Iowa Core Curriculum - ..Essential Content

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Mathematics

Essential Content

All students should acquire a deep and powerful understanding of mathematics. But which areas and topics of mathematics should be included in the school curriculum? In order to provide effective guidance to Iowa schools, the Iowa Core Curriculum for Mathematics identifies essential mathematical strands and essential concepts within those strands that all students should study in specified grade spans and in total by the end of high school.

This is the essential 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 Mathematical Strands
in the Iowa Core Curriculum
Kindergarten — Grade 8

Number and Operations
Algebra
Geometry and Measurement
Data Analysis and Probability

Essential Mathematical Strands
in the Iowa Core Curriculum
Grades 9 — 12

Algebra
Geometry
Statistics and Probability
Quantitative Literacy

(Note: Discrete Mathematics* topics are integrated throughout the above 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 objectives are symptomatic of and serve to exacerbate this problem. At the same time, in order to keep doors open for students and prepare them for the rapidly-changing world they will face as adults, we must provide a rich curriculum.

The need and goal of mathematics education is deep understanding of important mathematics. Thus, this document identifies essential concepts in four essential strands.

Characteristics of Essential Concepts:

Important mathematics
Mathematics needed to keep all options open for all students and prepare them for college and the modern world of work
A foundation for future learning of mathematics
A focus for curriculum design and instruction
More than just items in a laundry list of objectives
Consistent with professional recommendations for mathematics standards
Consistent with professional experience in mathematics curriculum development and instruction

In addition to an emphasis on essential concepts 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.

The topics identified here do not all require the same amount of time in the curriculum. For example, at the high school level, the topics of vertex-edge graphs or social decision making may take just a couple weeks or days in the entire high school curriculum, while other topics such as equations and inequalities or geometric properties and relationships will take much longer.

* "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 [NCTM's] 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)" (Navigating through Discrete Mathematics in Grades 6—12, Hart, Kenney, DeBellis, and Rosenstein, NCTM, 2008).