Mathematics
Complete downloadable Mathematics Model Core Curriculum document [ .pdf ]
Recent results of national and international tests show that the United States is facing a crisis in mathematics education. American high school students score near the bottom on the international TIMSS and PISA tests. Analysis of this poor performance shows that the U.S. mathematics curriculum is "a mile wide and an inch deep," trying to cover too many topics in not enough depth. All Iowa high school students must be better prepared in mathematics to successfully compete in the technology-rich, information-dense, global society. To achieve this we must redesign our mathematics curriculum so that it is focused on providing deep understanding of important mathematics.
In this document we identify the essential skills, content, and characteristics of the world-class mathematics curriculum that Iowa needs. This model core curriculum for high school mathematics is based on recommendations from the National Council of Teachers of Mathematics (NCTM, 2000), five years of experience with Iowa's Every Student Counts mathematics initiative (ESC), and best practices identified from reviews of research conducted by the National Research Council (2001), the International Bureau of Education (2000), the National Council of Teachers of Mathematics (2003), the federal What Works Clearinghouse Web site, and Iowa's Mathematics Content Network research review project.
In addition, the essential skills and content recommended in this model core curriculum document have been informed by a careful review of many background resources, including the Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics from the National Council of Teachers of Mathematics (NCTM, draft, 2006), the Mathematics Framework for the National Assessment of Educational Progress (NAEP, 2005), Guidelines for Assessment and Instruction in Statistics Education (GAISE Report, American Statistical Association, 2005), mathematics standards recommended by Achieve (2003 and in press), mathematics standards recommended by the College Board (in press), ACT core curriculum recommendations (2005), the mathematics curricula of Japan and Singapore, the National Center for the Study of Mathematics Curricula, mathematics standards in other states, and recommendations from Iowa’s Model Core Curriculum Lead Team.
In order to provide effective guidance and technical assistance for Iowa's schools, this document has drawn from the above resources to identify the essential skills, content, and characteristics of a world-class high school mathematics curriculum.
Essential Characteristics of a World-Class Curriculum in Mathematics
A world-class mathematics curriculum should be built around and focused on:
- Teaching for Understanding
- Problem-Based Instructional Tasks
- Distributed Practice that is Meaningful and Purposeful
- Mathematical Modeling
- Deep Conceptual and Procedural Knowledge
- Rigor and Relevance
- Effective Use of Technology
- Integrated Content
Essential Skills in a World-Class Curriculum in Mathematics
Students need powerful skills to be successful in the globally competitive workforce of the 21st century. Business and industry demand workers who can solve problems, work in teams, and are able to apply learning to new and changing situations, especially as workers change jobs and careers many times in their lifetimes. Therefore, students must acquire powerful, flexible, and widely-applicable mathematical skills by the time they graduate from high school. Many such skills have been discussed in surveys of businesses (e.g., the SCANS report) and in the NCTM Process Standards (NCTM, 2000). The skills identified here are taken substantively from the NCTM Process Standards.
Essential Skills:
- Problem Solving
- Communication
- Reasoning and Proof
- Ability to Recognize, Make, and Apply Connections
- Ability to Construct and Apply Multiple Connected Representations
Essential Content of a World-Class Curriculum in High School Mathematics
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 the sections above.
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).
Essential Strands:
- Algebra
- Geometry
- Statistics and Probability
- Quantitative Literacy
* "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, 2006).
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. Thus, we present here a short list of essential topics in each strand.
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
- Consistent with professional recommendations for mathematics standards
- 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.