts Less, What Counts More: Math Teachers Set New Priorities

From the National Council of Teachers of Mathematics’ Standards

Changes in Content and Emphases in Grades 9-12

Topics to Receive Increased Attention


  • 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


  • 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


  • 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


  • 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


  • Probability


Topics to Receive Decreased Attention


  • 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


  • 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


  • 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


  • 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