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Place value is a foundational competency for primary school mathematics and for this reason we have sought to investigate what the recent and current academic conversations are around this important concept. In this paper we present a survey of literature presented in the Australasian, European and Southern African contexts through a review of purposively selected conference proceedings and journals to establish what the conversations have been about the teaching and learning of place value in these research communities from 2013 to 2022.

For the twenty-eighth year, the Research and Theory Division of the Association for Educational Communications and Technology (AECT) is sponsoring the publication of these Proceedings. Papers published in this volume were presented at the National AECT Convention in Orlando, Florida. The Proceedings of AECT's Convention are published in two volumes. Volume 2 contains over 100 papers dealing with instruction and training issues. (Individual papers contain references, figures, and tables.) [For Volume 1, see ED499958.]

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan Melbourne primary schools who completed the Place Value Assessment Tool (PVAT). Each student's place value knowledge was categorised according to the Place Value Developmental Progression (PVDP). The results highlight the wide range of understanding in each year level and challenge the efficacy of a number magnitude-based progression in place value.

In this paper we compare the early years mathematics curricula of Germany, South Africa, and Australia in relation to the place value concept. Place value is an important topic as it underpins much of the number work completed by learners in the early years of schooling. We found that there were differences between the three curricula that could be summarised using five themes: namely, number range, place value structure, role of the zero, influence of language, and use of materials. We argue that how the different curricula deal with these five themes influences the quality of learning provided and we highlight key areas of concern. In concluding we identify three important implications for our future research project.

This paper reports on students' experiences of describing and representing variation in hypothetical data. Fifty-six students (8-9 years-old) experienced collecting and working with quantitative data for two years as part of a STEM education project. The task described here was an end-of-year survey question, with three parts about a hypothetical context for surveying students in two different Australian cities: recording the data, describing the potential variation in the data, and creating a representation of what the data might look like when only a descriptive account of the context and variables were provided. The data analysis framework utilised provides a means of determining students' readiness for further development of statistical ideas.

This paper reports on 73 Grades 3 to 6 students' written responses to equal groups, arrays, multiplicative comparison and Cartesian product word problems. It is part of a larger study relating to students' development of multiplicative thinking (MT). The potential of using multiplicative word problems as a diagnostic assessment to reveal students' transition barriers from additive thinking to MT was explored. The development of the assessment and some of the research findings are described here. Findings show that students experience different types of barriers during their transition from additive to MT. Some recommendations are given on how these barriers might be overcome during primary school years.

This paper reports on early years teachers and how often they should devote planning time to anticipating student responses in advance of the lesson. Sixty-five Foundation to Year 2 teachers (students 5-8 years of age) completed questionnaires at the beginning and end of a year-long research-based professional development program. Participants were learning to teach with sequences of challenging tasks. Post-program data showed a shift in the frequency of time participants believed teachers should devote to anticipating student responses prior to teaching. Supporting teachers' mathematical knowledge for teaching with an emphasis on how they plan and anticipate student responses has implications for improving practice and student outcomes.

Providing opportunities for students to demonstrate their mathematical thinking can be challenging. This paper reports on a case study conducted with a teacher and her class of Grade 3/4 students which investigated this phenomenon. Following collection of baseline data that showed her students were not demonstrating evidence of mathematical thinking, the teacher implemented teaching approaches designed to address this. The findings indicated the teaching approaches were effective and led to changes in the teacher's practice and professional growth. The study has implications for teachers who are looking to make changes to their practice based on evidence-informed teaching approaches.

There is an educational expectation that children's natural drawing will develop into proficient mathematical representations and formal diagrams, yet there is little research available to guide the assessment and development of children's mathematical drawing skills. The aim of this paper is to explore how Year 2 children (approx. 7 years) chose to represent their interpretations of a simple story that is suggestive of the take-away subtraction process, and what changes occurred when the drawing task was repeated 6 months later. Analysis of 13 pairs of drawings revealed changes in what the children drew (categories of number representations) and how they drew it (style). The findings suggest that substantial change in children's representational ability can occur in within 6 months.

Teachers often perceive barriers to integrating technology with Mathematics. In the study, teachers participated in professional development about considerations for and examples of integrating Digital Technologies into Mathematics learning in primary schools meeting the "Australian Curriculum: Mathematics and Digital Technologies" requirements. This exploratory multiple case study included preand post-surveys, mentoring conversations and interviews to explore their beliefs and perceived barriers to integrating mathematics and digital technologies. This paper provides insights into their perceived barriers to integrating digital technologies.

School Mathematics Leaders seek to improve the mathematical learning outcomes of the students in their schools. Recognising that improved learning is dependent on high quality teaching, leaders are often keen to support teachers' knowledge of mathematics content and pedagogy. This paper reports ways in which School Mathematics Leaders support and lead the professional development of teachers in team meetings. Results from survey data and case study research are reported in this paper to describe and highlight the supportive actions undertaken by School Mathematics Leaders as they provide professional learning opportunities for teachers.

This paper examines the types of teacher questions that assist young students to interpret and explain their critical mathematical thinking (CMT). Focusing on students who enter their first year of formal schooling (aged 5-6 years), this paper draws on data from a one-on-one task based clinical interview conducted with 16 students. Teacher questioning data were analysed for question type (probing, factual, guiding) and further analysed against the conceptualized critical mathematical thinking framework for young students. Findings indicated that when teachers used clarifying, noting relationships, and offering opinions style probing questions, young students were supported to interpret and explain their critical mathematical thinking.

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.

Mathematics self-efficacy is considered an important variable in mathematics education because of its links to mathematics achievement. This paper reports on the development of the "Self-efficacy-effort in Mathematics Scale" (SEEMS), an instrument that has strong theoretical and psychometric properties. Based on a sample of n = 224 Australian primary students and n =133 secondary students, the instrument demonstrated positive correlations with related measures of mathematics achievement and mathematics self-concept. Girls had higher mathematics achievement within the primary and secondary school data. There were no significant gender difference in mathematic self-concept scores for the primary and the secondary school students. For mathematics self-efficacy, a gender difference was only identified in the high school data. The implications of this research to mathematics education practices are reviewed in the paper.

These proceedings contain the papers of the 11th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2014), October 25-27, 2014, which has been organized by the International Association for Development of the Information Society (IADIS) and endorsed by the Japanese Society for Information and Systems in Education (JSISE). The CELDA 2014 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-agents systems. These developments have created both opportunities and areas of serious concerns. This conference aimed to cover both technological as well as pedagogical issues related to these developments. The conference included the Keynote Lecture: "Designing Learning Environments in a Digital Age: The Quest for What to Consider," by Professor Jan Elen, Faculty of Psychology and Educational Sciences, K.U. Leuven, Belgium. The conference included a panel entitled: "Competencies, Challenges, and Changes: A Global Conversation About 21st Century Teachers and Leaders" by Lynne Schrum, Rose Dolan, Dirk Ifenthaler, Ronghuai Huang, Dale Niederhauser, and Neal Strudler. Papers in the proceedings include: (1) Interactive Application in Spanish Sign Language for a Public Transport Environment (José Guillermo Viera-Santana, Juan C. Hernández-Haddad, Dionisio Rodríguez-Esparragón, and Jesús Castillo-Ortiz); (2) A Game-Based Assessment of Students' Choices to Seek Feedback and to Revise (Maria Cutumisu, Doris B. Chin, and Daniel L. Schwartz); (3) Investigating Teachers' Readiness, Understanding and Workload in Implementing School Based Assessment (SBA) (Norsamsinar Samsudin, Premila A/P Rengasamy, Jessnor Elmy Mat Jizat, Hariyaty Ab Wahid, and Norasibah Abdul Jalil; (4) The Effects of Frequency of Media Utilization on Decision Making of Media Choice (Yasushi Gotoh); (5) Comparing Novices & Experts in Their Exploration of Data in Line Graphs (Bruce H. Tsuji and Gitte Lindgaard); (6) Assessment Intelligence in Small Group Learning (Wanli Xing and Yonghe Wu); (7) Collaborative Creativity Processes in a Wiki: A Study in Secondary Education (Manoli Pifarré, Laura Marti, and Alex Guijosa); (8) LSQuiz: A Collaborative Classroom Response System to Support Active Learning Through Ubiquitous Computing (Ricardo Caceffo and Rodolfo Azevedo); (9) Impacts of MediaWiki on Collaborative Writing Among Teacher Students (Said Hadjerrouit); (10) Teachers' Perceptions of the Individual Case Studies' Literacy Performance and Their Use of Computer Tools (Odette Bourjaili Radi); (11) Exploring Opportunities to Boost Adult Students' Graduation--The Reasons Behind the Delays and Drop-Outs of Graduation (Päivi Aarreniemi-Jokipelto and Asta Bäck; (12) Effective Use of a Learning Management System to Influence On-Line Learning (Xu Hongjiang, Sakthi Mahenthiran, and Kenton Smith); (13) Order Effects of Learning with Modeling and Simulation Software on Field-Dependent and Field-Independent Children's Cognitive Performance: An Interaction Effect (Charoula Angeli, Nicos Valanides, Eirini Polemitou, and Elena Fraggoulidou); (14) Comparative Case Study on Designing and Applying Flipped Classroom at Universities (Cheolil Lim, Sunyoung Kim, Jihyun Lee, Hyeonsu Kim, and Hyeongjong Han); (15) Organizational Leadership Process for University Education (Ricardo Llamosa-Villalba, Dario J. Delgado, Heidi P. Camacho, Ana M. Paéz, and Raúl F. Valdivieso); (16) Academic versus Non-Academic Emerging Adult College Student Technology Use (Joan Ann Swanson and Erica Walker); (17) Creative Stories: A Storytelling Game Fostering Creativity (Antonis Koukourikos, Pythagoras Karampiperis, and George Panagopoulos); (18) An EVS Clicker Based Hybrid Assessment to Engage Students with Marking Criteria (Steve Bennett, Trevor Barker, and Mariana Lilley); (19) ICT Competence-Based Learning Object Recommendations for Teachers (Stylianos Sergis, Panagiotis Zervas, and Demetrios G. Sampson); (20) Improving Content Area Reading Comprehension with 4-6th Grade Spanish ELLs Using Web-Based Structure Strategy Instruction (Kausalai [Kay] Wijekumar, Bonnie J.F. Meyer, and Puiwa Lei); (21) Preparing Special Education Teachers to Use Educational Technology to Enhance Student Learning (Teresa Wallace and David Georgina); (22) ASK4Labs: A Web-Based Repository for Supporting Learning Design Driven Remote and Virtual Labs Recommendations (Panagiotis Zervas, Stefanos Fiskilis, and Demetrios G. Sampson); (23) Digital Storytelling: Emotions in Higher Education (Sandra Ribeiro, António Moreira, and Cristina Pinto da Silva); (24) Design in Practice: Scenarios for Improving Management Education (Lee Schlenker and Sébastien Chantelot); (25) Factors Influencing Students' Choice of Study Mode: An Australian Case Study (Dirk Ifenthaler, Maree Gosper, Matthew Bailey, and Mandy Kretzschmar); (26) Addressing Standardized Testing Through a Novel Assessment Model (Catherine C. Schifter and Martha Carey); (27) "It's Just Like Learning, Only Fun"--A Teacher's Perspective of Empirically Validating Effectiveness of a Math App (Ka Rene Grimes); (28) A User Centered Faculty Scheduled Development Framework (Shohreh Hadian and Nancy Sly); (29) Musical Peddy-Paper: A Collaborative Learning Activity Supported by Augmented Reality (José Duarte Cardoso Gomes, Mauro Jorge Guerreiro Figueiredo, Lúcia da Graça Cruz Domingues Amante, and Cristina Maria Cardoso Gomes); (30) Undergraduate Students' Experiences of Time in a MOOC: A Term of Dino 101 (Catherine Adams and Yin Yin); (31) The Answering Process for Multiple-Choice Questions in Collaborative Learning: A Mathematical Learning Model Analysis (Yasuyuki Nakamura, Shinnosuke Nishi, Yuta Muramatsu, Koichi Yasutake, Osamu Yamakawa, and Takahiro Tagawa); (32) Using Five Stage Model to Design of Collaborative Learning Environments in Second Life (Sevil Orhan and M. Kemal Karaman); (33) Students' Reflections Using Visualized Learning Outcomes and E-Portfolios (Takatsune Narumi and Yasushi Gotoh); (34) The Efficiency of Different Online Learning Media--An Empirical Study (Franziska J. Kößler and Marco M. Nitzschner); (35) Microblogging Best Practices (Shohreh Hadian and Maria-Elena Froese); (36) DIY Analytics for Postsecondary Students (Timothy Arndt and Angela Guercio); (37) Project "Flappy Crab": An Edu-Game for Music Learning (Cristina Maria Cardoso Gomes, Mauro Jorge Guerreiro Figueiredo, José Bidarra, and José Duarte Cardoso Gomes); (38) Higher Education Institutions (HEI) Students Take on MOOC: Case of Malaysia (Jessnor Elmy Mat-jizat, Norsamsinar Samsudin, and Rusliza Yahaya); (39) A Cross Cultural Perspective on Information Communication Technologies Learning Survey (Hale Ilgaz, Sacide Güzin Mazman, and Arif Altun); (40) An App for the Cathedral in Freiberg--An Interdisciplinary Project Seminar (Cindy Kröber and Sander Münster); (41) Possible Science Selves: Informal Learning and the Career Interest Development Process (Leila A. Mills); (42) A Case Study of MOOCs Design and Administration at Seoul National University (Cheolil Lim, Sunyoung Kim, Mihwa Kim, Songlee Han, and Seungil Seo); (43) Persistent Possible Science Selves (Leila A. Mills and Lin Lin); and (44) Towards a Collaborative Intelligent Tutoring System Classification Scheme (Rachel Harsley). Individual papers contain references. An author index is included.

Mathematical self-concept refers to the perceived ability that one has in being able to do mathematics. While it has been shown to be a significant predictor for how students learn and apply mathematics, little research has been conducted into the relationship between the mathematical self-concept of teachers and their pedagogical practices in the mathematics classroom. This paper reports on a section of the findings from a small mixed methods study that sought to ascertain the nature of primary teachers' mathematical self-concept and how it is related to their teaching practices. Findings suggest that a teachers' mathematical self-concept does not necessarily reflect the mathematics practices evident in their classroom.

The description "primary mathematics specialist" has become more frequently used in Australia in the past 10 years, suggesting sustained interest in deepening teacher expertise. Despite this, there is limited contextual research about how to prepare in-service teachers for such roles, and the organising structures needed to facilitate their progress. This paper describes background and emerging insights from a project offering sustained and supported learning experiences for in-service teachers to become primary mathematics specialist teachers in and across their school. Curriculum and contextual experiences designed around a theoretical framework of leadership development implemented over 2 years are described. Early insights include the "priming" influence of an extended focus on mathematical content and pedagogical knowledge on participants' confidence to lead others, and the benefits of being explicit about enabling structures that promote sustainable growth and change.

Primary mathematics leadership has become a focus for improving the teaching of mathematics within Australian primary schools. Much of the training and support for those in the role have concentrated on content knowledge, rather than leadership training. There are currently no guidelines or standards in place to support the complex and multi-faceted roles and responsibilities of primary mathematics leaders. This paper reports on the initial stage of a research project examining how primary mathematics leadership is conceptualised and experienced. It reports on survey findings regarding teachers and leaders' understanding of primary mathematics leadership.

All teachers of mathematics aim to provide productive learning experiences that cater for students in their care. The planning of effective and engaging mathematics lessons is complex and requires expertise. In a larger study survey data, observations and interviews were used to investigate the ways in which School Mathematics Leaders supported teachers to learn. This paper reports results from case study research and focuses on the actions of one School Mathematics Leader during planning meetings. Findings highlight a range of supportive actions, which included developing constructive working relationships with teachers, fostering knowledge of mathematical content and curriculum and facilitating collaborative team planning.

This paper outlines the rationale for, and some elements of, a particular approach to teaching and learning mathematics in the early years. The researchers worked with two school systems to offer both centrally delivered and school-based teacher professional learning, which included the application of illustrative teaching resources. The project gathered a range of data from teachers and leaders on their dispositions and knowledge, as well as the opportunities and constraints they experienced, and the influence these variables had on planning, teaching and student learning outcomes.

While interdisciplinary approaches in the STEM subjects are widely advocated there are concerns that disciplinary learning can be compromised, especially in mathematics. The Interdisciplinary Mathematics and Science (IMS) project is a three-year longitudinal study in four Victorian primary schools that has developed a pedagogical approach to mathematics and science learning where data modelling and representation are common to each. Investigations include astronomy, ecology, chemistry, fast plant growth, force and motion, water use, heat and temperature, body height, light and microorganisms. The paper describes the role of mathematics in the IMS pedagogical model and design of learning sequences.

The intangible concept of data, as part of statistical literacy, can be complex for young children to grasp. Inquiry as a pedagogy has potential for supporting student development of statistical literacy as the investigation process is driven by the inquiry question. The aim of this paper is to gain insight into how a teacher's communication processes with her students supported their emerging understandings about the abstract concept of data. In this exploratory case study, we present data from a Year 4 classroom (age 9) in a guided mathematical inquiry within the STEM context of agricultural science. The inquiry question the students addressed was, "How big is a leaf?" The inquiry focused on linking data to the real-life context the data represented.

In this paper we report on an aspect of a larger study and explore whether a framework for teacher STEM Capability Sets (SCS) enhanced teacher planning and the implementation of mathematics active STEM tasks. A case study approach was employed to understand how a classroom teacher used the digital resource, Gapminder, to teach a Year 5/6 cohort of students to interpret data as the basis for a STEM assessment. The research found that using the SCS as a guide, and emphasising mathematics in STEM learning and assessment, allowed the teacher to: reflect on existing STEM capabilities; observe the enhancement of other capabilities; and identify areas for future development.

The transition between arithmetic and algebraic thinking is challenging for students. One notable difficulty for students is understanding algebraic symbols--pronumerals. Researchers are exploring pedagogical approaches in seeking to address this issue. The current paper is contributing to this body of literature by illustrating how an online card matching game-based learning activity supports students' understanding of pronumerals.

This qualitative study investigates remote Australian primary school parents' attitudes towards their children's learning of mathematics and the role of technology. Using semi-structured interviews and thematic analysis, results revealed that parents aimed to provide the best mathematics learning opportunities for their children, yet they felt obsolete and isolated from their children's learning. Additionally, they valued the role of technology, but did not think school was providing adequate digital literacy skills. Discussion about what changes to the educational community are suggested to support parents in their children's learning.

Informed by teaching statistics across curriculum areas strategies, this study investigated the skills of 36 pre-service teachers (PSTs) who designed numeracy activities that focused on the statistics strand of the Australian curriculum. The data were analysed using descriptive statistics. The results showed that the PSTs designed numeracy activities focused on the science curriculum area. The results further showed that PSTs emphasised a few year levels and focused on collecting and recording data. The first stage of teaching statistics (designing effective questions) is often ignored in their activities. The approach adopted in this study can be used to identify PSTs' knowledge gaps and their professional learning requirements.

It is generally understood that both clear teacher instruction and orderly classroom climates support student achievement in mathematics. However, to what extent does instructional clarity "compensate" for classroom disorder? In this exploratory study, we analyse data from 8,864 Year 8 students sampled by TIMSS 2019 to investigate the relationship between instructional clarity, classroom disorder, and mathematics achievement. The findings demonstrate the deleterious effects of classroom disorder for mathematics achievement, even in the presence of high instructional clarity. The findings contribute to an emerging international body of work and reinforce the importance of teachers having an optimal combination of classroom skills to support student learning.

We explored primary pre-service teachers' beliefs about challenging mathematical tasks and the role they perceived their initial teacher education played in influencing those aspects. Fifty-seven pre-service teachers completed an online questionnaire, and four participants were individually interviewed. Results showed that most participants recognised the importance of teaching with challenging mathematical tasks even prior to exposure to such content in their teacher education program. The teacher education program was perceived to have positively impacted final year pre-service teachers' perspectives about challenging tasks. Implications for teacher education regarding challenging tasks are discussed.

Typically, more primary students qualify for mathematics intervention support than schools have the capacity to assist. This highlights the importance of every primary mathematics teacher having the expertise to design inclusive and responsive curricula and instruction for students who may experience difficulty. Our study addresses this issue through exploring how specialist intervention teachers can support the mathematics professional learning of teachers using co-teaching cycles. The findings provide insight about the challenges experienced by classroom teachers when teaching students who experience difficulty with mathematics, and the actions of the specialist intervention teachers that assisted the teachers' professional growth.

Despite curriculum expectations, many students, including a disproportionate number of girls, do not 'just know' (retrieve) single-digit addition facts by Year 3. The current study employed structured interviews to explore which strategies Year 3/4 students (n = 166) used when solving more difficult addition combinations. Results revealed that students preference the near-doubles strategy when the difference between the addends was one, the bridging-through-10 strategy when one of the addends was a nine, and the count-on-from-larger strategy when a derived strategy was more effortful. Moreover, whereas boys were more inclined to use derived strategies, girls were almost three times more likely to use the count-on-from-larger strategy.

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

The current study explored the reasons for students' preferences for the teach-first and task-first lesson structures, and whether students' preferences were influenced by their perceptions of the teacher's preference. Students (n=18) from two composite Year 3 and 4 classes (aged 8-10 years) completed a post-lesson drawing task and participated in a semi-structured interview following a series of lessons. Findings indicated students had a variety of reasons for their preference of lesson structure. Most focus students reported noticing aspects of the teacher's enjoyment during instruction. The results have implications for the way teachers inadvertently influence their students' own enjoyment of and preferences for instructional approaches.