Standards-Based Mathematics

Standards-based instruction in mathematics is designed to clearly identify what students should learn at each level. Standards provide more than a curriculum framework as they delineate the skills, concepts and knowledge that are to be mastered. For successful standards-based implementation, teachers must understand the rationale for using standards, know applicable national and state standards and use them as a basis for planning instruction, and implement best practices instructional strategies. Essential characteristics of an effective standards-based mathematics classroom include:

1. Lessons designed to address specific standards-based concepts or skills.

2. Student centered learning activities.

3. Inquiry and problem solving focused lessons.

4. Critical thinking and knowledge application skills

5. Adequate time, space, and materials to complete tasks.

6. Varied, continuous assessment, designed to evaluate both student progress and teacher effectiveness. (Teaching Today, 2005a)

The implementation of a standards-based math curriculum brings with it some special challenges. In addition to ensuring students are actively engaged, teachers should adhere to the following guidelines:

1. Create a safe environment where students feel comfortable.

2. Establish clear procedures and routines.

3. Provide both challenge and support.

4. Use carefully assigned and well-managed cooperative groups.

5. Make frequent real life connections.

6. Use an integrated curriculum.

7. Provide engaging educational experiences that are relevant to students.

8. Present activities where students produce and share products. (Teaching Today, 2005b, ¶ 3)

The Thomas B. Fordham Foundation has conducted three analyses of state mathematics standards. The most recent study was released in 2005. Although the weighting of the specific criteria has shifted, the same criteria: clarity of the standards, content, sound mathematical reasoning, and the absence of negative features, have been used to evaluate standards in each of the studies. Overall, only six states received grades of A of B. Twenty-nine states received grades of D or F, and 15 received Cs. The report identified nine major areas of concern including excessive emphasis on calculator use, memorization of basic number facts, lack of focus on the standard algorithms, insufficient focus on fractions, inadequate attention to mathematical patterns, counterproductive use of manipulatives, overemphasis on estimation skills, improper sequencing of statistics and probability standards, and a lack of standards that appropriately guide the development of problem-solving (Klein, 2005).

The study also offers suggestions for state policy makers seeking to strengthen their K-12 math standards. These recommendations include the use of standards developers who thoroughly understand mathematics, the development of coherent arithmetic standards that emphasize both conceptual understanding and computational fluency, avoid and rectify the nine major concerns related to math standards, and consider borrowing a complete set of math standards from one of the states with high-quality standards (Klein, 2005).