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An intelligent textbook may be defined as an interaction layer between the text and the student, helping the student master the content in the text. The Mobile Fact and Concept Training System (MoFaCTS) is an adaptive instructional system for simple content that has been developed into an interaction layer to mediate textbook instruction and so is being transformed into the Mobile Fact and Concept Textbook System (MoFaCTS). In this paper, we document the several terms of the logistic regression model we use to track performance adaptively. We then examine the contribution of each component of our model when it is fit to 4 semesters of Anatomy and Physiology course practice data. Following this documentation of the model, we explain how it is applied in the MoFaCTS system to schedule performance by targeting practice for each item at an optimal efficiency threshold. [This paper was published in the CEUR workshop proceedings (Vol. 2895).]

Bayesian Knowledge Tracing, a model used for cognitive mastery estimation, has been a hallmark of adaptive learning research and an integral component of deployed intelligent tutoring systems (ITS). In this paper, we provide a brief history of knowledge tracing model research and introduce pyBKT, an accessible and computationally efficient library of model extensions from the literature. The library provides data generation, fitting, prediction, and cross-validation routines, as well as a simple to use data helper interface to ingest typical tutor log dataset formats. We evaluate the runtime with various dataset sizes and compare to past implementations. Additionally, we conduct sanity checks of the model using experiments with simulated data to evaluate the accuracy of its EM parameter learning and use real-world data to validate its predictions, comparing pyBKT's supported model variants with results from the papers in which they were originally introduced. The library is open source and open license for the purpose of making knowledge tracing more accessible to communities of research and practice and to facilitate progress in the field through easier replication of past approaches. [For the full proceedings, see ED615472.]

Many scholars have argued that mathematics classrooms often offer narrow conceptions of mathematical excellence, recognizing only some kinds of thinking and some kinds of people as valuable, and conflating mathematical aptitude with overall intelligence. Play offers the potential to disrupt such classroom mathematical practices, by offering new and broader ways to exercise agency, and, relatedly, more expansive visions of who is seen as mathematically capable. Offering an in-depth analysis of the participation of two students as they engage in mathematics in their Kindergarten class, whole group rug time and small group play centers, we investigate how different activity structures create space for students to exercise agency in ways that demonstrate multiple forms of competence, creating liberating mathematical spaces. [For the complete proceedings, see ED658295.]

Dramatic differences in children's math knowledge at school entry are thought to originate in the Home Math Environment (HME), where parents and caregivers are the primary provider of experiences that influence children's early math knowledge development. Little is known about what informs parent decision-making around "mathematical parenting" (i.e., parents' cognitions, motivations, and behaviors that impact and influence child math development in the HME). This study uses the RESET Framework and survey instrument to investigate parents' mathematical parenting perceptions (n = 847) across the domains of Role, Expectations, Skills, Efficacy, and Time. Parent self-reports of early childhood math knowledge and of shared math activity are also examined to shed light on the factors that influence mathematical parenting of 4-5-year-old children in the home. [For the complete proceedings, see ED658295.]

The Indian Institute of Science is proud to host the fully in-person sixteenth iteration of the International Conference on Educational Data Mining (EDM) during July 11-14, 2023. EDM is the annual flagship conference of the International Educational Data Mining Society. The theme of this year's conference is "Educational data mining for amplifying human potential." Not all students or seekers of knowledge receive the education necessary to help them realize their full potential, be it due to a lack of resources or lack of access to high quality teaching. The dearth in high-quality educational content, teaching aids, and methodologies, and non-availability of objective feedback on how they could become better teachers, deprive our teachers from achieving their full potential. The administrators and policy makers lack tools for making optimal decisions such as optimal class sizes, class composition, and course sequencing. All these handicap the nations, particularly the economically emergent ones, who recognize the centrality of education for their growth. EDM-2023 has striven to focus on concepts, principles, and techniques mined from educational data for amplifying the potential of all the stakeholders in the education system. The spotlights of EDM-2023 include: (1) Five keynote talks by outstanding researchers of eminence; (2) A plenary Test of Time award talk and a Banquet talk; (3) Five tutorials (foundational as well as advanced); (4) Four thought provoking panels on contemporary themes; (5) Peer reviewed technical paper and poster presentations; (6) Doctoral students consortium; and (7) An enchanting cultural programme. [Individual papers are indexed in ERIC.]

ChatGPT and Bard, two chatbots powered by Large Language Models (LLMs), are propelling the educational sector towards a new era of instructional innovation. Within this educational paradigm, the present investigation conducts a comparative analysis of these groundbreaking chatbots, scrutinizing their distinct operational characteristics and applications as depicted in current scholarly discourse. ChatGPT emerges as an exemplary tool in task-oriented textual interactions, while Bard brandishes unique features such as Text-To-Speech (TTS) functionality, which enhances accessibility and inclusive education, as well as integration with Google Workspace applications. This research critically examines their utilization in various spheres such as pedagogy, academic research, Massive Open Online Courses (MOOCs), mathematics, and software programming. Findings accentuate ChatGPT's superior efficacy in content drafting, code generation, language translation, and providing clinically precise responses, notwithstanding Bard's significant potential encapsulated in its exclusive features. Furthermore, the study traverses' crucial ethical aspects, including privacy concerns and inherent bias, underscoring the profound implications of these Artificial Intelligence (AI) technologies on literature and advocating against the indiscriminate reliance on such models. [For the full proceedings, see ED636095.]

In response to the challenge of geometry's abstract and less engaging nature for students, this study explored the potential of connecting geometry to cultural elements, specifically geometric ornaments found in various cultures worldwide. Geometric ornaments, laden with cultural and spiritual significance, serve as a bridge between mathematics education and cultural contexts. The current research focused on in-depth interviews with 10 school students chosen randomly from two ninth-grade classes from an Arab middle school who were engaged in activities involving analyzing of geometric properties of ornaments, constructing ornaments using a compass and straightedge, and problem-solving exercises related to these ornaments. The qualitative data were analyzed to answer how the students perceived the learning of geometry in the context of geometric ornaments. The findings revealed a significant positive view of the students towards geometry after engaging in these activities. [For the full proceedings, see ED656038.]

"Geometry--Do" is a textbook about plane geometry. It will be divided into two volumes, "Geometry without Multiplication: White through Red Belt," and "Geometry with Multiplication: Blue through Black Belt. "The white- and yellow-belt chapters are neutral geometry; the remainder of "Volume One" and all of "Volume Two" is Euclidean geometry. It is primarily intended to teach geometry from the ground up, starting with the postulates and citing only already-proven theorems. It trains mathletes for competition, but it is not the usual grab-bag of unproven theorems chosen haphazardly and solely because they appeared in past exams. The early chapters prepare students for jobs in construction, architecture, surveying, graphic arts, and military defense. The later chapters teach geometry needed by engineers and military officers. In this lecture, the White Belt chapter is presented. I will address these people: Pure Mathematicians: Moise derides the "lighthearted use of the word let." I prove the crossbar theorem and other foundations not usually taught in high school, and I discuss Hilbert's "Foundations of Geometry." High-School Teachers: Randomly assigning letters to points is what makes geometry confusing. I have special symbols for midpoints, perpendicular feet, and infeet (where the angle bisector cuts the opposite side of a triangle) and exfeet. Administrators: I present clear distinctions between "Geometry--Do" and "Common Core" with examples that concerned parents can understand. Construction Workers: I invent the Aguilar A-Frame, give detailed instructions on squaring abasement foundation wider than a tape measure without exiting the rectangle, and discuss how building with wood differs from steel construction. Military Officers: I discuss troop positioning along a frontier that is plagued with cross-border raids, which assumes that friendly and enemy troops move at the same speed, and a parabola is the set of points equidistant from the focus and the directrix. [For the complete proceedings, see ED655360.]

To support online learners at a large scale, extensive studies have adopted machine learning (ML) techniques to analyze students' artifacts and predict their learning outcomes automatically. However, limited attention has been paid to the fairness of prediction with ML in educational settings. This study intends to fill the gap by introducing a generic algorithm that can orchestrate with existing ML algorithms while yielding fairer results. Specifically, we have implemented logistic regression with the Seldonian algorithm and compared the fairness-aware model with fairness-unaware ML models. The results show that the Seldonian algorithm can achieve comparable predictive performance while producing notably higher fairness. [This paper was published in: "LAK21: 11th International Learning Analytics and Knowledge Conference (LAK21), April 12-16, 2021, Irvine, CA, USA," ACM, 2021.]

Bridging the gap between mathematical learning at home and school has been an issue for education research for decades (Galindo & Sheldon, 2012). Expectations for mathematics do not often align for teachers and parents (Posey-Maddox & Hayley-Lock, 2016) and a limited view of what counts as mathematics persists. What needs more attention is the meaningful mathematical learning that happens at home but is rarely seen as mathematics. Parents frequently struggle in supporting their children's mathematical learning, but that struggle becomes productive when parents are recognized as mathematically capable. This paper shows how two mothers shift their perspectives of what counts as mathematics and recognize the rich content in their current interactions with young children. Making such connections between mathematics and parent action can strengthen the relationship between at-home and school learning. [For the complete proceedings, see ED630060.]

In this paper we address the question, how do quantitative reasoning and covariational reasoning present as students build structural conceptions of real-world situations. We use data from an exploratory teaching experiment with an undergraduate STEM major to illustrate the explanatory roles quantitative reasoning and covariational reasoning play in, (a) coordinating more than two interdependent quantities, (b) conceiving of real-world situations in more than one way, (c) constructing networks of quantitative relationships, and (d) creating a mathematical expression. We make the case that looking at mathematical model construction through the lens of quantitative reasoning and covariational reasoning may provide insights into students' mathematical decisions as they structure complex real-world scenarios. [For the complete proceedings, see ED630060.]

Several researchers have promoted reimagining functions and graphs more quantitatively. One part of this research has examined graphing "conventions" that can at times conflict with quantitative reasoning about graphs. In this theoretical paper, we build on this work by considering a widespread convention in mathematics teaching: putting related, derived graphical objects (e.g., the graphs of a function and its inverse or the graphs of a function and its derivative) on the same set of axes. We show problems that arise from this convention in different mathematical content areas when considering contextualized functions and graphs. We discuss teaching implications about introducing such related graphical objects through context on separate axes, and eventually building the convention of placing them on the same axis in a way that this convention and its purposes become more transparent to students. [For the complete proceedings, see ED630060.]

Consistency of learning behaviors is known to play an important role in learners' engagement in a course and impact their learning outcomes. Despite significant advances in the area of learning analytics (LA) in measuring various self-regulated learning behaviors, using LA to measure consistency of online course engagement patterns remains largely unexplored. This study focuses on modeling consistency of learners in online courses to address this research gap. Toward this, we propose a novel unsupervised algorithm that combines sequence pattern mining and ideas from information retrieval with a clustering algorithm to first extract engagement patterns of learners, represent learners in a vector space of these patterns and finally group them into groups with similar consistency levels. Using clickstream data recorded in a popular learning management system over two offerings of a STEM course, we validate our proposed approach to detect learners that are inconsistent in their behaviors. We find that our method not only groups learners by consistency levels, but also provides reliable instructor support at an early stage in a course. [This paper was published in: "LAK21: 11th International Learning Analytics and Knowledge Conference (LAK21), April 12-16, 2021, Irvine, CA, USA." ACM, 2021, pp. 226-236.]

In contrast to simple feedback, which provides students with the correct answer, elaborated feedback provides an explanation of the correct answer with respect to the student's error. Elaborated feedback is thus a challenge for AI in education systems because it requires dynamic explanations, which traditionally require logical reasoning and knowledge engineering to generate. This study presents an alternative approach that formulates elaborated feedback in terms of long-form question answering (LFQA). An off-the-shelf LFQA system was evaluated by human raters in a 2x2x2x2 ablation design that manipulated the context documents given to the LFQA model and the post-processing of model output. Results indicate that context manipulations improve performance but that postprocessing can have detrimental results. [This paper was published in: "Proceedings of the Eighth ACM Conference on Learning @ Scale," 2021, pp. 27-36.]

In the mathematical community, two notions of "function" are used: the set-theoretic definition as a univalent set of ordered pairs, and the Bourbaki triple. These definitions entail different interpretations and answers to mathematical questions that even a secondary student might be prompted to answer. However, mathematicians and mathematics educators are often not explicit about which definition they are using. This paper discusses these parallel usages and the related implications for the field of mathematics education. [For the complete proceedings, see ED629884.]

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.]

This study investigated how motivational orientations and learning strategies predict ninth graders' non-routine mathematical problem-solving anxiety. Non-routine mathematical problem-solving anxiety classification and prediction were investigated through TwoStep cluster analysis, linear discriminant analysis, and logistic regression. 274 ninth graders participated in the study. The participants were clustered based on their problem-solving achievements and test anxiety levels: high-level and low-level problem-solving anxiety. Extrinsic goal orientation, rehearsal, and peer learning were significant classifiers. Intrinsic goal orientation, self-efficacy, rehearsal, and help-seeking were significant predictors for ninth graders' non-routine mathematical problem-solving anxiety.

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.]

The problem of development of algorithmic competence of students -- future Computer Science teachers as a component of information competence is investigated. The aim of the study is to identify the conditions for effective algorithmization and programming learning, involving a modular representation of the content, blended learning, allocated in accordance with the B. Bloom's taxonomy classes of problems in Computer Science and Methods of its Teaching and the use of electronic learning resources. This paper specifies the concept of algorithmic competence of university students--students' readiness to design algorithms and programs, their use in professional activities in the process of Computer Science teaching, electronic learning resources (ELR) design, self-education in the field of Computer Science. Classes of problems for algorithmic competence development in accordance with B. Bloom's taxonomy (knowledge, comprehension, application, analysis, synthesis and evaluation) are identified. Classes of problems correspond to ELR of a certain structure and content. The efficiency of ELR use in students' algorithmic competence development is statistically confirmed. [For the complete proceedings, see ED608557.]

This paper will cover the design of a learning environment as a classroom regarding the Quadratic Equations, Functions and Graphs. The goal of the learning environment offered in the paper is to design a classroom where students will enjoy the process, use their skills they already have during the learning process, control and plan their learning process, and have the right of free choice of which way they can learn easily. Besides, it is alleged that in the paper, students will be more engaged, motivated and self-confident in this learning environment in terms of theories and approaches. Besides, students will have computers and graph calculators in the classroom, and some applications and programs will be provided such as Cabri, Maple, Derive, etc. [For the complete proceedings, see ED579395.]

This study examines the COVID-19 shift to online instruction and its impact on a charter school system (CSS) 3rd-10th grade students' academic achievement through the lens of noncognitive factors. We recruited 693 students and utilized qualitative and quantitative analyses. We found that students' NWEA math and ELA scores continued to increase although almost ninety percent of them completed 2020-2021 school year online. Second, students' self-efficacy, academic engagement, and growth mindset scores significantly explained some of the variance in students' NWEA math and ELA scores. Lastly, students indicated that they liked the comfort, family presence, safety, and personalization of the online learning most. They disliked the lack of social component of learning, technical, and focus and engagement problems most.

The Home Learning Environment (HLE) focuses on everyday learning habits in families to support children's competency development. In this study, we used multitrait-multimethod (MTMM) analyses to compare two theoretical dimensions and three methods for assessing the HLE and their associations with linguistic and mathematical competencies of kindergarten children. Our sample consisted of N = 190 children (M[subscript age] = 64 months, SD = 4.4). The MTMM matrix showed a substantial effect of common methods and indicated a one-dimensional HLE construct. A children's book title recognition test was the best predictor of children's linguistic and numeracy competencies. Even when controlling for child and family characteristics, the HLE was significantly related to both children's mathematical and linguistic competencies in a structural equation model.

To efficiently create books and other instructional content from videos and further improve accessibility of our course content we needed to solve the scene detection (SD) problem for engineering educational content. We present the pedagogical applications of extracting video images for the purposes of digital book generation and other shareable resources, within the themes of accessibility, inclusive education, universal design for learning and how we solved this problem for engineering education lecture videos. Scene detection refers to the process of merging visually similar frames into a single video segment, and subsequent extraction of semantic features from the video segment (e.g., title, words, transcription segment and representative image). In our approach, local features were extracted from inter-frame similarity comparisons using multiple metrics. These include numerical measures based on optical character recognition (OCR) and pixel similarity with and without face and body position masking. We analyze and discuss the trade-offs in accuracy, performance and computational resources required. By applying these features to a corpus of labeled videos, a support vector machine determined an optimal parametric decision surface to model if adjacent frames were semantically and visually similar or not. The algorithm design, data flow, and system accuracy and performance are presented. We evaluated our system using videos from multiple engineering disciplines where the content was comprised of different presentation styles including traditional paper handouts, Microsoft PowerPoint slides, and digital ink annotations. For each educational video, a comprehensive digital-book composed of lecture clips, slideshow text, and audio transcription content can be generated based on our new scene detection algorithm. Our new scene detection approach was adopted by ClassTranscribe, an inclusive video platform that follows Universal Design for Learning principles. We report on the subsequent experiences and feedback from students who reviewed the generated digital-books as a learning component. We highlight remaining challenges and describe how instructors can use this technology in their own courses. The main contributions of this work are: Identifying why automated scene detection of engineering lecture videos is challenging; Creation of a scene-labeled corpus of videos representative of multiple undergraduate engineering disciplines and lecture styles suitable for training and testing; Description of a set of image metrics and support vector machine-based classification approach; Evaluation of the accuracy, recall and precision of our algorithm; Use of an algorithmic optimization to obviate GPU resources; Student commentary on the digital book interface created from videos using our SD algorithm; Publishing of a labeled corpus of video content to encourage additional research in this area; and an independent open-source scene extraction tool that can be used pedagogically by the ASEE community e.g., to remix and create fun shareable instructional content memes, and to create accessible audio and text descriptions for students who are blind or have low vision. Text extracted from each scene can also used to improve the accuracy of captions and transcripts, improving accessibility for students who are hard of hearing or deaf.

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.]

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.]

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.]

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.]

The Computational Thinking recently has been recognised as one of the basic knowledge to be developed since childhood. Coding and computers are not just programming, but tools that help students to develop problem solving skills and more deep understand of the way things work. For these reasons, great attention has been focused on this topic both from a pedagogical and technological point of view. In this paper, a first approach to Computational Thinking using Arduino is presented. To this end, some learning activities have been designed to introduce middle school students, without any experience in coding, to the process of building the algorithm from simple exercises to more complex tasks. The pilot test involved 25 subjects, many of them do not like to study mathematics, science and technology, but the results were promising. The approach was appreciated by the students and the results of the questionnaires confirmed the learning effectiveness too. [For the complete proceedings, see ED600498.]

This paper describes a multiple criteria approach based on a hybrid method of Collaborative Filtering (CF) and ContentBased Filtering (CBF) for discovering the most relevant criteria which could affect the elective course recommendation for university students. In order to determine which factors are the most important, it is proposed a genetic algorithm which automatically discovers the importance of the different criteria assigning weights to each one of them. We have carried out an in-depth study using a real data set with more than 1700 ratings of Computer Science graduates at University of Cordoba. We have used different proposals and different weights for each criterion in order to discover what is the combination of multiple criteria which provides better results. [For the full proceedings, see ED593090.]

The significant amount of information available on the web has led to difficulties for the learner to find useful information and relevant resources to carry out their training. The recommender systems have achieved significant success in the area of e-commerce, they still have difficulties in formulating relevant recommendations on e-learning resources because of the different characteristics of learners. Most of the existing recommendation techniques do not take these characteristics into account. This problem can be mitigated by including learner information in the referral process. Currently many recommendation techniques have cold start problems and classification problems. In this paper, we propose an ontology-based collaborative filtering recommendation system for recommending learners' online learning resources based on a decision algorithm (DA). In our approach, ontology is used to model and represent domain knowledge about the learner and learning resources. Our approach is divided into four parts: (a) the creation of an ontology for the representation of the learner's knowledge and learning resources (b) the calculation of the similarity of the assessments according to the ontology and the prediction for the learner concerned; (c) generating the K best items by the collaborative filtering recommendation engine and (d) applying the DA on the proposed items to generate the final recommendations for the targeted learner. [For the complete proceedings, see ED590269.]

As mathematics educators, we teach and research a particular form of knowledge. However, in reacting to Platonic views of mathematics, we often overlook its unique characteristics. This paper presents a Kantian and Piagetian perspective that defines mathematics as a product of psychology. This perspective, based in human activity, unites mathematical objects, such as shape and number, while explaining what makes mathematics unique. In so doing, it not only privileges mathematics as a powerful form of knowledge but also empowers students to own its objects as their own constructions. Examples and interdisciplinary research findings (e.g., neuroscience) are provided to elucidate and support the perspective. [For the complete proceedings, see ED606531.]

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.]