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Science on a Sphere (SoS) is a compelling educational display installed at numerous museums and planetariums around the world; essentially the SoS display is a large spherical surface on which multicolor high-resolution depictions of (e.g.) planetary weather maps may be depicted. Fascinating as the SoS display is, however, it is in practice restricted to the use of museum professionals; students (and for that matter, older museum visitors) are unable to create their own displays for the surface. This paper describes a working software system, "Math on a Sphere" (MoS), that democratizes the SoS display by providing a simple programming interface to the public, over the World Wide Web. Briefly, our system allows anyone to write programs for spherical graphics patterns, and then to upload those programs at a planetarium or museum site and see the result on the giant sphere. This paper describes the implementation of the MoS system; sketches a sample project; and concludes with a more wide-ranging discussion of our user testing to date, as well as strategies for empowering children and students with greater control of public displays. [For the full proceedings, see ED562107.]

Intelligent Tutoring Systems (ITSs) have shown success in the domain of programming, in part by providing customized hints and feedback to students. However, many popular novice programming environments still lack these intelligent features. This is due in part to their use of open-ended programming assignments, which are difficult to support with existing hint generation techniques. In this paper, we present a new data-driven algorithm, based on the Hint Factory, to generate hints for these open-ended assignments. We evaluate our algorithm on historical student data and show that it can provide hints that successfully lead students to solutions from any state, help students achieve assignment objectives, and align with the student's future solution. [For the full proceedings, see ED592609.]

This paper describes how a new pre-service teacher engaged with mathematical content in order to learn it for teaching, during practicum. The results show that the PST learned mathematical content by initiating and carrying out a preparation phase prior to planning. This phase involved searching through internet sites and making notes that were then used to support her lesson planning and teaching. Implications for pre-service teacher education are also presented.

Mobile learning is a cognitively demanding application and more frequently the ubiquitous nature of mobile computing means that mobile devices are used in cognitively demanding environments. This paper examines the nature of this use of mobile devices from a Learning, Usability and Cognitive Load Theory perspective. It suggests scenarios where these fields interact and presents an experiment which determined that several sources of cognitive load can be measured simultaneously by the learner. The experiment also looked at the interaction between these cognitive load types and found that a distraction did not affect the performance or cognitive load associated with a learning task but it did affect the perception of the cognitive load associated with using the application interface. This paper concludes by suggesting ways in which mobile learning (and mobile computing) can benefit by developing cognitive load aware systems that could detect and change the difficulty of the learning task based on the cognitive state of the learner. [For the full proceedings, see ED562140.]

This paper explores how beliefs about mathematics may influence low-achieving adults' re-engagement with mathematics in the tertiary sector. Adult learners who have problematic mathematical histories often hold negative beliefs about the nature of mathematics and how it is learned. In New Zealand these adults are often required to re-engage in mathematical provision in the tertiary sector to gain qualifications for employment. The beliefs they hold about mathematics may negatively influence their approach to learning mathematics and their affective response to it. This paper explores several ways in which negative beliefs about mathematics may undermine adults' success.

Number sense is the foundation of arithmetic and algebra, yet relatively little research has deeply investigated what children do as they develop number sense. This case study provides insights into that development as it occurred during interactions with a multi-touch mathematics digital game, including conceptually congruent gestures. Findings extend and challenge extant research on number sense.

This paper uses the hammer-and-nail metaphor to highlight the rigidity and impulsiveness that can be found in student mathematical behaviour. The hammer-and-nail phenomenon can be attributed to two plausible causes: (1) the way the human mind works; and (2) the way mathematics is traditionally taught in school. In this paper, the following aspects of the hammer-and-nail metaphor are discussed: (1) its origin and its usefulness; (2) its manifestations among learners of mathematics; (3) related literature; (4) pedagogical causes; and (5) suggestions for teaching.

Why have an organisation like MERGA? This question will be addressed from past, present and future perspectives (1976, 2012, and 2025). One focus of the paper will be the need to improve mathematics curricula, and to improve the teaching and learning of mathematics, at all levels. I shall argue that we have not done enough to make sure that MERGA has delivered, is still delivering, and will continue to deliver the goods on such basic curriculum/teaching/learning issues. Part of the difficulty is that we researchers have not reached agreement on what we mean by "improvement". That is as much a political issue as anything else, of course, but the MERGA community needs to do more to make sure that the responsibility for defining what improvement means, and how it is assessed, is not in the wrong hands. A second focus of the paper will be some reflections on what the "A" in MERGA might represent. This Conference is being held in Singapore, and the challenge is for a wider vision of MERGA's role in Asia to be formulated and implemented.

In this paper we propose a refinement of Michener's (1978) well-known example classification based on data from university mathematicians. The refinement takes into account the mathematician's perspective on the role of examples in doing mathematics. More specifically, our work provides insight into the ways in which mathematicians talk about using examples in their scholarly work and their work with students. The proposed classification has the potential to inform our work as teachers as we strive to create opportunities to engage students in authentic mathematical work. [For the complete proceedings, see ED583989.]

We have explored educational methods for algorithmic thinking for novices and implemented a block programming editor and a simple learning management system. In this paper, we propose a program/algorithm complexity metric specified for novice learners. This metric is based on the variable usage in arithmetic and relational formulas in learner's algorithms. To evaluate the applicability of this metric for novice education, we discuss the differences between three previous program complexity metrics and our proposed metric. [For the full proceedings, see ED562093.]

Learning Style (LS) is an important parameter in the learning process. Therefore, learning styles should be considered in the design, development, and implementation of e-learning environments. Consequently, an important capability of an e-learning system could be the automatic determination of a student's learning style. In this paper, a set of features which are important in extracting the learning style automatically from students' behavior has been determined. These features, which are recognized based on Myers-Briggs Type Indicator's (MBTI), play a key role in predicting learning styles in an online course. The features are determined and ranked using pattern recognition techniques, such as K-means clustering algorithm, to show which features can be better to separate learning style dimensions. The results show several features can be used to predict learning styles with high precision. [For the complete proceedings, see ED562095.]

Whether teaching in a classroom or a Massive Online Open Course it is crucial to present the material in a way that benefits the audience as a whole. We identify two important tasks to solve towards this objective; (1) group students so that they can maximally benefit from peer interaction and (2) find an optimal schedule of the educational material for each group. Thus, in this paper we solve the problem of team formation and content scheduling for education. Given a time frame "d," a set of students S with their required need to learn different activities T and given "k" as the number of desired groups, we study the problem of finding "k" group of students. The goal is to teach students within time frame "d" such that their potential for learning is maximized and find the best schedule for each group. We show this problem to be NP-hard and develop a polynomial algorithm for it. We show our algorithm to be effective both on synthetic as well as a real data set. For our experiments we use real data on students' grades in a Computer Science department. As part of our contribution we release a semi-synthetic dataset that mimics the properties of the real data. [For complete proceedings, see ED560503.]

In this paper we consider discrimination-aware classification of educational data. Mining and using rules that distinguish groups of students based on sensitive attributes such as gender and nationality may lead to discrimination. It is desirable to keep the sensitive attributes during the training of a classifier to avoid information loss but decrease the undesirable correlation between the sensitive attributes and the class attribute when building the classifier. We illustrate, motivate, and solve the problem, and present a case study for predicting student exam performance based on enrollment information and assessment results during the semester. We evaluate the performance of two discrimination-aware classifiers and compare them with their non-discrimination-aware counterparts. The results show that the discrimination-aware classifiers are able to reduce discrimination with trivial loss in accuracy. The proposed method can help teachers to predict student performance accurately without discrimination. [For complete proceedings, see ED560503.]

Predicting the success or failure of a student in a course or program is a problem that has recently been addressed using data mining techniques. In this paper we evaluate some of the most popular classification and regression algorithms on this problem. We address two problems: prediction of approval/failure and prediction of grade. The former is tackled as a classification task while the latter as a regression task. Separate models are trained for each course. The experiments were carried out using administrate data from the University of Porto, concerning approximately 700 courses. The algorithms with best results overall in classification were decision trees and SVM while in regression they were SVM, Random Forest, and AdaBoost.R2. However, in the classification setting, the algorithms are finding useful patterns, while, in regression, the models obtained are not able to beat a simple baseline. [This work was partially funded by projects financed by the North Portugal Regional Operational Programme (ON.2--O Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF).] [For complete proceedings, see ED560503.]

Student modeling can help guide the behavior of a cognitive tutor system and provide insight to researchers on understanding how students learn. In this context, Bayesian Knowledge Tracing (BKT) is one of the most popular knowledge inference models due to its predictive accuracy, interpretability and ability to infer student knowledge. However, the most popular methods for training the parameters of BKT have some problems, such as identifiability, local minima, degenerate parameters and computational cost during fitting. In this paper we address some of the issues of one of these training models, BKT Brute Force. Instead of finding the parameter values that provide the lowest Residual Sum of Squares (RSS), we estimate this minimum RSS value from some a priori known values of the skill. From there we perform some preliminary analysis to improve our knowledge of the relationship between the RSS, from BKT-BF, and the four BKT parameters. [For complete proceedings, see ED560503.]

This paper reports on a project that aims to foster interdisciplinary collaboration between mathematicians and mathematics educators in pre-service teacher education. The project involves 23 investigators from six universities. Interviews were conducted with selected project participants to identify conditions that enable or hinder collaboration, and to identify learning mechanisms at the boundaries between disciplinary communities. A hybrid narrative constructed from the interviews is used to illustrate "transformation" as a learning mechanism that leads to new practices. [This project is funded by the Australian Government Office for Learning and Teaching (grant #MS13-3174).]

The purpose of this study was to explore the factorial structure of motivation and perception items from a student survey utilised as part of the Reframing Mathematical Futures II (RMFII) Project. Data was collected in 2017 from 442 students in Years 7 to 10 from various different States across Australia. An exploratory factor analysis identified four factors which were consistent with the studies the items were adapted from: Intrinsic and Cognitive Value of Mathematics, Instrumental Value of Mathematics, Mathematics Effort, and Social Impact of School Mathematics. An analysis of variance (ANOVA) also revealed that there were statistically significant differences between Year Level and State for some of these factors.

This paper explores the role examples play in mathematicians' conjecturing activity. While previous research has examined example-related activity during the act of proving, little is known about how examples arise during the formulation of conjectures. Thirteen mathematicians were interviewed as they explored tasks that required the development of conjectures. During the interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating systematic lists of examples that they examined for patterns. The results suggest pedagogical implications for explicitly targeting examples in conjecturing, and the study contributes to a body of literature that points to the benefits of exploring, identifying, and leveraging examples in proof-related activity. [For the complete proceedings, see ED597799.]

In this paper I present a case study to illustrate conflicts between different 'realizations' of the concept of 'continuous function' held by a university first year student. Sfard's commognitve framework is used in the analysis of a student's work on continuity. I point out how these conflicting realizations have arisen from the inconsistent definitions presented in text books and other mathematical resources. The study also points to the need of extending the notion of "commognitive conflict" in the framework. [For the complete proceedings, see ED597799.]

In this paper, we describe the process of students' self-assessment of their creativity and its development in the context of posing mathematical problems, presuming that such a process would support the development of their creativity. Examination of two case studies reveals that self-assessment of creativity may support its development provided that one possesses specific personal recourses; however, this process might suppress the creativity of those lacking the needed resources. Therefore, we suggest that self-assessment of creativity cannot stand on its own, and should be supplemented by teachers' feedback or other environmental 'scaffolding'. [For the complete proceedings, see ED597799.]

In this paper we examine a commonly suggested proof construction strategy from the mathematics education literature--that students first produce an informal argument and then use this as a basis for constructing a formal proof. The work of students who produce such informal arguments during proving activities was analyzed to distill three activities that contribute to students' successful translation of informal arguments into formal proofs. These are elaboration, syntactification, and rewarranting. We analyze how attempting to engage in these activities relates to success with proof construction. Additionally, we discuss how each individual activity contributes to the translation of an informal argument into a formal proof. [For the complete proceedings, see ED597799.]

To support teachers in their quest to incorporate reasoning as a mathematical proficiency as espoused in the Australian Curriculum: Mathematics, a professional learning research project using demonstration lessons was carried out. This paper reports on the impact of demonstration lessons on one participating teacher's pedagogical knowledge about reasoning. The growth in this teacher's knowledge was analysed using a phenomenographic framework established to evaluate teachers' development in mathematical reasoning. The results show that demonstration and subsequent trial lessons contributed to her growth.

This paper reports on an intervention program, "Prepare 2 Learn", that was designed taking into account a range of components from other successful intervention programs. The program is focussed on year 6 students from a school in Melbourne, Australia, who are falling approximately 6 months behind with the hope that extra help at an early stage may result in them reaching the required standard and realising their potential. While the students' academic results moved substantially a more pleasing result was the noticeable improvement in the students' approaches to their learning.

Self-belief can directly predict students' academic motivation and achievement. Research indicates that mathematical self-belief often decreases during the middle years of schooling. This study explored the mathematical self-belief development of 15 Year 7 students. Data were gathered from a survey, a mathematics achievement test and interviews. Results were analysed and interpreted from a multilevel perspective. Findings indicate that student-level characteristics, such as persistence, were the most influential on mathematical self-belief. While class-level contexts, such as ability grouping, were less influential, interpersonal relationships with teachers played a major role. [The research reported in this paper was part of a larger project supported by an Australian Research Council Linkage grant.]

This design-based research project investigated the development of functional thinking in algebra for the upper primary years of schooling. Ten teachers and their students were involved in a sequence of five cycles of collaborative planning, team-teaching, evaluating and revising five lessons on functional thinking for their students over one year. This paper focuses on two aspects of the study related to developing students' functional thinking by visualising the structure of a growing pattern in different ways. An appendix presents the assessment task used at the beginning of the lesson sequence.

This paper reports teachers' beliefs about the extent to which expertise in one-to-one teaching can be transferred to classroom teaching. The study involved 21 mathematics intervention specialists. Data collection involved a structured questionnaire with six openended questions. Participants were found to be very positive towards transferring strategies developed in one-to-one teaching to their classroom teaching. The strategies included using material settings, using particular questioning techniques, incorporating assessment into teaching, focusing on dimensions of mathematisation, valuing students' responses, teaching at the 'cutting edge', and using mathematical language.

This paper reports design and implementation outcomes at middle development advance of an educative program based on use and construction of widgets on Wolfram Alpha platform at higher education level for engineering and sciences areas. Widgets were based on Physics and Mathematics curricula under Project Oriented Learning and Blended Learning methodologies. Widgets constructed by teachers are first used by students to appropriate basic concepts of each course on a mobile learning basis; after, students construct their own widgets applying that concepts but involving different applied situations based on curriculum integration. Two phases of this activity help to develop basic and high level thinking. Description of design combining Wolfram Alpha widget developer, Weebly and Jotform tools to set up the widgets, institutional current advances on teachers training, courses involved and current outcomes of project are presented. [For the full proceedings see ED557171.]

This paper presents examples from 10 internal consultancies provided by the author within the Open University (United Kingdom) that reveal how teams develop and are integrated into the systems of a complex institution. These consultancies included: providing consulting services to a course team; counseling with a course team chair; serving as a participant-observer with staff in summer schools; interviewing learners in summer schools; evaluating the impact of new technology on staff; conducting a workshop for staff on group dynamics; providing consulting services to the Centre for Mathematics Education team; analyzing group dynamics in a video about learning and teaching mathematics; confidential counseling of team members; and providing consulting services to a course team on child development. The paper concludes that consultancy for organizational learning depends on an awareness of the mental models in use. The consultancies enabled the consultants to realize that transitions to higher levels of integration--individual, team and institution--is a social expression of mental development. The impact of a distance environment on staff and learners is noted and the provision of some face to face contact is urged. An appendix is included. (Contains 16 references.) (Author/CK)

Quantitative reasoning plays a crucial role in students' and teachers' successful modeling activities. In a semester-long teaching experiment with an undergraduate student, we explore how her conception of a graph plays a role in her ability to quantify and maintain quantitative structures. We characterize here Lydia's conception of a graph as one in which the graph entails several quantities she identified in a given dynamic situation, contradicting the conception of a graph as a representation of a multiplicative object consisting of only two quantities. We also discuss her thinking about her graph in terms of figurative and operative thought during a session in which we support her in disembedding and graphically representing quantities. [For complete proceedings, see ED581294.]

Expertise in a domain of knowledge is characterized by a greater fluency for solving problems within that domain and a greater facility for transferring the structure of that knowledge to other domains. Deliberate practice and the feedback that takes place during practice activities serve as gateways for developing domain expertise. However, there is a difficulty in consistently aligning feedback about a learner's practice performance with the intended learning outcomes of those activities -- especially in situations where the person providing feedback is unfamiliar with the intention of those activities. To address this problem, we propose an intelligent model to automatically label opportunities for practice (assessment questions) according to the learning outcomes intended by the course designers. As a proof of concept, we used a reduced version of Bloom's Taxonomy to define the intended learning outcomes. Using a factorial design, we employed term frequency-inverse document frequency (TF-IDF) and latent Dirichlet allocation (LDA) to transform questions from text to word weightages with support vector machine (SVM) and extreme learning machine (ELM) to train and automatically label the questions. We trained our models with 120 questions labeled by the subject matter expert of an undergraduate engineering course. Compared to existing works which create models based on a selfgenerated dataset, our proposed approach uses 30 untrained questions from online/textbook sources to validate the performance of our models. Exhaustive comparison analysis of the testing set showed that TF-IDF with ELM outperformed the other combinations by yielding 0.86 reliability (F1 measure) with the subject matter expert. [For the full proceedings, see ED596512.]

Since MOOC is suffering high dropout rate, researchers try to explore the reasons and mitigate it. Focusing on this task, we employ a composite model to infer behaviors of learners in the coming weeks based on his/her history log of learning activities, including interaction with video lectures, participation in discussion forum, and performance of assignments, etc. The prediction accuracy of our proposed model outperforms related methods. Besides, we try combining the model with suggested interventions, such as sending reminder emails to at-risk learners. Future work, which is currently underway, will evaluate its influence on mitigating dropout rate. [For the full proceedings, see ED596512.]

Augmented Graph Grammars are a graph-based rule formalism that supports rich relational structures. They can be used to represent complex social networks, chemical structures, and student-produced argument diagrams for automated analysis or grading. In prior work we have shown that Evolutionary Computation (EC) can be applied to induce empirically-valid grammars for student-produced argument diagrams based upon fitness selection. However this research has shown that while the traditional EC algorithm does converge to an optimal fitness, premature convergence can lead to it getting stuck in local maxima, which may lead to undiscovered rules. In this work, we augmented the standard EC algorithm to induce more heterogeneous Augmented Graph Grammars by replacing the fitness selection with a novelty-based selection mechanism every ten generations. Our results show that this novelty selection increases the diversity of the population and produces better, and more heterogeneous, grammars. [For the full proceedings, see ED596512.]

The 10th International Conference on Educational Data Mining (EDM 2017) is held under the auspices of the International Educational Data Mining Society at the Optics Velley Kingdom Plaza Hotel, Wuhan, Hubei Province, in China. This years conference features two invited talks by: Dr. Jie Tang, Associate Professor with the Department of Computer Science and Technology at Tsinghua University; and Dr. Ron Cole, President of Boulder Learning Inc. The main conference invited contributions to the Research Track and Industry Track. 122 submissions were received (71 full, 47 short, 4 industry). 18 full papers papers were accepted (25% acceptance rate) and 32 short papers for oral presentation (42% acceptance rate) and an additional 39 for poster presentations, 3 demonstrations. The industry track includes all 4 submitted industry papers and 1 paper initially submitted as a full paper. The EDM conference provides opportunities for young researchers, and particularly Ph.D. students, to present their research ideas and receive feedback from the peers and more senior researchers. This year, the Doctoral Consortium features 6 such presentations. In addition to the main program, the conference includes 3 workshops: (1) Graph-based Educational Data Mining (G-EDM 2017); (2) Sharing and Reusing Data & Analytics Methods with LearnSphere; and (3) Deep Learning with Educational Data; and 2 tutorials: (1) Why Data Standards are Critical for EDM and AIED; and (2) Principal Stratification for EDM Experiments. [For the 2016 proceedings, see ED592609.]

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, panel discussions, working group reports, new PhD reports, and summaries of ad hoc and poster sessions. Papers include the following: (1) The Most Unglamorous Job of All: Writing Mathematics Exercises (Yvan Saint-Aubin); (2) 40+ Years of Teaching and Thinking about University Mathematics Students, Proofs, and Proving (Annie Selden); (3) 'Elder Talk'-A Revisionist Version (Joel Hillel); (4) Teaching First Year Mathematics Courses in Transition from Secondary to Tertiary (Ann Arden, Wesley Maciejewski, Nadia Hardy); (5) L'anxiété mathématique chez les futurs enseignants du primaire : à la recherche de nouvelles réponses à des enjeux qui perdurent / Elementary Preservice Teachers and Mathematics Anxiety: Searching for New Responses to Enduring Issues (Manion LeBlanc, Jamie Pyper, Jo Towers) [Written in French and English]; (6) Social Media and Mathematics Education (Judy Larsen, Egan Chernoff, Viktor Freiman); (7) Quantitative Reasoning in the Early Years / Le raisonnement quantitatif dans les premières années du parcours scolaire (Doris Jeannotte, Lynn McGarvey)[Written in English and French ]; (8) Social, Cultural, Historical and Philosophical Perspectives on Tools for Mathematics (Yasmine Abtahi, Susan Gerofsky, Jean Francois); (9) Compréhension approfondie des mathématiques scolaires / Deep Understanding of School Mathematics (Richelle Marynowski, Sarah Dufour, Peter Liljedhal); (10) Modelling Mathematical Modelling / Modéliser la modélisation mathématique (France Caron)[Written in French and English]; (11) Collective Learning: Re-thinking the Environment, Artifacts and Classroom Interactions (Joyce Mgombelo); (12) A Psychological View of Teaching Proof Construction (John Selden); (13) Things Kids Think With: The Role of the Physical Properties of Mathematical Tools in Children's Learning in the Context of Addition of Fractions (Yasmine Abtahi); (14) Examining Mathematics Anxiety Among Classroom Teachers (Atinuke Adeyemi); (15) Teaching Teachers: A Look Inside Professional Development (Melania Alvarez); (16) Be Innovative but Don't Be Wrong: Are 21st Century Students Experiencing 21st Century Mathematics? (Jennifer Godfrey Anderson); (17) College Foundational Mathematics: Can the Affordances of ICT Enhance Self-regulation Skill of Students? / Mathématiques fondamentales du collège : est-ce que les apports des « TIC » peuvent améliorer l'autorégulation des compétences des élèves? (Carol Carruthers)[Written in English and French]; (18) Influence of the Learning Environment on Student Test Performance in Undergraduate Mathematics Courses (Amenda Chow); (19) The Role of Oral Communication Strategies in Accessing and Assessing Mathematical Understanding: Case Studies of Primary School Teachers' Perceptions of Teaching Mathematics and Teaching Literacy (Celia Kutas Chisu); (20) Reciprocal Partnership: An Intervention to Enhance Mathematics Self-efficacy and Achievement of First- and Second-semester College Students (Kerry Kwan); (21) Understanding the Interactions within a New Teacher Learning Community Composed of First Time Participants and a Novice Facilitator (Terry Wan Jung Lin); (22) Valued Kinds of Knowledge and Ways of Knowing in Mathematics and the Teaching and Learning of Mathematics: A Worldview Analysis (Gale L. Russell); (23) Opening Space: Complexity Thinking, Classroom Discourse, and Mathematics Learning in the Elementary Classroom / La technologie du forum ouvert: complexité, le discours de classe, et l'apprentissage de mathématiques en école élémentaire (Evan Throop-Robinson)[Written in English and French]; (24) Investigating Mathematics Teachers' Knowledge for Teaching and Their Learning Trajectories (Zhaoyun Wang]; (25) What/How Can We Learn from the Deaf Mathematics Classroom? (Christins M. Krause); (26) The Mathematical Association of Tanzania (MAT) Experience in CMESG Conference (Said A. Sima); (27) Toward a Hybrid Model to Describe Creative Acts in Mathematics Learning Environments (Ayman Aljarrah); (28) Problem Drift: Imaging Emerging Curricular Significance (Nat Banting); (29) Incorporating Writing into the Undergraduate Mathematics Curriculum (Lauren Dedieu); (30) Informing Local Materials Used for Concept-Rich Instruction Practice in Mathematics Class with Pre-service Teachers in Tanzanian Context (Emmanuel, Deogratias); (31) Les jeux technologiques dans les cours de mathématiques au secondaire (Caitlin, Furlong) [Written in French]; (32) De jeunes chercheurs à la rencontre de la philosophie des mathématiques (Sabrina Heroux, Sarah Mathieu-Soucy, Laura Broley) [Provided in French]; (33) Examining Parent Perspectives of Multiple Strategies (Jennifer Holm, Lynn McGarvey, Lixin Luo, Janelle McFeeters, and Iris Yin); (34) La dialectique perfection/imperfection : une nouvelle manière de penser l'activité mathématique (Marie-Line L. LaMarche, Jean-Francois Maheux) [Provided in French]; (35) Understanding School Leaders' Discourse in Regard to Mathematics Achievement (Jhonel Morvan); (36) I SEE What You're Saying: Visualization and the Growth of Mathematical Images (Jennifer Plosz); (37) Students' Relationships With Mathematics Revealed Through Drawings (Jennifer Plosz, Jo Towers, Kori Czuy, Ayman Aljarrah, Andrew Vorhies and Miwa Takeuchi); (38) Teacher Professional Learning in Tanzania: Experiences of Mathematics Teacher Leaders (Calvin Zakaria Swai); (39) "Perimeter is easier to work with than area": Students' Language Use in Group Work (Miwa Akoi Takeuchi); and (40) Toward an Understanding of Mathematics Teachers' Participation in Professional Learning Networks (Xiong Wang). Individual papers provide referenced. [For the 2016 proceedings, see ED581045.]

In this article, we suggest that the history in Mathematics Education combined with mobile technology, can provide analysis of concepts, theories and significant logical structures in the process of teaching and learning of Mathematics, as the main objective of this study is to analyze the students' motivation and learning using tablets in the classroom. From a collaborative work, high school students have created applications that told a little the Mathematics' history. A private school situated in the east side of São Paulo city conducted this experiment. With the participation of 4 teachers and 107 students of the first year of the high school, we observed that the tablet generated a stimulating and challenging environment in search of mathematical historical elements to explain concepts and theories so far not questioned by students in conventional classes. The results presented in the study indicate that the use of tablets in the work development was of paramount importance not only in the motivational issue, but also in getting knowledge about some mathematical theories put in its history. [For the complete proceedings, see ED579190.]

This work presents a proposed model in blended learning for a numerical methods course evolved from traditional teaching into a research lab in scientific visualization. The blended learning approach sets a differentiated and flexible scheme based on a mobile setup and face to face sessions centered on a net of research challenges. Model is presented being supported by previous research works about its performance in terms of effective evaluation and skill development. [For the complete proceedings, see ED579190.]

Mathematical reasoning features in curriculum documents around the world, but is understood and enacted poorly by teachers in classrooms. We explore teachers' noticing of reasoning during observed lessons. Two teams of primary teachers in Canada and Australia worked to plan, deliver, and observe lessons intended to include reasoning. They observed each other teaching a lesson that was planned with the assistance of a researcher, and later, a researcher observed each post-lesson discussion. Given the reported benefits of teachers' noticing of reasoning during peer-observed lessons, targeted professional learning support is required to further enact teachers' peer discourse to facilitate mathematical reasoning.

Examples play a critical role in the exploration and proving of conjectures. Although proof has been studied extensively, the precise ways in which examples might facilitate successful proofs are not well documented or understood. Working within a larger set of studies that argue for the value of examples in proof-related activity, in this paper we present a case study of one mathematician's work on a conjecture in which his strategic, intentional use of examples led to a proof of that conjecture. By examining his work in detail, we highlight specific mechanisms by which the mathematician's examples led to successful proof production. These mechanisms shed light on precise ways in which examples can directly lead to proof and inform our understanding of the conceptual landscape of the interplay between examples and proof. [For the complete proceedings, see ED584443.]