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The General Data Protection Regulation (GDPR) in the European Union contains directions on how user data may be collected, stored, and when it must be deleted. As similar legislation is developed around the globe, there is the potential for repercussions across multiple fields of research, including educational data mining (EDM). Over the past two decades, the EDM community has taken consistent steps to protect learner privacy within our research, whilst pursuing goals that will benefit their learning. However, recent privacy legislation may cause our practices to need to change. The right to be forgotten states that users have the right to request that all their data (including deidentified data generated by them) be removed. In this paper, we discuss the potential challenges of this legislation for EDM research, including impacts on Open Science practices, data modeling, and data sharing. We also consider changes to EDM best practices that may aid compliance with this new legislation. [For the complete proceedings, see ED630829.]

Students who take an online course, such as a MOOC, use the course's discussion forum to ask questions or reach out to instructors when encountering an issue. However, reading and responding to students' questions is difficult to scale because of the time needed to consider each message. As a result, critical issues may be left unresolved, and students may lose the motivation to continue in the course. To help address this problem, we build predictive models that automatically determine the urgency of each forum post, so that these posts can be brought to instructors' attention. This paper goes beyond previous work by predicting not just a binary decision cut-off but a post's level of urgency on a 7-point scale. First, we train and cross-validate several models on an original data set of 3,503 posts from MOOCs at University of Pennsylvania. Second, to determine the generalizability of our models, we test their performance on a separate, previously published data set of 29,604 posts from MOOCs at Stanford University. While the previous work on post urgency used only one data set, we evaluated the prediction across different data sets and courses. The best-performing model was a support vector regressor trained on the Universal Sentence Encoder embeddings of the posts, achieving an RMSE of 1.1 on the training set and 1.4 on the test set. Understanding the urgency of forum posts enables instructors to focus their time more effectively and, as a result, better support student learning. [For the complete proceedings, see ED630829.]

We examined changes in how mathematics coaches facilitated debriefing conversations after learning about a debrief conversational structure we created based on the principles of our content-focused coaching model. We compared participant coaches' first debriefing conversation, which occurred prior to learning about the debrief conversational structure to their second debriefing conversation, which occurred after learning about the debrief conversational structure. Findings indicate that in the second debriefing conversation, participant coaches participated more, prioritized different discursive moves, developed unique data collection systems to share observations from the co-taught lesson, and more frequently structured the conversation around content ideas related to the guiding principles of our content-focused coaching model. [For the complete proceedings, see ED657822.]

We examined the suggestions mathematics coaches provided to teachers as part of one-on-one coaching cycles. The purpose was to understand the object (content) of the suggestions, the lesson phase in which the suggestion would occur, and the clarity of the suggestion (how actionable the suggestion would be if the teacher followed the suggestion). Twenty-three coaching planning meetings were recorded, transcribed, and analyzed. Findings indicated that suggestions commonly focused on lesson design (how the lesson plan should be completed) or teacher questions (actual questions the teacher should ask). Almost half of the suggestions were about the explore phase (or middle) of the lesson and a majority of the suggestions were coded as medium or high clarity, meaning the coach clearly articulated what the suggestion would look like in the classroom. Implications for coaching and future coaching research are provided. [For the complete proceedings, see ED657822.]

We examined what and how experienced (mentor coaches) and novice coaches (coach participants) noticed as they analyzed a vignette of a coaching interaction between a coach and a teacher. We modified the van Es (2011) Learning to Notice Framework for a coaching context to analyze What and How coaches notice. We collected data from ten mentor coaches, who were experienced coaches and ten coach participants who were more novice coaches. We compared pre and post noticing for coach participants based on a two-year professional development model and compared the noticing to the mentor coaches. Findings indicate coach participant noticing for What and How coaches notice collectively shifted toward a greater focus on the teacher, included more interpretation, and was more specific from the beginning of the professional development to the end. The mentor coach noticing, on average, was more teacher-focused, interpretative, and specific than those of the coach participants. [For the complete proceedings, see ED657822.]

Drawing on data collected from one coaching cycle during mathematics instruction for one coach-teacher dyad, this study explores one instructional coach's discursive enactment of their coaching stance. Qualitative analyses indicate that there was dissonance between the coach's stance for coaching and their discursive enactment of coaching, and that the coach's disciplinary expertise seemed to influence the enactment of her coaching stance. Implications for research and practice are discussed. [For the complete proceedings, see ED657822.]

This quasi-experimental study seeks to improve the conceptual quality of summary essays by comparing two conditions, essay prompts with or without a list of 13 broad concepts, the concepts were selected across a continuum of the 100 most frequent words in the lesson materials. It is anticipated that only the most central concepts will be used as "anchors" when writing. Participants (n = 90) in an Architectural Engineering undergraduate course read the assigned lesson textbook chapter and attended lectures and labs, then in a final lab session were asked to write a 300-word summary of the lesson content. Data consists of the essays converted to networks and the end-of-unit multiple choice test. Compared to the expert network benchmark, the essay networks of those receiving the broad concepts in the writing prompt were not significantly different from those who did not receive these concepts. However those receiving the broad concepts were significantly more like peer essay networks (mental model convergence) and like the networks of the two PowerPoint lectures but neither were like the textbook chapter. Further, those receiving the broad concepts performed significantly better on the end-of-unit test than those not receiving the concepts. Term frequency analysis of the essays indicates as expected that the most network-central concepts had a greater frequency in essays, the other terms frequencies were remarkably the same for both the terms and no terms groups, suggesting a similar underlying conceptual mental model of this lesson content. To further explore the influence of anchoring concepts in summary writing prompts, essays were generated with the same two summary writing prompts using OpenAI (ChatGPT) and Google Bard, plus a new prompt that used the 13 most central concepts from the expert's network. The quality of the essay networks for both AI systems were equivalent to the students' essay networks for the broad concepts and for the no concept treatments. However, the AI essays derived with the 13 most central concepts were significantly better (more like the expert network) than the students and AI essays derived with broad concepts or no concepts treatments. In addition, Bard and OpenAI used several of the same concepts at a higher frequency than the students suggesting that the two AI systems have more similar knowledge graphs of this content. In sum, adding 13 broad conceptual terms to a summary writing prompt improved both structural and declarative knowledge outcomes, but adding 13 most central concepts may be even better. More research is needed to understand how including concepts and other terms in a writing prompt influences students' essay conceptual structure and subsequent test performance. [For the full proceedings, see ED636095.]

This qualitative study investigated how a TESOL pre-service foreign language teacher's perspective of translanguaging evolved throughout a 6-week minimester course focused on translanguaging. To support understanding of how Mel, the focal teacher, considered perspectives with which she previously disagreed, we drew on the concept of biographical reflexivity. We used thematic analysis to analyze data, which included the course syllabus and Mel's oral contributions that were audio recorded and transcribed verbatim. Findings show that as she worked to make sense of translanguaging as a theory, practice, and pedagogy by reflecting on her own experiences and juxtaposing them with course content, Mel wavered between agreement and disagreement regarding inequality, linguistic imperialism, discrimination, and identity development. Implications for future research and practice are discussed.

In real-world settings, vision language models (VLMs) should robustly handle naturalistic, noisy visual content as well as domain-specific language and concepts. For example, K-12 educators using digital learning platforms may need to examine and provide feedback across many images of students' math work. To assess the potential of VLMs to support educators in settings like this one, we introduce DrawEduMath, an English-language dataset of 2,030 images of students' hand-written responses to K-12 math problems. Teachers provided detailed annotations, including free-form descriptions of each image and 11,661 question-answer (QA) pairs. These annotations capture a wealth of pedagogical insights, ranging from students' problem-solving strategies to the composition of their drawings, diagrams, and writing. We evaluate VLMs on teachers' QA pairs, as well as 44,362 synthetic QA pairs derived from teachers' descriptions using language models (LMs). We show that even state-of-the-art VLMs leave much room for improvement on DrawEduMath questions. We also find that synthetic QAs, though imperfect, can yield similar model rankings as teacher-written QAs. We release DrawEduMath to support the evaluation of VLMs' abilities to reason mathematically over images gathered with educational contexts in mind.

Research into "gaming the system" behavior in intelligent tutoring systems (ITS) has been around for almost two decades, and detection has been developed for many ITSs. Machine learning models can detect this behavior in both real-time and in historical data. However, intelligent tutoring system designs often change over time, in terms of the design of the student interface, assessment models, and data collection log schemas. Can gaming detectors still be trusted, a decade or more after they are developed? In this research, we evaluate the robustness/degradation of gaming detectors when trained on older data logs and evaluated on current data logs. We demonstrate that some machine learning models developed using past data are still able to predict gaming behavior from student data collected 16 years later, but that there is considerable variance in how well different algorithms perform over time. We demonstrate that a classic decision tree algorithm maintained its performance while more contemporary algorithms struggled to transfer to new data, even though they exhibited better performance on unseen students in both New and Old data sets by themselves. Examining the feature importance values provides some explanation for the differences in performance between models, and offers some insight into how we might safeguard against detector rot over time. [For the full proceedings, see ED623995.]

Self-regulated learning (SRL) is a critical component of mathematics problem solving. Students skilled in SRL are more likely to effectively set goals, search for information, and direct their attention and cognitive process so that they align their efforts with their objectives. An influential framework for SRL, the SMART model, proposes that five cognitive operations (i.e., searching, monitoring, assembling, rehearsing, and translating) play a key role in SRL. However, these categories encompass a wide range of behaviors, making measurement challenging -- often involving observing individual students and recording their think-aloud activities or asking students to complete labor-intensive tagging activities as they work. In the current study, we develop machine-learned indicators of SMART operations, in order to achieve better scalability than other measurement approaches. We analyzed student's textual responses and interaction data collected from a mathematical learning platform where students are asked to thoroughly explain their solutions and are scaffolded in communicating their problem-solving process to their peers and teachers. We built detectors of four indicators of SMART operations (namely, assembling and translating operations). Our detectors are found to be reliable and generalizable, with AUC ROCs ranging from 0.76-0.89. When applied to the full test set, the detectors are robust against algorithmic bias, performing well across different student populations. [For the full proceedings, see ED623995.]

These proceedings are a written record of the research presented at the 44th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Nashville, Tennessee, and virtually. This year's conference theme is "Critical Dissonance and Resonant Harmony." The aim of this theme is to reflect not only the time and place that of gathering, but also the time and place in which to conduct academic work. Dissonance can be jarring to experience, whereas harmony can be pleasing. Nashville -- Music City -- which is no stranger to both dissonance and harmony. The papers accepted comprised 101 research reports, 140 brief research reports, 84 Posters, and 16 Working Groups or Research Colloquia. [Individual papers are indexed in ERIC.]

Considerable amount of research in educational data mining has focused on developing efficient algorithms for Knowledge Tracing (KT). However, in practice, many real-world learning systems used at scale struggle to implement KT capabilities, especially if they weren't originally designed for it. One key challenge is to accurately label existing items with skills, which often turns out to be a herculean task. In this paper, we investigate whether an increasingly popular approach to knowledge tracing, the use of neural network models, can be a partial solution to this problem. We conducted a case study within a commercial math blended learning system. Using the data collected from middle school students' use of the system over two years, we compare the performance of a neural network-based KT model (DKVMN) in three scenarios: 1) with the original (possibly unreliable) system-provided skill tags, 2) with coarser-grained domain tags based on state standards, and 3) without inputting any mappings between content and skills. Our results suggest that including the system-provided skills in the training of the model leads to the worst performance. The best performance is observed when the skills are entirely disregarded. This supports the possibility of bypassing the laborious step of item-skill tagging in real-world learning systems which were not originally designed to work with KT models, especially if the goal is only to predict the performance of a student on future items. We discuss the implications of our findings for practice and future research. [For the full proceedings, see ED623995.]

This study examined how mathematics coaches leverage written annotations to support professional discourse with teachers about important classroom events during synchronous debriefing conversations. Coaches and teachers created the annotations while asynchronously watching video of an implemented lesson as part of online video-assisted coaching cycles. More specifically, this project examined the extent to which a coach and teacher discussed the annotations during a debrief conversation in a coaching cycle. We present a rationale for needing new knowledge about the relationships between video annotations and professional discourse as well as the potential implications of such knowledge. [For the complete proceedings, see ED630060.]

We identify storylines about youth from minoritized cultures and/or languages in Norwegian news media to identify positionings made available to migrated and Indigenous mathematics students in this public discourse. Our search from 2003-2020 in a Norwegian media database including newspapers, journals, tabloids, etc., identified 1896 articles, reduced to 96 for relevancy. These storylines were identified: 'The majority language and culture are keys to learning and knowing mathematics', 'Mathematics is language- and culture-neutral', 'Minoritized mathematics students are motivated by gratitude', 'Extraordinary measures are needed to teach students from minoritized groups mathematics', 'Students from minoritized groups must put in extraordinary effort to learn mathematics', 'Students from minoritized groups' mathematics achievements are linked to culture and gender', and 'Students from minoritized groups underachieve.' [For the complete proceedings, see ED630060.]

Lack of diversity in the science community is a serious concern for social justice, scientific productivity, equity and efficacy. The first year of undergraduate education is of critical importance in increasing diversity in these fields. Peer-Led Team Learning (PLTL) has previously been shown to be associated with higher student achievement in gateway courses, particularly among students from populations that have been underserved and excluded within STEM fields (often referred to as underrepresented minorities, or URMs). We sought to determine whether participation in PLTL in an undergraduate introductory biology course is associated long-term retention rates among URM students in STEM majors. We used institutional data related to student recruitment and retention rates as well as pertinent demographic information over three and a half years subsequent to the introductory biology course experience. These data were combined with data on PLTL participation from the introductory biology course. Among students who did not engage in PLTL, URM students were significantly less likely to remain in STEM fields than non-URM students. However, no significant difference in STEM retention rates between URM and non-URM students was observed among those students who engaged in PLTL. Additionally, we found that retention rates were significantly higher for URM students who engaged in PLTL versus those who did not. These findings identify PLTL as a potential strategy to improve URM student recruitment and retention in STEM majors and indicate a need for further studies to determine the important aspects of PLTL that may lead to improved outcomes for URM students. [This paper was published in: "Proceedings of the 13th Annual Research Symposium," National Association of Biology Teachers, 2021.]

This study explores the collaborative process that two Korean-English and one Spanish-English bilingual Early Head Start family childcare educators, two instructional coaches, and the author engaged in as they co-created intentional bilingual approaches to supporting young emergent bilinguals. A thematic analysis of the design-based approach of teachers' experience and expertise, the author's observations and modeling, and regular honest feedback and conversations supported our collective work towards cultivating and sustaining spaces that reflected the linguistic realities of everyone present. This ongoing work showed that no single Head Start language approach was appropriate for all three teachers to draw on their entire linguistic repertoire while also providing rich and authentic multilingual learning experiences. This study problematizes the strict nature of monoglossic policymaking.

In this methodology paper, we present a methodology for characterizing how teachers use coaches' suggestions. We identified suggestions from planning conversations and explored the extent to which the teachers implemented the suggestions in enacted lessons. The planning conversations took place within online content-focused coaching cycles. A primary challenge confronting content-focused coaches when working one-on-one with teachers is finding a productive balance between giving suggestions and inquiring into teachers' practices through reflective questioning. This paper articulates a process for identifying suggestions made by a coach during a planning conversation and an analytic process for examining how a teacher takes up the suggestion during lesson implementation. We discuss the methodological challenges we encountered and tradeoffs in our decisions related to low- and high-inference claims. [For the complete proceedings, see ED629884.]

We share results of a study on the analytic stances of coaches' and teachers' as they annotated key moments from classroom video of the teacher's lessons. In the analysis, emphasis was on the analytic stances of the coaches and how their annotations related to trends in teachers' annotations. Findings indicate differences in how coaches and teachers noticed across the coaching cycles, suggesting the annotations were influenced by the interactions between the coaches and teachers and the teachers' perceptions of coaching process. As a result of our analysis, we characterized one coach as having a high ratio of questions to suggestions, another as having annotations coded as interpretation, another as having more evaluations and suggestions, and the fourth as having asked more questions. Some teachers mirrored the analytic stance of their coach over time and other teachers shifted their analytic stance in ways that suggest they were responsive to their coach's analytic stance. [For the complete proceedings, see ED629884.]

This paper briefly examines theories of affect and some of its possibilities and limits for mathematics education research. First, psychological, socio-cultural, embodied, and new materialist perspectives are considered. The paper juxtaposes emerging and older theories of affect in mathematics education with alternative approaches in the humanities and social sciences. Then, the paper briefly historicizes some of the changing and enduring economies for affect in mathematics education across three historicized "moments" of U.S. mathematics education reform circa the 1830s, 1890s, and 1930s. This section aims to consider some of the ways 'bodies' have become differently legible for theorizing affect in problematic ways with potential implications for future research. [For the complete proceedings, see ED629884.]

With the development of personalized learning in technological platforms, more data and information are given to instructors on what contents are appropriate for a learner's next step, with an aim of helping them support their students in navigating an optimized learning path that can promote an enhanced learning outcome. In this study, we collected data from an online learning platform, Learnta® TAD , which allows teachers to distribute tasks based on system recommendations. The recommendations are directed by the system's knowledge graph algorithm, determining whether the student is ready to learn the task (i.e. the task is within the student's Zone of Proximal Development), whether the student is not yet ready to learn the task, or whether the student has already mastered the task. We used the acquired data to investigate whether giving content in each of these groups results in different learning outcomes. Statistical methods such as subgroup analysis, Fisher's exact test, and logistic regression are conducted to address the proposed topic. Replicating a prior, smaller-scale study, our findings suggest that the student gains more mastery when assigned Ready-to-Learn tasks than when assigned Unready-to-Learn tasks, across Math and English, more and less successful students, and in-class and homework. Moreover, students who are given already mastered tasks perform better than those who are given Ready-to-Learn and Unready-to-Learn tasks across all groups. [For the full proceedings, see ED607784.]

Feature engineering, the construction of contextual and relevant features from system log data, is a crucial component of developing robust and interpretable models in educational data mining contexts. The practice of feature engineering depends on domain experts and system developers working in tandem in order to creatively identify actions and behaviors of interest. In this paper we outline a method of iterative feature engineering using the misclassifications of earlier models. By selecting cases where earlier models and ground truth disagree, we can focus attention on specific behaviors, or patterns of behavior, that a model is not using in its predictions. We show that iterative feature engineering on cases of false positives and false negatives improved a model predicting quitting in an educational video game by 15%. We close by discussing applications of this method for addressing model performance gaps across different classes of learners, as well as precautions against model overfitting with using this method of feature engineering. [For the full proceedings, see ED607784.]

There has been considerable interest in techniques for modelling student learning across practice problems to drive real-time adaptive learning, with particular focus on variants of the classic Bayesian Knowledge Tracing (BKT) model proposed by Corbett & Anderson, 1995. Over time researches have proposed many variants of BKT with differentiation based on their treatment of the underlying parameters: (a) general across student and questions; (b) individualized for students; and (c) individualized for questions. Yet at the same time, most of these variants are similar in that they utilize the same Hidden Markov (HMM) architecture to model student learning and share many of the same drawbacks, including less effective balancing between recent and historical student data and assuming that students learn at the same rate across all the attempts irrespective of if they get the question right. At the same time, these variants share the virtue of parameter interpretability, a virtue not seen in recent efforts to recast knowledge tracing as a deep learning problem. This paper proposes a different architecture that replaces learning rate with recency weights which capture student improvement wholly through data rather than assuming constant learning across attempts and manages recent and historical data more appropriately while retaining the interpretability of BKT parameters. The proposed model was tested on multiple public datasets from ASSISTments and Mindspark and performed similarly to classic BKT model on unseen data. [For the full proceedings, see ED607784.]

Demographic information often proves useful for finding subpopulations in educational data. Unfortunately, it is often not collected in the log files of online learning systems, which serve as one of the primary sources of data for the Educational Data Mining community. Recent work has sought to address this issue by investigating school-level differences in demographics, which can be used to discover trends in data where individual-level variation may be difficult or impossible to acquire. In this study, we use this approach to investigate the effect of demographic patterns on hint usage in an elementary level mathematics system, comparing this use to performance and motivational measures. In doing so, we expand upon the research into help-seeking behaviors, which typically takes a cognitive approach. Our results suggest the need to better understand what social factors are most likely to motivate help-seeking behaviors, particularly since research on their effectiveness has been mixed. [For the full proceedings, see ED599096.]

Replication of machine learning experiments can be a useful tool to evaluate how both "modeling" and "experimental design" contribute to experimental results; however, existing replication efforts focus almost entirely on modeling alone. In this work, we conduct a three-part replication case study of a state-of-the-art LSTM dropout prediction model. In our first experiment, we replicate the original authors' methodology as precisely as possible in collaboration with the original authors. In a second experiment, we demonstrate that this initial experiment likely overestimates the generalization performance of the proposed model due to the design of its validation. In a third experiment, we attempt to achieve the previously-reported performance in a more difficult, but more relevant, hold-out set design by exploring a large space of model regularization configurations. We demonstrate that we can reduce overfitting and improve generalization performance of the model, but cannot achieve the previously-reported level of performance. This work demonstrates the importance of replication of predictive modeling experiments in education, and demonstrates how experimental design and modeling decisions can impact the extent to which mode [For the full proceedings, see ED599096.]

Games in service of learning are uniquely positioned to offer immersive, interactive educational experiences. Well-designed games build challenge through a series of well-ordered problems or activities, in which perseverance is key for working through ingame failure and increasing game difficulty. Indeed, persistence through challenges during learning is beneficial not just in games but in other contexts as well, with grit and perseverance positively associated with academic performance and learning outcomes. However, recent studies suggest that not all persistence is positive, suggesting that many students end up "wheel-spinning", spending considerable time on a topic without achieving mastery. Thus, it is vital to differentiate productive and unproductive persistence in order to understand emergent student progress, particularly in the context of learning games and personalized learning systems, in which individual pathways differ greatly based on student needs. Leveraging Educational Data Mining methods, this study builds a detector of wheel-spinning behavior (differentiated from productive persistence) in an adaptive, game-based learning system. With the ability to predict unproductive persistence early, this detection model can be used to intelligently adapt to students needing further support in-system, as well as informing in-person intervention in a classroom setting--thus supporting a personalized, engaging learning experience in both formal and informal learning environments. [For the full proceedings, see ED599096.]

"Sensor-free" detectors of student affect that use only student activity data and no physical or physiological sensors are cost-effective and have potential to be applied at large scale in real classrooms. These detectors are trained using student affect labels collected from human observers as they observe students learn within intelligent tutoring systems (ITSs) in real classrooms. Due to the inherent diversity of student activity and affect dynamics, observing the affective states of some students at certain times is likely to be more informative to the affect detectors than observing others. Therefore, a carefully-crafted observation schedule may lead to more meaningful observations and improved affect detectors. In this paper, we investigate whether active (machine) learning methods, a family of methods that adaptively select the next most informative observation, can improve the efficiency of the affect label collection process. We study several existing active learning methods and also propose a new method that is ideally suited for the problem setting in affect detection. We conduct a series of experiments using a real-world student affect dataset collected in real classrooms deploying the ASSISTments ITS. Results show that some active learning methods can lead to high-quality affect detectors using only a small number of highly informative observations. We also discuss how to deploy active learning methods in real classrooms to improve the affect label collection process and thus sensor-free affect detectors. [For the full proceedings, see ED599096.]

Determining which students are at risk of poorer outcomes -- such as dropping out, failing classes, or decreasing standardized examination scores -- has become an important area of research and practice in both K-12 and higher education. The detectors produced from this type of predictive modeling research are increasingly used in early warning systems to identify which students are at risk and intervene to support better outcomes. In K-12, it has become common practice to re-build and validate these detectors, district-by-district, due to different data semantics and risk factors for students in different districts. As these detectors become more widely used, however, it becomes desirable to also apply detectors in school districts without sufficient historical data to build a district-specific model. Novel approaches that can address the complex data challenges a new district presents are critical for extending the benefits of early warning systems to all students. Using an ensemble-based algorithm, we evaluate a model averaging approach that can generate a useful model for previously-unseen districts. During the ensembling process, our approach builds models for districts that have a significant amount of historical records and integrates them through averaging. We then use these models to generate predictions for districts suffering from high data missingness. Using this approach, we are able to predict student-at-risk status effectively for unseen districts, across a range of grade ranges, and achieve prediction goodness comparable to previously published models predicting at-risk. [For the full proceedings, see ED599096.]

Informal inference is a critical practice for students to engage in if they are to understand formal statistical methods. However, during informal inference students often utilize complex ideas that many in-service teachers are not prepared for as they have not had the opportunity to think deeply about statistics and develop statistical knowledge for teaching (Groth, 2013). Research shows that engaging teachers in authentic inquiry of content supports the development of that content knowledge, and there is an urgent need to do so through professional developments (PDs). However, there is limited literature concerning PDs in statistics education, and a dearth of research focusing on teachers' engagement with informal inference tasks. This paper describes in detail how two teachers engaged with a seminal informal inference task during a PD, including their reasoning about variability and sample size when making inferences. [For the complete proceedings, see ED606556.]