The Mathematics Reform Movement

The reform movement in mathematics education can be traced to the mid-1980’s and was a response to the failure of traditional teaching methods, the impact of technology on curriculum and the emergence of new approaches to the scientific study of how mathematics is learned. Basic to the reform movement was a standards-based approach to the “what and how” of mathematics teaching (Battista, 1999).

In the new mathematics, the focus is on problem solving, mathematical reasoning, justifying ideas, making sense of complex situations and independently learning new ideas. Students must be provided with opportunities to solve complex problems, formulate and test mathematical ideas and draw conclusions. Students must be able read, write and discuss mathematics, use demonstrations, drawings and real-world objects, and participate in formal mathematical and logical arguments (Battista, 1999).

The driving force behind the standards-based approach to mathematics instruction has been the standards developed by the National Council of Teachers of Mathematics (NCTM). The Principles and Standards for School Mathematics, published by NCTM in 2000, outlines the principles and standards for developing a comprehensive school mathematics program. The document delineates six guiding principles related to equity, curriculum, teaching, learning, assessment and technology, and identifies five content and process standards outlining what content and processes students should know and be able to use. The content standards are organized around content strands related to numbers and operations, algebra, geometry, measurement and data analysis and probability. The process standards are organized around the areas of problem solving, reasoning and proof, communication, connections and representations (National Council of Teachers of Mathematics, 2000).

A set of basic assumptions about teaching and schooling practices is implicit in this reform movement. First, all students must have an opportunity to learn new mathematics. Second, all students have the capacity to learn more mathematics than we have traditionally assumed. Third, new applications and changes in technology have changed the instructional importance of some mathematics concepts. Fourth, new instructional environments can be created through the use of technological tools. Fifth, meaningful mathematics learning is a product of purposeful engagement and interaction which builds on prior experience (Romberg, 2000).

A recent concept paper published by the American Mathematical Society has been influential in identifying some common areas of agreement about mathematics education. The identified areas of agreement are based on three fundamental premises; basic skills with numbers continue to be important and students need proficiency with computational procedures, mathematics requires careful reasoning about precisely defined objects and concepts, and students must be able to formulate and solve problems. The areas of agreement emerging from these premises include: 

1. Mathematical fluency requires automatic recall of certain procedures and algorithms.

2. Use of calculators in instruction can be useful but must not impede the development of fluency with computational procedures and basic facts.

3. Using and understanding the basic algorithms of whole number arithmetic is essential.

4. Developing an understanding of the number meaning of fractions is essential.

5. Teachers must ensure that the use of “real-world” contexts for teaching mathematics maintains a focus on mathematical ideas.

6.Mathematics should be taught using multiple strategies, however, the teacher is responsible for selecting the strategies appropriate for a specific concept.

7. Mathematics teachers must understand the underlying meaning and justifications for ideas and be able to make connections among topics.

                                                           (Ball, Ferrini-Mundy, Kilpatrick, Milgram, Schmid, & Scharr, 2005).