From: "The Center" <ccsri@learningpt.org>
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Subject: The Center Newsletter, March 2008
Date: Wed, 19 Mar 2008 16:39:44 -0500
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March 2008

                                           

Getting to "Got It!"

Helping Mathematics Students Reach Deep Understanding

by Abner Oakes, Senior Program Associate, The Center for Comprehensive School Reform and Improvement at Learning Point Associates, and Jon R. Star, Ph.D., Assistant Professor, Harvard Graduate School of Education

It comes as no surprise that what teachers do in the classroom impacts students' learning of mathematics. During a single class period, a teacher makes countless decisions about how to present material, structure tasks, and guide student learning. Some decisions seem large, such as how to grade students and how to introduce new concepts. Other teacher decisions may seem less significant, such as the choice of how to position students' seats, which problems to assign for homework, or whether or not to ask students to raise hands before answering questions. In essence, effective teaching is effective decision-making, as the collection of big and small decisions made by mathematics teachers makes a tremendous difference in students' learning. How do teachers decide what to do when they teach? These decisions may be based on their training or professional development experiences, what they experienced as students, or what they have learned from colleagues. A recent practice guide titled Organizing Instruction and Study to Improve Student Learning aims to supplement and inform teachers' instincts and experiences by identifying research-based instructional strategies that teachers of all content areas can use to improve student learning.

The practice guide identifies the following seven recommendations (Pashler et al., 2007, p. 2):

1.      "Space learning over time. Arrange to review key elements of course content after a delay of several weeks to several months after initial presentation."

2.      "Interleave worked example solutions with problem-solving exercises. Have students alternate reading already worked solutions and trying to solve problems on their own."

3.      "Combine graphics with verbal descriptions. Combine graphical presentations (e.g., graphs, figures) that illustrate key processes and procedures with verbal descriptions."

4.      "Connect and integrate abstract and concrete representations of concepts. Connect and integrate abstract representations of a concept with concrete representations of