Several small-scale experimental studies in classrooms by Star and Rittle-Johnson demonstrate the value of comparison in mathematics learning: Students who learned by comparing and contrasting alternative solution methods made greater gains in conceptual knowledge, procedural knowledge, and flexibility than those who studied the same solution methods one at a time. This study will extend that prior work by developing, piloting, and then evaluating the impact of comparison on students' learning of mathematics in a full-year algebra course. Sixty Algebra I teachers will participate in a randomized controlled trial of the contrasting-examples instructional approach, using a delayed treatment design.
Our goal in this project was to develop and evaluate an Algebra I curriculum that incorporated the comparison of multiple problem solving strategies. Prior work in laboratory studies had found that this instructional approach was promising, but large scale intervention studies did not exist. To address this gap, we worked closely with experienced algebra teachers to develop and pilot test supplemental curriculum materials where two strategies for solving a math problem could be compared and discussed. When complete (see attached image for a sample of one of the curriculum pages), we then asked Algebra I teachers to use the materials for a full academic year and compared their students’ learning to those students in other Algebra I classrooms whose students did not use the materials. Our results indicate great promise in this curriculum approach; use of our materials was associated with gains in students’ procedural knowledge. In the large main study that was the centerpiece of this project, we found that teachers did not use our materials as frequently as we had hoped, and this may have prevented us for finding larger effects. However, we did find that as teachers grew more experienced in using our materials, the general instructional approach that our materials were based upon – giving students the opportunity to compare, contrast, discuss, and evaluate multiple strategies for solving algebra problems – began to pervade teachers' instruction more generally. On the whole, we believe that our project provides further evidence that comparison of multiple strategies is an important learning approach in mathematics. In addition, the curriculum materials that we have developed offer one potentially productive way for teachers to take advantage of the power of comparison.
