New Curriculum Makes Sense of Mathematics and Opens the Door for All Students to Learn

As a mathematics teacher looking at the challenge of the new Michigan Merit Curriculum high school graduation requirements, it is important to confront existing beliefs about what needs to be taught/learned and the instructional process used to facilitate successful learning of mathematics by all students. Research suggests that students—including those entering high school with low scores in mathematics—are more likely to pass high-level courses than low-level courses. Research also suggests that the skills and knowledge required in the work place are now very similar to those needed for success in college.

In 1992, the National Science Foundation (NSF) funded the development of K-12 mathematics curricula to reflect the kind of instruction envisioned by the National Council of Teachers of Mathematics (NCTM) standards. Five innovative high school programs emerged. Each provided the integration of math topics into an integrated core curriculum for all students. More information about these curricula and implementation guidelines may be found at the Curricular Options in Mathematics Programs for All Secondary Students (COMPASS) Center Web site at www.ithaca.edu/ compass. COMPASS is a secondary school implementation project funded in part by the National Science Foundation.

More Relevant Mathematics Curricula

Two of the five standards-based curricula available at COMPASS are ARISE Mathematics Modeling our World and Core-Plus Mathematics Contemporary Mathematics in Context. One example lesson from the ARISE curricula is about steroid testing. This unit interweaves the topics of probability, quadratic function family, and curve fitting and residual plots. The context relates math to chemistry, economics, physical education, and communication skills. Another example is the Matrix Models unit Core-Plus Mathematics. Using the contexts of economics, sociology, and biology, students develop the use of matrices to model brand switching, group behavior, and the spread of contamination in a food web. These units are indicative of the focus on both mathematical content and process found in the NSF programs.

In these programs, all students access the core mathematics through:

• The depth and level of abstraction to which topics are pursued.
• The use of technology as a tool for learning.
• A variety of degrees of difficulty in homework tasks.
• Active, problem-based learning.
• Multi-dimensional assessment.

All of these programs fulfill the Michigan Department of Education’s new High School Content Expectations (HSCE) mathematics requirements: one credit each of algebra I, geometry, and algebra II. In addition, many topics important for the 21st Century—most notably statistics and probability—are integrated each year.

Curricula Makes Math More Accessible to All

How do these programs make math more accessible to all students? What instructional methods ensure that all students can engage in meaningful learning? The key to answering these questions is that all of the five curricula organize math topics around mathematical modeling of relevant real-world situations. Examples of such situations include steroid testing, food web contamination, and brand switching. Real world mathematical modeling puts students in charge of looking at a situation, formulating a problem, and developing the mathematical tools to address the problem. Mathematics becomes a collaborative “sense-making” experience emphasizing connections across the strands of algebra, geometry, statistics, and discrete math. Students develop the habits of mind that foster communication and reasoning as they engage in sense making, problem solving, and conceptual thinking. This engagement creates lifelong learning skills needed for success in college or technical education, as well as for workforce preparation. The five innovative standards-based programs provide the rigor and relevance needed to address how all students can learn the mathematics that meet the new high school content expectations.

For more information, contact: Rose Martin, Mathematics Consultant, Lecturer, University of Michigan, rosemartin@tds.net.