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What Does Effective Mathematics Instruction Look Like?

— U.S. Department of Education
Updated on Dec 16, 2008

As a result of recent efforts to strengthen the mathematics curricula in our nation's schools, from basic through more advanced levels, the instruction that you can see in your child's mathematics classes may look quite a bit different from what you experienced when you were in elementary school. For instance, in effective math classrooms today, you can see the following:

Children are expected to know both basic arithmetic skills and the mathematical concepts that are the basis of these skills: They are learning and applying basic computational skills, and they will also be learning that mathematics is much more than knowing the "facts" and number operations. Young children are learning arithmetic - addition, subtraction, multiplication and division - and they also are using mathematical operations such as counting, measuring, weighing, reading charts and graphs and identifying patterns and shapes. Across the grades, children are practicing the use of their mathematics skills in many different ways, and they are using the language of math to talk about what they're doing. They are using mathematical operations that involve estimation, geometry, probability, statistics and the ability to interpret mathematical information. As they progress through school, children will increasingly show that they understand why they are using a particular math skill, recognize when they've made procedural errors and know what to do to correct those errors.

Children are involved actively in the study of mathematics: They are doing tasks that involve investigation, application and interpretation. They are talking about and writing explanations for their mathematical reasoning.

Children sometimes are working with one another: They sometimes collaborate to make discoveries, draw conclusions and discuss mathematical concepts and operations.

Children are striving to achieve high standards and are assessed regularly to determine their progress: The No Child Left Behind Act of 2001 (NCLB) calls for all children to be taught math by teachers who have the training needed to teach effectively, using curricula that are grounded in scientifically based research. The law requires annual math assessments of students in grades 3-8 according to state-defined standards and dissemination of the results to parents, teachers, principals and others. Curriculum based on state standards should be taught in the classroom; thus assessment would be aligned with instruction. In addition to assessments required by NCLB, teachers are using many different ways to determine if children know and understand mathematics concepts. Some of these ways are open-ended questions in which a student writes out the steps - or thought processes - used in solving a math problem; independent projects; and other written tests.

Children are learning to use calculators appropriately: They are using calculators not as crutches but as tools for performing operations with large numbers. Use of a calculator will not replace a thorough knowledge of basic mathematical operations.

Children are using computers appropriately: They are using computers to run software that poses interesting problem situations that would not be available to them without the use of technology.

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