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In Australia, all teachers are expected to explicitly attend to numeracy in the subjects they teach. Pre-service teachers, therefore, need to begin to develop effective numeracy teaching strategies but there is a limited research base to inform the design of courses that address this need. This paper reports on findings from a study investigating the impact of one such course. The paper draws on data from two pre-service teachers: two course tasks completed at the beginning of the course and interviews conducted at the end of the course. Data were analysed using the 21st Century Numeracy Model. Findings suggest there were changes to the pre-service teachers' understanding of numeracy and their capacity to embed numeracy in the subjects they will teach.

Engagement in mathematics education is an important factor in a successful student experience. This paper reports findings from a study of Year 5 student perceptions of engagement during a two-week, inquiry-based learning (IBL), problem-posing investigation. The study triangulated data from semistructured interviews, video observations and student work samples to understand the student's perspectives of IBL; however, this paper reports the interview data. The findings indicate that most of the students were behaviourally, emotionally, and cognitively engaged during the IBL investigation, and that the investigation provided an opportunity for students to experience levels of competence, relatedness, and autonomy need satisfaction.

Prospective secondary mathematics teachers in Australia are typically taught by mathematics educators and mathematicians who work in different faculties and seldom collaborate--a situation that can lead to conflicting views about how to teach mathematics. This paper reports on findings from semi-structured interviews with three mathematics teacher educators in a hybrid mathematics/mathematics education department. Valsiner's zone theory is used to analyse how their beliefs, institutional context and professional learning opportunities shape their identities as MTEs. Findings reveal that the MTEs had developed similar beliefs within supportive institutional context but drew on different sources of professional learning.

This study investigated how motivational orientations and learning strategies predict ninth graders' non-routine mathematical problem-solving anxiety. Non-routine mathematical problem-solving anxiety classification and prediction were investigated through TwoStep cluster analysis, linear discriminant analysis, and logistic regression. 274 ninth graders participated in the study. The participants were clustered based on their problem-solving achievements and test anxiety levels: high-level and low-level problem-solving anxiety. Extrinsic goal orientation, rehearsal, and peer learning were significant classifiers. Intrinsic goal orientation, self-efficacy, rehearsal, and help-seeking were significant predictors for ninth graders' non-routine mathematical problem-solving anxiety.

This submission contains the Proceedings of the 2012 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Laval University in Québec City, Québec. 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, a panel discussion, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc and poster sessions. Papers include: (1) Towards an Understanding of Ethical Practical Action in Mathematics Education: Insights from Contemporary Inquiries (Margaret Walshaw); (2) Old and New Mathematical Ideas from Africa: Challenges for Reflection (Paulus Gerdes); (3) Cooda, Wooda, Didda, Shooda: Time Series Reflections on CMESG/GCEDM (William Higginson); (4) Panel: What is Fundamental Mathematics for Learners? (Elaine Simmt, Darien Allan, Ralph Mason, Ruth Beatty, Peter Taylor, and Hélène Paradis); (5) Numeracy: Goals, Affordances, and Challenges (France Caron and Peter Liljedahl); (6) Diversities in Mathematics and their Relation to Equity (Beverly Caswell and David Wagner); (7) Technology and Mathematics Teachers (K-16) / La technologie et l'enseignant mathématique (K-16) (Chantal Buteau and Nathalie Sinclair); (8) La preuve en mathématiques et en classe / Proof in Mathematics and in Schools (David Reid and Denis Tanguay); (9) The Role of Text/books in the Mathematics Classroom / Le rôle des manuels scolaires dans la classe de mathématiques (Peter Appelbaum and Susan Gerofsky); (10) Preparing Teachers to Develop Algebraic Thinking in Primary and Secondary School / Préparer les enseignants au développement de la pensée algébrique au primaire et au secondaire (Hassane Squalli, Chris Suurtamm, and Viktor Freiman); (11) Collaboration Between Research in Mathematics Education and Teaching Mathematics: Case Study of Teaching Infinity in Calculus (Miroslav Lovric); (12) Dialogue sur la lecture de textes historiques dans la classe de mathématiques / Dialogue on Reading Original Texts in the Mathematics Classroom (Louis Charbonneau and David Guillemette) [Written in French]; (13) Teaching Toward Equity in Mathematics (Beverly Caswell); (14) Inequalities in the History of Mathematics: From Peculiarities to a Hard Discipline (Elena Halmaghi); (15) The Study of On-line Situations of Validation Experienced by 13- and 14-year-old Students With and Without the Aid of an Electronic Forum (Manon Leblanc); (16) Institutional Acculturation of the Researcher, Teacher, and Secondary 1 Students with Learning Difficulties in Problem Situations Involving Rational Numbers / Les effets d'une démarche d'acculturation sur l'action didactique conjointe de l'enseignant, des élèves et du chercheur, dans l'enseignement/apprentissage des nombres rationnels auprès d'élèves en difficultés d'apprentissage (Geneviève Lessard) [Written in French]; (17) Mathematics Education: An Aporetic of Epistemology, Language and Ethics (Jean-François Maheux); (18) Diverse Perspectives on Teaching "Math for Teachers": Living the Tensions (Susan Oesterle); (19) Conversations Held and Roles Played During Mathematics Teachers' Collaborative Design: Two Dimensions of Interaction (Armando Paulino Preciado Babb); (20) The Ordinary Yet Extraordinary Emotions and Motives of Preservice Mathematics Teachers (Oana Radu); (21) Élaboration et analyse d'une intervention didactique, co-construite entre chercheur et enseignant, visant le développement d'un contrôle sur l'activité mathématique chez les élèves du secondaire / Development and Analysis of a Didactic Intervention, Co-constructed Between Researcher and Teacher For the Development of a Control of the Mathematical Activity Among High School Students (Mireille Saboya) [Written in French]; (22) Publishing in the Journal of Mathematics Teacher Education (Olive Chapman and Margaret Walshaw); (23) Is It Possible to Measure the Effectiveness of a Specific Approach to Teaching Foundations Mathematics in a Post-Secondary Setting? / Est-il possible de mesurer l'efficacité d'une approche spécifique à l'enseignement mathématiques fondations dans un cadre de post-secondaire? (Taras Gula); (24) Challenges in Supporting Mathematics Teachers to Develop Their Teaching Practices (Lionel Lacroix); (25) Rapport sur le ad hoc éthique et éducation mathématique / Report on the Ethics and Mathematics Education Ad Hoc (Jean-François Maheux); (26) Reading Biographies and Autobiographies of Mathematicians: What Do They Tell Us About the Subject of Mathematics? (Veda Roodal Persad); (27) Online Environments for Mathematics Sharing and Collaboration (Geoffrey Roulet); (28) Ad Hoc Session on Planning for the Next Canadian Math Education Forum (CMEF) to be Held in May 2014 (Peter Taylor); (29) Preservice Elementary Teachers' Beliefs Toward Mathematics and Mathematics Teaching (Sean Beaudette, Alexandra Penn, and Geoffrey Roulet); (30) Gearing Up For Grade 9: A Learning Object (Laura Broley); (31) Students' Perceptions of the Role of Theory and Examples in College Level Mathematics (Dalia Challita and Nadia Hardy); (32) Une expérimentation de pratiques gagnantes en enseignement des mathématiques / An Experiment with Successful Practices in Mathematics Teaching (Lucie Deblois); (33) Blended Mathematical Collaboration Using a Wiki, Geogebra and Jing (Jill Lazarus and Geoffrey Roulet); (34) Some Things Technologies Can Tell Us About Technologies: An Instrumented Analysis of Two Successive Mathematics Curricula (Jean-François Maheux and Fabienne Venant); (35) Investigating the Teaching Practices of a Group of Mathematics Graduate Students (Tod L. Shockey and Sibylle Weck-Schwarz); (36) Mathematics For Young Children: Exploring What is Possible in Early Mathematics Education? (Diane Tepylo, Joan Moss, Catherine Bruce, Tara Flynn, Diana Chang, and Zachary Hawes); and (37) Mise à l'essai d'une situation d'enseignement-apprentissage en lien avec le métier du scénographe pour favoriser l'engagement mathématique des élèves du 1er cycle du secondaire (Josianne Trudel) [Written in French]. Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lectures at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, tables, and figures. [For the 2011 proceedings, see ED547245.]

In this paper we consider the problem of modelling when students end their session in an online mathematics educational system. Being able to model this accurately will help us optimize the way content is presented and consumed. This is done by modelling the probability of an action being the last in a session, which we denote as the End-of-Session probability. We use log data from a system where students can learn mathematics through various kinds of learning materials, as well as multiple types of exercises, such that a student session can consist of many different activities. We model the End-of-Session probability by a deep recurrent neural network in order to utilize the long term temporal aspect, which we experimentally show is central for this task. Using a large scale dataset of more than 70 million student actions, we obtain an AUC of 0.81 on an unseen collection of students. Through a detailed error analysis, we observe that our model is robust across different session structures and across varying session lengths. [For the full proceedings, see ED599096.]

Personalized education systems recommend learning contents to students based on their capacity to accelerate their learning. This paper proposes a personalized exercise recommendation system for online self-directed learning. We first improve the performance of knowledge tracing models. Existing deep knowledge tracing models, such as Dynamic Key-Value Memory Network (DKVMN), ignore exercises' concept tags, which are usually available in tutoring systems. We modify DKVMN to design its memory structure based on the course's concept list, and explicitly consider the exercise-concept mapping relationship during students' knowledge tracing. We evaluated the model on the 5th grade students' math exercising dataset in TAL, one of the biggest education groups in China, and found that our model has higher performance than existing models. We also enhance the DKVMN model to support more input features and obtain higher performance. Second, we use the model to build a student simulator, and use it to train an exercise recommendation policy with deep reinforcement learning. Experimental results show that our policy achieves better performance than existing heuristic policy in terms of maximizing the students' knowledge level. To the best of our knowledge, this is the first time that deep reinforcement learning has been applied to personalized mathematic exercise recommendation. [For the full proceedings, see ED599096.]

The Home Learning Environment (HLE) focuses on everyday learning habits in families to support children's competency development. In this study, we used multitrait-multimethod (MTMM) analyses to compare two theoretical dimensions and three methods for assessing the HLE and their associations with linguistic and mathematical competencies of kindergarten children. Our sample consisted of N = 190 children (M[subscript age] = 64 months, SD = 4.4). The MTMM matrix showed a substantial effect of common methods and indicated a one-dimensional HLE construct. A children's book title recognition test was the best predictor of children's linguistic and numeracy competencies. Even when controlling for child and family characteristics, the HLE was significantly related to both children's mathematical and linguistic competencies in a structural equation model.

Mathematical calculations are an important part of chemistry. Those problems are difficult for students, especially if the task is set with a limiting reactant. The aim of this study was development of a Procedure for evaluation of cognitive complexity of the Stoichiometric Tasks with a Limiting Reactant. The procedure created included an assessment of the difficulty of concepts and an assessment of their interactivity. As a research instrument for assessing performance, the test of knowledge was specifically constructed for this research. Each task in the test was followed by a seven-point Likert scale for the evaluation of the invested mental effort. The research included 58 upper-secondary students. The validity of the procedure was confirmed by a series of regression analyses where statistically significant correlation coefficients are obtained among the examined variables: students' achievement and invested mental effort from cognitive complexity (independent variable). [For the full proceedings, see ED620289.]

Examining students' inclinations to use algorithms and rules to solve a task was a fruitful area of research in chemical education in the last four decades. This research aimed to examine whether students read the task request carefully, considering its meaningfulness, or they approach it mechanically, applying a set of algorithms by default. The research sample consisted of students majoring in chemistry teaching at the University of Novi Sad, Faculty of Sciences who were in their final year of bachelor studies. The study was conducted during two academic years. The main instrument consisted of five quantitative problems, and each of the problems contained deceptive information that made the calculation nonsensical. The results revealed that most students applied an algorithmic approach without paying attention to the meaningfulness of the task requirements. Additionally, it has been shown that students rely heavily on memorizing formulas without a proper understanding of underlying concepts. [For the full proceedings, see ED620289.]

These proceedings contain papers of the 4th International Baltic Symposium on Science and Technology Education (BalticSTE2021) held in Šiauliai, Lithuania, June 21-22, 2021. This symposium was organized by the Scientific Methodical Center "Scientia Educologica" in cooperation with Scientia Socialis, Ltd. Lithuania. The proceedings are comprised of 16 short papers. Keynote speakers include: Paul Pace, Paolo Bussotti, Peter Demkanin, and Malgorzata Nodzynska. [Individual papers are indexed in ERIC.]

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl and Fre: (1) Working with Learners' Mathematics: Exploring a Key Element of Mathematical Knowledge for Teaching (Jill Adler, Zain Davis, Mercy Kazima, Diane Parker, and Lyn Webb); (2) A Comparison between Teachers' and Pupils' Tendency to Use a Representativeness Heuristic (Thekla Afantiti-Lamprianou, Julian S. Williams, and Iasonas Lamprianou); (3) Purposeful Task Design and the Emergence of Transparency (Janet G. Ainley, Liz Bills, and Kirsty Wilson); (4) A Developmental Model for Proportional Reasoning in Ratio Comparison Tasks (Silvia Alatorre and Olimpia Figueras); (5) Referential and Syntactic Approaches to Proof: Case Studies from a Transition Course (Lara Alcock and Keith Weber); (6) Teachers' Beliefs about Students' Development of the Pre-Algebraic Concept of Equation (Vassiliki Alexandrou-Leonidou and George N. Philippou); (7) Developing Students' Understanding of the Concept of Fractions as Numbers (Solange Amorim Amato); (8) Multiple Representations in 8th Grade Algebra Lessons: Are Learners Really Getting It? (Miriam Amit and Michael N. Fried); (9) Reform-Oriented Teaching Practices: A Survey of Primary School Teachers (Judy Anderson and Janette Bobis); (10) The Genesis of Signs by Gestures: The Case of Gustavo (Ferdinando Arzarello, Francesca Ferrara, Ornella Robutti, and Domingo Paola); (11) Students' Experience of Equivalence Relations: A Phenomenological Approach (Amir H. Asghari and David Tall); (12) How Series Problems Integrating Geometric and Arithmetic Schemes Influence Prospective Secondary Teachers' Pedagogical Understanding (Leslie Aspinwall, Kenneth L. Shaw, and Hasan Unal); (13) Dealing with Learning in Practice: Tools for Managing the Complexity of Teaching and Learning (Sikunder Ali Baber and Bettina Dahl); (14) Situations of Psychological Cognitive No-Growth (Roberto R. Baldino and Tania C. B. Cabral); (15) Good CAS Written Records: Insight from Teachers (Lynda Ball and Kaye Stacey); (16) Developing Procedure and Structure Sense of Arithmetic Expressions (Rakhi Banerjee and K. Subramaniam); (17) Struggling with Variables, Parameters, and Indeterminate Objects, or How to Go Insane in Mathematics (Caroline Bardini, Luis Radford, and Cristina Sabena); (18) Exploring How Power is Enacted in Small Groups (Mary Barnes); (19) A Framework for the Comparison of PME Research into Multilingual Mathematics Education in Different Sociolinguistic Settings (Richard Barwell); (20) Vygotsky's Theory of Concept Formation and Mathematics Education (Margot Berger); (21) Preservice Teachers' Understandings of Relational and Instrumental Understanding (Kim Beswick); (22) The Transformation of Mathematics in On-Line Courses (Marcelo C. Borba); (23) Using Cognitive and Situated Perspectives to Understand Teacher Interactions with Learner Errors (Karin Brodie); (24) Identification of Affordances of a Technology-Rich Teaching and Learning Environment (TRTLE) (Jill P. Brown); (25) The "A4-Project": Statistical World Views Expressed through Pictures (Michael Bulmer and Katrin Rolka); (26) A Whole-School Approach to Developing Mental Computation Strategies (Rosemary Callingham); (27) A Comparison of Perceived Parental Influence on Mathematics Learning among Students in China and Australia (Zhongjun Cao, Helen Forgasz, and Alan Bishop); (28) Using Word Problems in Malaysian Mathematics Education: Looking beneath the Surface (Kah Yein Chan and Judith Mousley); (29) Constructing Pedagogical Knowledge of Problem Solving: Preservice Mathematics Teachers (Olive Chapman); (30) Revisiting a Theoretical Model on Fractions: Implications for Teaching and Research (Charalambos Y. Charalambous and Demetra Pitta-Pantazi); (31) Students' Reflection on Their Sociomathematical Small-Group Interaction: A Case Study (Petros Chaviaris and Sonia Kafoussi); (32) Investigating Teachers' Responses to Student Misconceptions (Helen L. Chick and Monica K. Baker); (33) Studying the Distribution of Responsibility for the Generation of Knowledge in Mathematics Classrooms in Hong Kong, Melbourne, San Diego and Shanghai (David Clarke and Lay Hoon Seah); (34) Indigenous and Non-Indigenous Teaching Relationships in Three Mathematics Classrooms in Remote Queensland (Tom J. Cooper, Annette R. Baturo, and Elizabeth Warren); (35) Exploring the Strategies Used by Grade 1 to 3 Children through Visual Prompts, Symbols and Worded Problems: A Case for a Learning Pathway for Number (Ty Corvell Cranfield, Cally Kuhne, and Gary Powell); (36) Primary Students' Knowledge of the Properties of Spatially-Oriented Diagrams (Carmel Diezmann); (37) A Conceptual Framework for Studying Teacher Preparation: The Pirie-Kieren Model, Collective Understanding, and Metaphor (Maria A. Droujkova, Sarah B. Berenson, Kelli Slaten, and Sue Tombes); (38) Mathematical Modelling with 9-Year-Olds (Lyn English and James Watters); (39) Exploring "Lesson Study" in Teacher Preparation (Maria L. Fernandez); (40) Child-Initiated Mathematical Patterning in the Pre-Compulsory Years (Jillian Fox); (41) The Tacit-Explicit Nature of Students' Knowledge: A Case Study on Area Measurement (Cristina Frade); (42) Teachers as Interns in Informal Mathematics Research (John M. Francisco and Carolyn A. Maher); and (43) Exploring Excellence and Equity within Canadian Mathematics Classrooms (George Frempong). (Individual papers contain references.)

Mathematical reasoning is foundational to making sense of mathematics. Yet assessing mathematical reasoning can be challenging for teachers. This paper reports on a project where teachers taught two lessons with a specific focus on reasoning and came together with other teachers at their school to attempt to assess the reasoning of their students. Results, derived from an analysis of two post-lesson discussions about student work samples and associated completed assessment rubrics, provide insights into the challenges identified by 34 primary teachers at 4 Victorian government schools.

The Computational Thinking recently has been recognised as one of the basic knowledge to be developed since childhood. Coding and computers are not just programming, but tools that help students to develop problem solving skills and more deep understand of the way things work. For these reasons, great attention has been focused on this topic both from a pedagogical and technological point of view. In this paper, a first approach to Computational Thinking using Arduino is presented. To this end, some learning activities have been designed to introduce middle school students, without any experience in coding, to the process of building the algorithm from simple exercises to more complex tasks. The pilot test involved 25 subjects, many of them do not like to study mathematics, science and technology, but the results were promising. The approach was appreciated by the students and the results of the questionnaires confirmed the learning effectiveness too. [For the complete proceedings, see ED600498.]

This paper describes a multiple criteria approach based on a hybrid method of Collaborative Filtering (CF) and ContentBased Filtering (CBF) for discovering the most relevant criteria which could affect the elective course recommendation for university students. In order to determine which factors are the most important, it is proposed a genetic algorithm which automatically discovers the importance of the different criteria assigning weights to each one of them. We have carried out an in-depth study using a real data set with more than 1700 ratings of Computer Science graduates at University of Cordoba. We have used different proposals and different weights for each criterion in order to discover what is the combination of multiple criteria which provides better results. [For the full proceedings, see ED593090.]

Selecting courses in an open-curriculum education program is a difficult task for students and academic advisors. Course recommendation systems nowadays can be used to reduce the complexity of this task. To control the recommendation error, we argue that course recommendations need to be provided together with "statistical" confidence. The latter can be used for computing a statistically valid set of recommended courses that contains courses a student is likely to take with a probability of at least 1-[epsilon] for a user-specified significance level [epilsilon]. For that purpose, we introduce a generic algorithm for course recommendation based on the conformal prediction framework. The algorithm is used for implementing two conformal course recommender systems. Through experimentation, we show that these systems accurately suggest courses to students while maintaining statistically valid sets of courses recommended. [For the full proceedings, see ED607784.]

The study of the variational behavior of functions constitutes an important element in the understanding of the change of phenomena in real life. His understanding is an essential axis in the mathematical training of university students, especially those who pursue engineering careers. This article presents the results of a study whose objective was to determine the mistakes made by engineering students about the variational behavior of functions. The Duval Semiotics Records Theory was taken as a reference and a questionnaire was prepared with questions about identification of regions of variability for "x" and "y"; regions of growth, decrease, stability, extreme values and, analysis and description of the behavior of the function. The evaluation of the answers was done in a quantitative-qualitative way, from an exploratory and descriptive perspective, with 100 students participating in the civil engineering career. The results indicate that students do not make a real reflection on the variational behavior in intervals of the variables or in a global way. They have difficulty discriminating between the behavior of the function and the location of the function. They present cognitive difficulties that do not allow them to make an adequate conversion from one register to the other. Errors related to mathematical language were found, to the limitations to obtain spatial information, to establish erroneous inferences and to the inadequate development of previous knowledge, which does not allow them to properly evaluate the variational behavior of the functions. [For full proceedings, see ED621941.]

In this paper, we provide an overview of the "Maths Inside" project, funded by the Australian Maths and Science Partnership Program (AMSPP). The overall aim of the AMSPP is to improve uptake and participation of students in mathematics and science at secondary and tertiary levels. In this research project, we aim to improve student interest in mathematics and support mathematics teachers in their professional learning, through provision of rich and investigative learning resources, including video case studies of CSIRO scientists and mathematicians. Data collection on the outcomes of the project is ongoing and will be reported in subsequent papers.

Secondary mathematics pre-service teachers often have different experiences of mathematics and its teaching and learning during their initial teacher education. This paper documents the beliefs about mathematics, its teaching, and its learning, of mathematicians and mathematics educators who teach secondary mathematics pre-service teachers. The beliefs of the surveyed sample of eighty-two academics and differences between groups were characterised using descriptive statistics and one-way comparisons between groups ANOVA. Generally, respondents had a Problem-solving view of mathematics and those with education backgrounds were more in agreement with that method of teaching.

Pasifika cultures have a rich background of mathematics including a strong emphasis on patterns used within craft design (Finau & Stillman, 1995). However, there have been limited studies which have investigated the use of contextual Pasifika patterns in mathematics classrooms. The aim of this study was to explore how contextual Pasifika patterning tasks can potentially support young children to develop their understanding of growing patterns. Ten lessons using Pasifika and Maori patterns were undertaken with 27 Year 2 students (6-year-old). In this paper, analysis of one of the lessons is used to examine how a contextual task assisted these young students to generalise growing patterns.

This paper addresses the need for empirical research on the processes by which students create algorithms. I analyse the collaborative work of three high-school students on a contextualised graph theory task, in which they created an algorithm for maximising the happiness score of a seating arrangement. The group found an optimal arrangement but created an algorithm that did not fully account for this arrangement. The group's written algorithm reflected only the properties of their optimal arrangement that they explicitly noticed after creating the arrangement. And, these explicitly-noticed properties aligned with the group's predominant contextual considerations.

The analysis of log data generated by online educational systems is an important task for improving the systems, and furthering our knowledge of how students learn. This paper uses previously unseen log data from Edulab, the largest provider of digital learning for mathematics in Denmark, to analyse the sessions of its users, where 1.08 million student sessions are extracted from a subset of their data. We propose to model students as a distribution of different underlying student behaviours, where the sequence of actions from each session belongs to an underlying student behaviour. We model student behaviour as Markov chains, such that a student is modelled as a distribution of Markov chains, which are estimated using a modified k-means clustering algorithm. The resulting Markov chains are readily interpretable, and in a qualitative analysis around 125,000 student sessions are identified as exhibiting unproductive student behaviour. Based on our results this student representation is promising, especially for educational systems offering many different learning usages, and offers an alternative to common approaches like modelling student behaviour as a single Markov chain often done in the literature. [For the full proceedings, see ED596512.]

"Proceedings of International Conference on Social and Education Sciences" includes full papers presented at the International Conference on Social and Education Sciences (IConSES), which took place on October 7-10, 2019, in Denver, Colorado. The aim of the conference is to offer opportunities to share ideas, discuss theoretical and practical issues, and to connect with the leaders in the fields of education and social sciences. The IConSES invites submissions that address the theory, research, or applications in all disciplines of education and social sciences. The IConSES is organized for: faculty members in all disciplines of education and social sciences, graduate students, K-12 administrators, teachers, principals, and all interested in education and social sciences. [Individual papers are indexed in ERIC.]

These proceedings contain the papers of the 16th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2019), held during November 7-9, 2019, which has been organized by the International Association for Development of the Information Society (IADIS) and co-organised by University Degli Studi di Cagliari, Italy. The CELDA conference aims to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There have been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a fast pace and affecting academia and professional practice in many ways. Paradigms such as just-in-time learning, constructivism, student-centered learning and collaborative approaches have emerged and are being supported by technological advancements such as simulations, virtual reality and multi-agent systems. These developments have created both opportunities and areas of serious concerns. This conference aims to cover both technological as well as pedagogical issues related to these developments. Main tracks have been identified. However, innovative contributions that do not easily fit into these areas will also be considered as long as they are directly related to the overall theme of the conference -- cognition and exploratory learning in the digital age. The CELDA 2019 Conference received 87 submissions from more than 25 countries. Out of the papers submitted, 48 were accepted as full papers for an acceptance rate of 55%; 15 were accepted as short papers and one was accepted as a reflection paper. In addition to the presentation of full, short and reflection papers, the conference also includes one keynote presentation from an internationally distinguished researcher, Baltasar Fernández Manjón, Director of the e-Learning Research Group e-UCM, Complutense University of Madrid (UCM), Spain. [Individual papers are indexed in ERIC.]

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.

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 paper reports from a broad investigation of mathematics knowledge as dependent on interconnected concepts. The paper focuses specifically on illustrating how network analysis may be used in examining spatiotemporal relationships between learned mathematics concepts, or curriculum outcomes, and concepts inherent in assessment items. Connections both within and between year levels are shown, based on primary years' multiple-choice assessment items related to measurement. Network analysis provides a potentially powerful tool that may offer educators greater specificity in approaches to the design of revision and intervention through a view of complex rather than linear conceptual connectivity in mathematics learning. [For the complete proceedings, see ED597799.]

As a contribution to honour the foresight of Ken Clements and John Foyster in founding MERGA [Mathematics Education Research Group of Australasia] so many years ago this paper is not a research paper in the usual sense. Rather it sets out to sample the context of Mathematics Education in Australasia and beyond (then and now) and to highlight some challenges as seen by this author. In this personal view I do not intend to expand in detail upon particular strands of research in which I have been involved, although for purposes of illustration examples will be drawn from time to time from this and other work. MERGA is about both people and scholarly activity, and so this paper will make reference to both--for history, culture, and challenge are essential components of the development of any organisation.

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.]

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.]

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).]

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.

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.

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.]

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.

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.]

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.