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The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the paper reports on the creation and evaluation of a methodological tool for measuring the aforementioned construct. The tool was operationalized from analyses of 38 college students' problem-solving behaviors as well as their verbal self-reflections in semi-structured task-based interviews. Results showed decent validity and reliability evidence on the proposed research tool. This study contributes to a better conceptualization of learning orientation as a fundamental shaper of how students engage with mathematics; it also holds practical potential for enhancing mathematics classrooms. [For the complete proceedings, see ED658295.]

Access to body-based resources has been shown to augment cognitive processes, but not all movements equally aid reasoning. Interactive technologies, like dynamic geometry systems (DGS), potentially amplify the link between movement and geometric representation, thereby deepening students' understanding of geometric properties. This study investigated the influence of access to a DGS on students' geometric reasoning and gesture production compared to the impact of only spontaneous gestures. Access to simulations did not significantly increase the likelihood of students producing correct mathematical insights compared to spontaneous gestures. However, when controlling gesture production, DGS access became a significant predictor for transformational proof production. We also found that access to DGS influenced the type of gestures students produced during geometric reasoning tasks. This study underlines the vital role of gestures in geometric reasoning and suggests that while DGS offers benefits, spontaneous gestures remain a crucial embodied resource for exploring geometric concepts. [This paper was published in: "Proceedings of the 18th International Conference of the Learning Sciences - ICLS 2024," edited by R. Lindgren et al., International Society of the Learning Sciences, 2024, pp. 131-38.]

This qualitative study aims to investigate novice undergraduate mathematics students' first encounter with the First Isomorphism Theorem, which is, more often than not, the pinnacle of a typical introductory course in Group Theory. Several studies have reported on the challenges that this mathematical result poses to inexperienced mathematicians, mostly due to the numerous prerequisite abstract concepts. For the analysis of student responses, there has been used the Commognitive Theoretical Framework. This study suggests that the major challenges are due to the comprehension of the notions of kernel, image and isomorphism, and the application of FIT as a routine in the context of proofs.

This article seeks to explore the convergent validity of (and thus the consistency between) a few popular generative artificial intelligence (AI) robots in evaluating popular mobile learning apps' usability. The three robots adopted in the study were Microsoft Copilot, Google PaLM, and Meta Llama, which were individually instructed to accord rating scores to the eight major usability dimensions, namely, (1) content/course quality, (2) pedagogical design, (3) learner support, (4) technology infrastructure, (5) social interaction, (6) learner engagement, (7) instructor support, and (8) cost-effectiveness of 17 currently most popular mobile learning apps. For each of the three robots, the minimum, the maximum, the range, and the standard deviation of the rating scores for each of the eight dimensions were computed across all the mobile learning apps. The rating score difference for each of the eight dimensions between any pair of the above three robots was calculated for each app. The mean of the absolute value, the minimum, the maximum, the range, and the standard deviation of the differences for each dimensions between each pair of robots were calculated across all the apps. A paired sample t-test was then applied to each dimension for the rating score difference between each robot pair over all the apps. Finally, Cronbach's coefficient alpha of the rating scores was computed for each of the eight dimensions between all the three robots across all the apps. The computational results were to reveal whether the three robots awarded discrimination in evaluating each dimension across the apps, whether each robot, with respect to any other robot, erratically and/or systematically overrate or underrate any dimension over the apps, and whether there was high convergent validity of (and thus consistency between) the three robots in evaluating each dimension across the apps. Among other auxiliary results, it was revealed that the convergent validity of (and the consistency between) the three robots was marginally acceptable only in evaluating mobile learning apps' dimension of (1) content/course quality but not at all in the dimensions (2) pedagogical design, (3) learner support, (4) technology infrastructure, (5) social interaction, (6) learner engagement, (7) instructor support, and (8) cost-effectiveness. [For the full proceedings, see ED659933.]

Recognizing the limitations of the existing frameworks and models applied to estimate the learning loss caused by COVID-19 across the world by different studies, and the urgent need for estimating such loss at the different education levels, this paper, employs the Education Value Chain Analysis ( EVCA) approach as a new paradigm, attempts to develop and examine a more comprehensive and practical framework that would assist estimating the learning loss, determine its position(s) in the education system and the root causes behind its occurrence. The proposed framework seems to be superior, compared to the existing ones, in estimating learning loss. That would provide sufficient information to help in introducing effective measures and interventions to deal with such loss. For example, the framework would assist in estimating the loss that occurs within the main components of the education system (i.e., Input, process, and outcome). Besides, it helps estimate the loss of different education levels. In addition, the information provided by the framework would help determine the root causes of the learning loss. Hence. provides a checklist of the policy actions, informs the cost-effectiveness of policy interventions, and captures education system efficiency, effectiveness, and quality. Future studies are needed to validate and examine the applicability and usefulness of the proposed framework. [For the full proceedings, see ED652228.]

The study presented in this paper uses heuristics from computer linguistics and graph theory to analyze a systematic literature review on educational technology. A literature review was conducted to validate an expert-based taxonomy which was developed to ontologize delivered teaching and learning for easy reuse. The sample includes N = 121 publications. The findings indicate that the yielded key words that were generated through T-MITOCAR Artemis contained key features that were rated as being relevant to the experts and caused the expert-based taxonomy to be changed and restructured. The results of this study provide directions on how time-consuming elements of systematic literature reviews could partially be automated. [For the full proceedings, see ED636095.]

The purpose of this paper is to highlight issues related to students' personal inferences that arise when students verbally explain their justification for calculus statements. We conducted clinical interviews with three undergraduate students who had taken first-semester calculus but had not yet been exposed to formal proof writing activities through undergraduate mathematics courses. We analyzed these students' verbal justification of four statements, each of which described a different relationship between two quantified variables in calculus contexts. In this paper, we document students' personal inferences that were evoked in their justifications and discuss how they are similar to or different from the logical inferences that have been accepted and practiced by the mathematics community for mathematical arguments. [For the complete proceedings, see ED630210.]

This paper demonstrates how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. We examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance prediction; and (2) what types of in-game features were associated with student math knowledge scores. The results indicated that the Random Forest algorithm showed the best performance in predicting posttest math knowledge scores among the seven algorithms employed. Out of 37 features included in the model, the validity of the students' first mathematical transformation was the most predictive of their math knowledge scores. Implications for game learning analytics and supporting students' algebraic learning are discussed based on the findings.

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.]

In this paper, we offer a novel framework for analyzing the Opportunities for Reasoning-and-Proving (ORP) in mathematical tasks. By drawing upon some tenets of the commognitive framework, we conceptualize learning and teaching mathematics via reasoning and proving both as enacting reasoning processes (e.g., conjecturing, justifying) in the curricular-based mathematical discourse and as participation in the meta-discourse about proof, which is focused on the aspects of deductive reasoning. By cluster analysis performed on 106 tasks designed by prospective secondary teachers, we identify four types of tasks corresponding to four types of ORP: limited ORP, curricular-based reasoning ORP, logic related ORP, and fully integrated ORP. We discuss these ORP and the contribution of this framework in light of preparing beginning teachers to integrate reasoning and proving in secondary mathematics classrooms. [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.]

The purpose of this paper is to present an empirical investigation of the critical determinants for the adoption of learning analytics in higher education. A conceptual model was proposed to understand better the adoption of learning analytics in higher education by teaching staff. Structural equation modelling is used for testing and validating the proposed conceptual model based on the survey data collected from Australia, South Africa, and Zimbabwe. Five study hypotheses were statistically significant, while two were statically insignificant. A positive relationship was revealed between user preparedness, technology preparedness, perceived usefulness, and social influence with behavioural intentions to adopt learning analytics in higher education. Hypotheses between user preparedness and perceived usefulness as well as user preparedness and learning analytics adoption were rejected. This study contributes to the learning analytics adoption research by proposing and validating a research model for the adoption of learning analytics in higher education. [For the full proceedings, see ED639633.]

The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the representation of problems and in the formulation of conjectures or relationships that are important in the solution processes is highlighted. In this context, students have the opportunity to look for different ways to argue and support the relevance and validity of the conjectures. Results indicate that students extend their ways of reasoning so that allows them to move from empirical to formal arguments within problem solutions. [For the complete proceedings, see ED657822.]

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.]

Large language models (LLMs), such as Codex, hold great promise in enhancing programming education by automatically generating feedback for students. We investigate using LLMs to generate feedback for fixing syntax errors in Python programs, a key scenario in introductory programming. More concretely, given a student's buggy program, our goal is to generate feedback comprising a fixed program along with a natural language explanation describing the errors/fixes, inspired by how a human tutor would give feedback. While using LLMs is promising, the critical challenge is to ensure high precision in the generated feedback, which is imperative before deploying such technology in classrooms. The main research question we study is: "Can we develop LLMs-based feedback generation techniques with a tunable precision parameter, giving educators quality control over the feedback that students receive?" To this end, we introduce PyFiXV, our technique to generate high-precision feedback powered by Codex. The key idea behind PyFiXV is to use a novel run-time validation mechanism to decide whether the generated feedback is suitable for sharing with the student; notably, this validation mechanism also provides a precision knob to educators. We perform an extensive evaluation using two real-world datasets of Python programs with syntax errors and show the efficacy of PyFiXV in generating high-precision feedback. [For the complete proceedings, see ED630829.]

Problem decomposition into sub-problems or subgoals and recomposition of the solutions to the subgoals into one complete solution is a common strategy to reduce difficulties in structured problem solving. In this study, we use a datadriven graph-mining-based method to decompose historical student solutions of logic-proof problems into Chunks. We design a new problem type where we present these chunks in a Parsons Problem fashion and asked students to reconstruct the complete solution from the chunks. We incorporated these problems within an intelligent logic tutor and called them Chunky Parsons Problems (CPP). These problems demonstrate the process of problem decomposition to students and require them to pay attention to the decomposed solution while they reconstruct the complete solution. The aim of introducing CPP was to improve students' problem-solving skills and performance by improving their decomposition-recomposition skills without significantly increasing training difficulty. Our analysis showed that CPPs could be as easy as Worked Examples (WE). And, students who received CPP with simple explanations attached to the chunks had marginally higher scores than those who received CPPs without explanation or did not receive them. Also, the normalized learning gain of these students shifted more towards the positive side than other students. Finally, as we looked into their proof-construction traces in posttest problems, we observed them to form identifiable chunks aligned with those found in historical solutions with higher efficiency. [For the complete proceedings, see ED630829.]

Narrative inquiry is a type of qualitative research that explores human experiences through lived or told stories to understand a phenomenon. Narrative researchers collect data through spoken or written stories and life experiences of an individual (subject). The data is examined in chronological order to understand the meaning of the phenomenon being studied (Creswell, 2013). The researcher unfolds the hidden meanings in spoken or lived stories by analyzing the data in relation to social and cultural context. Narrative methodology is used to explain the behaviors or experiences of either an individual or a small group of people. Ethnography is a holistic approach to the study of cultural systems using both qualitative and quantitative methods with ontological and epistemological properties. It is greatly dependent on fieldwork. It is a process of discovery, making inferences, and continuing inquiries to achieve emic validity, while being an iterative process of learning episodes. It is also an open-ended emergent learning process, and not a rigid investigator-controlled experiment. [For the full proceedings, see ED656038.]

This study aimed to examine the validity and reliability evidence of Teacher Self-efficacy (TSE) scale (Tschannen-Moran & Hoy, 2001) for teacher in K-12 US schools. Particularly, our study gathered evidence for the internal structure validity, convergent validity, criterion validity and reliability of the TSES in US educational context. The survey was administered to Pre-K-12th grade teachers from a large school district in the Southwestern of the United States. The total sample size was 1,418. The majority of the sample was female (73.9%) and White (73.8%). Nearly half of the sample had BA in education (48.9%) and about 28% of them have master's degree in education. We conducted Confirmatory Factor Analysis (CFA) on Mplus. Data was screened, and all assumptions, normality, outliers and adequate sample size were met. We used CFA for internal structure, correlation for convergent validity evidence, and Analysis of Variance (ANOVA) for criterion validity evidence. Cronbach's Alpha and McDonald's Omega were used for reliability. Our results showed that the data fits the model well based on the goodness-of-fit statistics. This study provides evidence of the validity and reliability of TSE using this sample. [For the complete proceedings, see ED655360.]

Tychonov's 1935 solution of the heat equation, exhibiting nontrivial heat fluxes spontaneously appearing along an isolated conducting rod initially held at zero degrees, has intrigued some specialists for almost a century. No doubt those practicing heat engineers who took mathematics seriously were initially relieved to learn that the construction was valid only for infinitely long rods; the integrity of their published exchanger designs could be defended by citing this weakness, together with the known discrepancies between the heat equation and physical reality. Some mathematicians contrived additional hypotheses to disqualify the Tychonov solution. Recently a computer simulation was executed, revealing just how astonishingly unbridled the solution is. But there remain incongruities in this singular example that invite metaphysical speculation. We fuel the latter with a recap of the history from a lighthearted perspective, providing heat transfer engineering students with a rare insight into the practical value of the mathematicians' exacting obsession with generality. [For the complete proceedings, see ED655360.]

We investigate teacher beliefs about discourses for equation solving and the challenges these beliefs might pose for the implementation of instructional practices that promote deductive reasoning in algebra. To uncover these beliefs, we recorded three video explanations of solutions to the same linear equation with distinct discursive characteristics and analyzed seven secondary mathematics teachers' small-group critical discussions of these explanations. Three prevalent themes surfaced in our thematic analysis. Teacher beliefs about discourse for equation solving specified different roles and potential benefits of deductive explanations, estimated students' capacity to understand deductive explanations, and hypothesized differences between teachers' and students' potential to understand deductive reasoning. We discuss implications of these beliefs for opportunities to engage all learners in conceptual thinking about equations. [For the complete proceedings, see ED658295.]

Understanding how students reason with logical implication is essential for supporting students' construction of increasingly powerful ways of reasoning in proofs-based mathematics courses. We report on the results of an NSF-funded case study with a mathematics major enrolled in an introductory proofs course. We investigate the epistemological obstacles that she experienced and how they might relate to her treatment of logical implications as actions. Evidence shows that an action conception may pose challenges when students transform or quantify implications and may contribute to erroneous assumptions of biconditionality. Our report on available ways of operating with logical implications as actions is a first step in designing instructional tasks that leverage students' existing reasoning skills to support their continued development. [For the complete proceedings, see ED658295.]

Proof is a fundamental aspect of mathematics. However, in the high school curriculum, it often receives uneven attention that is focused on form rather than understanding. One avenue for addressing this issue is to change and strengthen teachers' conceptions of proof. To explore this idea, we followed a group of teachers as they participated in a summer mathematics research experience. During this experience, proof was not an isolated exercise but part of the mathematical process of discovery. In this study, we analyzed pre- and post-survey data and participants' critique of proofs to uncover the influence of the mathematics research experience on their concept of proof. We present data on the criteria participants used to evaluate proofs, their conception of proof, and how the mathematics research experience changed their conception of proof. [For the complete proceedings, see ED657822.]

Bramlett and Drake (2013) suggest that the ability of teachers to teach proof is crucial for students to learn and develop formal and informal proofs. Teachers need to be involved in the process of proving and have a firm understanding of the critical role of proofs in order to effectively engage their students in proving activities. It is unrealistic to expect K-12 teachers to educate students on proof if they themselves are not given opportunities to engage deeply in the process of proving and understand its significance (Bramlett & Drake, 2013). According to McClain (2010), it is important for teachers to help students understand proof and engage in proving tasks. However, there has been little research on how to teach proof in secondary school mathematics. Steele (2012) suggests that teachers should have the knowledge and skills to identify whether mathematical arguments constitute proofs or not and determine what counts as proof across different representations. Pedagogical beliefs toward proof may be influenced by teachers' beliefs about the nature and role of proof in mathematics, its role in school mathematics, and their beliefs about themselves as mathematical thinkers. In this case study, the researchers leveraged a qualitative method -- case study -- to study a pre-service teachers' belief about the process of proof and the role of visualization and technology in teaching proof. [For the complete proceedings, see ED657822.]

Nature of Science (NOS) has been enumerated as one of the important elements in education because robust conceptions of NOS is essential for individuals to be considered as scientific literate. As teachers are vital in imparting sound NOS conceptions to their students, they must possess sound NOS conceptions. However, studies have shown that teachers only possess naive conceptions of NOS which could be potentially passed down to their students during science instruction. So far, studies about in-service science teachers' conception on NOS were conducted in the West. The extensive literature search that was conducted on several renowned platforms found that the existing research available to the public focused on secondary school students or pre-service teachers but not in-service teachers. The conduct of this study bridges the gap in literature and informs relevant stakeholders about the current state of science education in Malaysia. This study shares the findings of a survey conducted with 33 in-service public school science teachers in Selangor, Malaysia. Results show that most teachers possess mixed conceptions about NOS. This study has implications on informing relevant stakeholders about the need of including NOS as a part of teacher training programmes and the need to conduct training sessions with in-service science teachers on NOS. [For the full proceedings, see ED654100.]

Assessment is a topic of concern to all stakeholders in our educational system. Pattern Based Questions are an assessment tool which is an alternative to the standardized assessment tool, and they are based on generative learning pedagogy, which shows promise in engaging all learners and usefulness in teaching and learning but validity has not yet been empirically established. Pattern-based questions seek to provide a qualitative expression of student understanding. It is the purpose of this research to empirically explore a correspondence between student response patterns and the students' expressed ways of thinking using a grounded theory approach and clinical interviews. Findings include rich descriptions of participants' ways of thinking about equivalent fractions as written in the PBQ. One response pattern was clearly differentiated from the others. Future research is discussed. [For the complete proceedings, see ED657822.]

Proof validation plays a significant role in students' understanding and learning of mathematical proofs. Recent studies have shown that university students were lacking skills in proof validation and were challenged by the implementation of the appropriate acceptance criteria when validating proofs. Drawing on Habermas' construct and rational questioning, the present study develops a proof validation framework that seeks to improve students' proof validation skills. The written responses of students' proof validation were analyzed based on their use of the proof validation framework in the context of a transition-to-proof course. The results showed that students primarily focused on the epistemic rationality component when they accept or reject the purported proof and that the students experienced difficulties with meeting the requirements of rationality components. Some educational implications are provided. [For the complete proceedings, see ED657822.]

The study was conducted to evaluate the implementation of the Concurrent Classroom (CC) modality, a type of hybrid learning modality wherein an in-person teacher teaches in-person and online students simultaneously. The study utilized a quantitative research design to assess the implementation of the CC based on its viability, functionality, and effectiveness. Grades 4 to 12 students, teachers, and subject coordinators participated in the study. Quantitative data were obtained from the self-rating survey, classroom observation rating and summative assessment results. Remarks about the implementation of the CC were also solicited. Obtained results show that the CC modality has high viability. It is practical, useful, and suitable for instructional delivery. CC also shows high functionality. It has enabled teachers and students to perform tasks that are expected from them. Lastly, it is an effective modality because it has produced favorable positive learning outcomes. Recommendations are focused on providing a targeted professional development to empower teachers in effectively handling CC classes, focusing on equitable cognitive engagement, active participation, and balanced support and attention for both in-person and online student groups. Also, provision and functionality of required devices, technical equipment, and connectivity in the CC learning environment must be ensured and emphasized. [For the full proceedings, see ED654100.]