Back to EMSC Home SED Home Disclaimers and Notices

Performance Indicator Alignment

Although the 2005 mathematics standard is different in structure from the previous standard documents, there are many similarities as indicated in the degree of alignment shown in the crosswalk. By listing performance indicators for both process and content strands, the 2005 standard places as much emphasis on instruction as on curriculum.  The performance indicators for the process strands stress instruction – how students learn and how teachers teach mathematics - and what mathematics is as a discipline. On the other hand, the performance indicators for the content strands stress curriculum – what students need to know and be able to do. The crosswalk included in this document primarily compares the content performance indicators of the 2005 Content Strands with those of the 1999 Core Curriculum. This in no way should be interpreted to mean that the process strands are of less importance than the content strands. They are both equally important. The performance indicators for the process strands were not included in the crosswalk because they basically did not have a counterpart in Standard 3 of the 1999 Core Curriculum. They are one of the major additions to the 2005 mathematics standard.

The following performance indicators from Math A and Math B have no counterpart in the content strands of the 2005 Core Curriculum at the high school level because they are included in the K-8 portion of the 2005 mathematics standard. This does not mean that they are not to be addressed at the high school level. 

 Math A

        Number and Numeration
            2B       Recognize the order of real numbers  

        Operations
            3C       Recognize and identify symmetry and transformations on figures

        Modeling/Multiple Representation

            4C       Use transformations in the coordinate plane 

Math B

        Number and Numeration

            2B       Recognize the order of real numbers

  2C       Apply the properties of the real numbers to various subsets of numbers

The following performance indicators from Math B have no direct counterpart in the content strands of the 2005 Core Curriculum at the high school level but are stressed within the five process strands.

        Problem Solving

   4A        Represent problem situations symbolically by using algebraic expressions, sequences,
   tree diagrams, geometric figures, and graphs

                  Representation

    4C       Choose appropriate representations to facilitate the solving of a problem

         Connections

     7G       Model real-world situations with the appropriate function

The following performance indicators from Math A and Math B do not have any direct counterpart in the 2005 Standard. This does not mean, however, that they are not addressed in the 2005 Standard. There is a comment for each performance indicator with an explanation as to how it is addressed in the 2005 Standard.

Math A

         Measurement

      5F      Apply proportions to scale drawings and direct variation

    Although not specifically stated, students would be expected to make these applications
    of proportions during their study of proportions in Math 7, Math 8, Algebra, and
    Geometry.

      5I       Use geometric relationships in relevant measurement problems involving geometric  
    concepts

                Although not specifically stated, students should continually use geometric relationships
    as they are involved in the measurement and geometry strands of the standard.

          Patterns/Functions

       7D      Model real-world situations with the appropriate function

                 Students should continually model real-world situations with the appropriate function
     while making connections in the Connections strand.

 Math B

        Number and Numeration

    2D       Recognize the hierarchy of the complex number system

Teachers should continually have students look at the development of our number system and see that each set of numbers is a subset of other sets; i.e., our number system develops in the following way: counting numbers, whole numbers, integers, rational numbers, irrational numbers, complex numbers and that each time a new type of number is introduced it has all the previous numbers as subsets. This is implied in the 2005 standard, but not specifically stated as a performance indicator.

        Modeling/Multiple Representation

    4D       Develop meaning for basic conic sections

               This is alluded to in G.G.1-G.G.7 (equations of conic sections) with basic meanings
               implied. Student activities should engage them in the basic meanings.

               4G       Represent graphically the sum and difference of two complex numbers

                           A2.N.9 requires operations with complex numbers, but the graphic sum and difference
                           of two complex numbers is not specifically indicated. Although not specifically stated, it
                           is expected that teachers would have students model the arithmetic operations
                           graphically.

                4H       Model quadratic inequalities both algebraically and graphically

               This performance indicator is a pre-requisite for the performance indicators in the new
   standard that deal with the solution of inequalities, but is not directly addressed.

    4I        Model the composition of transformations 

   Could be covered in the representation strand, but it is not directly stated there.

                4K       Use polynomial, trigonometric, and exponential functions to model real-world
                           relationships

               Students are expected to use polynomial, trigonometric, and exponential functions, but 
   the standard does not mention application in real-world settings. Applications in real-
   world settings should be a part of the Connections strand, but applications should be
   natural, not contrived.

    4N       Use graphing utilities to create and explore geometric and algebraic models

               Technology tools are implied to be fully integrated into the mathematics curriculum as    
   described by the new standard. Hence, the direct statement of this performance
   indicator is unnecessary.

Measurement

    5B      Understand error in measurement and its consequence on subsequent calculations

              Addressed somewhat in performance indicator A.M.3. Relative error in measuring
  square and cubic units when error occurs in linear measure.  No mention is made of
  consequence on subsequent calculations. Teachers would be expected to discuss this in
  the application of the performance indicator.

       Patterns/Functions

    7C     Translate among the verbal descriptions, tables, equations, and graphic forms of
  functions 

                          Implied in several performance indicators, but never directly addressed. Teachers
                          should continually show multiple representations throughout the entire curriculum.

                 7O     Apply the ideas of symmetry in sketching and analyzing graphs of functions

  Implied, but not specifically stated. Teachers would have students do this as they are
  engaged in activities involving the sketching and analyzing of graphs of functions.