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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.]

This paper reports on the potential for engaging students in an activity that considers the interconnectedness of the five Big Ideas of Statistics in the context of conducting random trials. In the study, two classes of Year 6 students (aged 11-12 years) used "TinkerPlots" to determine the sample space of a "Mystery Spinner." Analysed for this paper were data collected from entries made in completed workbooks while engaged in the learning activity and responses to relevant questions in an end-of-year questionnaire from 27 students. The results indicated using an activity that included a probability model contributed to students working mathematically with percentages and frequencies and supported the development of intuitions about randomness and informal inference. This was promoted by students analysing the variation in the distribution of data and describing their expectations about an unknown sample space.

Two case studies of Australian primary school students tracked changes in their data interpretation and representation over three years. Students were engaged in predictive reasoning tasks based on their interpretation of a data table showing temperature change over time. Students' explanations and graphical representations were collected at the beginning of Years 3 and 4 and the end of Years 4 and 5. The first case study was a student mathematically weaker than her peers while case study two was within the average range for her year. Despite differences in starting points, both case studies followed a similar developmental sequence of predicting, interpreting and representing, with the first case generally lagging one stage behind the second case. Similarities and contrasts between the two students are discussed.

These proceedings contain the papers and posters of the 11th International Conference on Mobile Learning 2015, which was organised by the International Association for Development of the Information Society, in Madeira, Portugal, March 14-16, 2015. The Mobile Learning 2015 Conference seeks to provide a forum for the presentation and discussion of mobile learning research which illustrate developments in the field. The following are included in these proceedings: (1) Evolution or Revolution? Diffusion and Adaptation of (Smart) Mobile Phones among Children and Adolescents (Gitte Bang Stald); (2) Wearables and the "Anatomy" of Information: Biodata, Privacy, and Ethics (Amber Hutchins and Jake McNeill); (3) Scaffolding Java Programming on a Mobile Phone for Novice Learners (Chao Mbogo, Edwin Blake and Hussein Suleman); (4) Implementation of an Intelligent Tutorial System for Socioenvironmental Management Projects (Gil Vera, Víctor Daniel and Gabriel Awad); (5) Patterns of Mobile Technology Use in Teaching: A Pilot Study (Tami Seifert); (6) Developing Students' Professional Digital Identity (Thomas Cochrane and Laurent Antonczak); (7) Impact of Contextuality on Mobile Learning Acceptance: An Empirical Study Based on Language Learning App (Stephan Böhm and Georges Philip Constantine); (8) Do Mobile Learning Devices Enhance Learning in Higher Education Anatomy Classrooms? (Kate Wilkinson and Phil Barter); (9) It's Not Just the Pedagogy: Challenges in Scaling Mobile Learning Applications into Institution-Wide Learning Technologies (Peter Bird and Mark Stubbs); (10) Mobile Learning and Teacher Education: Researching MLEARN Pilot Development (Don Passey and Joana Zozimo); (11) Mobile-Assisted Language Learning: Student Attitudes to Using Smartphones to Learn English Vocabulary (Neil Davie and Tobias Hilber); (12) Active Students in Webinars (Line Kolås, Hugo Nordseth and Jørgen Sørlie Yri); (13) Expanding the Media Mix in Statistics Education through Platform-Independent and Interactive Learning Objects (Hans-Joachim Mittag); (14) Research on Mobile Learning Activities Applying Tablets (Eugenijus Kurilovas, Anita Juskeviciene and Virginija Bireniene); (15) Learner Centered Experiences with Flipped Classroom and Mobile Online Webinars in Distance Education Program (Lisbeth Amhag); (16) Walk Like an Egyptian: A Serious, Pervasive Mobile Game for Tourism (Fatema Mohsen Gabr and Slim Abdennadher); (17) Educational Materials for Mobile Learning (Kosuke Kaneko, Yoshihiro Okada, Motofumi Yoshida, Hitoshi Inoue and Naomi Fujimura); (18) Boosting up JSL Learners' Outside-Class Learning Time with Learning Log System (Noriko Uosaki, Hiroaki Ogata and Kousuke Mouri); (19) An Integrated Learning Management System for Location-Based Mobile Learning (Christian Sailer, Peter Kiefer and Martin Raubal); (20) The Influence of Affordances on Learner Preferences in Mobile Language Learning (Maria Uther and Adrian Banks); (21) Microlearning as Innovative Pedagogy for Mobile Learning in MOOC (Despina Kamilali and Chryssa Sofianopoulou); (22) Cross-Platform User Interface of e-Learning Applications (Michal Stoces, Jan Masner, Jan Jarolímek, Pavel Šimek, Jirí Vanek and Miloš Ulman); (23) Technology Trends in Mobile Computer Supported Collaborative Learning in Elementary Education from 2009 to 2014 (Mia Carapina and Ivica Boticki); (24) Challenges of Using Learning Analytics Techniques to Support Mobile Learning (Marco Arrigo, Giovanni Fulantelli and Davide Taibi); (25) Effectiveness and Utility of Terminal Tablet as Electric Textbooks for Nursing Practicum (Yumiko Nakamura, Kaori Fukayama and Yukie Majima); (26) A Study on the Process of Development of Collective Intelligence for Utilization of Unused Space of Abandoned Schools (Uk Kim and Junyoung Yang); (27) Implementation of an Adaptive Learning System Using a Bayesian Network (Keiji Yasuda, Hiroyuki Kawashima, Yoko Hata and Hiroaki Kimura); (28) Mathematics and Mobile Learning (Fayez Sayed); and (29) A Framework to Support Global Corporate M-Learning: Learner Initiative and Technology Acceptance across Cultures (Wendy Farrell). An author index is provided. (Individual papers contain references.)

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.]

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.]

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 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)

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.]

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.

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.]

Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school Mathematics teacher taught a lesson in Statistics where the students had the task create a pie graph representing the data. Results show us that their procedural vision of Statistics lead them to focus more on a graphical representation and thus led to avoid all statistical reasoning development (Garfield, 2002).

The research reported here uses a pre/post-test model and stimulated recall interviews to assess teachers' statistical reasoning about comparing distributions, when enrolled in a graduate-level statistics education course. We discuss key aspects of the course design aimed at improving teachers' learning and teaching of statistics, and the resulting different ways of reasoning about comparing distributions that teachers exhibited before and after the course.

The theme of this year's conference is "Critical Responses to Enduring Challenges in Mathematics Education." The theme of this year's conference invites mathematics education scholars to reflect upon and critically respond to enduring challenges in teaching and learning mathematics for all students. To ignite discussion within the field, the organizers of this conference organized the conference around four focal-enduring challenges, each of which is featured in one of four plenary talks: (1) teaching as responsive to various conceptions of mathematics; (2) addressing the needs of marginalized populations in school mathematics; (3) the impact of teacher evaluation and high-stakes assessment in teaching; and (4) the role of assessment in teaching and learning. It is the hope of the organizers that the conference will catalyze collective reflection, collaborative inquiry, and discussion about various means for responding to and addressing these, and other, challenges. Submissions received numbered 528. The overall acceptance rate was 64%. The conference program includes 92 Research Report sessions, 96 sessions, 136 Posters, and 12 Working Groups. Chapters include: (1) Plenary Papers; (2) Special Session; (3) Curriculum and Related Factors; (4) Early Algebra, Algebra, and Number Concepts; (5) Geometry and Measurement; (6) Mathematical Processes; (7) Statistics and Probability; (8) Student Learning and Related Factors; (9) Teacher Education and Knowledge; (10) Teaching and Classroom Practice; (11) Technology; (12) Theory and Research Methods; and (13) Working Groups. [Individual plenary and research papers are available in ERIC. Financial and personnel support was provided by the Michigan State University CREATE for STEM Institute.]

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)

This paper argues for a renewed focus on statistical reasoning in the elementary school years, with opportunities for children to engage in data modeling. Data modeling involves investigations of meaningful phenomena, deciding what is worthy of attention, and then progressing to organizing, structuring, visualizing, and representing data. Reported here are some findings from a two-part activity (Baxter Brown's Picnic and Planning a Picnic) implemented at the end of the second year of a current three-year longitudinal study (grade levels 1-3). Planning a Picnic was also implemented in a grade 7 class to provide an opportunity for the different age groups to share their products. Addressed here are the grade 2 children's predictions for missing data in Baxter Brown's Picnic, the questions posed and representations created by both grade levels in Planning a Picnic, and the metarepresentational competence displayed in the grade levels' sharing of their products for Planning a Picnic. [For the complete proceedings, see ED585874.]

Problems teaching probability in Tonga (in the South Pacific) led to the question how language and culture affect the understanding of probability and uncertainty. The research uses a discursive approach to find the endorsed narratives which underlie Tongans' reasoning in situations of uncertainty. I aim to justify the claim that the Tongan Language and the Tongan way of life interact to make the concept of uncertainty unimportant and the concept of probability almost redundant in day to day discourse. [For the complete proceedings, see ED597799.]