Mathematics - Essential Content

Essential Content of a World-Class Curriculum in High School Mathematics

This section specifies the recommended content that all students should study by the end of high school. This is the core content needed by all students to keep all their options open for college and the world of work. Those students intending mathematics-based majors in college should take additional mathematics in high school (not specified here). The recommended content includes legacy content and future content (Prensky, 2001, as described in the Charge for the Model Core Curriculum Project).

Essential Strands

(*Discrete Mathematics topics are integrated throughout the above strands.)
 

Essential Topics in Each Strand
Click on the essential strands listed above to see the essential topics for each strand.

All students should acquire a deep and powerful understanding of mathematics. But which areas and topics of mathematics should be included in the high school curriculum? In order to provide effective guidance to Iowa's high schools, this document identifies essential mathematical strands and essential topics within those strands. It is expected that students enter this world-class high school mathematics curriculum with a strong background gained in a high-quality K-8 mathematics program that is consistent with the essential characteristics and skills described in those respective sections.The recommended content includes legacy content and future content (Prensky, 2001, as described in the Charge for the Model Core Curriculum Project).

Essential Strands

The most telling criticism of the U.S. mathematics curriculum is that it is "a mile wide and an inch deep." We cannot continue to teach too many topics in too little depth. Long lists of recommended topics are symptomatic of and serve to exacerbate this problem. The need and goal for mathematics education is deep understanding of important mathematics. Thus, we present here a short list of essential topics in each strand. (Click on the Essential Strands listed above.)

Characteristics of Essential Topics:

  • Serve to identify important mathematics
  • Provide a focus for curriculum design and instruction
  • Not a laundry list of objectives
  • Lay the foundation for future learning of mathematics
  • Are consistent with professional recommendations for mathematics standards
  • Are consistent with professional experience in mathematics curriculum development and instruction

In addition to an emphasis on essential topics in each strand, it is also important to weave together general themes of mathematics. Mathematics has been described as a science of patterns, in particular patterns of number, shape, change, chance, and data (cf. Steen, 1990). These themes need to be woven together throughout the study of the mathematical strands.

 

* "Discrete mathematics is an important branch of contemporary mathematics that is widely used in business and industry. ... Discrete mathematics is often described by listing the topics it includes, such as vertex-edge graphs, systematic counting, iteration and recursion, matrices, voting methods, and fair division. ... Three key topics of discrete mathematics that are integrated within Principles and Standards are combinatorics, iteration and recursion, and vertex-edge graphs. ... Other discrete mathematics topics that may be included in the school curriculum include the mathematics of information processing (e.g., error-correcting codes and cryptography), and the mathematics of democratic and social decision making (e.g., voting methods, apportionment, fair division, and game theory)" (NCTM, 2007).