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In numerous studies, intelligent tutoring systems (ITSs) have proven effective in helping students learn mathematics. Prior work posits that their effectiveness derives from efficiently providing eventually-correct practice opportunities. Yet, there is little empirical evidence on how learning processes with ITSs compare to other forms of instruction. The current study compares problem-solving with an ITS versus solving the same problems on paper. We analyze the learning process and pre-post gain data from N = 97 middle school students practicing linear graphs in three curricular units. We find that (i) working with the ITS, students had more than twice the number of eventually-correct practice opportunities than when working on paper and (ii) omission errors on paper were associated with lower learning gains. Yet, contrary to our hypothesis, tutor practice did not yield greater learning gains, with tutor and paper comparing differently across curricular units. These findings align with tutoring allowing students to grapple with challenging steps through tutor assistance but not with eventually-correct opportunities driving learning gains. Gaming-the-system, lack of transfer to an unfamiliar test format, potentially ineffective tutor design, and learning affordances of paper can help explain this gap. This study provides first-of-its-kind quantitative evidence that ITSs yield more learning "opportunities" than equivalent paper-and-pencil practice and reveals that the relation between opportunities and learning gains emerges only when the instruction is effective.

In this study we present results of a discourse analysis of the interactions between two partners, Uma and Sean, through a feminist lens. During roughly five hours of small group work in a teaching experiment, how each partner used language to position each other's thinking as mathematically significant and establish a collaborative environment varied dramatically. Specifically, Uma shouldered the burden of continuously working to maintain collaboration, oftentimes at the expense of having her thinking positioned as mathematically significant. On the other hand, Sean regularly offered little opportunity for Uma to engage openly with his thinking, which ultimately constrained Uma's opportunities to learn. [For the complete proceedings, see ED630210.]

Teaching robotics courses online is challenging due to the complexity of the interdisciplinary topics involved. One of the most challenging topics is 3D coordinate transformations. Students often struggle to grasp the concept of 3D coordinate transformations and their relevance to real-world robotic applications. This paper applies the Scholarship of Teaching and Learning methodology to address this challenge and shares the self-evaluation assignments given to students to gradually enhance their ability to solve a real-world robotic navigation problem -- a crucial skill required in almost all robotic applications. Each assignment includes an informative description that explains the purpose of the task and its connection to the next assignment. Manageable MATLAB resources are provided in each assignment, allowing students to study fundamental Matlab scripts and use MATLAB Grader for self-evaluation before submission. The instructor provides feedback on incorrect answers through MATLAB Grader. The assignments focus on problem-solving and can be automatically graded, building upon prior work done by the instructor. The paper will also detail strategies for motivating students to engage with these challenging assignments and how the instructor assists distracted students in catching up with any missing assignments. [For the full proceedings, see ED656038.]

In this paper duality between real world phenomenon and mathematics will be discussed. This duality exists for many years which considerably remarked in the history of mathematics curriculum. One of the good potential for filling the gap between real world phenomenon and mathematical ideas would be modelling tasks which require performing the modelling cycle. In this paper after discussion about modelling in more details, two modelling cycles will be elaborated in the context of mathematical tasks that are related to everyday life. Main ideas behind different modelling cycles is starting point that would be from real world situation. Then gradually mathematical elements of real world phenomenon identified and mathematics problem will have shaped in a form that could be solved through mathematical problem solving techniques. Furthermore, it would be important phase that call interpretation of mathematics answer and check it in front of real world situation. This paper will be followed by discussion about learning theories that support the idea of modelling. Finally, two educational challenges (Design good modelling tasks and assessing of students performance) in mathematical modelling activity will be discussed. [For the complete proceedings, see ED655360.]

This paper explores how learning analytics data provided by a math problem-solving educational technology platform informed 5th and 6th grade teachers' instructional decisions around socioemotional learning (SEL). MathSpring is an educational technology tool that provides teachers with data on students' effort, progress, and emotions while students are solving math problems. This paper presents findings from qualitative analyses of 11 classroom observations, 10 observation follow-up chats, and 35 teacher interviews that were collected as part of a randomized control trial conducted in the northeastern United States. The analyses include teachers who used the program with their students (treatment group) and teachers who implemented math instruction as usual (control group). Teachers in the treatment group viewed analytic data on students' effort and progress, which informed the discussions they had with their students around SEL topics including setting goals, the importance of effort, and using productive problem-solving strategies. Findings from these analyses suggest that analytic data on effort and progress can inform teachers' discussions of math-related SEL concepts with their students. [This paper was published in: "The 14th Learning Analytics and Knowledge Conference (LAK '24), March 18-22, 2024, Kyoto, Japan," ACM, 2024.]

Perseverance is critical for students' achievement and may be particularly important after COVID-19. This paper includes analyses of teacher and principal interviews and student educational technology usage data to examine students' perseverance during math problem-solving across three cohorts of students during and after COVID-19. Data were collected as part of a randomized control trial examining the efficacy of an educational technology platform, MathSpring, in supporting students' math achievement. The results indicated that teachers and principals were concerned with their students' perseverance, and students' usage data similarly demonstrated that students may have reduced perseverance when solving math problems after COVID-19. Teachers and students may benefit from using tools that help foster perseverance in math class. MathSpring and other educational technology tools that support perseverance could be useful for encouraging students to put forth effort when solving math problems, which could in turn support students' math learning outcomes.

In a research study designed to investigate the emergence of collective creativity in elementary classroom settings, and in which teachers' decision-making practices were analyzed alongside both the teachers' observed teaching practices in their classrooms and their students' problem solving actions, the first author developed four metaphors for collective mathematical creativity and linked the entailments of these metaphors to teachers' actions. In this paper, we discuss in detail these entailments and teacher actions, present a framework for collective creativity, and reflect on the implications for practice and further research. [For the complete proceedings, see ED657822.]

Transactive discussion during collaborative learning is crucial for building on each other's reasoning and developing problem solving strategies. In a tabletop collaborative learning activity, student actions on the interface can drive their thinking and be used to ground discussions, thus affecting their problem-solving performance and learning. However, it is not clear how the interplay of actions and discussions, for instance, how students performing actions or pausing actions while discussing, is related to their learning. In this paper, we seek to understand how the transactivity of actions and discussions is associated with learning. Specifically, we ask what is the relationship between discussion and actions, and how it is different between those who learn (gainers) and those who do not (non-gainers). We present a combined differential sequence mining and content analysis approach to examine this relationship, which we applied on the data from 32 teams collaborating on a problem designed to help them learn concepts of minimum spanning trees. We found that discussion and action occur concurrently more frequently among gainers than non-gainers. Further we find that gainers tend to do more reflective actions along with discussion, such as looking at their previous solutions, than non-gainers. Finally, gainers discussion consists more of goal clarification, reflection on past solutions and agreement on future actions than non-gainers, who do not share their ideas and cannot agree on next steps. Thus this approach helps us identify how the interplay of actions and discussion could lead to learning, and the findings offer guidelines to teachers and instructional designers regarding indicators of productive collaborative learning, and when and how, they should intervene to improve learning. Concretely, the results suggest that teachers should support elaborative, reflective and planning discussions along with reflective actions. [For the complete proceedings, see ED630829.]

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.

This conceptual paper discusses two frameworks, developed independently by the lead author, that will provide the conceptual foundation for the identification and evaluation of mental computation strategies students demonstrate during an upcoming research project entitled Mental Computation in Year 5. These frameworks will be used by the lead author during an intervention to investigate the application of mental computation strategies in problem solving tasks involving duration of time. It is an intended outcome of the project that the two frameworks will be useful for teachers and students in upper primary school to provide feedback regarding the teaching and learning of mental computation.

Worldwide interest in Lesson Study (LS) and the opportunities offered for student learning through the use of a Structured Problem-Solving Approach (SPSA), as typically adopted in Japanese LS research lessons in mathematics, have left largely unanswered questions about the extent to which these can be replicated elsewhere. This paper presents a case study of one primary school teacher's learning experiences, and his views about LS and SPSA, as a result of participating in a project introducing SPSA through LS in three Fijian primary schools. The results reveal that engaging in the LS process was instrumental in supporting this teacher's implementation of SPSA in his mathematics classroom. The findings are important for teacher professional learning (PL) in Pacific cultural contexts.

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.

The phenomenon of teachers designing their own instructional materials is gaining more attention in research. Different aspects of this enterprise have been examined--its potential to reveal the complexity of teachers' instructional planning considerations, the design principles employed by teachers to realise instructional goals, among others. In the study reported in this paper, the focus was on its utility as a form of teacher professional development. In particular, evidence was sought for this claim: not only is teacher-designed instructional materials a useful tool for professional development, it can capture usable knowledge teachers appropriate from professional development.

The development of students' mathematical problem-solving skills is contingent upon the approaches and methods employed by primary school teachers. This research endeavors to scrutinize the effectiveness of primary school teachers in their roles within the problem-solving process, with particular attention directed toward their inquiry techniques, instructional approaches, and responses to student errors. Employing as a explanatory mixed-design research, firstly quantitative data were obtained from the primary school teachers (N=116) and analyzed by applying the questionnaire form developed by the researchers; additionally, qualitative data were obtained by conducting focus group interviews with a subset of participants (N=6) based on the information obtained from these data. Thereby, teachers get the opportunity to share their ideas in the process. Second phase of the research aimed to develop the active roles of the participants in the problem-solving process. The research outcomes underscore that teachers frequently gravitate toward questioning techniques and teaching methods that promote a nuanced comprehension of the problem. There also appears to be an underutilization of inquiries pertaining to prediction, generalization, and collaborative group work. Furthermore, the research unveils an array of strategies employed by teachers to rectify student errors. These encompass commonly employed techniques such as question-answer, exemplification, and lecture responses, irrespective of the specific type of question posed. [This paper was published in: "EJER Congress 2023 International Eurasian Educational Research Congress Conference Proceedings," Ani Publishing, 2023, pp. 476-492.]

This paper aims at using a Use-Modify-Create approach to explore students' mathematical problem solving by means of computational thinking (CT) and programming activities. The data collection method is participant observation, in which the researcher also has the role as teacher, guiding the group activities. In our study, two groups of students at the undergraduate level solving a mathematical task. The main finding of the study shows that the progression through the Use-Modify-Create continuum did not work as expected and that the connections between mathematical thinking, computational thinking, and programming proved difficult for the students. Conclusions so far are drawn from the study to promote mathematical problem solving by means of computational thinking and programming in a Use-Modify-Create context. [For the full proceedings, see ED636095.]

Nurses are a vital resource of health care systems, a resource that must be valued, bearing in mind that their work has a role in social indicators of health, and also determines topics such as equality and equity, fairness and justice, which support the kind of societies we all want to live in. In the training process, they learn, in the middle of a team, to plan, to put into practice and evaluate general medical care based on acquired knowledge and skills. Future nurses must not only be prepared to meet the needs of the individual, the family, the community, but also to have confidence in their own intellectual and clinical abilities so that they can work responsibly and autonomously, facing at the same time with increasingly complex requirements of healthcare. The refinement of medical training is subsequently achieved by developing the ability to solve problems, to make decisions, to practice leadership in medical care. The acquisition of leadership skills has been identified as a need in training nurses, both from the researches of internal and international professional bodies and from those of clinical units. By harmonizing this need with public educational policies, the unit of learning outcomes "Leadership and professional communication" was implemented in the professional training standard. This paper aims to gain insight into the relationship between the values of leadership and the development of a good educational policy in training nurses, with a fundamental impact on the provision of health care in an efficient, integrated and safe manner for the patient. [For the full proceedings, see ED654100.]

The paper presents an attempt made to use the Arduino platform and the Scratch for Arduino (S4A) environment for the implementation of an educational project for 6th grade primary school students in a classroom attended by refugee, immigrants, and indigenous students. The aim was to investigate the opportunity to use educational robotics as tools to support the social interactions and social inclusion of refugee children in the classroom community. The research was a case study implemented in a primary school in rural Greece. Students had to work in groups to design, build, and program a construction that simulates an "escape room." Students of each group solving a riddle of the other groups must discover a code to unlock the door of the "escape room," based on a series of six worksheets of increasing difficulty to create their final construction. The research tools were a diagnostic questionnaire, an evaluation questionnaire, specially designed worksheets, an observation sheet for participatory observation, and sociometric test tools. Based on the findings it could be supported that educational robotics are able to support social interactions of refugee children to a certain extent. The intervention supported social interactions and collaboration among students but without solving the problem of difficulties in the social integration of refugee students in the classroom community. Verbally all students stated that they had not any problem cooperating with refugee students, but this was not strongly reflected in practice. Greek students interacted strongly with immigrant students and refugee students seemed to prefer interacting with immigrant students too. [For the full proceedings, see ED656038.]

Career development is an important aspect of every young person's life as it helps them identify their skills, interests and goals and find the right career path for themselves. Career skills are a broad range of competencies and abilities that are necessary for success in the workplace. Developing them through education, training and experience can help students identify them and achieve their career goals. Design thinking is a powerful approach for this purpose. With its components-problem solving, innovation and creativity, collaboration and teamwork, iterative approaches, and empathy-design thinking can help students develop the skills they need to succeed in a wide range of professional fields. The specificity of the hackathon as a form of organization further contributes to building these essential skills that are directly related to students' career development. This paper explores the possibilities of forming career skills in students through design thinking hackathons. [For the complete proceedings, see ED655360.]

This paper explores the correlation between mental calculation performance and the frequency of using written algorithms in mental calculation tasks. Mental calculation is a mathematical tool used in everyday life situations during and after our formal education. After presenting an overview of the professional literature on this topic, the paper will present calculation methods and show how represented they are in the Curriculum. For the empirical part of the research, a total of 233 Croatian students aged 10 to 22 years were tested and interviewed. The previously mentioned correlation was then analyzed. An overview of the interview results will be presented as well. It was found that school mathematics does not always contribute to the development and flexibility in using mental calculation strategies because of the student preference for acquired written algorithms. Definitely, recommendation is shifting the focus from written calculation and procedures to the mental, discussing the associated strategies and different concepts of number. In this way, formal education could contribute to what students really need later on, in both private and professional situations in which they may find themselves on a daily basis. [For the full proceedings, see ED630948.]

This paper describes our work to determine the naturalistic images that first-time second-semester university calculus students possess for series convergence. We found that the students we interviewed most frequently determined whether a series converged by imagining a process of appending summands into a running total and examining whether this running total appeared to approach an asymptotic value. We provide examples and three corresponding implications of this "asymptotic running total" that informed students' actions while determining series convergence or the value of convergence. Our paper adds to the research literature by confirming students' meanings for limits reported for other topics (e.g., limit of sequence, function, Taylor series) apply to infinite series and proposing relationships between previously reported meanings for series convergence. [For the complete proceedings, see ED630210.]

This paper focuses on Emergent bilinguals (EBs) who traditionally face unequal opportunities to learn mathematics, harming their identities. The purpose of this paper is to illustrate how a fifth grade teacher cultivated the development of her EBs' mathematical identities by giving them opportunities to participate in cognitively demanding activities. Drawing on a conception of mathematical identity as something that changes in response to different situations, we illustrate how a fifth-grade teacher positively impacted her students' mathematical identities. The results reveal that when teachers use instructional strategies such as distributing mathematical authority, positioning students as mathematically capable, and incorporating students' languages as a resource for instruction, their EBs have multiple opportunities to build positive mathematical identities. [For the complete proceedings, see ED630210.]

Computational thinking is a way of thinking for problem solving and is one of the basic skills of the 21st century that is very important to be applied in science learning as an effort to prepare for disruption in the industrial era 4.0 and society 5.0. This study aims to find a new method that has proven its effectiveness to apply problem solving skills. The Research and Development (R and D) method with the ADDIE model (Analysis, Design, Develop, Implementation and Evaluation) was carried out to develop a Problem Project Based Learning (PPjBL) model with a Computational Thinking (CT) approach based on CoSpaces-Edu Paper Cube Augmented Reality. This research has produced a product in the form of a Problem Project Based Learning (PPjBL) model with a Computational Thinking (CT) approach based on CoSpaces-Edu Paper Cube Augmented Reality which has been validated by experts on very feasible and effective criteria to be applied as a science learning design. [ABSTRACT FROM AUTHOR]

Past research has yielded ample knowledge regarding the design of analytics-based tools for teachers and has found beneficial effects of several tools on teaching and learning. Yet there is relatively little knowledge regarding the design of tools that support teachers when a class of students uses AI-based tutoring software for self-paced learning. To address this challenge, we conducted design-based research with 20 middle school teachers to create a novel real-time dashboard, Tutti, that helps a teacher monitor a class and decide which individual students to help, based on analytics from students' tutoring software. Tutti is fully implemented and has been honed through prototyping and log replay sessions. A partial implementation was piloted in remote classrooms. Key design features are a two-screen design with (1) a class overview screen showing the status of each student as well as notifications of recent events, and (2) a deep dive screen to explore an individual student's work in detail, with both dynamic replay and an interactive annotated solution view. The project yields new insight into effective designs for a real-time analytics-based tool that may guide the design of other tools for K-12 teachers to support students in self-paced learning activities. [This paper was published in: "Proceedings, European Conference on Technology Enhanced Learning, EC-TEL 2022. Lecture Notes in Computer Science, vol 13450," edited by I. Hilliger et al., Cham: Springer, 2022, pp. 16-30.]

Collaborative learning is a complex process during which two or more learners exchange opinions, construct shared knowledge, and solve problems together. While engaging in this interactive process, learners' satisfaction toward their partners plays a crucial role in defining the success of the collaboration. If intelligent systems could predict peer satisfaction early during collaboration, they could intervene with adaptive support. However, while extensive studies have associated peer satisfaction with factors such as social presence, communication, and trustworthiness, there is no research on automatically predicting learners' satisfaction toward their partners. To fill this gap, this paper investigates the automatic prediction of peer satisfaction by analyzing 44 middle school learners' interactions during collaborative coding tasks. We extracted three types of features from dialogues: (1) linguistic features indicating semantics; (2) acoustic-prosodic features including energy and pitch; and (3) visual features including eye gaze, head pose, facial behaviors, and body pose. We then trained several regression models to predict the peer satisfaction scores that learners received from their partners. The results revealed that head position and body location were significant indicators of peer satisfaction: lower head and body distances between partners were associated with more positive peer satisfaction. This work is the first to investigate the multimodal prediction of peer satisfaction during collaborative problem solving, and represents a step toward the development of real-time intelligent systems that support collaborative learning. [For the full proceedings, see ED623995.]

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of information and demonstrate cognitive flexibility in their use of visualisation, diagrams, language, and symbols.

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment Framework for multiplicative thinking, it has been difficult to move students through Zone 4 at the same rate. A closer examination of item responses at this level reveal that a disposition to notice and work with relationships between quantities may explain this phenomenon.

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.

In this paper, we present a case study of a secondary mathematics teacher, Isaac (pseudonym), and his considerations for teaching with multiple methods for solving missing-value problems. While his students preferred methods that drew more closely on their intuitive understanding of proportionality, Isaac emphasised the algorithmic cross-multiplication method. Analysis of Isaac's introduction and use of the cross-multiplication method suggest his key considerations were linked demonstrating the efficiency of the cross-multiplication method, while also helping students to make making meaning from the cross-multiplication method.

From mathematics education, a great variety of studies have focused on analyzing the presence of digital technology from different points of view. Those who work with proof and argumentation have resisted presenting results with a technological component, due to the idea of formality associated with those terms, which has increased the existing tension between the theoretical and empirical nature of mathematics. Taking into consideration that with the presence of environments such as dynamic geometry software (DGS) the student can access to dynamic representations, we seek to understand the impact of the interaction with these representations on the arguments proposed by the students. For this, we carried out an exploratory and descriptive study whose results show that the interaction with dynamic representations provides students with validation tools different from those on paper. [For the complete proceedings, see ED630210.]