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Bridging the Bridge to Algebra: Measuring and Optimizing the Influence of Prerequisite Skills on a Pre-Algebra Curriculum

Year: 2007
Name of Institution:
Carnegie Mellon University
Goal: Development and Innovation
Principal Investigator:
Pavlik, Philip
Award Amount: $1,120,955
Award Period: 4 years
Award Number: R305B070487

Description:

Purpose: Relatively little research has focused on the development of curricula and instructional methods designed to improve skills that are required for learning and doing algebra. The purpose of this project is to develop an automated tutorial intervention that is intended to improve learning in a pre-algebra curriculum. In particular, the goal of this intervention is to help children learn new complex math skills by attending to prerequisite math skills. In many theories of learning, complex skills are posited to be learned more easily or more deeply when students are already fluent or skillful in the component skills at the time of learning. This research team will develop and test an intelligent computer tutor intended to help students learn pre-algebra skills key to success in algebra. The tutor will be designed to tailor practice specifically to each student's individual skill set.

Project Activities: The research team will extend an existing intelligent tutor to deliver practice of pre-algebra skills. The computer tutor will be designed to deliver practice sessions that target discrete prerequisite math skills. The system will use a personalized model of each student's learning to determine when and how much practice is needed for each prerequisite skill in order to maximize progress. Using personalized models of instruction allows the computer tutor to target needed prerequisite skills for each student while avoiding unnecessary review of skills the student has already mastered. The new intervention will be tested using a randomized within-subjects experimental design.

Products: Products from this project include software designed to aid middle school students in the learning of prerequisite pre-algebra skills, and published reports on the initial impact of the software on student achievement in pre-algebra and algebra.

Structured Abstract

Purpose: This research team will develop and test an intelligent computer tutor that is intended to help students practice key prerequisite pre-algebra skills. The tutor will be designed to tailor practice specifically to each student's individual skill set.

Setting: The research setting is middle schools in a large, metropolitan school district in California.

Population: The study population includes primarily urban, low-income, Hispanic students in grades 6-8.

Intervention: The project extends the Bridge to Algebra cognitive tutor, currently produced by Carnegie Learning Inc., by creating a highly controlled system to deliver practice of prerequisite pre-algebra skills. The computer tutor will be designed to deliver practice sessions that target discrete prerequisite math skills. The system will use a personalized model of each student's learning to determine when and how much practice is needed for each prerequisite skill in order to maximize progress in the Bridge to Algebra tutor. Using personalized models of instruction allows the computer tutor to target needed prerequisite skills for each student while avoiding unnecessary review of skills the student has already mastered.

Research Design and Methods: The new intervention will be tested using a randomized within-subjects experimental design. To compare the effects of the intervention with the effects of existing instructional practice, half of the students, chosen randomly, use the new version of the Bridge to Algebra tutor in the fall semester, and the other half use the new version of the Bridge to Algebra tutor in the spring semester. This design compares the same student's progress during experimental treatment versus during existing instructional practice. Math performance will be measured at the beginning of the year, at the end of the fall semester just prior to the crossover from experimental to control condition (or vice versa), and at the end of the academic year.

Control Condition: During the control periods, students use the existing Bridge to Algebra tutor.

Key Measures: The primary measure consists of a random sample of math assessment items taken from the Trends in International Mathematics and Science Survey (TIMSS) grade 8 questions. Primary measures computed from data logged by the Bridge to Algebra tutor and intervention software include individual problem performance accuracy and latency.

Data Analytic Strategy: For the analysis of crossover efficacy studies, the research team is conducting repeated measures analyses of variance of TIMSS test scores and Bridge to Algebra dependent measures.

Publications from this project:

Pavlik Jr., P.I., Anderson, J.R. (2008). Using a Model to Compute the Optimal Schedule of Practice, Journal of Experimental Psychology: Applied, 14: 101–117.

Frishkoff, G., Levin, L., Pavlik, P., Idemaru, K., and de Jong, N. (2008). A Model-based Approach to Second-Language Learning of Grammatical Constructions. In V. Sloutsky, B. Love and K. McRae (Eds.), Proceedings of the 30th Conference of the Cognitive Science Society (pp. 916–921). Washington, D.C.

Pavlik, P.I., Cen, H., Wu, L., and Keodinger, K.R. (2008). Using Item-Type Performance Covariance to Improve the Skill Model of an Existing Tutor. In R.S. Baker and J.E. Beck (Eds.), Proceedings of the 1st International Conference on Educational Data Mining (pp. 77–86). Montreal, Canada: UQAM.

Pavlik Jr., P.I., Bolster, T., Wu, S., Koedinger, K.R., and MacWhinney, B. (2008). Using Optimally Selected Drill Practice to Train Basic Facts. In B. Woolf, E. Aimer and R. Nkambou (Eds.), Proceedings of the 9th International Conference on Intelligent Tutoring Systems. (vol 5091, pp 593–602). Berlin, Germany: Springer.