Object-oriented (OO) programs, which use subtyping and dynamic dispatch, make specification and verification difficult because the code executed by a method call may dynamically be dispatched to an overriding method in any subtype, even ones that did not exist at the time the program was specified. Modular reasoning for such programs means allowing one to add new subtypes to a program without re-specifying and re-verifying it. In a 2015 ACM TOPLAS paper we presented a model-theoretic characterization of a Hoare-style modular verification technique for sequential OO programs called ``supertype abstraction,'' defined behavioral subtyping, and proved that behavioral subtyping is both necessary and sufficient for the validity of supertype abstraction. The present paper is aimed at graduate students and other researchers interested in formal methods and gives a comprehensive overview of our prior work, along with the motivation and intuition for that work, with examples.
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Student Subtyping via EM-Inverse Reinforcement Learning.
Abstract: In the learning sciences, heterogeneity among students usually leads to different learning strategies or patterns and may require different types of instructional interventions. Therefore, it is important to investigate student subtyping, which is to group students into subtypes based on their learning patterns. Subtyping from complex student learning processes is often challenging because of the information heterogeneity and temporal dynamics. Various inverse reinforcement learning (IRL) algorithms have been successfully employed in many domains for inducing policies from the trajectories and recently has been applied for analyzing students’ temporal logs to identify their domain knowledge patterns. IRL was originally designed to model the data by assuming that all trajectories have a single pattern or strategy. Due to the heterogeneity among students, their strategies can vary greatly and the design of traditional IRL may lead to suboptimal performance. In this paper, we applied a novel expectation-maximization IRL (EM-IRL) to extract heterogeneous learning strategies from sequential data collected from three simulation environments and real-world longitudinal students’ logs. Experiments on simulation environments showed that EM-IRL can successfully identify different policies from the heterogeneous sequences with different strategies. Furthermore, experimental results from our educational dataset showed that EM-IRL can be used to obtain different student subtypes: a “learning-oriented” subtype who learned the material as much as possible regardless of the time in that they spent significantly more time than the other two subtypes and learned significantly; an“efficient-oriented”subtype who learned efficiently in that they not only learned significantly but also spent less time than the first subtype; a “no learning” subtype who spent less amount of time than first subtype and failed to learn.
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- Award ID(s):
- 1651909
- NSF-PAR ID:
- 10214149
- Date Published:
- Journal Name:
- In Proceedings of the 13th International Conference on Educational Data Mining (EDM) 2020.
- Page Range / eLocation ID:
- pp 269-279
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Due to the potentially significant benefits for society, forecasting spatio-temporal societal events is currently attracting considerable attention from researchers. Beyond merely predicting the occurrence of future events, practitioners are now looking for information about specific subtypes of future events in order to allocate appropriate amounts and types of resources to manage such events and any associated social risks. However, forecasting event subtypes is far more complex than merely extending binary prediction to cover multiple classes, as 1) different locations require different models to handle their characteristic event subtype patterns due to spatial heterogeneity; 2) historically, many locations have only experienced a incomplete set of event subtypes, thus limiting the local model’s ability to predict previously “unseen” subtypes; and 3) the subtle discrepancy among different event subtypes requires more discriminative and profound representations of societal events. In order to address all these challenges concurrently, we propose a Spatial Incomplete Multi-task Deep leArning (SIMDA) framework that is capable of effectively forecasting the subtypes of future events. The new framework formulates spatial locations into tasks to handle spatial heterogeneity in event subtypes, and learns a joint deep representation of subtypes across tasks. Furthermore, based on the “first law of geography”, spatiallyclosed tasks share similar event subtype patterns such that adjacent tasks can share knowledge with each other effectively. Optimizing the proposed model amounts to a new nonconvex and strongly-coupled problem, we propose a new algorithm based on Alternating Direction Method of Multipliers (ADMM) that can decompose the complex problem into subproblems that can be solved efficiently. Extensive experiments on six real-world datasets demonstrate the effectiveness and efficiency of the proposed model.more » « less
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Background/Context: After-school programs that focus on integrating computer programming and mathematics in authentic environments are seldomly accessible to students from culturally and linguistically diverse backgrounds, particularly bilingual Latina students in rural contexts. Providing a context that broadens Latina students’ participation in mathematics and computer programming requires educators to carefully examine how verbal and nonverbal language is used to interact and to position students as they learn new concepts in middle school. This is also an important stage for adolescents because they are likely to make decisions about their future careers in STEM. Having access to discourse and teaching practices that invite students to participate in mathematics and computer programming affords them opportunities to engage with these fields. Purpose/Focus of Study: This case study analyzes how small-group interactions mediated the positionings of Cindy, a bilingual Latina, as she learned binary numbers in an after-school program that integrated computer programming and mathematics (CPM). Setting: The Advancing Out-of-School Learning in Mathematics and Engineering (AOLME) program was held in a rural bilingual (Spanish and English) middle school in the Southwest. The after-school program was designed to provide experiences for primarily Latinx students to learn how to integrate mathematics with computer programming using Raspberry Pi and Python as a platform. Our case study explores how Cindy was positioned as she interacted with two undergraduate engineering students who served as facilitators while learning binary numbers with a group of three middle school students. Research Design: This single intrinsic case focused on exploring how small-group interactions among four students mediated Cindy’s positionings as she learned binary numbers through her participation in AOLME. Data sources included twelve 90-minute video sessions and Cindy’s journal and curriculum binder. Video logs were created, and transcripts were coded to describe verbal and nonverbal interactions among the facilitators and Cindy. Analysis of select episodes was conducted using systemic functional linguistics (SFL), specifically language modality, to identify how positioning took place. These episodes and positioning analysis describe how Cindy, with others, navigated the process of learning binary numbers under the stereotype that female students are not as good at mathematics as male students. Findings: From our analysis, three themes that emerged from the data portray Cindy’s experiences learning binary numbers. The major themes are: (1) Cindy’s struggle to reveal her understanding of binary numbers in a competitive context, (2) Cindy’s use of “fake it until you make it” to hide her cognitive dissonance, and (3) the use of Spanish and peers’ support to resolve Cindy’s understanding of binary numbers. The positioning patterns observed help us learn how, when Cindy’s bilingualism was viewed and promoted as an asset, this social context worked as a generative axis that addressed the challenges of learning binary numbers. The contrasting episodes highlight the facilitators’ productive teaching strategies and relations that nurtured Cindy’s social and intellectual participation in CPM. Conclusions/Recommendations: Cindy’s case demonstrates how the facilitator’s teaching, and participants’ interactions and discourse practices contributed to her qualitatively different positionings while she learned binary numbers, and how she persevered in this process. Analysis of communication acts supported our understanding of how Cindy’s positionings underpinned the discourse; how the facilitators’ and students’ discourse formed, shaped, or shifted Cindy’s positioning; and how discourse was larger than gender storylines that went beyond classroom interactions. Cindy’s case reveals the danger of placing students in “struggle” instead of a “productive struggle.” The findings illustrated that when Cindy was placed in struggle when confronting responding moves by the facilitator, her “safe” reaction was hiding and avoiding. In contrast, we also learned about the importance of empathetic, nurturing supporting responses that encourage students’ productive struggle to do better. We invite instructors to notice students’ hiding or avoiding and consider Cindy’s case. Furthermore, we recommend that teachers notice their choice of language because this is important in terms of positioning students. We also highlight Cindy’s agency as she chose to take up her friend’s suggestion to “fake it” rather than give up.more » « less
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Abstract Introduction Cross-sectional surveys found behavioral heterogeneity among dual users of combustible and electronic cigarettes. Yet, prior classification did not reflect dynamic interactions between cigarette and e-cigarette consumption, which may reveal changes in product-specific dependence. The contexts of dual use that could inform intervention were also understudied.
Methods This study conducted secondary analysis on 13 waves of data from 227 dual users who participated in a 2-year observational study. The k-means method for joint trajectories of cigarette and e-cigarette consumption was adopted to identify the subtypes of dual users. The time-varying effect model was used to characterize the subtype-specific trajectories of cigarette and e-cigarette dependence. The subtypes were also compared in terms of use contexts.
Results The four clusters were identified: light dual users, predominant vapers, heavy dual users, and predominant smokers. Although heavy dual users and predominant smokers both smoked heavily at baseline, by maintaining vaping at the weekly to daily level the heavy dual users were able to considerably reduce cigarette use. Yet, the heavy dual users’ drop in cigarette dependence was not as dramatic as their drop in cigarette consumption. Predominant vapers appeared to engage in substitution, as they decreased their smoking and increased their e-cigarette dependence. They were also more likely to live in environments with smoking restrictions and report that their use of e-cigarettes reduced cigarette craving and smoking frequency.
Conclusions Environmental constraints can drive substitution behavior and the substitution behavior is able to be sustained if people find the substitute to be effective.
Implications This study characterizes subtypes of dual users based on the dynamic interactions between cigarette use and e-cigarette use as well as product-specific trajectories of dependence. The subtypes differ in not only sociodemographic characteristics but also contexts of cigarette and e-cigarette use. Higher motivation to use e-cigarettes to quit smoking and less permissive environment for smoking may promote substitution of cigarettes by e-cigarettes.
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Abstract Capturing evidence for dynamic changes in self‐regulated learning (SRL) behaviours resulting from interventions is challenging for researchers. In the current study, we identified students who were likely to do poorly in a biology course and those who were likely to do well. Then, we randomly assigned a portion of the students predicted to perform poorly to a science of learning to learn intervention where they were taught SRL study strategies. Learning outcome and log data (257 K events) were collected from
n = 226 students. We used a complex systems framework to model the differences in SRL including the amount, interrelatedness, density and regularity of engagement captured in digital trace data (ie, logs). Differences were compared between students who were predicted to (1) perform poorly (control,n = 48), (2) perform poorly and received intervention (treatment,n = 95) and (3) perform well (not flagged,n = 83). Results indicated that the regularity of students' engagement was predictive of course grade, and that the intervention group exhibited increased regularity in engagement over the control group immediately after the intervention and maintained that increase over the course of the semester. We discuss the implications of these findings in relation to the future of artificial intelligence and potential uses for monitoring student learning in online environments.Practitioner notes What is already known about this topic
Self‐regulated learning (SRL) knowledge and skills are strong predictors of postsecondary STEM student success.
SRL is a dynamic, temporal process that leads to purposeful student engagement.
Methods and metrics for measuring dynamic SRL behaviours in learning contexts are needed.
What this paper adds
A Markov process for measuring dynamic SRL processes using log data.
Evidence that dynamic, interaction‐dominant aspects of SRL predict student achievement.
Evidence that SRL processes can be meaningfully impacted through educational intervention.
Implications for theory and practice
Complexity approaches inform theory and measurement of dynamic SRL processes.
Static representations of dynamic SRL processes are promising learning analytics metrics.
Engineered features of LMS usage are valuable contributions to AI models.
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Accepted Manuscript1.0
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