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In order to discuss the role of mathematics education in developing students' STEM Capabilities and 21st Century skills, it is necessary to define what is meant by these terms given the extent to which they are broadly used in global contexts. A literature review aimed at providing clarity, through affording a concise interpretation of each term for the Australian context, enabled the development of a working framework for defining 21st Century skills and STEM capabilities. This paper provides working definitions and reports on initial findings from a larger three-phase study aimed at exploring secondary mathematics teachers' beliefs, attitudes and practices, towards the role mathematics education plays in developing students' STEM capabilities and 21st Century skills.

This paper reports on teachers' perceptions of students learning as part of a project examining teacher practice and student learning when using "ScratchMaths" in their classroom programmes. The project used design-based methodology, incorporating video-recorded classroom excerpts; teacher interviews; and teacher analysis and review of their practice. The teachers identified the students' problem solving, using unplugged activities, and collaborating using explicit mathematical and coding language as ways to facilitate mathematical thinking. They also recognised that their practice became more faciliatory, with their understanding of coding developing through learning with their students.

In this paper, we report on the pedagogical actions of one teacher in eliciting and developing students' mathematical reasoning during one mathematics lesson. The findings illustrate that through the careful design and planning of a contextually relevant task (the construction of a manu tukutuku), and the implementation of specific teacher actions, a group of marginalised students were provided access to exploring the concept of equivalence.

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.

As imperceptible as it is, mathematics is fundamental and is present on several occasions in our daily lives, but among 65 countries Brazil still ranks 53rd in education. The lack of investment in primary education has affected students learning since the early years. From this perspective, this paper proposed to verify teaching/learning in mathematics discipline for elementary school students through playful games, a fun method that can be used at various times and aims to review and fix the content in a practical way and interactive. For this, a game named "Mathematical rods" was elaborated a renewal of the hobby "Cat rods". The operations present in the game are simple, focused on basic mathematics and can still be adapted depending on the level of knowledge of the students. The game was applied to three groups of six 9th grade students of the State College Professor Izidoro Luiz Ceravolo, located in the city of Apucarana, Paraná in Brazil. Therefore, in addition to dynamic and creative, we conclude that this educational interpretation is easy and accessible, a tool that can be used in any public institution, contributing to the learning process of students. [For the complete proceedings, see ED631021.]

It is expected that students who learn Indonesian will be able to communicate both orally and in writing. However, students continue to face numerous difficulties when confronted with Indonesian conversation, such as feeling uncomfortable, stammering, or simply remaining silent when they are asked about their opinions. As such, this study will consolidate the findings of past studies on the topic of increasing speaking skills, particularly for elementary school students, using a literature review technique. This study collects data from Google Scholars and papers published in 2020-2021 which are filtered using the keyword "speaking skills for elementary school students." The study's findings suggest the need for role models and learning material that are age-appropriate for elementary school students. The range of enjoyable learning models, distinctive learning media, and even the combination of various models and media can serve as references for teachers aiming for establishing a meaningful learning environment, particularly for elementary school students looking to enhance their speaking skills. [For the full proceedings, see ED630948.]

Many studies use instructional designs that include two or more artifacts (digital manipulatives, tables, graphs) to support students' development of reasoning about covarying quantities. While students' forms of covariational reasoning and the designs are often the focus of these studies, the way students' interactions and transitions between artifacts shape their actions and thinking is often neglected. By examining the transitions that students make between artifacts as they construct and reorganize their reasoning, our study aimed to justify claims made by various studies about the nature of the synergy of artifacts. In this paper, we present data from a design experiment with a pair of sixth-grade students to discuss how their transitions between artifacts provided a constructive space for them to reason about covarying quantities in graphs. [For the complete proceedings, see ED630210.]

This paper describes how fifth-grade English Learner students (ELs) in an urban school district develop the mathematics register during a problem-solving lesson. It provides examples of students' work to illustrate how they use the mathematics register to communicate their mathematical ideas orally and in writing. The teacher implemented teaching practices such as mathematics discourse to facilitate their students' development of the mathematics register during the problem-solving lesson. Students were engaged in a problem-solving task that involved fractions. Findings provide insights into EL students' challenges when learning the mathematics register and inform instruction about the importance of incorporating teaching practices such as paraphrasing and assessing others' reasoning to support students in learning the mathematics register through problem-solving. [For the complete proceedings, see ED630210.]

This study examined the role of student generated drawings to offload cognitive demands of a mathematical problem. We used Unit Transformation Graphs to compare students' thought processes when they had to solve the problem mentally, and when they were allowed to use pen and paper. The results indicated that the possibility to rely on drawings helped the participants to free up working memory resources and complete a cognitively demanding fractional task. [For the complete proceedings, see ED630210.]

The frequentist and classical models of probability provide students with different lenses through which they can view probability. Prior research showed that students may bridge these two lenses through instructional designs that begin with a clear connection between the two, such as coin tossing. Considering that this connection is not always clear in our life experiences, we aimed to examine how an instructional design that begins with a scientific scenario that does not naturally connect to theoretical probability, such as the weather, may support students' bridging of these two models. In this paper, we present data from a design experiment in a sixth-grade classroom to discuss how students' shifts of reasoning as they engaged with such a design supported their construction of bridges between the two probability models. [For the complete proceedings, see ED630210.]

This paper examines the possibilities of designing a formative assessment that gathers information about novice elementary teachers' skills with modeling content and makes sense of such information. A decomposition of the practice of modeling content was developed and used to design the assessment. Participants included ten first-year teachers who graduated from a range of different teacher education programs. The findings reveal that our formative assessment works to gather information about teachers' capabilities with modeling content and that the associated tools support making sense of the information gathered. [For the complete proceedings, see ED630210.]

In this proposal, we share research that explores the potential benefits of a novel Making experience within mathematics teacher preparation that we hypothesized would inform the pedagogical and curricular thinking of prospective teachers of elementary mathematics (PMTs). That experience had PMTs exploring at the intersection of content, pedagogy, and design to digitally design, 3D print, and share an original manipulative with a child to promote their mathematical thinking. We share several vignettes of our research that aim to discern some of the potential benefits the experience might offer PMTs. These take a variety of theoretical and methodological approaches at the intersections of teacher knowledge, identity, pedagogy, and design. Implications of our findings for teacher preparation and professional learning are provided throughout the paper and in its conclusion. [For the complete proceedings, see ED630210.]

Remaining continually curious about students' mathematical thinking is challenging, yet worthwhile, in teaching practice. This paper describes and analyzes two video-based professional learning (PL) activities designed to help teachers go beyond their initial perceptions of what students understand and to identify what else they might learn about students' thinking. The findings suggest the potential of the activities to evoke different types of curiosity about student-thinking and the conditions that may support such questioning. [For the complete proceedings, see ED630210.]

Learning Trajectories have the potential to be used as a tool to advance equity by explicitly connecting to anti-deficit framing and asset-based instruction. This plenary paper highlights research on three use cases for learning trajectories (LT) with an intentionality around promoting equity: 1) the use of LT based Lesson Study with vertical teams of teachers to position students as capable and teachers as knowledgeable, 2) the use of LT coupled with anti-deficit framing in curriculum design research to provide students with access to rigorous educational resources and asset based instruction, 3) the use of LT with formative assessment to develop preservice teachers' equitable teaching practices to advance students understanding. The presenter invites the PMENA community to consider how learning trajectories can be coupled with powerful equity-focused research and frameworks to disrupt the status quo, broaden the notion of learning mathematics, eliminate labeling, and dismantle inequitable structures and hierarchy in the mathematics classroom. [For the complete proceedings, see ED630210.]

This paper frames children's mathematics as mathematics. Specifically, it draws upon our knowledge of children's mathematics and applies it to understanding the prime number theorem. Elementary school arithmetic emphasizes two principal operations: addition and multiplication. Through their units coordination activity, children construct two mathematical worlds: an additive world and a multiplicative world. Understanding how children might map between their additive and multiplicative worlds provides insights into the prime number theorem. It also helps us appreciate the power of children's mathematics, constructed through the coordination of their own mental actions. [For the complete proceedings, see ED630210.]

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and provide examples of how this approach can help challenge a settled mathematics learning status quo about the kind of algebra students can learn, when they can learn it, and how all students can be successful. Empirically derived learning progressions are an important part of designing early algebra innovations that can open new curricular pathways for teaching and learning algebra, creating accessible and effective avenues of learning for all students. [For the complete proceedings, see ED630210.]

The development and use of learning trajectories is a body of research that has made enormous contributions to the field of mathematics education, offering insight into the teaching and learning of topics at all levels. Simultaneously, the work of building learning trajectories can benefit from explicitly adopting an anti-deficit stance, incorporating ways to center student voices from an asset-based perspective. In this paper I propose two related constructs to support this work: decentering and second-order models. In decentering, researchers work to set aside their own knowledge to understand students' reasoning as viable. This can support models of student mathematics that position student thinking as rational, powerful, and productive. I provide one example of the work of decentering and discuss ways to build learning trajectories that emphasize students' strengths and competencies. [For the complete proceedings, see ED630210.]

This theoretical paper describes how Community-based Mathematical Modeling can advance equity and cultivate civic empathy in elementary school settings. We provide a framework for community-based mathematical modeling instruction consisting of five goals: facilitating connections, fostering engagement, promoting rigor, cultivating civic empathy, and elevating justice. We illustrate how these goals work together to advance equity and cultivate civic empathy through classroom vignettes of community-based modeling lessons. Through this theoretical synthesis, implications for community-based mathematical modeling instruction will be discussed. [For the complete proceedings, see ED630210.]

The 360 Degree Global Education Model (360 Global Ed Model) provides a comprehensive framework for creating meaningful interdisciplinary student team learning through international service learning. Providing successful multi-disciplined undergraduate education necessitates creating a foundation for productive team-science based learning between disciplines. The pedagogical foundation employed by Breitkreuz and Songer within the 360 Global Ed model creates a shared values student dialogue for enhancing undergraduate team learning and performance. This paper provides a summary of the 360 Global Ed Model, a discussion of methods used to create a student shared dialogue ("Team Learning Foundation"), lessons learned, and student outcomes. Methods for shared dialogues include creating a team-defined mission, team-defined behavioral standards, building shared cultural understandings and expectations for developing cultural intelligence, and developing realistic expectations for interpersonal understandings through use of self-assessments. Student team-led projects provide an authentic context impetus for implementing the team learning foundation. [For the full proceedings, see ED631133.]

The integration of Syrian children into the Turkish national educational system has been an important issue in the field of Turkish educational policy since 2011 when the Syrian crisis caused millions of people to seek asylum in Turkey. After Temporary Education Centers (TECs) in refugee camps were phased out due to the changing inclusive education policies, Promoting Integration of Syrian Children into the Turkish Education System project (PIKTES) was introduced by the Ministry of National Education (MoNE) in 2016 in 26 cities across the country mainly to alleviate the linguistic challenges of Syrian refugees and facilitate their social integration into the society. The present qualitative type of study aims to describe and analyze the inclusive education practices for Syrian students at primary state schools. Data collected from five experienced Turkish teachers of integration classrooms via semi-structured interviews. The reflexive thematic analysis revealed three main themes as systemic shortcomings, Syrian families' indifference, and insufficient professional support for the teachers. The themes present the challenges of inclusive education in Turkey from the initial stages in TECs to the recent practices within the scope of the PIKTES project. Findings shed light on how to redesign inclusive education for refugees in the Turkish context. [This paper was published in:"EJERCongress 2022 Conference Proceedings," Ani Publishing, 2022, pp. 372-385.]

THS is applied to Science High Schools, Social Sciences High Schools, Anatolian Technical Programs of Vocational and Technical Anatolian High Schools and Project schools for student selection. With THS, approximately 10 percent of more than one million students are placed in a secondary education institution based on their preferences. The purpose of this study was to examine the relationship between the success of the THS Science test of the students who have just graduated from middle school and who took the THS exam and their middle school science course scores, gender, and socio-economic level. In this ex post facto research, a total of 101 students were involved in the sample. Majority of the students were male (n=54, 53.5%). Pearson correlation analysis revealed that THS science score of participants were significantly and positively correlated with their 6th, 7th, and 8th grade science scores. The results of independent samples t-test demonstrated that there was no significant difference in THS science scores for male and female participants. Finally, the results of one-way ANOVA indicated that there were significant differences in THS science scores by participants' socio-economic levels. Accordingly, students with high socio-economic level had higher scores from THS science test than students with moderate and low socio-economic levels. Based on this particular finding, policy makers are recommended to reconsider their efforts to provide equality of opportunity in education. [This paper was published in: "EJERCongress 2022 Conference Proceedings," Ani Publishing, 2022, pp. 225-231.]

This study aims to investigate the views of primary school principals regarding pre-school education. The study was carried out with ten primary school principals in the city of Zonguldak during the 2021-2022 academic year. The case study method, one of the qualitative research types, was used in the research. Based on the purpose of the research, the semi-structured interview technique was used to collect the data. A personal information form and an interview form prepared by the researchers were used to collect data in the study. In the research, it used the content analysis technique for the data obtained as a result of the semi-structured interviews. When the findings are examined, it shows that the primary school principals involved had positive perceptions regarding pre-school education. The primary school principals stated that pre-school education supports a child's psychomotor, linguistic, and cognitive development, and facilitates the preparation of children for primary school and their adaptation to school. Having a qualified pre-school educational institution in suitable conditions for children with interior and exterior space, it was stated that physical conditions and equipment should be planned in such a way that children can move freely. Some say that pre-school teachers should love their profession, be tolerant, give importance to their professional development, establish good relations with children and be role models to make pre-school education qualified. It was stated that the school principals had budget problems in pre-school education. They said that they sought support from the school-parent union and collected dues to solve these problems. Preparing physically suitable environments to carry out pre-school education more effectively, they expressed their suggestions to have auxiliary personnel, not to provide uninterrupted training, and to allocate the budget. [This paper was published in: "EJERCongress 2022 Conference Proceedings," Ani Publishing, 2022, pp. 152-165.]

Bullying, which is a global public health problem, has serious effects on children and adolescents. If peer-bullying behaviors among primary-school children with various effects ranging from low academic achievement, anxiety and depression to suicide and substance abuse are not detected and intervened in a timely manner, they have the risk of continuing to increase in frequency. School climate is one of the most important factors in the emergence and elimination of bullying behaviors. Therefore, it is important to examine the frequency and types of bullying behaviors among primary-school children and the views of children about school climate, to reveal the in-school factors affecting peer-bullying and to create effective intervention programs. In this study, it was aimed to determine the frequency and type of bullying behaviors experienced at primary-school level in Çankiri Province and to examine students' opinions about school climate. The sample of the research consists of 590 primary-school students selected through cluster sampling from Çankiri Province. The data of the study were collected using the Colorado School Climate Survey. Descriptive analyzes were done on the data with the help of SPSS program. The research showed that physical and relational bullying is the most common type of bullying among primary-school students, and in case of bullying, the victims most often get help from their family or an adult at school. [This paper was published in: "EJERCongress 2022 Conference Proceedings," Ani Publishing, 2022, pp. 264-279.]

Learning analytics includes interventions that will support learning and improve learning environments. Despite the fact that learning analytics is a promising field of study, the lack of empirical evidence on the effects of learning analytics-based interventions has been widely addressed in recent years. In this context, insights validated by experimental studies may play a crucial role. Therefore, there is a need for a report describing the methodological aspects and effects of current experimental interventions based on learning analytics. This systematic review provides an in-depth examination of learning analytics research that reports experimental findings to evaluate learning analytics-based interventions. The PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) 2020 protocol provided the basis for the work of this systematic review. This review contained 52 papers that met the inclusion and exclusion criteria. The results show that student-facing dashboards are the most common learning analytics-based intervention. Evidence from how user data is handled for interventions demonstrates that the most common method is the distillation of data for human judgment. This study confirms that a significant proportion of experimental studies employing learning analytics interventions have demonstrated significant effects on learning outcomes. The effectiveness of learning analytics-based interventions is also addressed in this review in terms of motivation, engagement, and system usage behaviors. The findings of this study will contribute to the literature in terms of describing the experimentally validated findings of learning analytics-based interventions in depth.

This study aims to explore an educational learning environment that supports students to learn conceptual modelling with the unified modelling language (UML). In this study, we call the describing models "UML programming." In this paper, we show an educational UML programming environment for science, technology, engineering, art, and mathematics (STEAM) related subjects (especially for Technology or Engineering) in schools, which are able to apply from elementary school to university. At first, we explain why, what, and how doing the UML programming. In this study, we use a state machine diagram for UML programming. To draw this model, the students just put some states in rectangular shape and transitions in arrow shape. Two types of educational model notations in state machine diagram are introduced. Then, some advanced functions of the SRPS are described. They are an educational model editor, and management of users, learning tasks and models submitted by students. Next, two case studies with the SRPS are shown. One case study is adopted to the summer camp for 5th- and 6th-grade students. The participants were 20 students and were engaged in 4 hours workshop. We used a car-type robot with two DC motors, a one-touch sensor, and one infrared sensor connected to a micro:bit. The other case study is a formal technology class at one Japanese public junior high school. One teacher and five classes worked on UML programming for traffic lights. Each class had 20 9th-grade students. One student at this school was given a traffic light robot with three Light-emitting diode (LED) lights, a one-touch sensor, and one infrared sensor connected to a micro:bit. Finally, on the basis of these two case studies using our environment, we discuss the potential for innovative STEAM education with UML programming.

This paper presents a summary of Dr. Clinton Lee (Andy) Anderson's 40+ years Military (US Army) Educator Service implementing Dr. Malcolm S. Knowles' perspective on andragogy. Some specifics of Anderson's implementation include five Adult Basic Education (ABE) characteristics of facilitating Knowles' andragogy, six differences between teaching and facilitating adult learning and teaching children, fourteen self-actualization of andragogical, self-directed learning initiatives implemented in US Army education, ten general characteristics of adult learning in andragogy, and fifteen directions of growth in ABE learners' maturation. [For full proceedings, see ED628982.]

Classroom instruction in China and in the United States have sharp differences. Typically, constructivist learning theory shapes American classroom instruction whereas Confucian educational culture shapes Chinese classroom instruction. Furthermore, typically, Chinese classrooms adopt a direct instructional approach whereas American classrooms adopt an indirect instructional approach. Awareness of such differences in classroom instruction informs educators of the educational backgrounds of students coming from different educational environments and cultures, enabling educators to better serve different student populations. Additionally, it is worth noting that educational culture worldwide is converging as indicated by world culture theory. This paper presents different classroom instruction in China and the U.S., and inspires educators to learn from the differences, reflect on their own instruction, and eventually innovate and improve their instruction. [For the full proceedings, see ED628982.]

Providing high-level support to students on NGSS inquiry practices can be challenging; however, teacher dashboards can help teachers provide just-in-time instruction to students, both in-person and online. Prior work has shown some success with a dashboard that alerts teachers in real time on students' science inquiry difficulties, but teachers differed in their use of the alerts. To further support teachers, we designed a second iteration, in which the alerts included actionable, evidence-based Teacher Inquiry Practice Supports (TIPS), a series of suggested scaffolds that teachers can use to support students on the practices with which they are struggling. In this study, we investigate how the discursive support patterns from one teacher differed when using the dashboard alerts "without" TIPS followed by "with" TIPS. Findings suggest that TIPS influenced how the teacher incorporated different types of support for her students, and further, that the support given varied across different virtual lab stages. [This paper was published in: "ICLS2022 Proceedings," International Society of the Learning Sciences, 2022, pp. 297-304.]

Historically, learning for young students has occurred in formal, in-person classroom environments, but the distance learning context has opened a myriad of learning modalities. To this end, we aim to better understand how deploying learning experience design (LXD) approach supports or hinders children's engagement while participating in an online, video based math course. This study operationalized LXD through the integration of evidence-based pedagogical instructional design and human-centered user experience (UX) design. Findings suggest that students' situational interest and mind-wandering significantly mediate the relationship between user experiences and online engagement. These results provide practical implications for how researchers, designers, and instructors can intentionally iterate the learning experience to reduce mind-wandering and sustain children's online engagement with learning theories as we consider the future of online teaching and learning modalities. [This paper was published in: "ICLS2022 Proceedings," International Society of the Learning Sciences (ICLS), 2022, pp. 472-479.]

This paper describes a work in progress to design and evaluate an e-learning intervention that utilizes the Internet of Things (IoT) to increase awareness of the dangers of ultraviolet (UV) radiation exposure and promote sun protection practices early in life. The authors' previous work in a pre-test post-test control group study (Study 1) involved children in using IoT devices to collect and analyze real-time UV radiation data. Preliminary data were promising in this small-scale study, but the latter did not use a validated instrument to measure children's UV knowledge, attitudes, and behaviors. This second study has a dual aim. First, it reports on the results of a systematic literature review that aimed to identify validated questionnaires that a) measure attitudes toward UV light protection, b) are appropriate for primary school, and c) are suitable for evaluating e-learning prevention interventions if they are used as a pre-test and post-test. Second, it describes how the intervention of Study 1 will be re-enacted through an e-learning platform that allows for deepening student understanding and engagement through gamification and allows for visualizing students' understanding in real-time. [For the full proceedings, see ED639633.]

The COVID-19 has impacted education all over the world, especially many African countries where the experience of the pandemic has been distressing. While the need for distance learning was clear from the outset of the pandemic, achieving effective reach to learners was more complex, multifaceted and challenging task, facing to many issues: Closing equity and adapting and using technologies for hybrid learning that engages pupils. Early childhood and primary level students are seen to be most likely to be disadvantaged by the crisis and least likely to be able to access the technologies required for learning. These problems faced governments worldwide but has been particularly severe in most African countries where there is a wide disparity in technology use and access for the 'elite and for less advantaged pupils mostly in rural areas. his paper describes the first stage of a study that aims to characterize the ubiquitous learning scenario for marginalized regions and challenges brought by the COVID-19 pandemic to the Tunisian primary education context. This scenario aims to enhance learners to embrace change, learn, and keep attached to the learning process by interactive SMS based game. This scenario has been tested on the second level of science education in six Tunisian elementary schools in a rural region. A preliminary analysis showed that the proposed learning activities motivate Tunisian pupils who become more closer to learning than before. The experience should be generalized in the other Tunisian regions and classrooms. [For the full proceedings, see ED638044.]

Mexico is a country where seismic events occur in a daily basis. Since 1990, the national seismological service has reported various earthquakes, in some cases they usually imperceptible, it doesn't ensure that the population cannot be injured, there for, it is important to keep the entire population informed and prepared in the event of an earthquake. This project will present a proposal for a serious videogame with the intention of bringing the young public, between nine and twelve years old, closer to earthquake prevention in a playful way through a narrative based on children studies and official civil protection guidelines. This videogame is developed with de Godot game engine platform, using as the main source of information the research project developed by the students of the master's degree in Information Design and Communication about strategies focused on children to promote informed behavior for safety in the case of seismic related situations (Gros, 2009). The videogame poses scenarios of elementary school, where a series of challenges are presented to the gamer as simulating real situations with the intention that the player learn how to avoid getting hurt and manage to reach to meeting point safely. This paper shows the related work in the domain of games focused to promote the information about safety during earthquakes, the design and the advances in the development the proposal. [For the full proceedings, see ED638044.]

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.)

This document is the fourth 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 42 research reports by presenters with last names beginning between Mul and Wu: (1) Case Studies of Children's Development of Structure in Early Mathematics: A Two-Year Longitudinal Study (Joanne Mulligan, Michael Mitchelmore, and Anne Prescott); (2) A Case Study of How Kinesthetic Experiences Can Participate in and Transfer to Work with Equations (Ricardo Nemirovsky and Chris Rasmussen); (3) The Construction of Proportional Reasoning (Stephen Norton); (4) The Transition of a Secondary Mathematics Teacher: From a Reform Listener into a Believer (Jo Clay Olson and Karmen Kirtley); (5) Substantive Communication of Space Mathematics in Upper Primary School (Kay Owens); (6) Transforming Korean Elementary Mathematics Classrooms to Student-Centered Instruction (JeongSuk Pang); (7) The Effect of Improved Automaticity and Retrieval of Basic Number Skills on Persistently Low-Achieving Students (John Pegg, Lorraine Graham, and Anne Bellert); (8) Degrees of Freedom in Modeling: Taking Certainty out of Proportion (Irit Peled and Ronit Bassan-Cincinatus); (9) "I Know That You Don't Have to Work Hard": Mathematics Learning in the First Year of Primary School (Bob Perry and Sue Dockett); (10) Disentangling Mentors' Role in the Development of Prospective Teachers' Efficacy Beliefs in Teaching Mathematics (George Philippou and Charalambos Y. Charalambous); (11) Linear Functions and a Triple Influence of Teaching on the Development of Students' Algebraic Expectation (Robyn Pierce); (12) Engaging the Learner's Voice? Catechetics and Oral Involvement in Reform Strategy Lessons (Adrian J. Pinel); (13) Teaching Projectile Motion to Eliminate Misconceptions (Anne Prescott and Michael Mitchelmore); (14) An Investigation of a Preservice Teacher's Use of Representations in Solving Algebraic Problems Involving Exponential Relationships (Norma Presmeg and Rajeev Nenduradu); (15) On Embodiment, Artifacts, and Signs: A Semiotic-Cultural Perspective on Mathematical Thinking (Luis Radford, Caroline Bardini, Cristina Sabena, Pounthioun Diallo, and Athanase Simbagoye); (16) Generalization Strategies of Beginning High School Algebra Students (Joanne Rossi Becker and Ferdinand Rivera); (17) Synchronizing Gestures, Words and Actions in Pattern Generalizations (Cristina Sabena, Luis Radford, and Caroline Bardini); (18) Analyzing Student Modeling Cycles in the Context of a "Real World" Problem (Roberta Y. Schorr and Miriam Amit); (19) Negotiating about Perceived Value Differences in Mathematics Teaching: The Case of Immigrant Teachers in Australia (Wee Tiong Seah); (20) Development of Mathematical Norms in an Eighth-Grade Japanese Classroom (Yasuhiro Sekiguchi); (21) Solving Additive Problems at Pre-Elementary School Level with the Support of Graphical Representation (Ana Coelho Vieira Selva, Jorge Tarcisio da Rocha Falcao, and Terezinha Nunes); (22) From the Everyday, through the Authentic, to Mathematics: Reflecting on the Process of Teaching Mathematics through the Everyday (Godfrey Sethole); (23) Personal Experiences and Beliefs in Early Probabilistic Reasoning: Implications for Research (Sashi Sharma); (24) Assimilating Innovative Learning/Teaching Approaches into Teacher Education: Why Is It so Difficult? (Atara Shriki and Ilana Lavy); (25) Student Thinking Strategies in Reconstructing Theorems (Tatag Yuli Eko Siswono); (26) A Comparison of How Textbooks Teach Multiplication of Fractions and Division of Fractions in Korea and in U.S. (Ji-Won Son); (27) Mathematical Knowledge of Pre-Service Primary Teachers (Beth Southwell and Marina Penglase); (28) Analysing Longitudinal Data on Students' Decimal Understanding Using Relative Risk and Odds Ratios (Vicki Steinle and Kaye Stacey); (29) Girls Journey toward Proportional Reasoning (Olof Bjorg Steinthorsdottir); (30) University Student Perceptions of CAS Use in Mathematics Learning (Sepideh Stewart and Michael O. J. Thomas); (31) Prospective Teachers' Understanding of Proof: What if the Truth Set of an Open Sentence Is Broader than that Covered by the Proof? (Andreas J. Stylianides, Gabriel J. Stylianides, and George Philippou); (32) Planning and Teaching Mathematics Lessons as a Dynamic, Interactive Process (Peter Sullivan, Robyn Zevenbergen, and Judy Mousley); (33) Teacher Factors in Integration of Graphic Calculators into Mathematics Learning (Michael O. J. Thomas and Ye Yoon Hong); (34) Students' Overreliance on Linearity: An Effect of School-Like Word Problems (Wim Van Dooren, Dirk De Bock, Dirk Janssens, and Lieven Verschaffel); (35) A Process of Abstraction by Representations of Concepts (N. C. Verhoef and H. G. B. Broekman); (36) Argumentation Profile Charts as Tools for Analysing Students' Argumentations (Jill Vincent, Helen Chick, and Barry McCrae); (37) Characterizing Middle School Students' Thinking in Estimation (Tanya N. Volkova); (38) Reviewing and Thinking the Affect/Cognition Relation (Margaret Walshaw and Tania Cabral); (39) Young Children's Ability to Generalise the Pattern Rule for Growing Patterns (Elizabeth Warren); (40) Consolidating One Novel Structure whilst Constructing Two More (Gaye Williams); (41) Spreadsheets, Pedagogic Strategies and the Evolution of Meaning for Variable (Kirsty Wilson, Janet Ainley, and Liz Bills); and (42) A Study of the Geometric Concepts of the Elementary School Students Who Are Assigned to the van Hiele Level One (Der-bang Wu and Hsiu-Lan Ma). (Individual papers contain references.)

Developing models and using mathematics are two key practices in internationally recognized science education standards, such as the Next Generation Science Standards (NGSS). However, students often struggle with these two intersecting practices, particularly when developing mathematical models about scientific phenomena. Formative performance-based assessments designed to elicit fine-grained data about students' competencies on these practices can be leveraged to develop embedded AI scaffolds to support students' learning. In this paper, we present the design and initial classroom test of virtual labs that automatically assess fine-grained sub-components of students' mathematical modeling competencies based on their actions within the learning environment. We describe how we leveraged underlying machine-learned and knowledge-engineered algorithms to trigger scaffolds, delivered proactively by a pedagogical agent, that address students' individual difficulties as they work. Results show that the students who received automated scaffolds for a given practice on their first virtual lab improved on that practice for the next virtual lab on the same science topic in a different scenario (a near-transfer task). These findings suggest that real-time automated scaffolds based on fine-grained assessment can foster students' mathematical modeling competencies related to the NGSS.

This paper looks at Computer Assisted Language Learning (CALL) in the primary school setting and the problems, possibilities, and potential associated with this context. CALL normalisation is a key feature of successful CALL usage. This paper looks at CALL normalisation in the primary school context through three different lenses: Leakey's (2011) 3P's, Bax's (2003) CALL normalisation, and Chambers and Bax's (2006) CALL normalisation. The paper provides an overview of the use of a CALL resource for primary school students over a period of three years, with students ranging in age from seven to 12, both boys and girls with a number of different teachers across two different schools. It finishes up with some reflections and tips for others looking to work in this particular area. [For the complete volume, "CALL for Widening Participation: Short Papers from EUROCALL 2020 (28th, Online, August 20-21, 2020)," see ED610330.]

Playing games on mobile devices has become an integral part of younger generations' lives. Mobile games foster, among other things, deep concentration. This paper reports on design guidelines derived from observations of six elementary school pupils' engagement over a six-week period during an after-school reading club program. Each meeting consisted of three activities as well as reading text on the Microsoft immersive reader on an iPad, and playing a competitive reading game app, 'Henry rennt', which are both designed to support reading. Pupils were engaged in informal conversation with the researchers about both applications, and the authors informally observed the pupils' engagement with the apps and each other. Patterns of engagement and comments from pupils informed the design of a new reading app. This work reports these general patterns and concludes with new research areas to pursue as a result, including the impact of: social setting on playing, in-game teaching with avatars on engagement, and speed as a measurement of skill mastery. Finally, the applicability of children's engagement patterns is validated with adult students of German as a second language who used the app. [For the complete volume, "CALL for Widening Participation: Short Papers from EUROCALL 2020 (28th, Online, August 20-21, 2020)," see ED610330.]

The paper examines how the game Minecraft can be used as a new digital learning environment in the context of second language teaching and learning. It explores how the concepts of digital space and digital place within the new 3D digital environment can contribute to reshaping the language learners' experience and promote greater engagement in the target language. The study involved one language teacher and his grade 6 (upper elementary) students in a French immersion program in Canada. Digital artifacts created by the students in Minecraft were collected and qualitative analysis was carried out. The findings reveal that the use of a new digital environment allows for the emergence of a sense of digital place (emotional connection), greater engagement, and a sense of agency and control on the part of learners. Higher levels of collaboration, creativity, and imagination were also observed in the language tasks. [For the complete volume, "CALL for Widening Participation: Short Papers from EUROCALL 2020 (28th, Online, August 20-21, 2020)," see ED610330.]

In the U.S., state guidance to schools in response to the COVID-19 pandemic was politicized. We used state-level political affiliation to explore whether access to curricular resources differed pre-pandemic or during pandemic remote teaching and teachers' reported control over curricular resources during pandemic teaching. We found that pre-pandemic the percentage of teachers in Republican states reported higher levels of resources overall, and use of core and teacher-created curricular resources in particular. They also reported having greater control over their curricular decision-making during the pandemic. There were no state-level differences in teachers' level of preparation for pandemic teaching, but teachers in Democrat states reported a greater proportion of their students had sufficient resources for online learning. We discuss the implications of these findings in terms of teacher control and state policies. [For the complete proceedings, see ED657822.]

Research on pre-service teachers' discussion practices has focused on decompositions of practice into subskills, while acknowledging the importance of the role of context, identity, and relationships between interactive moves. We focused on 66 elementary preservice teachers' (PSTs') framing-launching moves in discussions after problem-solving in a Mursion[superscript TM] custom simulation. PSTs used five moves: gathering information about student processes, focusing on problem features, task and non-task oriented social interactions, and partner talk. Empirical findings of PSTs' intentions and tacit actions coupled with study findings of the diversity in PSTs' framing moves, highlight the complexity of teacher decision making involved in discussion subsills such as framing. We argue that PSTs' framing moves are motivated by an array of intentions including the mathematics aims of discussions. [For the complete proceedings, see ED657822.]

Preservice teachers (PSTs) are expected to possess a relational understanding (i.e., knowing how to do and why) of mathematics for ambitious instruction. This study aimed to shed some light on the possibilities of supporting PSTs' development of relational understanding of fractions through engaging them in writing collective argumentation. Drawing data from a larger project; we explored the development of a PST's understanding of fractions through the engagement of collective argumentation. The results indicated that the PST's relational understanding of fractions developed from both structural and content perspectives. Some educational implications for teacher education are discussed. [For the complete proceedings, see ED657822.]

In today's technology, there are rapid advances in the field of artificial intelligence. With the increasing involvement of artificial intelligence in daily activities, great changes are taking place in our habits. At this point, the necessity of educating students in accordance with the age of artificial intelligence emerges. Students' acquaintance with current technologies requires that the education provided is up to date. From these developments artificial intelligence, and its effects on society should be conveyed to students. The aim of the study is to implement the curriculum developed for middle school students to learn about the ethical dimension of artificial intelligence and to reveal students' views on the subject. Within the framework of the Artificial Intelligence and Ethics curriculum, 25 sixth grade students were trained. At the end of the training, a semistructured interview form was applied to the students. Students' views on the ethical dimension of artificial intelligence were revealed. As a result, education has been contributed with an artificial intelligence and ethics curriculum suitable for middle school students. In general, the approach of including the ethical dimension of artificial intelligence in education shows that middle school students can evaluate artificial intelligence as a personal and social issue beyond just having knowledge about its functioning. [For the full proceedings, see ED652261.]

It is estimated that up to 13% of children have been exposed to three or more adverse childhood experiences. The problem addressed by this study was the lack of adequate and appropriate teacher preparation in the support needed to combat the negative effects of adverse childhood experiences which can inadvertently intensify the academic, behavioral, emotional, social, and health challenges faced by children exposed to trauma. The purpose of this study was to explore teacher perceptions of pre-service and in-service professional development training provided to support the needs of elementary students that have been exposed to adverse childhood experiences in "at-risk", rural communities. Implications of the finding include the need for teacher preparation programs to include training on adverse childhood experiences and strategies to support children exposed to trauma, for school districts to gather input from faculty on in-service topics that are relevant to needs within the classroom, for school districts to provide more in-depth hands-on and proactive training on strategies to support children exposed to adverse childhood experiences, and on self-care to combat compassion fatigue. [For the full proceedings, see ED652228.]

Spatial analytics receive increased attention in educational data mining. A critical issue in stop detection (i.e., the automatic extraction of timestamped and located stops in the movement of individuals) is a lack of validation of stop accuracy to represent phenomena of interest. Next to a radius that an actor does not exceed for a certain duration to establish a stop, this study presents a reproducible procedure to optimize a range parameter for K-12 classrooms where students sitting within a certain vicinity of an inferred stop are tagged as being visited. This extension is motivated by adapting parameters to infer teacher visits (i.e., on-task and off-task conversations between the teacher and one or more students) in an intelligent tutoring system classroom with a dense layout. We evaluate the accuracy of our algorithm and highlight a tradeoff between precision and recall in teacher visit detection, which favors recall. We recommend that future research adjust their parameter search based on stop detection precision thresholds. This adjustment led to better cross-validation accuracy than maximizing parameters for an average of precision and recall (F1 = 0.18 compared to 0.09). As stop sample size shrinks with higher precision cutoffs, thresholds can be informed by ensuring sufficient statistical power in offline analyses. We share avenues for future research to refine our procedure further. Detecting teacher visits may benefit from additional spatial features (e.g., teacher movement trajectory) and can facilitate studying the interplay of teacher behavior and student learning. [For the complete proceedings, see ED630829.]

We explore multi-modal machine learning-based approaches (facial expression recognition, auditory emotion recognition, and text sentiment analysis) to identify "negative moments" of teacher-student interaction during classroom teaching. Our analyses on a large (957 videos, each 20min) dataset of classroom observations suggest that: (1) Negative moments occur sparsely and are laborious to find by manually watching videos from start to finish; (2) Contemporary machine perception tools for emotion, speech, and text sentiment analysis show only limited ability to capture the diverse manifestations of classroom negativity in a fully automatic way; (3) Semi-automatic procedures that combine machine perception with human annotation may hold more promise for finding authentic moments of classroom negativity; Finally, (4) even short 10 sec negative moments contain rich structure in terms of the actions and behaviors that they comprise. [For the complete proceedings, see ED630829.]

Teachers increasingly rely on online social media platforms to supplement their educational resources, greatly influencing PK-12 education through the swift and extensive diffusion of teacher-curated resources. Understanding this diffusion process is crucial, but current educational studies primarily report resource diffusion through small-scale analyses, such as teacher interviews or anecdotal accounts. To bridge this gap, we conduct a pioneering, large-scale, quantitative, and data-driven analysis of the diffusion of teacher-curated resources on Pinterest, a platform widely embraced by educators. Our study begins by defining a resource's diffusion tree, which encapsulates the cascade of resource sharing across the social network. Based on this diffusion tree, we identify three measures to characterize a resource's diffusion process: volume, virality, and velocity. Equipped with these three measures, we conduct an in-depth analysis of the diffusion of over one million resources curated by thousands of teachers on Pinterest. Our investigation concludes by examining the correlation between a resource's attributes and its curator's attributes and the diffusion of the resource. [For the complete proceedings, see ED630829.]

Recent research seeks to develop more comprehensive learner models for adaptive learning software. For example, models of reading comprehension built using data from students' use of adaptive instructional software for mathematics have recently been developed. These models aim to deliver experiences that consider factors related to learning beyond performance in the target domain for instruction. We investigate the extent to which generalization is possible for a recently developed predictive model that seeks to infer students' reading comprehension ability (as measured by end-of-year standardized test scores) using an introductory learning experience in Carnegie Learning's MATHia intelligent tutoring system for mathematics. Building on a model learned on data from middle school students in a single school district in a mid-western U.S. state, using that state's end-of-year English Language Arts (ELA) standardized test score as an outcome, we consider data from a school district in a south-eastern U.S. state as well as that state's end-of-year ELA standardized test outcome. Generalization is explored by considering prediction performance when training and testing models on data from each of the individual school districts (and for their respective state's test outcomes) as well as pooling data from both districts together. We conclude with discussion of investigations of some algorithmic fairness characteristics of the learned models. The results suggest that a model trained on data from the smaller of the two school districts considered may achieve greater fairness in its predictions over models trained on data from the other district or both districts, despite broad, overall similarities in some demographic characteristics of the two school districts. This raises interesting questions for future research on generalizing these kinds of models as well as on ensuring algorithmic fairness of resulting models for use in real-world adaptive systems for learning. [For the complete proceedings, see ED630829.]

Within the last decade, different educational data mining techniques, particularly quantitative methods such as clustering, and regression analysis are widely used to analyze the data from educational games. In this research, we implemented a quantitative data mining technique (clustering) to further investigate students' feedback. Students played educational games within a week on the educational games platform, Legends of Learning and after a week, we asked them to fulfill the feedback survey about their feelings on the use of this platform. To analyze the collected data from students, firstly, we prepared clusters and selected one prototype student closest to the centroid of each cluster to interview. Interviews were held to explain the clusters more and due to time and resource limitations, we were unable to interview all (N=60) students, thus only the most representative students were interviewed. In addition to the students, we conducted an interview with the teacher as well to get her detailed feedback and observations on the usage of educational games. We also asked students to take an exam before and after the research to see the impact of games on their grades. Our results depict that though educational games can increase students' motivation, they may negatively impact some students' grades. And even though playing games made students feel interested and fun, they would not like to play them on a daily basis. Hence, using educational games for a certain duration such as subject revision weeks may positively influence students' grades and motivation. [For the complete proceedings, see ED630829.]

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.