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Does your school or district have a vision of what high quality math instruction “looks like” and “sounds like”?
Oftentimes, I have the opportunity to observe math instruction across several grade bands. My vision for the quality of math instruction should be just as important as reading instruction. There are some specific teacher behaviors that “matter” in the teaching of mathematics. This is an example of what math instruction should “sound and look like”:
Demonstrate acceptance of students’ divergent ideas.
They challenge students to think more deeply about the problems they are solving and ask them to explain the solutions. Such an approach also helps students develop confidence in their own abilities to do mathematics and gain an even firmer grasp of key concepts and processes.
Influence learning by posing challenging and interesting questions.
Teachers should present questions that stimulate students’ curiosity and encourage them to investigate further. The questions should encourage students to rely on themselves and their peers for ideas about mathematics and problem-solving.
Project a positive attitude about mathematics and about students’ ability to “do” mathematics.
This includes demonstrating enthusiasm for the content as well as a belief that all students are capable of learning the material, with lessons designed to encourage curiosity, interest, and skill-building. Certain instructional characteristics also are associated with effective mathematics instruction. By integrating the following approaches into classroom instruction, teachers can promote both student learning and motivation.
Students are actively engaged in doing mathematics.
They should not be sitting back watching other students solve problems.
Students are provided with a variety of opportunities to communicate mathematically.
During a lesson, students should have many opportunities to communicate their ideas. They may draw a picture to represent their ideas or write them in mathematics journals. Whole-class discussions should provide opportunities to hear about and perhaps challenge other students’ ideas in an environment of respect and understanding.
Students are using manipulatives and other tools.
The long-term use of mathematics manipulatives is positively related to student achievement and attitudes about mathematics. It is not enough, however, to simply provide students with manipulatives; they must be taught how to use these materials. Several steps can be taken to ensure students benefit from a lesson involving manipulatives. First, the teacher should use manipulatives that support the lesson learning targets. Next, before allowing students to handle the materials, the teacher should demonstrate how to use the manipulatives and the procedures for handling them. And finally, the lesson design should encourage the active participation of all students (Ross and Kurtz 1993).
