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This paper explores the construction of classroom contexts facilitative of student engagement in Mathematics. Employing a form of discourse analysis framed within a participation approach to learning, the paper provides insights into the construction of such contexts. The affordances and constraints of constructing such a context are discussed in the light of the writings of one Year 7 teacher as she employed Collective Argumentation to re-construct her classroom context to better engage students in the learning of Mathematics.

The aim of the larger study, of which this paper is a part, is to investigate the decline in Year 10 male students' participation in senior calculus mathematics courses at an independent boys' school located in metropolitan Queensland. This paper draws on Sealey and Noyes's (2010) relevance framework to conduct document analysis and interviews with leaders and teachers concerning the relevance of mathematics. In both cases results indicated that there was a limited understanding of relevance of mathematics.

"Let's Count" is an early mathematics program that has been designed by The Smith Family and the authors to assist educators in early childhood contexts in socially disadvantaged areas of Australia to work in partnership with parents and other family members to promote positive mathematical experiences for young children (3-5 years). A longitudinal evaluation of "Let's Count" was undertaken in 2012-2014 involving 337 children in two treatment groups and 125 children in a comparison group. This paper shares preliminary results from the evaluation. Overall the findings demonstrate that "Let's Count" was effective. [The research reported in this paper was funded by The Smith Family and the Origin Energy Foundation as part of the "Let's Count Longitudinal Evaluation."]

"Let's Count" is a preschool mathematics intervention implemented by The Smith Family from 2012 to the present in "disdvantaged" communities across Australia. It is based on current mathematics and early childhood education research and aligns with the Early Years Learning Framework. Let's Count has been shown to be effective in enhancing mathematics learning and dispositions of young children, early childhood educators and families through a longitudinal evaluation undertaken from 2012-2015. This paper reports on the development, implementation and evaluation of "Let's Count" and its likely future trajectory.

Collaboration between mathematicians and mathematics educators may provide a means of improving the quality of pre-service teacher education for prospective teachers of mathematics. Some preliminary findings of a project that investigates this type of interdisciplinary collaboration, both within and across institutions, are reported on in this paper. Interviews were conducted with selected participants to identify the nature of the boundary encounters and brokering involved between disciplinary communities in order to create new practices and transfer these practices to a new institutional context. [This work was funded by the Australian Government Office for Learning and Teaching (grant #MS13-3174).]

Reasoning is an important aspect in the understanding and learning of mathematics. This paper reports on a case study presenting one Australian primary teacher's reflections regarding the role played by a professional learning program in her developing understanding of mathematical reasoning. Examination of the transcripts of two interviews identified changes in her perceptions of mathematical reasoning by mapping interview responses against the Mathematical Reasoning Framework (Herbert et al., 2015). This change indicates that a well planned program of professional learning based on a demonstration is efficacious in developing teachers' understanding of mathematical reasoning.

This paper presents initial data from a study being undertaken into the potential effects of a mentoring program for teacher education students who have self-identified as suffering from mathematics anxiety. The first phase of the study saw 8 primary teacher education students opt into a program matching them in pairs with 4 mentor teachers who had been selected by their principals after meeting 6 criteria that identified them as highly capable mentors in mathematics education. The mentees worked with the mentors in classrooms for 8 weeks. After the program the students were interviewed. Data from these students is explored here with particular emphasis on an artefact presented by one of the students about her journey through the process.

A central premise of this project is that teachers learn from the act of teaching a lesson and that this learning is evident in the planning and teaching of a subsequent lesson. We are studying the knowledge construction of mathematics teachers utilising multi-camera research techniques during lesson planning, classroom interactions and reflection. This paper reports on the learning of two Year 7 teachers, one in Melbourne and one in Chicago, teaching the same initial lesson focusing on division, remainders and context. Both teachers claimed to have learned about their students' mathematical thinking after teaching the initial lesson, but found planning a second lesson to accommodate this learning challenging.

Although an understanding of time is crucial in our society, curriculum documents have an undue emphasis on reading time and little emphasis on core underlying ideas. Given this context, a one-to-one assessment interview, based on a new framework, was developed and administered to investigate students' understanding of core ideas undergirding the notion of time: succession, duration and measurement. This paper reports on the development and implementation of the interview and initial results for Year 3/4 students.

This paper presents a hypothesised learning trajectory for a Year 3 Indigenous student en route to generalising growing patterns. The trajectory emerged from data collected across a teaching experiment (students n = 18; including a pre-test and three 45-minute mathematics lessons) and clinical interviews (n = 3). A case study of one student is presented as a representative of high achieving students' progression and shifts in learning. Results suggest that students are capable of functional thinking, which contradicts the notion of young students can only engage with recursive pattern sequences. In addition, particular teaching actions assisted in promoting shifts in developing students' capability to generalise growing patterns.

Teachers of senior secondary mathematics are required to contend with a number of challenges including covering the prescribed curriculum, differentiating the content for a range of learners, and preparing students for externally imposed assessment tasks. The flipped classroom is gaining in popularity as an approach that can be used to address these challenges. This paper provides a framework that can be used to interpret the affordances of a flipped classroom within the context of teaching secondary mathematics and the motivational factors that influence the uptake of the approach. Data analysed through the framework showed that students believed that the approach enabled them to have autonomy over their learning and achieve their goals. The study has implications for senior secondary teachers and students, particularly in terms of meeting the challenges of curriculum coverage and preparation for externally imposed assessment tasks.

This paper explores how young Indigenous students' (Year 2 and 3) generalise growing patterns. Piagetian clinical interviews were conducted to determine how students articulated growing pattern generalisations. Two case studies are presented displaying how students used gesture to support and articulate their generalisations of growing patterns. This paper presents a hypothesised cultural learning semiotic model that was a result of the interactions that occurred between the non-Indigenous researcher, the Indigenous students and the Indigenous Education Officers.

This paper reports on the experiences of newcomers at the 36th Annual MERGA Conference. The paper applies Wenger's (1998) social learning theory to explore the kinds of feedback that might assist newcomers. Questionnaire responses to describe the experience of ten newcomers and interview responses from five of the ten are reported. The participants identified the stimulating presentations and being immersed in an environment conducive to rich dialogue as important factors that contributed to a positive experience. The newcomers felt welcomed by the MERGA community and were able to contribute, particularly those who had previous experience in research or at other conferences.

Traditionally, the domain of higher education, the 'flipped classroom' is gaining in popularity in secondary school settings. In the flipped classroom, digital technologies are used to shift direct instruction from the classroom to the home, providing students with increased autonomy over their learning. While advocates of the approach believe it is more engaging and effective than traditional instruction, there is little empirical research into the benefits of this approach, particularly in relation to mathematics instruction. This paper adds to the limited research by reporting on students and parents' experiences with a flipped classroom in a senior mathematics class. The results indicated that there were five main components that influenced students' motivation to engage with the flipped classroom approach. The study has particular implications for students and secondary mathematics teachers who have limited time to make the curriculum comprehensible for students and to prepare them for external assessment tasks.

This paper compares the counting and whole number knowledge and skills of primary school children in Australia and Germany at the end of Grade 1 and Grade 2. Children's learning was assessed using the Early Numeracy Interview and associated Growth Point Framework. The findings highlight substantial differences between the two groups that vary for the four whole number content domains that have been investigated. These variations are likely due to different curriculum emphases in the two countries.

A central premise of this project is that teachers learn from the act of teaching a lesson and that this learning is evident in the planning and teaching of a subsequent lesson. In this project, the knowledge construction of mathematics teachers was examined utilising multi-camera research techniques during lesson planning, classroom interactions and reflection. Our goal is a refined understanding of classroom events that create opportunities for teacher learning. This paper reports what one Year 5 teacher appeared to learn from the process.

The intent of this paper is to stress the importance of narrative and story, and to share the experience of opening the windows of memory to look into the past and uncover fascinating and valuable histories as portrayed in a current study. The longitudinal study of an educator follows his life story and his role in education. Set in Victoria, it explores the founding of the State's education system and highlights progressive developments. The life story reveals the history of the system and evolving philosophies that influenced the life of the subject. The study considers the philosophies and how they influenced the subject's thinking and actions. Using windows as a metaphor, Part 1 of the paper includes discussion regarding the appropriacy of narrative as a research tool, considers the notion of memory and introduces the research subject. Part 2 gives insights into three distinct periods and the part played by three men who guided Victoria's educational development and growth throughout the twentieth century. In relation to each is a brief discussion of their influence on the career of the research subject.

This paper addresses data arising from initial discussion with school principals concerning the implementation of a doctoral project at their schools. The doctoral project involved the prep teacher working with the preschool teacher to support children's numeracy practices as they made the transition to school. The findings presented in this paper suggest that numeracy might not be a key priority for schools as children make the transition from preschool to primary school, despite government policy, frameworks and curriculum documentation advocating the otherwise.

Autoethnography is adopted as the procedure and orientation for this PhD study which aims to explore the cultural identity of the Chinese families and its influences on their children's mathematics learning. The purpose of this paper is two-fold. First, readers are invited to travel with the researcher a journey in which she explores her diasporic identity by engaging in the stories of others. This will be done by examining how her understanding of her own Chinese identity was challenged by those of the participants in the interviews. Second, through her experience and reflections, readers are provided with an insider's lens to understand some of the data collected in the interviews. Data are collected through interviews, journals, observations and fieldwork memos. As an autoethnographic study, it is not the aim of this thesis to provide a generalization of data. Rather, rich data sets which are partially contrastive and partially congruent to one another challenged the homogeneity of Chineseness. This paper discusses how the researcher uses her dual positionality to explore blurred boundaries between the observer and the observed, insider and outsider. It highlights how self is an important instrument in both the collection and analysis of data.

This paper explores the role of professional learning community and collegial discussion as important supports for developing teacher expertise in the teaching and learning of mathematics in rural and remote regions of Queensland, Australia. The research reported in this paper is from the first year of a longitudinal research and development project. Findings suggest that teachers in rural and remote schools with a small number of mathematics teachers may benefit from access to the mathematics professional learning community of a larger rural school.

The importance of leadership in changing schools and building quality programs is the focus of this paper. While leadership is often seen as a management aspect of school life, the role of leadership in curriculum change may be quite different from that of school leadership visa-vis the principal. In small remote schools where there are many factors impacting on school reform, this paper explores curriculum leadership where the schools successfully performed against numeracy benchmarks. Features of curriculum leadership are drawn from these cases to develop a framework for considering effective leadership in remote Indigenous contexts.

This paper reports on a study that explored the use of cognitively challenging tasks with low-attaining mathematics students and in particular, their teachers' attempts at scaffolding. A major finding was that responding appropriately to scaffolding opportunities was challenging for the teachers. In this paper two main factors are discussed which impacted on the teachers' responses to scaffolding opportunities: teacher knowledge of appropriate tools and representations for particular mathematical concepts, and teacher response to student prior knowledge and understanding.

These proceedings contain the papers of the 13th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2016), October 28-30, 2016, which has been organized by the International Association for Development of the Information Society (IADIS), co-organized by the University of Mannheim, Germany, and endorsed by the Japanese Society for Information and Systems in Education (JSISE). 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. These proceedings contain the following keynote lectures: (1) From Digital to Double Blended Learning (Jeroen J. G. van Merrienboer); and (2) Open Educational Resources: Educational Technology as a Driver for Educational Reform? (Michael Kerres). Full papers in these proceedings include: (1) A Service-Learning Project Using Crowdfunding Strategy: Students' Experience and Reflection (Jessnor Elmy Mat-jizat and Khalizul Khalid); (2) Towards a Theory-Based Design Framework for an Effective E-Learning Computer Programming Course (Ian S. McGowan); (3) An Ontology for Learning Services on the Shop Floor (Carsten Ullrich); (4) The Impact of Technology Integration upon Collegiate Pedagogy from the Lens of Multiple Disciplines (Joan Ann Swanson); (5) A Learning Support System Regarding Motion Trigger for Repetitive Motion Having an Operating Instrument (Hiroshi Toyooka, Kenji Matsuura, and Naka Gotoda); (6) Task-Based Assessment of Students' Computational Thinking Skills Developed through Visual Programming or Tangible Coding Environments (Takam Djambong and Viktor Freiman); (7) Framework for Intelligent Teaching and Training Systems--A Study of the Systems (Nikolaj Troels Graf von Malotky and Alke Martens); (8) Mobile Device Usage in Higher Education (Jan Delcker, Andrea Honal, and Dirk Ifenthaler); (9) Features Students Really Expect from Learning Analytics (Clara Schumacher and Dirk Ifenthaler); (10) Music Technology Competencies for Education: A Proposal for a Pedagogical Architecture for Distance Learning (Fátima Weber Rosas, Leticia Rocha Machado, and Patricia Alejandra Behar); (11) Increasing Students' Science Writing Skills through a PBL Simulation (Scott W. Brown, Kimberly A. Lawless, Christopher Rhoads, Sarah D. Newton, and Lisa Lynn); (12) The Effect of Choosing versus Receiving Feedback on College Students' Performance (Maria Cutumisu and Daniel L. Schwartz); (13) The Impact of Middle-School Students' Feedback Choices and Performance on Their Feedback Memory (Maria Cutumisu and Daniel L. Schwartz); (14) Numerical Acuity Enhancement in Kindergarten: How Much Does Material Presentation Form Mean? (Maria Lidia Mascia, Maria Chiara Fastame, Mirian Agus, Daniela Lucangeli, and Maria Pietronilla Penna); (15) A Video Game for Learning Brain Evolution: A Resource or a Strategy? (Luisa Fernanda Barbosa Gomez, Maria Cristina Bohorquez Sotelo, Naydu Shirley Roja Higuera, and Brigitte Julieth Rodriguez Mendoza); (16) Communication Vulnerability in the Digital Age: A Missed Concern in Constructivism (Fusa Katada); (17) Online Learners' Navigational Patterns Based on Data Mining in Terms of Learning Achievement (Sinan Keskin, Muhittin Sahin, Adem Ozgur, and Halil Yurdugul); (18) Amazed by Making: How Do Teachers Describe Their PBL Experience (Dalit Levy and Olga Dor); (19) Group Work and the Impact, If Any, of the Use of Google Applications for Education (Jannat Maqbool); (20) Fractangi: A Tangible Learning Environment for Learning about Fractions with an Interactive Number Line (Magda Mpiladeri, George Palaigeorgiou, and Charalampos Lemonidis); (21) Evaluation of Learning Unit Design with Use of Page Flip Information Analysis (Izumi Horikoshi, Masato Noguchi, and Yasuhisa Tamura); (22) Einstein's Riddle as a Tool for Profiling Students (Vildan Özeke and Gökhan Akçapinar); (23) Exploring Students' E-Learning Effectiveness through the Use of Line Chat Application (Tassaneenart Limsuthiwanpoom, Penjira Kanthawongs, Penjuree Kanthawongs, and Sasithorn Suwandee); (24) Factors Affecting Perceived Satisfaction with Facebook in Education (Penjuree Kanthawongs, Penjira Kanthawongs, and Chaisak Chitcharoen); (25) Interactive Video, Tablets and Self-Paced Learning in the Classroom: Preservice Teachers' Perceptions (Anthia Papadopoulou and George Palaigeorgiou); (26) Cognitive Design for Learning: Cognition and Emotion in the Design Process (Joachim Hasebrook); (27) Investigating the Potential of the Flipped Classroom Model in K-12 Mathematics Teaching and Learning (Maria Katsa, Stylianos Sergis, and Demetrios G. Sampson; (28) Learning Analytics to Understand Cultural Impacts on Technology Enhanced Learning (Jenna Mittelmeier, Dirk Tempelaar, Bart Rienties, and Quan Nguyen); (29) Widening and Deepening Questions in Web-Based Investigative Learning (Akihiro Kashihara and Naoto Akiyama); (30) Year 9 Student Voices Negotiating Digital Tools and Self-Regulated Learning Strategies in a Bilingual Managed Learning Environment (Ulla Freihofner, Simone Smala, and Chris Campbell); (31) Purposeful Exploratory Learning with Video Using Analysis Categories (Meg Colasante); (32) Building a Learning Experience: What Do Learners' Online Interaction Data Imply (Mehmet Kokoç and Arif Altun); (33) Rules for Adaptive Learning and Assistance on the Shop Floor (Carsten Ullrich); and (34) Participation and Achievement in Enterprise MOOCs for Professional Learning (Florian Schwerer and Marc Egloffstein). Short papers included in these proceedings include: (1) Connectivist Communication Networks (Ingolf Waßmann, Robin Nicolay, and Alke Martens); (2) Learning and Skills Development in a Virtual Class of Educommunications Based on Educational Proposals and Interactions (Maria Cristina Bohorquez Sotelo, Brigitte Julieth Rodriguez Mendoza, Sandra Milena Vega, Naydu Shirley Roja Higuera, and Luisa Fernanda Barbosa Gomez); (3) The Relationship among ICT Skills, Traditional Reading Skills and Online Reading Ability (I-Fang Liu and Hwa-Wei Ko); (4) Towards Concept Understanding Relying on Conceptualisation in Constructivist Learning (Farshad Badie); (5) E-Learning in Chemistry Education: Self-Regulated Learning in a Virtual Classroom (Rachel Rosanne Eidelman and Yael Shwartz); (6) Relationship of Mobile Learning Readiness to Teacher Proficiency in Classroom Technology Integration (Rhonda Christensen and Gerald Knezek); (7) Human Computer Interaction (HCI) and Internet Residency: Implications for Both Personal Life and Teaching/Learning (Linda Crearie); (8) A Portfolio for Optimal Collaboration of Human and Cyber Physical Production Systems in Problem-Solving (Fazel Ansari and Ulrich Seidenberg); (9) Innovative Collaborative Learning Strategies for Integrated Interactive E-Learning in the 21st Century (Barbara Son); (10) Educational Criteria for Evaluating Simple Class Diagrams Made by Novices for Conceptual Modeling (Mizue Kayama, Shinpei Ogata, David K. Asano, and Masami Hashimoto); (11) Digital Natives and Digital Divide: Analysing Perspective for Emerging Pedagogy (Uriel U. Onye and Yunfei Du); (12) E-Learning System Using Segmentation-Based MR Technique for Learning Circuit Construction (Atsushi Takemura); (13) Students' Google Drive Intended Usage: A Case Study of Mathematics Courses in Bangkok University (Krisawan Prasertsith, Penjira Kanthawongs, and Tan Limpachote); (14) An Empirical Study on the Impact of Self-Regulation and Compulsivity towards Smartphone Addition of University Students (Penjira Kanthawongs, Felicito Angeles Jabutay, Ruangrit Upalanala, and Penjuree Kanthawongs); (15) Adaptive Game Based Learning Using Brain Measures for Attention--Some Explorations (Jelke van der Pal, Christopher Roos, Ghanshaam Sewnath, and Christian Rosheuvel); (16) Evaluation of the Course of the Flight Simulators from the Perspective of Students and University Teachers (Feyzi Kaysi, Bünyamin Bavli and Aysun Gürol); (17) Development of Critical Thinking with Metacognitive Regulation (Yasushi Gotoh); (18) Enacting STEM Education for Digital Age Learners: The "Maker" Movement Goes to School (Dale S. Niederhauser and Lynne Schrum); (19) New Scenarios for Audience Response Systems in University Lectures (Daniel Schön, Stephan Kopf, Melanie Klinger, and Benjamin Guthier); (20) Academic Retention: Results from a Study in an Italian University College (Maria Lidia Mascia, Mirian Agus, Maria Assunta Zanetti, Eliano Pessa, and Maria Pietronilla Penna); and (21) Learning How to Write an Academic Text: The Effect of Instructional Method and Reflection on Text Quality. Reflection papers in these proceedings include: (1) Teachers' Attitude towards ICT Use in Secondary Schools: A Scale Development Study (Mehmet Kemal Aydin, Ali Semerci, and Mehmet Gürol); and (2) Inventing the Invented for STEM Understanding (Alicia Stansell, Tandra Tyler-Wood, and Christina Stansell). An author index is included. Individual papers contain references.

This paper reports on one phase of a long-term project investigating mathematical content knowledge of pre-service teachers. A cohort of second year PSTs conducted a diagnostic assessment and a series of associated tutoring sessions with a primary aged child. The focus here is on the PSTs' ability to make appropriate task choices following the diagnostic process. Results of the study suggest that PSTs are capable of making sound choices of tasks and associated resources based on their mathematical and pedagogical content knowledge following a targeted diagnostic assessment process.

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.]

With persistent concerns about student engagement, interest and participation in mathematics, this research investigated the range of practices 31 Year 7 mathematics teachers reported using and how they perceived these practices influenced student engagement in mathematics. In-depth interviews revealed similarities in teachers' perceptions of student engagement but differences in what teachers did to address engagement through their practices. This paper reports on teacher practices identified as promoting and hindering student engagement in mathematics.

Information and communication technologies (ICT) are positioned in policy/syllabus documents as an essential resource in the teaching of mathematics. Given their youth and lifelong experience with technology, early career teachers (ECTs) are expected to excel in their use of ICT; however, we are not clear on the viability of these expectations and the reality of their teaching practices. This paper draws on data from three separate studies to explore how ECTs use technology in their teaching. Although their use of Interactive Whiteboards did not pose challenges, use of iPads did, and the teachers' mathematical knowledge for teaching appeared to be directly related to how they used their technology.