Supermath: An Alternative Approach to Improving Math Performance in Grades 4 through 9
Stanley Pogrow · Phi Delta Kappan · 2004
Stanley Pogrow shares a decade's worth of experience in developing an approach to teaching math to upper-elementary and middle school students that simultaneously increases basic skills, improves problem solving, raises test scores, and sparks student interest in math. For details, read on. MY WORK over the past 24 years has focused on using technology to produce more sophisticated forms of learning after the third grade. This work started with the Higher Order Thinking Skills (HOTS) program for Title I and learning-disabled students. (For more information on the HOTS program, visit www.hots.org.) We used lessons learned from this pioneering effort as we developed Supermath, an alternative approach to teaching math to all students. Supermath provides interesting opportunities for districts to better meet the accountability challenges of No Child Left Behind (NCLB) while also producing reflective mathematics learning as celebrated in the November 2003 issue of the Kappan. Background Of Supermath In the early 1990s, the National Science Foundation (NSF) funded the development of Supermath as part of an effort to produce new and innovative approaches to and materials for teaching mathematics. In designing Supermath, we sought to develop an approach that would simultaneously increase students' basic skills, problem-solving ability, test scores, and interest in math. We aimed to achieve these results for both advantaged and disadvantaged students and to be far more successful in doing so than conventional approaches, even those that used technology, had been. Given these ambitious goals, it was clear that the Supermath materials would have to be creative and engaging and would have to incorporate and systematize powerful curricular and pedagogical techniques. The use of technology to improve learning has traditionally focused on presenting content in an individualized fashion and then testing students. Fancy graphics and animation are used to intrigue the students. Technology serves to automate instruction rather than to create new forms of instruction. While this approach has value, it generally produces gains only in the early grades -- and primarily on the program vendor's test. There are more creative simulations and tools available on which to build new approaches to instruction. But, while valuable and able to provide for exploratory learning, these technologies tend to be hit or miss and place heavy burdens on teachers to figure out how to use them effectively. It is also hard to demonstrate the impact that these simulations and tools have on improved content skills and test scores. HOTS demonstrated that it was possible to use technology systematically in ways that produced progressive outcomes -- comprehension and self- concept -- while also producing even greater gains on traditional achievement measures, such as test scores. The primary lesson from HOTS is that developing a more powerful approach to learning requires insight into what is inhibiting learning and ideas about how to overcome these inhibitors. Then, and only then, should one think about using technology to improve instruction and student performance. In the case of HOTS, I discovered that for disadvantaged students the key inhibitor of reading comprehension and general learning was not understanding understanding, a problem that could be addressed only through intensive conversations about ideas.1 Based on this insight, HOTS uses technology to provide students a common experience that serves as the basis for shared conversations, much as a family uses life experience as the basis for dinner-table conversation. In this approach to technology use, curriculum and training were designed to generate an environment conducive to sophisticated and intensive Socratic conversation and to maintain it over the one- to two-year period needed to develop students' sense of understanding. Using technology indirectly to promote conversation, as a table setter so to speak, worked powerfully. …