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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.]

The purpose of this paper is to determine whether the changes that were found to occur pre- to post intervention in students' cognitive structures (Mills, 2013; Knezek, Christensen, Tyler-Wood, & Periathiruvadi, 2013) continued to persist two years later. Major findings were: a) semantic perception of science and STEM as a career became more aligned with interest in being a scientist, from pretest to post test time during the treatment year and continued to be aligned two years later; b) semantic perception of engineering moved from alignment with science and STEM as a career at time 1, to alignment with semantic perception of technology and creative tendencies after the treatment year, at time 2, and remained aligned with technology two years later, at time 3; and c) semantic perception of mathematics was separated from the other constructs during the pre-post treatment year and remained largely separated two years later. Data mining techniques were also used to explore changes in relationships among these and other constructs over time. [For the full proceedings, see ED562107.]

In the last decades there have been several attempts to use computers in Music Education. New pedagogical trends encourage incorporating technology tools in the process of learning music. Between them, those systems based on Artificial Intelligence are the most promising ones, as they can derive new information from the inputs and visualize them in several meaningful ways. This paper presents an application of machine learning to music performance which is able to discover the similarities and differences between a given performance and those from other musicians. Such a system would help students to better learn how to perform a certain piece of music, allowing them to compare with other students or master performers. [For the full proceedings, see ED562127.]

Problem solving task design is not only the design of a non-routine problem to be solves by the students. Our task design also requires a supporting document, the practical worksheet, which would act as a cognitive scaffold for the students in the initial stages of the problem solving process before they can internalize the metacognitive strategies and automate the use of these strategies when faced with a new problem. A further enhancement of the scaffolding that can be provided by the teacher as she facilitates forty or more students working on the practical worksheet is a set of scaffolding cards. In this paper, we describe the cards and the preliminary use of these cards to facilitate problem solving for teachers in a professional development workshop.

This paper identifies the strategies Singaporean and Australian students (n = 1,187) employed to solve a 24-item mathematics test. A mathematics-processing framework is proposed, which describes the way primary-aged students successfully process graphic and non-graphic mathematics tasks. There were distinct differences in the way in which the students from the respective countries approached the tasks with the Singaporean students more likely to employ strategies that were explicitly taught and practiced in the classroom, whereas the Australian students tended to employ a more diverse range of approaches.

The learning and teaching of mathematics are key elements for primary school teachers, and various approaches for teaching mathematics to pre-service teachers are evident in mathematics education. This paper reports on a project to develop a critical approach to using mathematical subject knowledge in choosing learning examples and examines data from United Kingdom pre-service teachers' lessons. The data suggests pre-service teachers have no structured method for choosing examples, which impacts on the quality of the learning experiences of students.

The use of high-stakes assessment to measure students' mathematical performance has become commonplace in schools all over the world. Such assessment instruments provide national or international comparisons of student (and potentially teacher performance). Each form of assessment is specialised in nature and is characteristic of the culture and intent of the governing bodies. The purpose of this paper is to highlight differences and similarities between two national high-stakes assessments and the possible implications to students' sense making.

Rhetoric about the importance of students being equipped to apply mathematics to relevant problems arising in their lives, individually, as citizens, and in the workplace has never been matched by serious policy or curricular support. This paper identifies and elaborates authenticity implications for addressing this issue, and describes aspects of a modelling challenge in which students were mentored to engage in problem solving located in real world settings. Characteristics of the approach and selected student responses to the challenge are provided.

"Make It Count" was a large scale, government-funded, project aimed at improving the mathematics learning of Indigenous students. NAPLAN Numeracy test results were used as one measure of the effect of the program. In this paper we report on the performance on these tests of Indigenous students in schools involved in the project. Group data and, where available, longitudinal data for individual students are reported.

What types of performance do we encourage in our mathematics students? How do these performances reflect students' identity constructions? This paper uses a performance metaphor for identity to analyse interviews with teachers and students in their first year of secondary school. "Perseverance" is valued by teachers, yet many mathematics classrooms appear not to provide the opportunities to persevere and students do not perform identities of perseverance. Rather, "quickness" and "just knowing" the answer are considered part of a successful mathematics identity.

Students develop understanding of mathematics when they translate between and within different mathematical representations. This paper explores a student-generated story and content descriptors from the Australian Curriculum: Mathematics to highlight how primary school students can represent mathematical concepts through exploring the links between everyday physical objects, pictures, oral/written language, models and mathematical symbols. This active experience enhances the students' capacity to represent mathematical concepts and ideas, symbolise these, and eventually learn to abstract and generalise.

A current concern is student learning outcomes and these are largely a function of teachers' knowledge and their practice. This position paper is premised on the notion that certain knowledge is required for the teaching of mathematics. An exploration of literature demonstrates that such professional knowledge development can be supported by Learning Trajectories (LT). We propose to use LT as theoretical lens to examine pre-service teachers' Content and Pedagogical Content knowledge and advance a research design.

Lots of researches have showed that plagiarism becomes a severe problem in higher education around the world, especially in programming learning for its essence. Therefore, an effective strategy for plagiarism surveillance in program learning is much essential. Some literature focus on code similarity algorithm and the related tools can help to deal with the tedious and time-consuming task of detecting plagiarism to some extent. However, it is somewhat cursory to determine plagiarized programs only with automatic tool. Meanwhile, there is little research on incentive strategy of plagiarism surveillance. In this paper, we focus on the incentive mechanism of programming plagiarism surveillance. We aim to use some incentive strategy for plagiarism to gain the students' learning outcome. In the context of a programming learning information system EduPCR, a fishbone model is proposed, which consists of three aspects: problem, reason, and strategy. The questionnaire and interview conducted to survey the students' attitude about the incentive model show that the incentive model is welcome and practical in programming plagiarism surveillance. Our research is not only valuable for the programming learning but also for plagiarism surveillance of documents in other formats in academia. [For the complete proceedings, see ED557168.]

In this paper, I examine the utility of a mathematics learning trajectory as a tool to support teachers' attention to students' mathematical thinking. I present findings from one second grade teacher's use of a learning trajectory as she planned a sequence of three mathematics lessons. Findings suggest learning trajectories support teachers in choosing appropriate tasks and learning goals, and in anticipating students' likely approaches and difficulties. Learning trajectories, as representations of student thinking, provide teachers with a means of evaluating evidence of student learning of intended goals and afford them with a range of instructional moves based on their students' current conceptions. [For the complete proceedings, see ED584829.]

Examples play a critical role in mathematical practice, particularly in the exploration of conjectures and in the subsequent development of proofs. Although proof has been an object of extensive study, the role that examples play in the process of exploring and proving conjectures has not received the same attention. In this paper, we present a framework that characterizes ways in which mathematicians utilize examples when investigating conjectures and developing proofs. The data consist of 133 mathematicians' responses to two open-ended survey questions. The framework offers categories for the types of examples, uses of examples, and example strategies that mathematicians discussed in reference to their work with conjectures. In addition to presenting the framework, we also discuss potential educational implications of the results. [For the complete proceedings, see ED584829.]

This paper presents the results from an initial lesson in a series of design experiments focusing on young Indigenous students' understandings of growing patterns. Indigenous students in Year 2 and 3 (n = 16) participated in pre lesson activities and a 45 minute lesson on growing patterns. Tentative findings from this study suggest that; (a) Year 2 and 3 Indigenous students are capable of working with growing patterns; (b) contextual artefacts assisted with communication; and (c) gesture played an important two-fold role in the lessons and communication of the mathematics experienced.

In this paper, the RBC+C framework (Hershkowitz, Schwartz, & Dreyfus, 2001) is used to analyse and describe construction and consolidation of mathematical knowledge by primary pupils in a whole-class setting. I describe a lesson that concerned what is commonly termed the Handshakes problem. One pupil spontaneously established a connection with a related problem in which the class had engaged a month previously. There followed a conversation in which an older construct was consolidated while a new construct emerged--the nature of this intertwined construction and consolidation is discussed.

In this paper, we problematize an ontological characterization of change within a complex system by illustrating how epistemological premises of interactionist, individualist, and collectivist theoretical perspectives reveal only specific aspects of a changing system. Methodological considerations resulting from our recognition that change is characterized subjectively within various theoretical perspectives are made. [For the complete proceedings, see ED584829.]

This paper examines ten K-8 preservice teachers' visual representations of fraction operations using the four main pattern blocks. Data consist of figures made using the pattern blocks, drawn colored representations, and detailed written comments and algebraic formalism. The theoretical framework is drawn from representational theories and analyses of fraction operations, and work on coordination of different levels of units. The main result is that only those teachers meaningfully coordinating the different referent units in the fraction situations, were the ones consistent in their representations and reasoning, and in successfully establishing referential commutativity for multiplication of fractions. [For the complete proceedings, see ED585874.]

In this paper we report on a study examining how teacher perspectives on mathematics content and pedagogy changed after the teachers' schools participated for one year in the Mathematics Coaching Program. Teacher narrative responses to questions about student work samples provided qualitative data for analysis. Questions asked for teacher input on student thinking and instructional decisions. Responses reveal teacher change in the area of the program goals of movement toward an integrated procedural/conceptual perspective on content and a learner responsive perspective on pedagogy. [For the complete proceedings, see ED585874.]

Using an innovative recruitment tool, the social network site Facebook, survey data were gathered from samples of the Australian general public and from around the world. Views on the gendering of mathematics, science, and ICT were gathered. In this paper we report the findings from six of the 15 questions on the survey, and only from respondents in predominantly English-speaking countries. The findings reveal that the majority was not gender-stereotyped about mathematics and related careers. However, if a gendered view was held, it was overwhelming to endorse the male stereotype. Male respondents' views were more strongly gendered than were females'. [For the complete proceedings, see ED585874.]

We present an analysis of log data from a semester's use of the OpenDSA eTextbook system with the goal of determining the most difficult course topics in a data structures course. While experienced instructors can identify which topics students most struggle with, this often comes only after much time and effort, and does not provide real-time analysis that might benefit an intelligent tutoring system. Our factors included the fraction of wrong answers given by student, results from Item Response Theory, and the rate of model answer and hint use by students. We grouped exercises by topic covered to yield a list of topics associated with the harder exercises. We found that a majority of these exercises were related to algorithm analysis topics. We compared our results to responses given by a sample of experienced instructors, and found that the automated results match the expert opinions reasonably well. We investigated reasons that might explain the over-representation of algorithm analysis among the difficult topics, and hypothesize that visualizations might help to better present this material. [For the full proceedings, see ED592609.]

In recent years, substantial improvements were obtained in the effectiveness of data driven algorithms to validate the mapping of items to skills, or the Q-matrix. In the current study we use ensemble algorithms on top of existing Q-matrix refinement algorithms to improve their performance. We combine the boosting technique with a decision tree. The results show that the improvements from both the decision tree and Adaboost combined are better than the decision tree alone and yield substantial gains over the best performance of individual Q-matrix refinement algorithm. [For the full proceedings, see ED592609.]

User clustering algorithms have been introduced to analyze users' learning behaviors and help to provide personalized learning guides in traditional Web-based learning systems. However, the explicit and implicit coupled interactions, which means the correlations between user attributes generated from learning actions, are not considered in these algorithms. Much significant and useful information which can positively affect clustering accuracy is neglected. To solve the above issue, we proposed a coupled user clustering algorithm for Wed-based learning systems. It respectively takes into account intra-coupled and inter-coupled relationships of learning data, and utilizes Taylor-like expansion to represent their integrated coupling correlations. The experiment result demonstrates the outperformance of the algorithm in terms of efficiently capturing correlations of learning data and improving clustering accuracy. [For the full proceedings, see ED592609.]

The 9th International Conference on Educational Data Mining (EDM 2016) is held under the auspices of the International Educational Data Mining Society at the Sheraton Raleigh Hotel, in downtown Raleigh, North Carolina, in the USA. The conference, held June 29-July 2, 2016, follows the eight previous editions (Madrid 2015, London 2014, Memphis 2013, Chania 2012, Eindhoven 2011, Pittsburgh 2010, Cordoba 2009 and Montreal 2008). The EDM conference is the leading international forum for high-quality research that leverages educational data, learning analytics, and machine learning to answer research questions that shed light on the learning processes. This year's conference features three invited talks by: Rakesh Agrawal, President and Founder of Data Insights Laboratories; Marcia C. Linn, Professor of the University of California at Berkeley; and Judy Kay, Professor of the University of Sydney. Judy Kay's invited paper entitled "Enabling people to harness and control EDM for lifelong, life-wide learning" is also presented in the proceedings. Together with the "Journal of Educational Data Mining" ("JEDM"), the EDM 2016 conference supports a "JEDM" Track that provides researchers a venue to deliver more substantial mature work than is possible in a conference proceedings and to present their work to a live audience. The papers submitted to this track followed the "JEDM" peer review process; three papers have been accepted to the track and were presented at the conference. The abstracts of the invited talks, panels and accepted "JEDM" Track papers can be found in these proceedings. [For the 2015 proceedings, see ED560503.]

This paper examines literature on the development of self-knowledge for possible selves--how an individual thinks about oneself and one's potential future selves (Markus & Nurius, 1986). Future science selves research, a recent offshoot of possible selves theories, centers on the development and loss of future possible scientific selves and factors such as academics, apprenticeships, or serious science gaming that may influence the science self and science career interest. Science career persistence is thought to be related to scientific exposure, reflection in real-world contexts, mentoring programs, and intensive math and science academic programs. While serious science gaming may prove to encourage science selves by providing positive virtual science-related experiences, there is limited research on best learning contexts or long-range effects of academic science gaming on adolescents. [For the complete proceedings, see ED557311.]

We studied the linguistic norms of mathematical proof writing at the undergraduate level by asking two mathematicians and five mathematics undergraduate students to read seven partial proofs based on student-generated work and to identify and discuss uses of mathematical language that were out of the ordinary with respect to standard mathematical proof writing. By asking participants to discuss the seriousness of each breach, we not only identify and discuss some of these linguistic norms, but also describe important differences between the ways in which mathematicians and students understand them. [For the complete proceedings, see ED583989.]

In this study, we surveyed 570 Calculus I and Calculus II students at two large public universities in the Northeastern region of the United States. We explored the relationship between these students' career goals in mathematics and other STEM fields, with their mathematics identity and self-identified personality attributes. Our findings suggest that mathematics identity can be used as a way of explaining persistence in mathematics and other STEM fields. We also found certain personality attributes to be correlated with persistence in these fields and these personality attributes varied based on gender. We conclude with a detailed analysis of our findings and some implications. [For the complete proceedings, see ED583989.]

An examination of past research, policies, and reforms in mathematics education suggests that there have always been, and remain, tensions in conceptualizing the aims and goals of mathematics teaching and learning. While the disproportionality and conditions of marginalized learners is a cause for concern, it is important to understand that addressing the needs of these learners may not have been the primary goal of prior policies and reforms in mathematics education. Derrick Bell, a former attorney with the National Association for the Advancement of Colored People (NAACP) during the Civil Rights Era, employed his interest-convergence principle to explain how the United States Supreme Court issued the landmark ruling in "Brown v Board of Education of Topeka, Kansas" ("Brown I") in 1954. The Supreme Court's ruling in the "Brown" case revoked the "separate but equal" doctrine, which legally sanctioned segregation in public education and all aspects of daily life. Bell (2004) argued that the "Brown" decision was not the result of America coming to terms with its democratic ideals or moral sensibilities. Rather, the Supreme Court was more interested in providing "immediate credibility to America's struggle with communist countries to win the hearts and minds of emerging third world people" than in doing what was morally right (p. 233). "Brown" provided the impetus for legislation, such as the Elementary and Secondary Education Act (ESEA) of 1965 and it reauthorizations Improving America's School Act of 1994 and No Child Left Behind Act (NCLB) of 2001 (Zion & Blanchett, 2011). These along with other legislations and mandates established requirements that address the need to ensure that all students in the United States are provided equal educational opportunities. Although not fully realized, the requirements of these legislative acts and mandates created pressure to address the historical inequity in educational opportunity, achievement, and outcomes. Zion and Blanchett (2011) argued that the reason why large scale improvement in outcomes for all students have yet to be realized is that the problem has not yet been framed appropriately. The problem must be framed as part of the history and legacy of racism, and as an issue of civil rights and social justice, viewed through a critical lens. This article use a critical lens to apply the interest-convergence principle informed largely by the work of legal scholar, Derrick Bell (1980 & 2004), to examine motivating factors of policies and reform efforts in mathematics education. Specifically, this article makes the case that policies and reforms in mathematics education were not designed to address the needs of marginalized learners; rather these policies and reforms are often designed and enacted to protect the economic, technological, and social interests of the dominant culture. [For the complete proceedings, see ED583989.]