Review three goals for 21st century teaching. Investigate national achievement trends for grade 8. Identify NCTM's content and process standards for grades 6–8.

Using NCTM Standards

Standards have been around for more than 20 years, and, as educators, we're getting used to them. But, as we all know, the standards movement isn't without its critics. James Bohan (2002) believes that the way standards are currently used practically ensures that mathematics teaching won't change, because using standards as a guide doesn't, on its own, promote teaching for understanding. According to Bohan,

• Standards are similar to the modern math of the 1960s, meaning that "this too shall pass."
• Teaching facts, skills, and procedures is less demanding than teaching problem solving, reasoning, communication, and connections.
• Facts, skills, and procedures are easily assessed and glowing results can appear to indicate a high level of mathematical understanding that doesn't actually exist.

What's Your Response?

Of course, the standards movement has plenty of proponents as well. And whether you agree with Bohan or not, it's hard to argue with the movement's stated goal, namely, to improve education. Toward this end, the National Commission on Mathematics and Science Teaching for the 21st Century, an active proponent of the standards movement, published a report to the nation in 2000 establishing three interrelated goals for mathematics and science education:

Goal 1: Establish an ongoing system to improve the quality of mathematics and science teaching in grades K–12.

Goal 2: Increase significantly the number of mathematics and science teachers and improve the quality of their preparation.

Goal 3: Improve the working environment and make the teaching profession more attractive for K–12 mathematics and science teachers. (pp. 8–9)

A year later, the 2001 No Child Left Behind Act (NCLB) echoed the commission's call for improved teaching through professional development and reinforced the idea that teacher excellence is critical to student achievement. In summary, the NCLB Act mandates that

• All students must be taught by quality teachers.
• Productive support programs must be provided.
• Math and science education needs to be strengthened.

The Role of Assessment

Because states and the federal government have designed different standards, assessing progress can be confusing for many parents. For example, their child's school may show improvement on state standardized tests but show insufficient progress on the National Assessment of Educational Progress (NAEP) assessment tests. One reason for this discrepancy may simply be a difference in interpretation. For instance, the state's averages may not correlate with NAEP's levels as defined by the National Assessment Governing Board (NAGB). Learn more about NAGB attainment levels.

In spite of such assessment inconsistencies, it does appear that, since 1990, grade 8 students have made steady progress, as indicated in this chart showing NAGB attainment levels from the National Center for Educational Statistics.

Source: From The Nation's Report Card: Mathematics 2000 (p. 517), by the National Center for Educational Statistics, 2001, Washington D.C.:  U.S. Department of Education, Office of Educational Research and Improvement.

Despite the clear progress, the chart also indicates that 34 percent of all children were not yet achieving at the Basic level in 2000. Thirty-four percent! According to Kathleen Kennedy Manzo and Michelle Galey (2003), this trend continues with the latest NAEP results, in which only 67 percent of 8th graders reached at least the Basic level of achievement.

What About Your School?

NCTM's Standards

In its effort to support improved student achievement, the NCTM came up with a set of standards composed of two parts: content and process. Content standards offer the details of what students should know and be able to do, and the process standards support more general integrative procedures that should be reinforced throughout mathematics programs in order to help children meet the more detailed content standards. First established in 1989, the standards were revised in 2000 to reflect the need for changes to address the achievement gap between U.S. and non-U.S. students.

Content Standards

The following links provide more detailed explanations of each content standard's components.

1. Number and Operations

a. Understand numbers, ways of representing numbers, relationships among numbers, and number systems

b. Understand meanings of operations and how they relate to one another

c. Compute fluently and make reasonable estimates

2. Algebra

a. Understand patterns, relations, and functions

b. Represent and analyze mathematical situations and structures using algebraic symbols

c. Use mathematical models to represent and understand quantitative relationships

d. Analyze change in various contexts

3. Geometry

a. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

b. Specify locations and describe spatial relationships using coordinate geometry and other representational systems

c. Apply transformations and use symmetry to analyze mathematical situations

d. Use visualization, spatial reasoning, and geometric modeling to solve problems

4. Measurement

a. Understand measurable attributes of objects and the units, systems, and processes of measurement

b. Apply appropriate techniques, tools, and formulas to determine measurements

5. Data Analysis and Probability

a. Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

b. Select and use appropriate statistical methods to analyze data

c. Develop and evaluate inferences and predictions that are based on data

d. Understand and apply basic concepts of probability

Process Standards

The following links provide more detailed explanations of the process standards.

1. Problem Solving

2. Reasoning and Proof

3. Communication

4. Connections

5. Representation

Some NCTM Standards-Based Activities

Mathematics Fun

The Magic of Mathematics

The Practitioner's Corner

Patrick Bathras discusses the role of standards in a high-quality mathematics program. Read more.

• Standards: Here Today, Here Tomorrow
  Successful standards-based reform depends on clear standards, well-crafted tests, and fair accountability. Several strategies can help educators put those critical pieces in place.
• How and Why Standards Can Improve Student Achievement: A Conversation with Robert J. Marzano
  Marzano is senior fellow at the Mid-continent Research for Education and Learning (McREL) Institute.

Standards have become an accepted component of our public school system. Some, however, while not questioning the intent of standards, do question whether the standards themselves offer sufficient guidance for teachers. John Marshall (2003), for example, wonders about the standards' lack of real-world context for mathematical concepts.

Neither the sample text I was examining nor the two versions of the NCTM standards appear to give a context in which "square roots" are used. Yet all say it is their aim to see math around us. (p. 195)

What suggestions do you have for teaching this topic — square roots — in a meaningful way so that students learn the role of square roots in life?

• Eisenhower National Clearinghouse for Mathematics and Science Education (ENC)
  The ENC's site provides links to curriculum and professional development resources, articles on education topics, and online lesson plans, student activities, and teacher learning tools.
• National Center for Improving Student Learning and Achievement in Mathematics and Science
  The center works with teachers and schools to study and develop ways to advance K–12 students' learning of mathematics and science.
• National Council of Supervisors of Mathematics (NCSM)
  The NCSM Web site is a resource for those interested in leadership in mathematics education.

Assessment Activity

In Lesson 3, we'll examine how brain-based learning can help make learning more meaningful.

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