Student Modeling in the ACT Programming Tutor: Adjusting a Procedural Learning Model With Declarative Knowledge

This paper describes a successful effort to increa se the predictive validity of student modeling in the ACT Programming Tutor (APT). APT is an intelligent tutor con - structed around a cognitive model of programming kn owledge. As the student works, the tutor estimates the student's growing knowledge of the component production rules in a process called knowledge tracing. Knowledge tracing employs a simple two-state lear ning model and Bayesian updates and has proven quite accurate in predicting student posttest performance, although with a small systematic tende ncy to overestimate test performance. This paper describes a simple three-state model in which the student may acquire non- ideal programming rules that do not transfer to the test environment. A series of short tests assess students' declarative knowledge and th ese assessments are used to adjust knowledge tracing in the tutor. The resulting model eliminates over-prediction of posttest performance and more accurately predicts individual differences among students. Mastery learning holds out the promise that virtual ly all students can master a domain if the do- main knowledge is analyzed into a hierarchy of component knowledge units and if learning is structured so that students master prerequisites be fore moving to higher level knowledge (Bloom, 1968; Carroll, 1963; Keller, 1968). Meta-analyses c onfirm that mastery learning yields higher achievement levels (Kulik et al., 1990), but achiev ement gains in conventional mastery learning fall short of early expectations (Resnick, 1977; Sl avin, 1987). The ACT Programming Tutor (APT) is an intelligent tutoring system that employs a detailed cognitive model of programming knowledge in an attempt to achieve mastery learning. Our goal in the tutor is to monitor the student's growing proce dural knowledge in the course of problem solv- ing, provide sufficient learning opportunities for mastery and accurately predict students' test performance. This paper describes an important step forward in this modeling process: By incor- porating an independent measure of students' prereq uisite declarative knowledge we substantially improve the predictive validity of the modeling pro cess. In this paper we briefly describe the learning envi ronment, the cognitive model, the learning and performance assumptions that underlie knowledge tracing, and the empirical validity of knowledge tracing. We describe a battery of declara tive knowledge assessments we have devel- oped and describe the improved predictive accuracy that is achieved by incorporating them into the model.