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The Proceedings of PME-XVII has been published in three volumes because of the large number of papers presented at the conference. Volume I contains a brief Plenary Panel report, 4 full-scale Plenary Addresses, the brief reports of 10 Working Groups and 4 Discussion Groups, and a total of 23 Research Reports grouped under 4 themes. Volume II contains 37 Research Reports grouped under 7 themes. Volume III contains 28 Research Reports grouped under 5 themes, 25 Oral Communications, and 19 Poster Presentations. In summary, the 3 volumes contain 88 full-scale Research Reports, 4 full-scale Plenary Addresses, and 59 briefer reports. Conference subject matter can be conveyed through a listing of the 15 themes under which Research Reports were grouped: Advanced Mathematical Thinking; Algebraic Thinking; Assessment and Evaluation; Pupil's Beliefs and Teacher's Beliefs; Computers and Calculators; Early Number Learning; Functions and Graphs; Geometrical and Spatial Thinking; Imagery and Visualization; Language and Mathematics; Epistemology, Metacognition, and Social Construction; Probability, Statistics, and Combinatorics; Problem Solving; Methods of Proof; Rational Numbers and Proportions; Social Factors and Cultural Factors. Each volume contains an author index covering all three volumes. (MKR)

Understanding the affect expressed by learners is essential for enriching the learning experience in Massive Open Online Courses (MOOCs). However, online learning environments, especially MOOCs, pose several challenges in understanding the different types of affect experienced by a learner. In this paper, we define two categories of emotions, explicit emotions as those collected directly from the student through self-reported surveys, and implicit emotions as those inferred unobtrusively during the learning process. We also introduce positivity as a measure to study the valence reported by students chronologically, and use it to derive insights into their emotion patterns and their association with learning outcomes. We show that implicit and explicit emotions expressed by students within the context of a MOOC are independent of each other, however, they correlate better with students' behavior compared to their valence. [For the full proceedings, see ED599096.]

Six of the seven papers in this collection focus on regional library activities in Africa, Asia and Oceania, and Latin America and the Caribbean: (1) "Libraries and Information Services in a Changing World: The Challenges African Information Services Face at the End of the 1980s" (Dejen Abate, Ethiopia); (2) "The Computer and Knowledge Information Development in Malaysia: Some Perspectives" (Edward Lim Huck Tee); (3) "New Development of Scientific and Technical Information Services in China" (Wang Jiabin, China); (4) "El Papel de las Asociaciones Profesionales (The Role of Professional Associations)" (Maria Casas de Faunce, Puerto Rico, in Spanish only); (5) "Library and Information Services in a Changing World: An African Point of View" (A. Olugboyega Banjo, Nigeria); and (6)"Report of the Activities of the Regional Section for Asia and Oceania 1986-1987" (J. S. Soosai, Malaysia). The seventh paper was delivered at a joint meeting of the Division of Regional Activities and the Division of Libraries Serving the General Public: "Library Development Worldwide: The Role of the British Council" (Gillian Roche, United Kingdom). (CGD)

Two papers on library statistics describe national programs to collect such statistics in a Western European country and a developing country in Africa: "Establishment and Organisation of National Library Statistics: The Nigerian Experience," by J. A. Dosunmu; and "German Library Statistics," by Peter Gruber. Dosunmu's paper describes the objectives and activities of a task force established by the Nigerian Library Association to gather and compile statistics on libraries in Nigeria. A list of definitions and instructions and a questionnaire on library statistics prepared for UNESCO by the task force accompany the text. Gruber's paper describes the development and publication of German library statistics and outlines the types of statistics contained in the publications. A table listing the number of libraries in the Federal Republic of Germany according to size of holdings is included. (JL)

This volume contains the papers and comments from the Workshop on Mathematics Education, a special session of the 15th Conference on Stochastic Processes and Their Applications, held in Nagoya, Japan, July 2-5, 1985. Topics covered include: (1) probability; (2) statistics; (3) deviation; (4) Japanese mathematics curriculum; (5) statistical education; (6) programmable calculators; (7) limit theorems; (8) Poisson distribution; (9) French curriculum for high school and college; (10) middle school curriculum, People's Republic of China; (11) New Zealand curriculum; and (12) reforms in Korean curriculum. (JM)

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.]

In today's polarizing political climate, there is a need to build citizens' statistical literacy to combat misinformation and support data-based arguments. To that aim, we investigate K-12 standards documents for their alignment with the American Statistical Association's Guidelines for the Assessment and Instruction in Statistics Education (GAISE II). We found that the states that explicitly reference GAISE or had standards that explicitly addressed the statistical investigative process did not offer consistent opportunities for students to engage in each element of the investigative process and at each developmental level. We discuss the implications of the findings and provide recommendations for policy makers and standards writers. [For the complete proceedings, see ED630060.]

In this study, we investigated how sixth and seventh grade students used CODAP to make sense of roller coaster data while engaged in Exploratory Data Analysis (EDA). Using instrumentation theory, we examined students' instrumentation approaches, as well as the types of instrumental orchestration utilized by teachers as they interacted with student pairs during EDA. [For the complete proceedings, see ED630060.]

In Intelligent Tutoring Systems (ITS), methods to choose the next exercise for a student are inspired from generic recommender systems, used, for instance, in online shopping or multimedia recommendation. As such, collaborative filtering, especially matrix factorization, is often included as a part of recommendation algorithms in ITS. One notable difference in ITS is the rapid evolution of users, who improve their performance, as opposed to multimedia recommendation where preferences are more static. This raises the following question: how reliably can we use matrix factorization, a tool tried and tested in a static environment, in a context where timelines seem to be of importance. In this article we tried to quantify empirically how much information can be extracted statically from datasets in education versus datasets in multimedia, as the quality of such information is critical to be able to accurately make predictions and recommendations. We found that educational datasets contain less static information compared to multimedia datasets, to the extent that vectors of higher dimensions only marginally increase the precision of the matrix factorization compared to a 1-dimensional characterization. These results show that educational datasets must be used with time information, and warn against the dangers of directly trying to use existing algorithms developed for static datasets. [For the full proceedings, see ED615472.]

Increasingly, mathematics is being positioned as a tool to support students' understandings of social (in)justice and their own unique social positioning in the world. To this end, this study analyzes the impact of curricular reform efforts in an elementary mathematics content course. The course focused on fractions and statistics, and the course content was taught through tasks designed to support prospective teachers in understanding and critiquing the world. The authors found that through the course, prospective teachers' content knowledge increased and their knowledge of the world's demographics and social inequities increased. [For the complete proceedings, see ED629884.]

Texts presenting novel statistics can shift learners attitudes and conceptions about controversial science topics. However, not a lot is known about the mechanisms underlying this conceptual change. The purpose of this study was to investigate two potential mechanisms that underlie learning from novel statistics: numerical estimation skills and epistemic cognition. This research investigated two treatments--a numerical estimation and epistemic cognition intervention--that were expected to enhance people's ability to make sense of key numbers about climate change. Results indicated that undergraduate students (N = 516) who were given instruction on numerical estimation strategies before shown novel climate change statistics had fewer misconceptions when compared with people who did not. Findings provide emerging evidence that supporting mathematical reasoning skills can enhance conceptual change in science. [For the complete proceedings, see ED629884.]

These proceedings are a written record of the research presented at the 42nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in Mazatlán, Mexico, virtually beginning May 27, 2021 and in-person June 2-6, 2021. The conference was originally scheduled to take place October 14-18, 2020; it was postponed, due to the COVID pandemic. In accordance with the major goals of PME-NA that include promoting international contacts and stimulating interdisciplinary research, the theme was proposed as "Entre Culturas/Across Cultures". The goal of the theme was an academic exchange that would reflect the ample diversity of ways of teaching and learning of mathematics, and of the tools and communities involved in mathematics education; as well as an exploration of how the differences in cultures imply a need to consider how research results can be taken into account in varying contexts. The papers comprise 80 Research Reports, 190 Brief Reports, 147 Poster Presentations, 10 Working Groups, 2 Research Colloquia, and Plenary and special lectures. The program also includes a special tribute to Eugenio Filloy and a tribute to the PME-NA members who were affected by the COVID-19 pandemic. [These proceedings were produced with Cinvestav (Centro de Investigación y de Estudios Avanzados del IPN), México and AMIUTEM (Asociación Mexicana de Investigadores del Uso de Tecnología en Educación Matemática, A.C.), México. Individual papers are indexed in ERIC.]

The idea of variation is a foundation of statistical reasoning, and many curriculum documents, including the "Australian Curriculum", include variation in the learning required for the primary years. In this paper, we consider the design of activities that can exemplify the idea of variation for young students and investigate how students can use graphs to support discussions about variation. The use of appropriate contexts and the provision of physical experiences of the phenomena seemed to help students make sense of graphical representations and allowed them to discuss how variation was exemplified in the graphs.

The aim of this investigation is to explore the preservice teachers' reasoning about variation (variability or spread) when they analyze data in situations that involve risk. In particular, in this communication the responses to two problems of a questionnaire administered to 96 preservice teachers are reported. The problems are of comparing groups of data in situations of risk: stakes in games and the life expected after medical treatments. The questionnaire was applied before the preservice teachers began a course of statistical information processing and the results showed the difficulty found by students to interpret variation in this type of contexts. For these results it is necessary to reflect on the instruction of future teachers about the meanings of measures of center dispersion and dispersion to contribute to an improvement in their academic training. [This paper is written in both Spanish and English. For complete proceedings, see ED581294.]

This study employs a cross-case analysis in order to explore the demands and opportunities that arise when information problem-solving tasks are introduced into college mathematics classes. Professors at three universities collaborated with me to develop statistics-related activities that required students to engage in research outside the classroom. This paper will focus on one aspect of the study: a comparison of how the teachers balanced mathematical content with information problem solving in the tasks that they created. These tasks incorporated mathematics in a variety of ways, ranging from tasks in which the mathematical component was crucial to others where mathematics served solely as a marker of credibility. This research has the potential to provide tools for understanding how to productively incorporate information-literacy instruction into the mathematics classroom without losing sight of mathematical goals. [For complete proceedings, see ED581294.]

The author has attended and presented at most ASCUE meetings since 1994, and has worked professionally in research and development, industry, military, government, business, and private and public academia--moving between computer science, software engineering, and business fields at both the undergraduate and graduate level, and even running academic computing for a few years. This paper/session will present/discuss definitions, implications, and relationships of and between the areas of computer science, software engineering, information technology, and business information systems. Included will be perspectives of the history of the past, specific needs of the present, and general directions and predictions of the future, and the implications to academia, business, and other areas. [For the full proceedings, see ED575713.]

The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the preliminary phase of a large national study designed to move beyond the hypothetical and to provide an evidence-based foundation for learning progressions in mathematical reasoning in three key areas of the curriculum: Algebraic Reasoning, Geometrical and Spatial Reasoning, and Statistical Reasoning. [References after each paper.]

Data is everywhere. As a result the need for data scientists with the correct skill set to analyze and interpret the data has escalated. Not surprisingly, data scientists are currently one of the most wanted professions. Tertiary institutions are faced with the challenge of producing students with the correct blend of theoretical knowledge and practical skills. In an attempt to provide current post-graduate students with these skills, a flipped class room approach was adopted to teach students data warehousing as part of the data science curriculum. This paper used the four pillars of F-L-I-P (FLN 2014) to analyze data obtained from lecturer implementation experience and student course evaluation forms. It was shown that great strides have been made in this course in the adoption of the flipped class room although there is room for improvement in order to achieve flipped learning. The outcome of the study directly contributes to the improvement of subsequent implementations of the module. [For full proceedings, see ED571459.]

In the spirit of questioning, crossing, and blurring disciplinary borders with(in) mathematics education, this paper proposes a theoretical framework that merges conceptions of critical literacy and statistical literacy for high school mathematics curriculum. I begin by discussing the political nature of education and then situate this work within the goals of education for active citizenship. Next, I provide a detailed background of both critical and statistical literacy from multiple educational research perspectives. Lastly, by synthesizing notions of critical and statistical literacy, I present a theoretical framework for a critical statistical literacy in the context of high school mathematics curriculum. [For the complete proceedings, see ED583608.]

The goal of the proposed working group is to create a space for those interested in researching issues around the teaching and learning of statistics to meet, discuss, synthesize past research, and begin to strategize ways of leveraging multiple perspectives and expertise to identify and address current challenges in statistics education. The nature of statistics being a methodological discipline make it such that statistics education is made up of a diverse array of people from various backgrounds, disciplines, fields, interests and expertise. We propose this working group to create a space for dialogue among people with diverse perspectives to tackle important issues in the teaching and learning of statistics. Diverse perspective help to look at problems in new ways and come up with new solutions. However, we also want to pragmatically make progress towards a goal, which requires some common direction as well. To balance these tensions we frame our work in the notion of learning environments as a way of organizing past work as well as ideas for future projects into a meaningful structure. Additionally we are layering on the consideration of teachers and teaching in the design and enactment of learning environments. [For the complete proceedings, see ED606556.]

These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67 research reports, 184 brief research reports, 126 posters, and 13 working groups. Chapters include the following: (1) Plenaries; (2) Curriculum, Technology, and Assessment; (3) Early Algebra, Algebra, and Number Concepts; (4) Equity and Justice; (5) Geometry, Measurement, Statistics, and Probability; (6) In-Service Teacher Education and Professional Development; (7) Instructional Leadership, Policy, and Institutions/Systems; (8) Mathematical Knowledge for Teaching; (9) Mathematical Processes; (10) Precalculus, Calculus, and Higher Mathematics; (11) Pre-Service Teacher Education; (12) Student Learning and Related Factors; (13) Teaching and Classroom Practice; (14) Theory, Research Methods, and Miscellaneous Topics; and (15) Working Groups. [These proceedings were co-published by University of Missouri, St. Louis. Individual plenary and research papers are available in ERIC.]

This study reports on the capabilities of 53 Year 4 students as they completed the final stages of their first complete statistical investigation. In the context of becoming acquainted with students in a sister school in another city, students in both schools wrote and refined questions, which were answered by all students in an on-line survey. Using data from both schools, students chose at least one question to analyse and present their findings comparing the two cities and/or groups of students. Of interest are the representations created for the questions chosen, the conclusions drawn, the variation observed, the certainty about the conclusion, and the comments about what had been learned about writing survey questions.

It is acknowledged that there are connections between language use and mathematics in mathematics education, and the potential challenges this issue can pose have been investigated by researchers. Yet how the challenges can be overcome in statistics classrooms, where language is even more important as a medium of instruction, has received very little scrutiny. This article reports on research carried out in three New Zealand largely Pasifika dominated Year-12 classes. Findings from the teacher reflection aspect of the study indicate that teachers can struggle with how to use home language and real-life contexts to maximise learning in their classrooms. Some strategies to incorporate students' home language in their learning worked better than others. However, more research is needed to explore language issues and the barriers they might present in statistics education in greater depth.

The "doer effect" is the assertion that the amount of interactive practice activity a student engages in is much more predictive of learning than the amount of passive reading or watching video the same student engages in. Although the evidence for a doer effect is now substantial, the evidence for a causal doer effect is not as well developed. To address this, we mined data for evidence of a causal doer effect across multiple domains. We examined data from two online courses in Psychology, one in Biology, one in Statistics, and two in Information Science, applying causal discovery algorithms in Tetrad to each. Assuming that factors driving a student's choices regarding how to spend their time in an online course are temporally prior to their performance on quizzes and exams, we found evidence of a causal relationship in every domain we studied. We did not find evidence that a unique causal model held in every domain we studied, but when we estimated the size of the causal relationships in the models we found in each domain, we did find evidence in every case that doing has a much stronger quantitative effect on learning than either reading or watching video. This work may be the first EDM effort to explore the generalizability of a causal claim about learning across multiple datasets from a variety of courses and contexts of use. It makes vivid the role of causal data mining algorithms in educational research. The evidence presented furthers the case for doer effect causality, but also recommends a need for richer data with more student background and learning process variables to better isolate causal directionality without assumptions about temporal order and unmeasured confounds. [For the full proceedings, see ED593090.]

Adaptive online courses are designed to automatically customize material for different users, typically based on data captured during the course. Assessing the quality of these adaptive courses, however, can be difficult. Traditional assessment methods for (machine) learning algorithms, such as comparison against a ground truth, are often unavailable due to education's unique goal of affecting both internal user knowledge, which cannot be directly measured, as well as external, measurable performance. Traditional metrics for education like quiz scores, on the other hand, do not necessarily capture the adaptive course's ability to present the right material to different users. In this work, we present a mathematical framework for developing scalable, efficiently computable metrics for these courses that can be used by instructors to gauge the efficacy of the adaptation and their course content. Our metric framework takes as input a set of quantities describing user activities in the course, and balances definitions of user consistency and overall efficacy as inferred by the quantity distributions. We support the metric definitions by comparing the results of a comprehensive statistical analysis with a sample metric evaluation on a dataset of roughly 5,000 users from an online chess platform. In doing so, we find that our metrics yield important insights about the course that are embedded in the larger statistical analysis, as well as additional insights into student drop-off rates. [For the full proceedings, see ED593090.]

Western Governors University has the mission to improve quality and expand access to post-secondary educational opportunities by providing a means for individuals to learn independent of time and place thus the mobility of our coursework is essential. Technological advances facilitate this mission. While all degrees are based entirely on the demonstration of competency, candidates come to their programs with varying skills. For this reason, our Probability and Statistics course is individualized to adapt with the candidate's learning style. Technology based learning resources are developed continuously to create non-traditional Probability and Statistical education resources. [For the complete proceedings, see ED590269.]