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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.

Ascertaining young children's attitudes towards mathematics has its challenges. Methodologically, limitations exist regarding the type of research techniques that can be employed. The use of children's drawings as a data source has both methodological affordances and issues. The study was conducted with 106 children in Years 2 and 3 from three South Australian primary schools. This paper identifies some of the methodological affordances and issues of using children's drawings to ascertain and describe their attitudes towards mathematics. [This paper is the third in a symposium of three papers. For the first paper, "Drawings Reveal Young Students' Multiplicative Visualisation," see ED616196. For the second paper, "Investigating Students' Drawings as a Representational Mode of Mathematical Fluency," see ED616197.]

In test equating, one critical equating property is the group invariance property which indicates that the equating function used to convert performance on each alternate form to the reporting scale should be the same for various subgroups. To mitigate the impact of disrupted learning on the item parameters during the COVID-19 pandemic, a pre-equated approach was frequently implemented for student scoring in the spring 2021 administration of large-scale assessments. This study examines how much the group invariance property was satisfied for various subgroups when pre-equating was applied to large-scale assessments in spring 2021. While most studies for invariance property have been for post-equating, this study investigated the invariance property with pre-equating. Due to the potential impact on live calibration and equating, many large-scale assessment programs have opted to reuse previously administered forms and applied pre-equating rather than developing new forms and post-equating in 2021. This study included grades 6 and 8 ELA and Math from a spring 2021 large-scale assessment program and examined the invariance property for four subgroups: gender, SES, ethnicity, and LEP. Three different scoring methods were studied: unrounded equated scores, rounded equated scores, and MLE as IRT pattern scoring. As evaluation criteria, RMSD and REMSD indices were included (Dorans & Holland, 2000). The effect size was also used for evaluating the equating function differences between each subgroup's categories and the population. Invariance property is often studied when post-equating is performed with alternate forms under common (i.e., anchor) item design. In this case, the quality and number of anchor items between alternate forms influence the equating results and invariance property. In general, if anchors are close to a minimal test version, equating results can be better with many anchor items. Pre-equating design fully satisfies the requirement of the maximum number of anchor items because all items can be used as anchor items. Therefore invariance property can be better achieved than post-equating with some common items under the same condition. RMSD and REMSD values for ELA, where students' performances were not much impacted by the pandemic, showed the same results. However, there were some deviations in the invariance property for Math where students' performances appeared to be impacted.

The purpose of the current research study was to investigate the extent to which student performance was influenced by the disruption to learning that occurred due to the COVID-19 pandemic. To explain observed differences in performance, we compared outcomes from a state-wide summative testing program between students who were administered the test in 2019 and 2021. Because the background and demographic characteristics of the two testing populations differed on several variables, including race/ethnicity, locale, and subgroup membership, propensity score matching was used to develop comparable groups for analyses. Independent samples t-tests were then conducted to assess whether there were significant differences in mean scaled scores and domain subscores between the two matched groups. In addition, the same procedures were used to develop and analyze differences for specific student subgroups (students with disabilities, economically disadvantaged students, and English language learners). Overall, results indicated that the 2021 test-takers earned lower scores than students who tested in 2019 for all subjects and grade levels, except English Language Arts (ELA) grade 8. Moreover, larger score differences were observed for mathematics than ELA. Lastly, results from subgroup analyses indicated that in mathematics all subgroups earned significantly lower scores in 2021 than 2019, whereas in ELA grades 5 through 7, English Language Learners and economically disadvantaged subgroups earned lower scores in 2021 than 2019. The results of this study suggest that after controlling for differences between the 2021 and 2019 populations, student performance was likely influenced by the disruption to learning due to pandemic-related factors.

Noticing children's mathematical thinking is foundational to teaching that is responsive to children's thinking. To better understand the range of noticing expertise for teachers engaged in multiyear professional development, we assessed the noticing of 72 upper elementary school teachers using three instructional scenarios involving fraction problem solving. Through a latent class analysis, we identified three subgroups of teachers that reflected different profiles of noticing expertise. Consideration was given to the noticing component skills of attending to children's strategy details, interpreting children's understandings, and deciding how to respond on the basis of children's understandings. We share theoretical and practical implications for not only the three profiles but also our choice to explore separately two versions of deciding how to respond (deciding on follow-up questions and deciding on next problems). [For the complete proceedings, see ED630060.]

People often view mathematics as abstract, cold, and irrelevant to real-life, and their school experiences influence such views. In this case study, we investigated the mathematics learning experiences of two women who participated in an afterschool girls STEM club 26 years ago. We explored their experiences in and out of school and how such experiences informed their images of mathematics. Data were collected from a survey, focus group interviews, and individual interviews. Using qualitative analysis, we learned that their school mathematics experiences influenced the participants' images of mathematics. The findings also revealed the participants' continuous and discontinuous learning experiences between school and out-of-school mathematics. This study suggests creating spaces to develop curricula that bridge the gap between school and out-of-school learning experiences. [For the complete proceedings, see ED630060.]

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

In this study, we investigated two students', ages ten and eleven, emotions while they engaged in mathematical problem solving. During three task-based interviews, the students explored parts of the unsolved problem the Graceful Tree Conjecture. While they were engaged in the interviews, they self-identified the emotions of frustration and joy they were feeling using the Wong-Baker Scale. The students displayed the interplay of the emotions of frustration and joy or which we consider to be productive struggle. A descripted case of Georgia is included to describe her emotions while problem solving. [For the complete proceedings, see ED629884.]

This study examines pre-service teachers' (PSTs') views of tasks that engage students in mathematical argumentation. Data were collected in two different mathematics courses for elementary school education majors (n = 51 total PSTs). Analyzed were (a) written journals in which PSTs defined tasks that promote student engagement in argumentation, (b) tasks PSTs posed to engage students in mathematical argumentation, and (c) accompanying explanations in which PSTs motivated tasks they posed. The analysis revealed that PSTs interpret tasks that foster argumentation in terms of activities of argumentation that a task elicits and space for argumentation that the task provides. Several features that PSTs associated with each of the two major task characteristics were identified. While posing tasks to engage students in argumentation, PSTs did not place equal emphasis on all of the identified features. [For the complete proceedings, see ED629884.]

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

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

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

This paper describes the genesis of YuMi Deadly Maths, a school change process that has been used in over 200 schools to develop mathematics teaching and learning to improve students' employment and life chances. The paper discusses the YuMi Deadly Maths approach to mathematics content and pedagogy, implemented through a process of PD and school change, and looks at the strengths and weaknesses of the process and the challenges it faces.

We explore the epistemological issues that arise when considering STEM as a curricular and instructional construct. Our approach is somewhat unique in that we are not focused on the curricular or instructional boundaries of STEM education, but consider the nature of the cognitive activity at play during STEM-focused activity, with an emphasis on mathematical thinking. We focus specifically on the epistemological underpinnings of mathematics and other STEM disciplines, and the possibility of an epistemology of STEM as a curricular construct. The implications on students' STEM ways of thinking (SWoT) are discussed in detail from a theoretical and empirical lens. Future research directions are identified. [For the complete proceedings, see ED606556.]

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

The purpose of this study was to explore the factorial structure of motivation and perception items from a student survey utilised as part of the Reframing Mathematical Futures II (RMFII) Project. Data was collected in 2017 from 442 students in Years 7 to 10 from various different States across Australia. An exploratory factor analysis identified four factors which were consistent with the studies the items were adapted from: Intrinsic and Cognitive Value of Mathematics, Instrumental Value of Mathematics, Mathematics Effort, and Social Impact of School Mathematics. An analysis of variance (ANOVA) also revealed that there were statistically significant differences between Year Level and State for some of these factors.

This submission contains the Proceedings of the 2017 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at McGill University in Montreal, Quebec June 2-6. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, panel discussions, working group reports, new PhD reports, and summaries of ad hoc and poster sessions. Papers include the following: (1) The Most Unglamorous Job of All: Writing Mathematics Exercises (Yvan Saint-Aubin); (2) 40+ Years of Teaching and Thinking about University Mathematics Students, Proofs, and Proving (Annie Selden); (3) 'Elder Talk'-A Revisionist Version (Joel Hillel); (4) Teaching First Year Mathematics Courses in Transition from Secondary to Tertiary (Ann Arden, Wesley Maciejewski, Nadia Hardy); (5) L'anxiété mathématique chez les futurs enseignants du primaire : à la recherche de nouvelles réponses à des enjeux qui perdurent / Elementary Preservice Teachers and Mathematics Anxiety: Searching for New Responses to Enduring Issues (Manion LeBlanc, Jamie Pyper, Jo Towers) [Written in French and English]; (6) Social Media and Mathematics Education (Judy Larsen, Egan Chernoff, Viktor Freiman); (7) Quantitative Reasoning in the Early Years / Le raisonnement quantitatif dans les premières années du parcours scolaire (Doris Jeannotte, Lynn McGarvey)[Written in English and French ]; (8) Social, Cultural, Historical and Philosophical Perspectives on Tools for Mathematics (Yasmine Abtahi, Susan Gerofsky, Jean Francois); (9) Compréhension approfondie des mathématiques scolaires / Deep Understanding of School Mathematics (Richelle Marynowski, Sarah Dufour, Peter Liljedhal); (10) Modelling Mathematical Modelling / Modéliser la modélisation mathématique (France Caron)[Written in French and English]; (11) Collective Learning: Re-thinking the Environment, Artifacts and Classroom Interactions (Joyce Mgombelo); (12) A Psychological View of Teaching Proof Construction (John Selden); (13) Things Kids Think With: The Role of the Physical Properties of Mathematical Tools in Children's Learning in the Context of Addition of Fractions (Yasmine Abtahi); (14) Examining Mathematics Anxiety Among Classroom Teachers (Atinuke Adeyemi); (15) Teaching Teachers: A Look Inside Professional Development (Melania Alvarez); (16) Be Innovative but Don't Be Wrong: Are 21st Century Students Experiencing 21st Century Mathematics? (Jennifer Godfrey Anderson); (17) College Foundational Mathematics: Can the Affordances of ICT Enhance Self-regulation Skill of Students? / Mathématiques fondamentales du collège : est-ce que les apports des « TIC » peuvent améliorer l'autorégulation des compétences des élèves? (Carol Carruthers)[Written in English and French]; (18) Influence of the Learning Environment on Student Test Performance in Undergraduate Mathematics Courses (Amenda Chow); (19) The Role of Oral Communication Strategies in Accessing and Assessing Mathematical Understanding: Case Studies of Primary School Teachers' Perceptions of Teaching Mathematics and Teaching Literacy (Celia Kutas Chisu); (20) Reciprocal Partnership: An Intervention to Enhance Mathematics Self-efficacy and Achievement of First- and Second-semester College Students (Kerry Kwan); (21) Understanding the Interactions within a New Teacher Learning Community Composed of First Time Participants and a Novice Facilitator (Terry Wan Jung Lin); (22) Valued Kinds of Knowledge and Ways of Knowing in Mathematics and the Teaching and Learning of Mathematics: A Worldview Analysis (Gale L. Russell); (23) Opening Space: Complexity Thinking, Classroom Discourse, and Mathematics Learning in the Elementary Classroom / La technologie du forum ouvert: complexité, le discours de classe, et l'apprentissage de mathématiques en école élémentaire (Evan Throop-Robinson)[Written in English and French]; (24) Investigating Mathematics Teachers' Knowledge for Teaching and Their Learning Trajectories (Zhaoyun Wang]; (25) What/How Can We Learn from the Deaf Mathematics Classroom? (Christins M. Krause); (26) The Mathematical Association of Tanzania (MAT) Experience in CMESG Conference (Said A. Sima); (27) Toward a Hybrid Model to Describe Creative Acts in Mathematics Learning Environments (Ayman Aljarrah); (28) Problem Drift: Imaging Emerging Curricular Significance (Nat Banting); (29) Incorporating Writing into the Undergraduate Mathematics Curriculum (Lauren Dedieu); (30) Informing Local Materials Used for Concept-Rich Instruction Practice in Mathematics Class with Pre-service Teachers in Tanzanian Context (Emmanuel, Deogratias); (31) Les jeux technologiques dans les cours de mathématiques au secondaire (Caitlin, Furlong) [Written in French]; (32) De jeunes chercheurs à la rencontre de la philosophie des mathématiques (Sabrina Heroux, Sarah Mathieu-Soucy, Laura Broley) [Provided in French]; (33) Examining Parent Perspectives of Multiple Strategies (Jennifer Holm, Lynn McGarvey, Lixin Luo, Janelle McFeeters, and Iris Yin); (34) La dialectique perfection/imperfection : une nouvelle manière de penser l'activité mathématique (Marie-Line L. LaMarche, Jean-Francois Maheux) [Provided in French]; (35) Understanding School Leaders' Discourse in Regard to Mathematics Achievement (Jhonel Morvan); (36) I SEE What You're Saying: Visualization and the Growth of Mathematical Images (Jennifer Plosz); (37) Students' Relationships With Mathematics Revealed Through Drawings (Jennifer Plosz, Jo Towers, Kori Czuy, Ayman Aljarrah, Andrew Vorhies and Miwa Takeuchi); (38) Teacher Professional Learning in Tanzania: Experiences of Mathematics Teacher Leaders (Calvin Zakaria Swai); (39) "Perimeter is easier to work with than area": Students' Language Use in Group Work (Miwa Akoi Takeuchi); and (40) Toward an Understanding of Mathematics Teachers' Participation in Professional Learning Networks (Xiong Wang). Individual papers provide referenced. [For the 2016 proceedings, see ED581045.]

Mathematical reasoning features in curriculum documents around the world, but is understood and enacted poorly by teachers in classrooms. We explore teachers' noticing of reasoning during observed lessons. Two teams of primary teachers in Canada and Australia worked to plan, deliver, and observe lessons intended to include reasoning. They observed each other teaching a lesson that was planned with the assistance of a researcher, and later, a researcher observed each post-lesson discussion. Given the reported benefits of teachers' noticing of reasoning during peer-observed lessons, targeted professional learning support is required to further enact teachers' peer discourse to facilitate mathematical reasoning.

I investigate the sustainability of lesson study as mathematics teachers who participated in a 3-year professional development partnership engage in a district scale-up lesson study professional experience. This study answers three questions: (1) what are K-12 teachers' conceptions of sustaining mathematics lesson study, (2) what practices of lesson study continued after the grant as reported by participants, and (3) what are supportive and constraining factors in continuing lesson study after external funding ends when there is both reported desire from teachers as well as some district support? Survey and interview data are analyzed using grounded theory and social network analysis for patterns in and structure to activities. Findings suggest rich conceptions of lesson study, the continuation of particular lesson study practices, and the importance of integration and linkage as factors that supported or hindered lesson study. [For the complete proceedings, see ED583989.]

In this study we examine the use of cumulative and exploratory talk types in a year 5 computer supported collaborative learning environment. The focus for students in this environment was to participate in mathematical problem solving, with the intention of developing the proficiencies of problem solving and reasoning. Findings suggest that students engaged in exploratory talk may more regularly attempt the use of technical (tier 3) mathematical vocabulary.

Mathematics anxiety affects primary pre-service teachers' engagement with and future teaching of mathematics. The study aimed to assess the level and range of mathematics anxiety in first year pre-service teachers entering their teacher education course, and to investigate the sources of this anxiety as perceived and identified by them. Data collection methods included the RMARS survey, and Critical Incident Technique. The results indicate that the most common negative impacts on pre-service teacher mathematical self-concept involved experiences with teachers. However, their current mathematics anxiety is most commonly aroused under testing or evaluation situations.

This study investigated potential gender differences in a sample of 807 Year 6 Singaporean students in relation to two variables: spatial visualisation ability and cognitive style. In contrast to the general trend, overall there were no significant gender differences on spatial visualisation ability. However, gender differences were prevalent among students who possessed high spatial visualisation ability, in favour of boys. In terms of cognitive style, there were significant gender differences in the spatial imagery and verbal information processing dimensions. Boys gave higher ratings to their spatial-imagery encoding and processing preferences than their verbal information processing preferences. Some of these findings are in contrast to studies undertaken in the educational-psychology literature. Implications are drawn regarding pedagogical practices in Singaporean schools.

The aim of this study was to determine the role of semiotics in assisting young Indigenous students to engage with and identify the general structure of growing patterns. The theoretical perspective of semiotics underpinned the study. Data are drawn from two Year 3 students, including analysis of pretest questions and two conjecture-driven lessons. Results indicate that particular semiotic signs (iconic signs) contribute to how young Indigenous students attend to, and identify the structure of growing patterns.