CMU PACT CENTER            Algebra/Geometry

Dear Math Educator:

I want to thank you and take this opportunity to share the CMU PACT Center's progress in enhancing student achievement in middle and high school mathematics. PACT Center Mathematics provides full course curriculum, curriculum-integrated software (Intelligent Cognitive Tutors), teacher workshops, Principal's Implementation Guide, and in-service support (software installation, two site visits, telephone and e-mail) beginning with pre-algebra and algebra 1 through geometry and algebra 2 . The technology behind the software has been developed over the last fifteen years, based on a theory by Dr. John Anderson, the Walter VanDyke Bingham Professor of Psychology and Computer Science. This software is a cognitive psychology and expert system-based model of classroom curriculum that is implemented on inexpensive Apple Macintosh computers (Windows version due in fall 98). This software/curriculum/teacher support combination has impressive educational effectiveness statistics with students on both ends of the learning curve, including challenging high risk student populations. In the five years the CMU PACT Center Program/Algebra 1 has been in the Pittsburgh Public Schools, we find:

• Algebra problem solving test scores improve 100% compared to students taking traditional algebra 1 courses
• Algebra 1 students score 8% to 15% better on standardized tests then their peers in traditional algebra classes using tests such as the Iowa Algebra Readiness Test (new version), and appropriate questions from the Scholastic Achievement Test ("SAT").
• In the first group of students in which this data is available, the CMU PACT Center Mathematics/Algebra 1 students are more than twice likely to complete geometry and enroll in algebra 2
• CMU PACT Center Mathematics affords students and teachers the opportunity for student-centered teaching
• Non-academic math students including special populations take algebra successfully
• Teachers like it and the students are turned on to math

Each Intelligent Cognitive Tutor contains a psychological model of the cognitive processes behind successful and near successful student performance. This allows the software to monitor each student's progress through a problem solution. When help is needed, the ICT knows where the student is and can provide hints that are individualized to each student's particular approach to the problem. In controlled studies, this learning technology has reduced the time to standardized attainment levels by two thirds. Intelligent Cognitive Tutors also monitor the student's learning from problem to problem. A sophisticated statistical estimation procedure identifies student strengths and weaknesses. This assessment information is used to individualize problem selection and optimally pace students through the curriculum. Data from students using the CMU PACT Center Mathematics/ Algebra 1 demonstrated a one standard deviation performance improvement. This level of improvement is 50% of that expected if each student had their own high quality human tutor, but without the attendant human resource and cost limitation.

In the most common PACT Center Mathematics implementation, students in a classroom setting work in cooperative problem solving groups three days a week. During this time, the teacher functions as a guide and coach. Students can use traditional and modern classroom tools including paper, pencils, calculators, and graphing calculators. Two days a week students work on computers using the PACT Center Mathematics software. During this time each student addresses their individual needs to attain mastery.

During the 97-98 school year, almost 4,000 students per day use the CMU PACT Center Mathematics/ Algebra 1. These students attend public schools and private middle and high schools in the East, Midwest, South and U.S. Armed Forces Associated Schools in Europe.

CMU's Pittsburgh Advanced Cognitive Tutoring Center is developing and implementing the prototype Intelligent Cognitive Tutors and curriculum for geometry and algebra . These will complete testing this year and be available in September, 1998.

We look forward to talking with you about the CMU PACT Center Mathematics and have enclosed additional material for your review. Please don't hesitate to call should you have any questions or would like to visit classrooms using the CMU PACT Center Mathematics.

Sincerely,

Albert T. Corbett, Ph.D.             Kenneth R. Koedinger, Ph.D.
Research Scientist                   Research Scientist