A Measurement Model of Microgenetic Transfer for Improving Instructional Outcomes

Abstract

Efforts to improve instructional task design often make reference to the mental structures, such as Bschemas^(e.g., Gick & Holyoak, 1983) or Bidentical elements^(Thorndike & Woodworth, 1901), that are common to both the instructional and target tasks. This component based (e.g., Singley & Anderson, 1989) approach has been employed in psychometrics (Tatsuoka, 1983), cognitive science (Koedinger & MacLaren, 2002), and most recently in educational data mining (Cen, Koedinger, & Junker, 2006). A typical assumption of these theory based models is that an itemization of Bknowledge components^shared between tasks is sufficient to predict transfer between these tasks. In this paper we step back from these more cognitive theory based models of transfer and suggest a psychometric measurement model that removes most cognitive assumptions, thus allowing us to understand the data without the bias of a theory of transfer or domain knowledge. The goal of this work is to help provide a methodology that allows researchers to analyse complex data without the theoretical assumptions clearly part of other methods. Our experimentally controlled examples illustrate the non-intuitive nature of some transfer situations which motivates the necessity of the unbiased analysis that our model provides. We explain how to use this Contextual Performance Factors Analysis (CPFA) model to measure learning progress of related skills at a fine granularity. This CPFA analysis then allows us to answer questions regarding the best order of practice for related skills and the appropriate amount of repetition depending on whether students are succeeding or failing with each individual practice problem. We conclude by describing how the model

Optimal Knowledge Component Extracting Model for Knowledge-Concept Graph Completion in Education

“…Knowledge tracing (KT), which originated around the time of Corbett and Anderson [7], traces and predicts students' changing learning status. Knowledge tracing techniques include BKT, probabilistic models of dynamic Bayesian knowledge tracing (DBKT) [39], logistic models such as performance factor analysis (PFA) [40], and deep learning models such as DKT [8] with nonlinear model functionality.…”

“…In general, the test data for a question included information about the time the student responded together with KC data related to the question. For learning data that includes the dimension of time, there is a trend to apply RNNs [40], [41] that model how students' knowledge levels change over time to the concept of basic DKT, which is also characterized as long short-term memory (LSTM). LSTM is in the RNN family but compensates for the shortcomings of the vanishing gradient approach [42].…”

Estimating Programming Exercise Difficulty using Performance Factors Analysis

“…For the purpose of model selection, we begin by comparing the Additive Factors Model (AFM) [22], Performance Factors Analysis (PFA) [27] as well as its recency-weighted modification [23] and the Recent-Performance Factors Analysis (R-PFA) [25]. We also include modifications of these models, S-only, R-only and R-AFM, introduced in [25], in our study.…”

Generalizing automated detection of the robustness of student learning in an intelligent tutor for genetics.

“…The efforts listed above have leveraged models of student knowledge that can successfully infer the probability that a student knows a specific skill from the student’s history of correct responses and noncorrect responses (e.g., errors and hint requests) for that skill up until that time (cf. Corbett & Anderson, 1995; Martin & VanLehn, 1995; Pavlik, Cen, & Koedinger, 2009; Shute, 1995). In recent years, the debate about how to best model student knowledge has continued, with an increasing number of explicit comparisons of models’ ability to predict future performance within the tutoring software studied (cf.…”

“…In recent years, the debate about how to best model student knowledge has continued, with an increasing number of explicit comparisons of models’ ability to predict future performance within the tutoring software studied (cf. Gong, Beck, & Heffernan, 2010; Pardos, Gowda, Baker, & Heffernan., 2011; Pavlik et al, 2009; Wang & Heffernan, 2011).…”