Strategies to Enhance Math Instruction

Thanks its partnership with publisher Eye on Education, EducationWorld is pleased to present this tip from Mathematics Coaching Handbook: Working with Teachers to Improve Instruction, by Pia Hansen. The book serves as a reference to help prepare and support effective math coaches. Here, we offer five strategies that coaches can present to teachers (or teachers can use directly in their classrooms) to enhance their mathematics instruction.

1. Manipulatives
   The use of manipulative materials, visual models (sketches) and cooperative partner work encourages the discussion of mathematics and prepares students for writing about their conjectures. For example, students can build growing patterns with colored tile and explain the “rule” to their classmates. Then a chart is created to show the numeric sequence.
2. Observational Language
   Students can use language to deepen their understanding of mathematical concepts. In this lesson, fourth-grade students are given index cards and asked to share their mathematical observations about rectangles. The fact that the rectangle is white or made out of paper is not relevant to the properties of rectangles. Then students are asked to construct posters with peers about other polygon shapes and present their work to the class.
3. Trial and Error
   Rather than being told about a mathematical concept, students can first use trial and error to discover the concept for themselves. For example, a teacher gives students a variety of jar lids, tubes and cans from circular wastebaskets. She gives each student (or group of students) a tape measure and asks them to measure the diameter (distance across) and circumference (distance around) of each item on their table. These measurements are recorded onto a data sheet. Then participants are asked to examine the ratio between these measurements (discover Pi, between 3.1 and 3.2). Older students can graph the relationship (the horizontal axis representing the diameter and the vertical axis representing the circumference) onto grid paper. The slope of these equivalent ratios should make a line close to 3.1.
4. Word Resource Cards
   Word Resource Cards can help develop rich mathematical language especially when graphic representations (pictures) are attached to the vocabulary word. These cards also have a student-friendly definition on the back. Teachers can post them in pocket charts during the unit of study and then move them to a math word wall. It is recommended that these words be grouped by strand. For example, all the geometry words would be together, angle words together, two-dimensional shapes together, and so on. English language learners benefit from this explicit vocabulary support.
5. K-W-C (Know-Want-Conditions) Chart
   K-W-C charts are especially helpful for students who may have difficulties with word problems. By graphically organizing what they know, want to find out, and any special conditions, students can create concrete representations of an abstract word problem.

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