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With the increased number of MOOC offerings, it is unclear how these courses are related. Previous work has focused on capturing the prerequisite relationships between courses, lectures, and concepts. However, it is also essential to model the content structure of MOOC courses. Constructing a precedence graph that models the similarities and variations of learning paths followed by similar MOOCs would help both students and instructors. Students can personalize their learning by choosing the desired learning path and lectures across several courses guided by the precedence graph. Similarly, by examining the precedence graph, instructors can 1) identify knowledge gaps in their MOOC offerings, and 2) find alternative course plans. In this paper, we propose an unsupervised approach to build the precedence graph of similar MOOCs, where nodes are clusters of lectures with similar content, and edges depict alternative precedence relationships. Our approach to cluster similar lectures based on PCK-Means clustering algorithm that incorporates pairwise constraints: Must-Link and Cannot-Link with the standard K-Means algorithm. To build the precedence graph, we link the clusters according to the precedence relations mined from current MOOCs. Experiments over real-world MOOC data show that PCK-Means with our proposed pairwise constraints outperform the K-Means algorithm in both Adjusted Mutual Information (AMI) and Fowlkes-Mallows scores (FMI). [For the full proceedings, see ED607784.]

Noticing children's mathematical thinking is foundational to teaching that is responsive to children's thinking. To better understand the range of noticing expertise for teachers engaged in multiyear professional development, we assessed the noticing of 72 upper elementary school teachers using three instructional scenarios involving fraction problem solving. Through a latent class analysis, we identified three subgroups of teachers that reflected different profiles of noticing expertise. Consideration was given to the noticing component skills of attending to children's strategy details, interpreting children's understandings, and deciding how to respond on the basis of children's understandings. We share theoretical and practical implications for not only the three profiles but also our choice to explore separately two versions of deciding how to respond (deciding on follow-up questions and deciding on next problems). [For the complete proceedings, see ED630060.]

Isomorphism and homomorphism are topics central to abstract algebra, but research on mathematicians' views of these topics, especially with respect to sameness, remains limited. This study examines 197 mathematicians' views of how sameness could be helpful or harmful when studying isomorphism and homomorphism. Instructors saw benefits to connecting isomorphism and sameness but expressed reservations about homomorphism. Pedagogical considerations and the dual function-structure nature of isomorphism and homomorphism are also explored. [For the complete proceedings, see ED630060.]

This study aims to describe how preservice secondary mathematics teachers (PSMTs) reason about different function representations. The study focuses on two PSMTs' reasonings across static and dynamic representations of functions. Sfard's (2008) Theory of Commognition guided our analysis. Findings indicate that while static representations restrict attention given to covariation, dynamic representations support PSMTs' reasoning about covariation including making connections to how covariation is represented in static graphs. [For the complete proceedings, see ED630060.]

This article describes the results of an investigation based on a Models and Modeling Perspective [MMP]. We present the evolution of the models built by university students when solving a model development sequence designed to promote their learning of the exponential function. As a result, we observed that students' thinking was modified, expanded, and refined, as they developed different iterations of their models. Students' models evolved by creating, first, linear models that required direction; second, models where there was no dissociation between linear and exponential behavior; then, situated exponential models; and finally, sharable, and reusable exponential models. [For the complete proceedings, see ED630060.]

People often view mathematics as abstract, cold, and irrelevant to real-life, and their school experiences influence such views. In this case study, we investigated the mathematics learning experiences of two women who participated in an afterschool girls STEM club 26 years ago. We explored their experiences in and out of school and how such experiences informed their images of mathematics. Data were collected from a survey, focus group interviews, and individual interviews. Using qualitative analysis, we learned that their school mathematics experiences influenced the participants' images of mathematics. The findings also revealed the participants' continuous and discontinuous learning experiences between school and out-of-school mathematics. This study suggests creating spaces to develop curricula that bridge the gap between school and out-of-school learning experiences. [For the complete proceedings, see ED630060.]

The demand for U.S. temporary workers has doubled since the 1990s, especially after the technology boom. American employers have benefited from hiring foreign talent for STEM occupations. Despite the mandatory prevailing wage regulations, temporary skilled immigrants have been criticized for their "willingness" to work for lower wages. This integrated literature review aims to clarify the wage gap between skilled immigrants and natives in STEM occupations. This research design utilized a systematic literature review to identify relevant studies, collect data, and analyze data using thematic coding. Findings included two major themes: the wage gap as a "myth" and the wage gap as a "reality." Practical and policy implementations will be discussed based on the findings of this integrated literature review. [For the complete volume, "American Association for Adult and Continuing Education Inaugural 2020 Conference Proceedings (Online, October 27-30, 2020)," see ED611534.]

Mathematical calculations are an important part of chemistry. Those problems are difficult for students, especially if the task is set with a limiting reactant. The aim of this study was development of a Procedure for evaluation of cognitive complexity of the Stoichiometric Tasks with a Limiting Reactant. The procedure created included an assessment of the difficulty of concepts and an assessment of their interactivity. As a research instrument for assessing performance, the test of knowledge was specifically constructed for this research. Each task in the test was followed by a seven-point Likert scale for the evaluation of the invested mental effort. The research included 58 upper-secondary students. The validity of the procedure was confirmed by a series of regression analyses where statistically significant correlation coefficients are obtained among the examined variables: students' achievement and invested mental effort from cognitive complexity (independent variable). [For the full proceedings, see ED620289.]

Examining students' inclinations to use algorithms and rules to solve a task was a fruitful area of research in chemical education in the last four decades. This research aimed to examine whether students read the task request carefully, considering its meaningfulness, or they approach it mechanically, applying a set of algorithms by default. The research sample consisted of students majoring in chemistry teaching at the University of Novi Sad, Faculty of Sciences who were in their final year of bachelor studies. The study was conducted during two academic years. The main instrument consisted of five quantitative problems, and each of the problems contained deceptive information that made the calculation nonsensical. The results revealed that most students applied an algorithmic approach without paying attention to the meaningfulness of the task requirements. Additionally, it has been shown that students rely heavily on memorizing formulas without a proper understanding of underlying concepts. [For the full proceedings, see ED620289.]

These proceedings contain papers of the 4th International Baltic Symposium on Science and Technology Education (BalticSTE2021) held in Šiauliai, Lithuania, June 21-22, 2021. This symposium was organized by the Scientific Methodical Center "Scientia Educologica" in cooperation with Scientia Socialis, Ltd. Lithuania. The proceedings are comprised of 16 short papers. Keynote speakers include: Paul Pace, Paolo Bussotti, Peter Demkanin, and Malgorzata Nodzynska. [Individual papers are indexed in ERIC.]

In this study, we investigated two students', ages ten and eleven, emotions while they engaged in mathematical problem solving. During three task-based interviews, the students explored parts of the unsolved problem the Graceful Tree Conjecture. While they were engaged in the interviews, they self-identified the emotions of frustration and joy they were feeling using the Wong-Baker Scale. The students displayed the interplay of the emotions of frustration and joy or which we consider to be productive struggle. A descripted case of Georgia is included to describe her emotions while problem solving. [For the complete proceedings, see ED629884.]

This study examines pre-service teachers' (PSTs') views of tasks that engage students in mathematical argumentation. Data were collected in two different mathematics courses for elementary school education majors (n = 51 total PSTs). Analyzed were (a) written journals in which PSTs defined tasks that promote student engagement in argumentation, (b) tasks PSTs posed to engage students in mathematical argumentation, and (c) accompanying explanations in which PSTs motivated tasks they posed. The analysis revealed that PSTs interpret tasks that foster argumentation in terms of activities of argumentation that a task elicits and space for argumentation that the task provides. Several features that PSTs associated with each of the two major task characteristics were identified. While posing tasks to engage students in argumentation, PSTs did not place equal emphasis on all of the identified features. [For the complete proceedings, see ED629884.]

This report proposes a framework for describing student analogical reasoning activities in abstract algebra that moves beyond the traditional literature-based treatment of analogical mapping. The Analogical Reasoning in Mathematics (ARM) framework captures the activities that students engage in when anticipating, creating, and reasoning from mathematical analogies. This considers activities along several dimensions including: inter/intra domain activity, foregrounded/backgrounded domain, and attention to similarity/difference. These dimensions are integrated with Gentner's (1983) analogical mapping framework to characterize student activity when they are presented with tasks where reasoning by analogy can productively support their mathematical investigations. By characterizing these activities, we can better develop tasks to support students in productively analogizing between mathematical domains. [For the complete proceedings, see ED629884.]

We report on findings from two one-on-one teaching experiments with prospective middle school teachers (PTs). The focus of each teaching experiment was on identifying and explicating the mental processes and types of intermediate, supporting reasoning that each PT used in their development of combinatorial reasoning. The teaching experiments were designed and facilitated to guide each PT toward reinventing multiple combinatorial formulas. Drawing on a subset of this data, we describe the development of the PTs' mental processes and reasoning as they came to construct formulas for counting permutations and arrangements without repetition, and we analyze our findings through a psychological constructivist framework. [For the complete proceedings, see ED629884.]

One important aspect of teaching is reviewing tasks in preparation for instruction. The goal of the multicase study of four secondary teachers was to examine the interplay between their mathematical knowledge for teaching [MKT] and what they attend to when reviewing a mathematics task. We engaged secondary mathematics teachers in a semi-structured, clinical interview focused on a nonroutine mathematical task involving exponential growth. The results suggest experienced teachers may not explicitly attend to learning opportunities in their review of a task, and their own mathematical work contributes to their anticipation of student work and thinking. This work highlights how researchers focused on MKT can use clinical interviews as a tool for extracting and describing a teacher's MKT. [For the complete proceedings, see ED629884.]

We report our findings and perspective to document the knowledge exhibited by three experienced high school teachers in their instructional decisions for lessons on the equation of an exponential function. We describe the nature of the mathematical ideas and connections teachers promoted in discourse and the decisions that supported the emergence and connections of the mathematics. Despite similarities in the structure of the mathematical activities, differences existed in the ideas that emerged in the three teachers' discussions regarding the relationship between the exponent value and the independent variable. We describe links between collections of teacher decisions to their influences on the mathematics discourse. [For the complete proceedings, see ED629884.]

Using neurodiversity as our theoretical framework, rather than a deficit or medical model, we analyze the narratives of five dyslexic research mathematicians to find common strengths and challenges for dyslexic thinkers at the highest level of mathematics. We report on 3 themes: (1) highly visual and intuitive ways of mathematical thinking; (2) pronounced issues with memorization of mathematical facts and procedures; and (3) resilience as a strength of dyslexia that matters in mathematics. We introduce the idea of Neurodiversity for Mathematics, a research agenda to better understand the strengths (as well as challenges) of neurodiverse individuals and to use that knowledge to design better mathematical learning experiences for all. [For the complete proceedings, see ED629884.]

Metacognition is a valuable tool for learning, since it is closely related to self-regulation and awareness of one's own affect. However, methods for automatically detecting and studying metacognition are scarce. Thus, in this paper we describe an algorithm for automatic detection of metacognitive language in writing. We analyzed text from the forums of two online, university-level science courses, which revealed common patterns of phrases that we used for automatic metacognition detection. The algorithm we developed exhibited high accuracy on expert-labeled metacognitive phrases (Spearman's rho = 0.878 and Cohen's kappa = 0.792), and provides a reliable, fast method for automatically annotating text corpora that are too large for manual annotation. We applied this algorithm to analyze relationships between students' metacognitive language and their academic performance, finding small correlations with course grade and medium-sized differences in metacognition across courses. We discuss how our algorithm can be used to advance metacognitive studies and online educational systems.

One of the essential problems, in educational data mining, is to predict students' performance on future learning materials, such as problems, assignments, and quizzes. Pioneer algorithms for predicting student performance mostly rely on two sources of information: students' past performance, and learning materials' domain knowledge model. The domain knowledge model, traditionally curated by domain experts, maps learning materials to concepts, topics, or knowledge components that are presented in them. However, creating a domain model by manually labeling the learning material can be a difficult and time-consuming task. In this paper, we propose a tensor factorization model for student performance prediction that does not rely on a predefined domain model. Our proposed algorithm models student knowledge as a soft membership of latent concepts. It also represents the knowledge acquisition process with an added rank-based constraint in the tensor factorization objective function. Our experiments show that the proposed model outperforms state-of-the-art algorithms in predicting student performance in two real-world datasets, and is robust to hyper-parameters. [For the full proceedings, see ED599096.]

One significant challenge in the field of measuring ability is measuring the current ability of a learner while they are learning. Many forms of inference become computationally complex in the presence of time-dependent learner ability, and are not feasible to implement in an online context. In this paper, we demonstrate an approach which can estimate learner skill over time even in the presence of large data sets. We use a rating system derived from the Elo rating system and its relatives, which are commonly used in chess and sports tournaments. A learner's submission of a course assignment is interpreted as a single match. We apply this approach to Coursera's online learning platform, which includes millions of learners who have submitted assignments tens of millions of times in over 3000 courses. We demonstrate that this provides reliable estimates of item difficulty and learner ability. Finally, we address how this scoring framework may be used as a basis for various applications that account for a learner's ability, such as adaptive diagnostic tests and personalized recommendations. [For the full proceedings, see ED599096.]

In this paper we consider the problem of modelling when students end their session in an online mathematics educational system. Being able to model this accurately will help us optimize the way content is presented and consumed. This is done by modelling the probability of an action being the last in a session, which we denote as the End-of-Session probability. We use log data from a system where students can learn mathematics through various kinds of learning materials, as well as multiple types of exercises, such that a student session can consist of many different activities. We model the End-of-Session probability by a deep recurrent neural network in order to utilize the long term temporal aspect, which we experimentally show is central for this task. Using a large scale dataset of more than 70 million student actions, we obtain an AUC of 0.81 on an unseen collection of students. Through a detailed error analysis, we observe that our model is robust across different session structures and across varying session lengths. [For the full proceedings, see ED599096.]

Clustering of educational data allows similar students to be grouped, in either crisp or fuzzy sets, based on their similarities. Standard approaches are well suited to identifying common student behaviors; however, by design, they put much less emphasis on less common behaviors or outliers. The approach presented in this paper employs fuzzing clustering in the identification of these outlier behaviors. The algorithm is an iterative one, where clustering is applied, outliers identified, the data restricted to the outliers, and the process repeated. This approach produces a clustering that is crisp between each iteration and fuzzy within. It arose as a consequence of trying to cluster student progress trajectories in an adaptive learning platform. Included are results from applying the repeated fuzzy clustering algorithm to data from multiple courses and semesters at the University of Central Florida, (N=5,044). [For the full proceedings, see ED599096.]

Personalized education systems recommend learning contents to students based on their capacity to accelerate their learning. This paper proposes a personalized exercise recommendation system for online self-directed learning. We first improve the performance of knowledge tracing models. Existing deep knowledge tracing models, such as Dynamic Key-Value Memory Network (DKVMN), ignore exercises' concept tags, which are usually available in tutoring systems. We modify DKVMN to design its memory structure based on the course's concept list, and explicitly consider the exercise-concept mapping relationship during students' knowledge tracing. We evaluated the model on the 5th grade students' math exercising dataset in TAL, one of the biggest education groups in China, and found that our model has higher performance than existing models. We also enhance the DKVMN model to support more input features and obtain higher performance. Second, we use the model to build a student simulator, and use it to train an exercise recommendation policy with deep reinforcement learning. Experimental results show that our policy achieves better performance than existing heuristic policy in terms of maximizing the students' knowledge level. To the best of our knowledge, this is the first time that deep reinforcement learning has been applied to personalized mathematic exercise recommendation. [For the full proceedings, see ED599096.]

Short forms of psychometric scales have been commonly used in educational and psychological research to reduce the burden of test administration. However, it is challenging to select items for a short form that preserve the validity and reliability of the scores of the original scale. This paper presents and evaluates multiple automated methods for scale short form creation based on metaheuristic optimization algorithms that incorporate validity criteria based on internal structure and relationships with other variables. The ant colony optimization (ACO) algorithm, tabu search (TS), simulated annealing (SA) and genetic algorithm (GA) are examined using confirmatory factor analysis (CFA) of scales with one factor, three factor, and bi-factor factorial structure. The results indicate that SA created short forms with best model fit for scales with one and three factor structures, but ACO was able to obtain highest reliability. For scales with bi-factor structure, SA provide short forms with best model fit, but TS obtained highest reliability. Overall, the SA algorithm is recommended because it produced consistently best model fit and reliability that was only slightly lower than the ACO or TS algorithms. [For the full proceedings, see ED599096.]