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1. Does deep knowledge tracing model interactions among skills?

   Montero, S. ; Arora, A. ; Kelly, S. ; Milne, B. ; Mozer, M. C. ( July 2018 , Proceedings of the Eleventh International Conference on Educational Data Mining)

   Personalized learning environments requiring the elicitation of a student’s knowledge state have inspired researchers to propose distinct models to understand that knowledge state. Recently, the spotlight has shone on comparisons between traditional, interpretable models such as Bayesian Knowledge Tracing (BKT) and complex, opaque neural network models such as Deep Knowledge Tracing (DKT). Although DKT appears to be a powerful predictive model, little effort has been expended to dissect the source of its strength. We begin with the observation that DKT differs from BKT along three dimensions: (1) DKT is a neural network with many free parameters, whereas BKT is a probabilistic model with few free parameters; (2) a single instance of DKT is used to model all skills in a domain, whereas a separate instance of BKT is constructed for each skill; and (3) the input to DKT interlaces practice from multiple skills, whereas the input to BKT is separated by skill. We tease apart these three dimensions by constructing versions of DKT which are trained on single skills and which are trained on sequences separated by skill. Exploration of three data sets reveals that dimensions (1) and (3) are critical; dimension (2) is not. Our investigation gives us insightmore »into the structural regularities in the data that DKT is able to exploit but that BKT cannot.« less
2. Extending Deep Knowledge Tracing: Inferring Interpretable Knowledge and Predicting Post System Performance

   Scruggs, R. ; Baker, R.S. ; McLaren, B.M. ( January 2020 , Proceedings of the 28th International Conference on Computers in Education)

   Recent student knowledge modeling algorithms such as Deep Knowledge Tracing (DKT) and Dynamic Key-Value Memory Networks (DKVMN) have been shown to produce accurate predictions of problem correctness within the same learning system. However, these algorithms do not attempt to directly infer student knowledge. In this paper we present an extension to these algorithms to also infer knowledge. We apply this extension to DKT and DKVMN, resulting in knowledge estimates that correlate better with a posttest than knowledge estimates from Bayesian Knowledge Tracing (BKT), an algorithm designed to infer knowledge, and another classic algorithm, Performance Factors Analysis (PFA). We also apply our extension to correctness predictions from BKT and PFA, finding that knowledge estimates produced with it correlate better with the posttest than BKT and PFA’s standard knowledge estimates. These findings are significant since the primary aim of education is to prepare students for later experiences outside of the immediate learning activity.
3. Deep Learning vs. Bayesian Knowledge Tracing: Student Models for Interventions.

   Mao, Y. ( January 2018 , Journal of educational data mining)

   Bayesian Knowledge Tracing (BKT) is a commonly used approach for student modeling, and Long Short Term Memory (LSTM) is a versatile model that can be applied to a wide range of tasks, such as language translation. In this work, we directly compared three models: BKT, its variant Intervention-BKT (IBKT), and LSTM, on two types of student modeling tasks: post-test scores prediction and learning gains prediction. Additionally, while previous work on student learning has often used skill/knowledge components identified by domain experts, we incorporated an automatic skill discovery method (SK), which includes a nonparametric prior over the exercise-skill assignments, to all three models. Thus, we explored a total of six models: BKT, BKT+SK, IBKT, IBKT+SK, LSTM, and LSTM+SK. Two training datasets were employed, one was collected from a natural language physics intelligent tutoring system named Cordillera, and the other was from a standard probability intelligent tutoring system named Pyrenees. Overall, our results showed that BKT and BKT+SK outperformed the others on predicting post-test scores, whereas LSTM and LSTM+SK achieved the highest accuracy, F1-measure, and area under the ROC curve (AUC) on predicting learning gains. Furthermore, we demonstrated that by combining SK with the BKT model, BKT+SK could reliably predict post-test scoresmore »using only the earliest 50% of the entire training sequences. For learning gain early prediction, using the earliest 70% of the entire sequences, LSTM can deliver a comparable prediction as using the entire training sequences. The findings yield a learning environment that can foretell students’ performance and learning gains early, and can render adaptive pedagogical strategy accordingly.« less
4. Modeling Hint-Taking Behavior and Knowledge State of Students with Multi-Task Learning

   Chaudhry, R. ; Singh, H. ; Dogga, P. ; Saini, S. K. ( January 2018 , Proceedings of the 11th International Conference on Educational Data Mining)

   Interactive learning environments facilitate learning by providing hints to fill the gaps in the understanding of a concept. Studies suggest that hints are not used optimally by learners. Either they are used unnecessarily or not used at all. It has been shown that learning outcomes can be improved by providing hints when needed. An effective hinttaking prediction model can be used by a learning environment to make adaptive decisions on whether to withhold or provide hints. Past work on student behavior modeling has focused extensively on the task of modeling a learner’s state of knowledge over time, referred to as knowledge tracing. The other aspects of a learner’s behavior such as tendency to use hints has garnered limited attention. Past knowledge tracing models either ignore the questions where a hint was taken or label hints taken as an incorrect response. We propose a multi-task memory-augmented deep learning model to jointly predict the hint-taking and the knowledge tracing task. The model incorporates the effect of past responses as well as hints taken on both the tasks. We apply the model on two datasets – ASSISTments 2009-10 skill builder dataset and Junyi Academy Math Practicing Log. The results show that deep learningmore »models efficiently leverage the sequential information present in a learner’s responses. The proposed model significantly out-performs the past work on hint prediction by at least 12% points. Moreover, we demonstrate that jointly modeling the two tasks improves performance consistently across the tasks and the datasets, albeit by a small amount.« less
5. Juror Scientific Reasoning Skills and Discussion of Scientific Evidence During Deliberation

   McCowan, K. ( March 2020 , Annual Conference of the American Psychology-Law Society.)

   Abstract We investigate the link between individual differences in science reasoning skills and mock jurors’ deliberation behavior; specifically, how much they talk about the scientific evidence presented in a complicated, ecologically valid case during deliberation. Consistent with our preregistered hypothesis, mock jurors strong in scientific reasoning discussed the scientific evidence more during deliberation than those with weaker science reasoning skills. Summary With increasing frequency, legal disputes involve complex scientific information (Faigman et al., 2014; Federal Judicial Center, 2011; National Research Council, 2009). Yet people often have trouble consuming scientific information effectively (McAuliff et al., 2009; National Science Board, 2014; Resnick et al., 2016). Individual differences in reasoning styles and skills can affect how people comprehend complex evidence (e.g., Hans, Kaye, Dann, Farley, Alberston, 2011; McAuliff & Kovera, 2008). Recently, scholars have highlighted the importance of studying group deliberation contexts as well as individual decision contexts (Salerno & Diamond, 2010; Kovera, 2017). If individual differences influence how jurors understand scientific evidence, it invites questions about how these individual differences may affect the way jurors discuss science during group deliberations. The purpose of the current study was to examine how individual differences in the way people process scientific information affects the extentmore »to which jurors discuss scientific evidence during deliberations. Methods We preregistered the data collection plan, sample size, and hypotheses on the Open Science Framework. Jury-eligible community participants (303 jurors across 50 juries) from Phoenix, AZ (Mage=37.4, SD=16.9; 58.8% female; 51.5% White, 23.7% Latinx, 9.9% African-American, 4.3% Asian) were paid $55 for a 3-hour mock jury study. Participants completed a set of individual questionnaires related to science reasoning skills and attitudes toward science prior to watching a 45-minute mock armed-robbery trial. The trial included various pieces of evidence and testimony, including forensic experts testifying about mitochondrial DNA evidence (mtDNA; based on Hans et al. 2011 materials). Participants were then given 45 minutes to deliberate. The deliberations were video recorded and transcribed to text for analysis. We analyzed the deliberation content for discussions related to the scientific evidence presented during trial. We hypothesized that those with stronger scientific and numeric reasoning skills, higher need for cognition, and more positive views towards science would discuss scientific evidence more than their counterparts during deliberation. Measures We measured Attitudes Toward Science (ATS) with indices of scientific promise and scientific reservations (Hans et al., 2011; originally developed by the National Science Board, 2004; 2006). We used Drummond and Fischhoff’s (2015) Scientific Reasoning Scale (SRS) to measure scientific reasoning skills. Weller et al.’s (2012) Numeracy Scale (WNS) measured proficiency in reasoning with quantitative information. The NFC-Short Form (Cacioppo et al., 1984) measured need for cognition. Coding We identified verbal utterances related to the scientific evidence presented in court. For instance, references to DNA evidence in general (e.g. nuclear DNA being more conclusive than mtDNA), the database that was used to compare the DNA sample (e.g. the database size, how representative it was), exclusion rates (e.g. how many other people could not be excluded as a possible match), and the forensic DNA experts (e.g. how credible they were perceived). We used word count to operationalize the extent to which each juror discussed scientific information. First we calculated the total word count for each complete jury deliberation transcript. Based on the above coding scheme we determined the number of words each juror spent discussing scientific information. To compare across juries, we wanted to account for the differing length of deliberation; thus, we calculated each juror’s scientific deliberation word count as a proportion of their jury’s total word count. Results On average, jurors discussed the science for about 4% of their total deliberation (SD=4%, range 0-22%). We regressed proportion of the deliberation jurors spend discussing scientific information on the four individual difference measures (i.e., SRS, NFC, WNS, ATS). Using the adjusted R-squared, the measures significantly accounted for 5.5% of the variability in scientific information deliberation discussion, SE=0.04, F(4, 199)=3.93, p=0.004. When controlling for all other variables in the model, the Scientific Reasoning Scale was the only measure that remained significant, b=0.003, SE=0.001, t(203)=2.02, p=0.045. To analyze how much variability each measure accounted for, we performed a stepwise regression, with NFC entered at step 1, ATS entered at step 2, WNS entered at step 3, and SRS entered at step 4. At step 1, NFC accounted for 2.4% of the variability, F(1, 202)=5.95, p=0.02. At step 2, ATS did not significantly account for any additional variability. At step 3, WNS accounted for an additional 2.4% of variability, ΔF(1, 200)=5.02, p=0.03. Finally, at step 4, SRS significantly accounted for an additional 1.9% of variability in scientific information discussion, ΔF(1, 199)=4.06, p=0.045, total adjusted R-squared of 0.055. Discussion This study provides additional support for previous findings that scientific reasoning skills affect the way jurors comprehend and use scientific evidence. It expands on previous findings by suggesting that these individual differences also impact the way scientific evidence is discussed during juror deliberations. In addition, this study advances the literature by identifying Scientific Reasoning Skills as a potentially more robust explanatory individual differences variable than more well-studied constructs like Need for Cognition in jury research. Our next steps for this research, which we plan to present at AP-LS as part of this presentation, incudes further analysis of the deliberation content (e.g., not just the mention of, but the accuracy of the references to scientific evidence in discussion). We are currently coding this data with a software program called Noldus Observer XT, which will allow us to present more sophisticated results from this data during the presentation. Learning Objective: Participants will be able to describe how individual differences in scientific reasoning skills affect how much jurors discuss scientific evidence during deliberation.« less