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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.]

In Australia, all teachers are expected to explicitly attend to numeracy in the subjects they teach. Pre-service teachers, therefore, need to begin to develop effective numeracy teaching strategies but there is a limited research base to inform the design of courses that address this need. This paper reports on findings from a study investigating the impact of one such course. The paper draws on data from two pre-service teachers: two course tasks completed at the beginning of the course and interviews conducted at the end of the course. Data were analysed using the 21st Century Numeracy Model. Findings suggest there were changes to the pre-service teachers' understanding of numeracy and their capacity to embed numeracy in the subjects they will teach.

Engagement in mathematics education is an important factor in a successful student experience. This paper reports findings from a study of Year 5 student perceptions of engagement during a two-week, inquiry-based learning (IBL), problem-posing investigation. The study triangulated data from semistructured interviews, video observations and student work samples to understand the student's perspectives of IBL; however, this paper reports the interview data. The findings indicate that most of the students were behaviourally, emotionally, and cognitively engaged during the IBL investigation, and that the investigation provided an opportunity for students to experience levels of competence, relatedness, and autonomy need satisfaction.

Prospective secondary mathematics teachers in Australia are typically taught by mathematics educators and mathematicians who work in different faculties and seldom collaborate--a situation that can lead to conflicting views about how to teach mathematics. This paper reports on findings from semi-structured interviews with three mathematics teacher educators in a hybrid mathematics/mathematics education department. Valsiner's zone theory is used to analyse how their beliefs, institutional context and professional learning opportunities shape their identities as MTEs. Findings reveal that the MTEs had developed similar beliefs within supportive institutional context but drew on different sources of professional learning.

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).]

In test equating, one critical equating property is the group invariance property which indicates that the equating function used to convert performance on each alternate form to the reporting scale should be the same for various subgroups. To mitigate the impact of disrupted learning on the item parameters during the COVID-19 pandemic, a pre-equated approach was frequently implemented for student scoring in the spring 2021 administration of large-scale assessments. This study examines how much the group invariance property was satisfied for various subgroups when pre-equating was applied to large-scale assessments in spring 2021. While most studies for invariance property have been for post-equating, this study investigated the invariance property with pre-equating. Due to the potential impact on live calibration and equating, many large-scale assessment programs have opted to reuse previously administered forms and applied pre-equating rather than developing new forms and post-equating in 2021. This study included grades 6 and 8 ELA and Math from a spring 2021 large-scale assessment program and examined the invariance property for four subgroups: gender, SES, ethnicity, and LEP. Three different scoring methods were studied: unrounded equated scores, rounded equated scores, and MLE as IRT pattern scoring. As evaluation criteria, RMSD and REMSD indices were included (Dorans & Holland, 2000). The effect size was also used for evaluating the equating function differences between each subgroup's categories and the population. Invariance property is often studied when post-equating is performed with alternate forms under common (i.e., anchor) item design. In this case, the quality and number of anchor items between alternate forms influence the equating results and invariance property. In general, if anchors are close to a minimal test version, equating results can be better with many anchor items. Pre-equating design fully satisfies the requirement of the maximum number of anchor items because all items can be used as anchor items. Therefore invariance property can be better achieved than post-equating with some common items under the same condition. RMSD and REMSD values for ELA, where students' performances were not much impacted by the pandemic, showed the same results. However, there were some deviations in the invariance property for Math where students' performances appeared to be impacted.

The purpose of the current research study was to investigate the extent to which student performance was influenced by the disruption to learning that occurred due to the COVID-19 pandemic. To explain observed differences in performance, we compared outcomes from a state-wide summative testing program between students who were administered the test in 2019 and 2021. Because the background and demographic characteristics of the two testing populations differed on several variables, including race/ethnicity, locale, and subgroup membership, propensity score matching was used to develop comparable groups for analyses. Independent samples t-tests were then conducted to assess whether there were significant differences in mean scaled scores and domain subscores between the two matched groups. In addition, the same procedures were used to develop and analyze differences for specific student subgroups (students with disabilities, economically disadvantaged students, and English language learners). Overall, results indicated that the 2021 test-takers earned lower scores than students who tested in 2019 for all subjects and grade levels, except English Language Arts (ELA) grade 8. Moreover, larger score differences were observed for mathematics than ELA. Lastly, results from subgroup analyses indicated that in mathematics all subgroups earned significantly lower scores in 2021 than 2019, whereas in ELA grades 5 through 7, English Language Learners and economically disadvantaged subgroups earned lower scores in 2021 than 2019. The results of this study suggest that after controlling for differences between the 2021 and 2019 populations, student performance was likely influenced by the disruption to learning due to pandemic-related factors.

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.]

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.

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.]