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Definitions are an integral aspect of mathematics. In particular, they form the backbone of deductive reasoning and facilitate precision in mathematical communication. However, when multiple non-equivalent definitions for the same term exist, their ability to serve these purposes can be called into question. While ambiguity can be productive, the lack of an agreed upon definition can make the truth value of certain mathematical statements unclear. In this study, we presented pre-service and in-service mathematics teachers with three mathematical claims in which definitional ambiguity was a consideration; then, we asked them to determine the correctness of each claim, justify their positions, and anticipate what reasoning might lead to a possible counterargument. Based on their responses, we identified several factors that influenced the participants' approaches in each situation as well as cross-cutting themes that describe their considerations. Finally, we consider the pedagogical implications of employing such a task in teacher preparation programs and in-service teacher education.

Young children's early math experiences are culturally situated, occurring in the context of everyday family interactions and routines. Yet, we know little about the math experiences in culturally and linguistically minoritized families, including those from Latine communities. In this article, we provide the first review of research on family math in the homes of young Latine children in the United States. We identify shared patterns and inconsistencies across studies on family math cognitions and math practices, and their relations with children's outcomes. We argue for the need to use a sociocultural lens to examine and understand family math, and offer recommendations that center families' experiences to generate foundational knowledge, capture within-group variation, and use more flexible and culturally relevant measures.

In this paper we discuss the types of knowledge used by six middle school students as they engaged with a debugging task designed to integrate ideas from computer science, mathematics and science. Our findings show that the computational thinking practice of debugging is a rich source of opportunities to integrate these different disciplines. The analysis illustrates how the types of knowledge the students did and did not use at each step of the debugging process were related to their ability to succeed at each step. Our work contributes to theory and practice by uncovering implications for studying debugging through two refined frameworks and for designing debugging tasks to support transdisciplinary learning.

In this study, we discuss how the use of student personas can support pre-service teachers developing digital mathematics learning resources and improve mathematics teacher training programs. The use of modern technologies in schools requires that pre-service teachers prepare for new challenges, including the development of digital learning resources. To be able to develop such resources during teacher training, pre-service mathematics teachers without direct contact with students need insights into particular characteristics of mathematics students. We argue that personas, a tool and approach adopted from user experience research, can provide such insights. For this purpose, we interviewed four pre-service mathematics teachers who were developing digital learning resources in the span of a semester. We analyzed the data using grounded qualitative content analysis approaches and identified the following key aspects of personas usage for mathematics teacher training: (A) personas can act as an information tool, (B) personas can act as a planning and feedback tool, (C) the use of personas can trigger reflection processes for pre-service teachers, and (D) sustained work with personas may increase its impact. Our results indicate that personas can offer pre-service teachers support when developing digital learning resources and contribute to their professional development.

In this paper, I analyze the impact of culture and metaphor on cryptology education. I will compare and contrast the historically grounded metaphors of cryptology-is-warfare and encryption-is-security to a set of counter-metaphors: cryptology-is-privacy and encryption-is-communication. Using this explicit understanding of conceptual metaphor, I present design recommendations and metaphorizing activities for educators building their undergraduate cryptology course.

Household composition has diversified and encompasses the number of parents and the types of extended relatives in homes with implications for a child's development. Yet, few studies have included Latinx children of immigrant parents. To fill this gap, I draw upon the Early Childhood Longitudinal Study, 2011-cohort to analyze the household composition and academic performance of Latinx children of immigrant parents and Latinx children of U.S.-born parents from kindergarten through fifth grade. I use an ecological framework to situate household composition as a microsystem component. Results indicated that Latinx children of immigrant parents were less likely to have lived with a single parent and more likely to have lived with horizontal relatives, like aunts or uncles, compared to Latinx children of U.S.-born parents. However, they were as likely as Latinx children of U.S.-born parents to have lived with grandparents or with grandparents and other extended relatives. Structural factors largely shaped household composition. Importantly, household composition states did not compensate for the academic disparities in math and reading between Latinx children of immigrant parents and Latinx children of U.S.-born parents. However, the presence of extended relatives did have a partial effect in some household composition states.

It is difficult for mathematics teachers to find and utilize relevant historical content for their students. In this study, we aimed to examine how prospective mathematics teachers (PMTs) evaluate the history of mathematics (HM) in curriculum resources and how they integrate the HM into lesson plans. We collected data through PMTs' evaluation reports on the analysis of textbooks, lesson plans, and lesson plan reflections. PMTs evaluated textbooks critically, acknowledging the limits and recognizing the possibilities. They mostly provided negative evaluations and criticized the quality of HM in the textbooks. The findings revealed that PMTs' evaluations of the analysis of HMs in textbooks served as a bridge to assist their utilization of HMs in lesson plans. When PMTs incorporated HM into their lesson plans in an effort to engage students in the learning of mathematics, the HM integration reached higher levels of cognitive demand. However, they performed less well when incorporating pedagogical instructions and student thinking. The theoretical and practical implications of the study are discussed.

Purpose: This study aims to describe and examine the effectiveness of the mathematics-based learning method, called Accountamatics (Accounting from Mathematics perspective). The Accountamatics method is rooted in the principles of double-entry bookkeeping and the rules of debits and credits, which were initially documented by Luca Pacioli, a Mathematics Professor, in a mathematics book. Design/methodology/approach: This study uses a quasi-experimental design, spanning a duration of one semester, to examine its research objectives. The participants included 230 students from the Faculty of Economics and Business in Indonesia, who were accredited by AACSB. Control variables, including gender, majors and study backgrounds, were taken into consideration. The data was analyzed using a linear regression test, followed by a comparative t-test. Findings: The study findings show a significant positive impact of the Accountamatics method on student performance when compared to traditional learning approaches. Furthermore, the analysis indicates that the control variables examined in the study did not have a significant effect on student performance. Thus, it can be inferred that the implementation of the Accountamatics method has a beneficial effect on the academic performance of college students. Practical implications: The study findings provide valuable insights for faculty members in higher education institutions, highlighting the potential benefits of incorporating mathematics-based teaching in accounting as an alternative approach for business students. These findings contribute to the existing knowledge on innovative teaching methods that can enhance the study of accounting within the business curriculum. Originality/value: Over the span of around 25 years, extensive research has been conducted to compare traditional teaching methods with innovative approaches. However, the results have not consistently shown that the innovative methods outperform their traditional counterparts. In response to this, the Accountamatics method has been developed, building upon the fundamental knowledge in accounting that has been used since 1494. Despite its historical significance, this method is sometimes regarded as limited to technical knowledge in the modern era.

The aim of this study was to summarize evidence about the relations between parent math support in children aged 3-5 years (from several countries in America, Asia, and Europe) and concurrent and longitudinal math outcomes. The (bio)ecological model of human development guided our hypotheses. The design and reporting of this meta-analysis used the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). We screened 2,163 abstracts, from which 135 full-text studies were assessed for eligibility. Forty-five studies fulfilled our inclusion criteria and were retained (representing 244 effect sizes); 90 studies were discarded as they did not include preschool children or measures of both parent math support and children's math skills. Meta-analysis using Correlated and Hierarchical Effect (CHE) models showed a significant positive association between parent math support and child math skills for both concurrent and longitudinal studies. On average, higher parent math support was associated with better math skills in children, albeit these being small effect sizes. We found non-significant or inconclusive moderator effects related to formal vs. informal parent math support, type of children's math skills, participants' characteristics (e.g., child age and child/parent gender), parent education, and study characteristics. There was a significant moderator effect of the specificity of parent math support, with global assessments showing higher correlations with math outcomes than specific assessments. The publication bias analysis showed small-study effects for longitudinal but not for concurrent studies. Conclusions are drawn regarding the importance of promoting parent math support and informing future intervention studies.

The latest technologies in natural language processing provide creative, knowledge retrieval, and question-answering technologies in the design of intelligent education, which can provide learners with personalized feedback and expert guidance. Entrepreneurship education aims to cultivate and develop the innovative thinking and entrepreneurial skills of students, making it a practical form of education. However, a knowledge retrieval and question-answering teaching assistant system for entrepreneurship education has not been proposed. This observation motivated us to develop a reading comprehension framework to address the challenges of domain-specific knowledge gaps and the weak comprehension of complex texts encountered by intelligent education models in practical applications. The proposed framework mainly includes: question understanding, relevant knowledge retrieval, mathematical calculation, and answer prediction. The techniques involved in the aforementioned modules mainly include text embedding, similarity retrieval, graph convolution, and long short-term memory network. By integrating this model into entrepreneurship courses, learners can participate in real-time discussions and receive immediate feedback, creating a more dynamic and interactive learning environment. To assess the effectiveness of the proposed model, this article conducts answer prediction on single-choice exercises related to entrepreneurship education courses. This study employs the potential of using a question-and-answer format to enhance intelligent entrepreneurship education, paving the way for a more effective and engaging online learning experience.

This study investigated the underexplored topic of teacher preparation program admissions processes by interviewing faculty and analyzing program documents. We investigated how 31 K-12 mathematics and science teacher preparation programs (MSTPPs) and faculty attend to diversity, equity, inclusion, and social and racial justice (DEIJ). Specific foci included applicant recruitment and selection, components of applications (e.g., forms, essays, and interviews), and how applicants' DEIJ-related information and orientations factor into admissions. We found that all MSTPPs participating in the study collected information related to DEIJ (e.g., applicants' ethnoracial backgrounds, citizenship), and all interviewed faculty expressed an interest in increasing the diversity of applicants and admitted students. Faculty expressed preferences for applicants who evidenced positive DEIJ orientations, such as recognizing social and ethnoracial injustices, but at the same time, differences were evident in how MSTPPs and faculty attended to DEIJ. Considerations, implications, and dilemmas for teacher preparation programs and faculty are discussed.

The logistic differential equation is ubiquitous in calculus and differential equations textbooks. If the model is developed from first principles in these courses, it is usually done in an abstract mathematical way, rather than in one based in ecology. In this short note, we look at examples of how the model is derived in mathematical texts and compare them to that in an ecology text.

We conducted a systematic review to generate a comprehensive understanding of cisgendered girls' mathematical identity within the United States to better understand: (a) how mathematical identity is associated with girls' participation, engagement, and achievement in mathematics; (b) the factors related to girls' mathematical identity; and (c) strategies for developing strong mathematical identities within girls. We identified 76 articles that examined mathematical identity in young girls and women. Our review suggests that positive girls' mathematical identity was consistently linked with increased performance, participation and persistence in mathematics. Factors and strategies affecting girls' mathematical identity included the role of parental attitudes and beliefs; societal and cultural influences; and the intersections of sex and race. Practical implications for researchers and practitioners are also discussed.

In designing an intelligent tutoring system, a core area of the application of AI in education, tips from the system or virtual tutors are crucial in helping students solve difficult questions in disciplines like mathematics. Traditionally, the manual design of general tips by teachers is time-consuming and error-prone. Generative AI, like ChatGPT, presents a new channel for designing general tips. This study utilized prompt engineering and Chain of Thought to summarize general tips for given mathematical problems (one geometry problem and one algebra problem) and their solutions. A Turing test was conducted to compare ChatGPT-generated general tips with human-designed ones. Results from 121 human evaluators, each assessing 6 ChatGPT-generated and 6 human-designed general tips for each of two mathematical problems, showed that the average score for ChatGPT-generated tips is less than that of human-designed tips at a statistically significant level (p < 0.05), and Zero-Shot CoT achieved the best score. However, no evaluator could distinguish the tip types exactly. The average precision, recall and F-value of all ChatGPT-generated tips are less than 40%. AI-generated general tips can serve as a valuable reference for teachers to enhance efficiency and students' mathematical learning.

When student achievement is assessed, we seek to elicit a student's maximum performance -- a goal requiring the assumption that the student is fully engaged. Otherwise, to the extent that disengagement occurs, test performance is likely to suffer. Effectively managing test-taking disengagement requires an understanding of the testing conditions under which disengagement is more likely. This study investigated the association between disengagement and the time-of-day testing occurred for a widely used low-stakes, computer-adaptive achievement test in grades 2-8. Disengagement was measured using two indicators: response time effort (RTE) and performance decline. Results showed clear evidence for a time-of-day effect for RTE, with the prevalence of students exhibiting low RTE (<0.90) tripling during the school day in Math, and nearly doubling in Reading. In contrast, the prevalence of significant performance decline showed little change across time of day. Reasons for differences in results for the two disengagement indicators are discussed.

This study aims to classify subtypes of mathematics disability (MD) using a novel classification method, cognitive diagnostic models (CDMs), and examine whether domain-general skills, namely, linguistic, working memory, and spatial skills, were related to the identification of the subtypes. Participants were 454 children (246 boys; age: M ± SD = 88.66 ± 5.92 months), including 204 MD children and a control group of 250 low-achieving children, who were identified from a sample of 3,384 second graders in China. Six MD subtypes were classified: the symbolic and concept deficits group, the verbal and concept deficits group, the pervasive deficits group, the concept deficits group, the mapping and concept deficits group, and the unknown deficits group. The reliability and validity of using CDMs to identify MD subtypes were evaluated. Different constellations of working memory, spatial, and linguistic skills were found to contribute to different MD subtypes. Identifying subtypes of MD and their domain-general correlates sheds light on appropriate interventions targeting different MD subtypes.

Questionnaires in educational research assessing students' attitudes and beliefs are low-stakes for the students. As a consequence, students might not always consistently respond to a questionnaire scale but instead provide more random response patterns with no clear link to items' contents. We study inter-individual differences in students' intra-individual random responding profile across 19 questionnaire scales in the TIMSS 2015 eighth-grade student questionnaire in seven countries. A mixture IRT approach was used to assess students' random responder status on a questionnaire scale. A follow-up latent class analysis across the questionnaire revealed four random responding profiles that generalized across countries: A majority of consistent nonrandom responders, intermittent moderate random responders, frequent random responders, and students that were exclusively triggered to respond randomly on the confidence scales in the questionnaire. We discuss the implications of our findings in light of general data-quality concerns and the potential ineffectiveness of early-warning monitoring systems in computer-based surveys.

This study sought to explain the differences in the computational thinking skills of primary school students. The survey model was adopted for the research. In the study, in which 780 primary school students participated, the relationship between computational thinking skills and factors at the student (gender, parent education status, internet access, attitude toward science, attitude toward math) and school level (school status, technology use, classroom size) were analyzed and a prediction model was tested. Personal information forms, computational thinking tests, and attitude scales toward science and math were used in the study. The findings of the study showed that primary school students' computational thinking skills were most closely related to the mother's educational level, attitudes toward math, and use of technology in lessons.

Considering the prevalence of mathematics teacher shortages in the United States, together with declining enrollments in teacher preparation programs, it is crucial for districts and teacher preparation programs alike to investigate new recruitment initiatives. In this pilot study, a university aimed to increase high school students' interest in mathematics and mathematics teaching through a 1-week summer mathematics camp led by university undergraduates who were participating in an experiential learning program in mathematics teaching. The undergraduates engaged the high school students in activities chosen to allow exploration and discovery related tp advanced mathematics topics. High school students expressed highly positive perceptions of the mathematics camp outcomes. Furthermore, participants experienced increased interest in mathematics at the end of the week and approximately one-third of participants attributed the camp to improving their likelihood of entering a teacher preparation program. Participants highlighted the positive classroom environment and focus on social emotional learning as strong contributors to the success of the camp. Implications for future research and practice are discussed.

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

Changes in society demand constantly evolving education systems. Teachers' practice is crucial to the successful implementation of educational reforms. A major obstacle for practicing teachers in implementing reform mathematics is that they have not experienced it themselves as learners. Consequently, teachers require extended, practice-based professional development to support them in the implementation phase of reform endeavours. Japanese Lesson Study has increased in popularity internationally as a professional development model due to its potential to facilitate teachers to learn in and from the practice of teaching. This self-study examines two mathematics teacher educators' first experience of facilitating Lesson Study with Irish primary in-service teachers. Reflection on the Lesson Study carried out with in-service teachers in 8 urban schools revealed three critical incidents that promoted deeper understanding of the context. The findings provide insights into the realities of managing and leading Lesson Study with in-service teachers, in particular the various barriers affecting teacher engagement. Alternative approaches to practice to address these challenges are also identified.

The purpose of this study was to examine associations between caseload, social determinants, health needs, students meeting grade-level English and Math standards, and attendance. Data from the Washington State Open Data Portal and Report Card were combined with District Health Assessment data from 264 school districts. Analyses of variance and linear stepwise regression analyses were conducted. Key findings indicate significant differences in English and Math outcomes by caseloads, with higher caseload districts have lower percentages of students meeting English and Math standards, but not attendance. Caseload is a significant predictor of students meeting English and Math standards, after controlling for social determinants and district health needs. Findings point to the complexity of school nursing work and builds a foundation to guide future nursing research. Large prospective studies that allow for comprehensive measurement of structure, process and outcomes variables are needed to advance school nursing research.

Purpose: This paper defines and assesses student learning patterns under the influence of problem-based learning (PBL) and their classification into a reasonable minimum number of classes. Study utilizes PBL implemented in an undergraduate Statistics and Operations Research course for techno-management students at a private university in India. Design/methodology/approach: Study employs an in situ experiment using a conceptual model based on learning theory. The participant's end-of-semester GPA is Performance Indicator. Integrating PBL with classroom teaching is unique instructional approach to this study. An unsupervised and supervised data mining approach to analyse PBL impact establishes research conclusions. Findings: The administration of PBL results in improved learning patterns (above-average) for students with medium attendance. PBL, Gender, Math background, Board and discipline are contributing factors to students' performance in the decision tree. PBL benefits a student of any gender with lower attendance. Research limitations/implications: This study is limited to course students from one institute and does not consider external factors. Practical implications: Researchers can apply learning patterns obtained in this paper highlighting PBL impact to study effect of every innovative pedagogical study. Classification of students based on learning behaviours can help facilitators plan remedial actions. Originality/value: 1. Clustering is used to extract student learning patterns considering dynamics of student performances over time. Then decision tree is utilized to elicit a simple process of classifying students. 2. Data mining approach overcomes limitations of statistical techniques to provide knowledge impact in presence of demographic characteristics and student attendance.

This paper describes how the notion of the strongly didactic contract can serve to characterize the teaching adopted to implement a task in probability. It is particularly focused on the reality of mathematical work performed by students and teachers. For this research, classroom sessions were developed in an in-service teacher training course designed (and adapted) according to the Japanese Lesson Study model. Through the combined use of the Theory of Didactical Situations (TDS) and the Theory of Mathematical Working Spaces (ThMWS), a coding of the sessions observed was developed. Based on this coding, different patterns emerged which gave each session a specific rhythm and identity from which it was possible to recognize and characterize different strongly didactic contracts. The study highlights the difference between the potential contracts intended by the teachers and those observed in practice. The tools, and especially the coding, developed for the study could be used for future research on instructional situations or in-service teacher training.

Purpose: This qualitative study extends jigsaw lesson study (JLS) by focusing specifically on the impact of feedback on teacher candidates' (TCs') professional knowledge and instructional growth in the teacher-educator classroom. Design/methodology/approach: For this study, JLS took place in two different methods courses and followed the lesson study (LS) framework using the small group rotations of JLS. In each course, the JLS small group teams taught another team before receiving feedback and revising their lessons. Then they would teach another group. After each iteration, teams debriefed and reviewed the feedback to revise their lessons and prepare for reteaching. Following the JLS process, TCs reflected on the impact of feedback in a post-survey that was analyzed, coded and aligned with their lesson iterations and revisions. Findings: Both integrated language arts (ILA) and math TCs reported that receiving peer feedback improved their lessons, instructional materials, revisions and student engagement. Through collaboration, TCs valued peer dialog, multiple perspectives and TCs learned to provide and receive constructive feedback professionally. Overall, feedback and collaboration helped strengthen their lesson planning as they considered multiple perspectives. Feedback helped TCs consider differentiation and the diversity of learners as well as student engagement while building their professional knowledge. Originality/value: Although a previous study has shown an impact of JLS in ILA teacher-education courses with a broader scope in mathematics courses, this study focused on the JLS process in two teacher-education courses. Furthermore, current research tends to focus on the LS process, but this study focused specifically on TCs' perceptions of the impact of feedback of their professional and instructional growth.

The heterogeneity in the developmental trajectories of math motivational beliefs (i.e., expectancies for success and subjective task value beliefs) was examined among Asian and Latinx male and female students from Southern California across Grades 8 through 10 (n = 2,710; 50% female; 85% Latinx; 15% Asian; M[subscript age] = 13.77). By conducting growth mixture modeling, we identified two classes of stable trajectories for expectancies for success; five classes of stable, decreasing, or increasing trajectories for interest and utility value; and three classes of stable, decreasing, or increasing trajectories for attainment value. The group comparisons demonstrated that variability exists in adolescents' motivational belief development at the intersection of their race/ethnicity and gender for some trajectories. For example, Latina adolescents were more likely to maintain moderate expectancies for success than high expectancies for success compared to Latino and Asian male adolescents, but Asian female adolescents did not differ in their level of expectancies for success from the two male groups. Also, we found Latina adolescents displayed smaller decreases in interest compared to Asian female adolescents and in utility value compared to Latino adolescents. The findings from the present study challenge traditional stereotypes in math and highlight positive motivational belief development in students who are marginalized in math (e.g., Latina adolescents).

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

This article considers starting with an existing SIMIODE modeling scenario [Winkel, B. (2015). 1-031-CoolIt-ModelingScenario. SIMIODE (Version 2.0). "QUBES Educational Resources." https://doi.org/10.25334/3WG8-EC31] that develops Newton's law of cooling by considering data on the cooling of a beaker of water in a room, and expanding upon it to create a longer project modeling the temperature of a building with an internal heat pump that is also subject to a sinusoidal varying outside temperature. The proposed project was undertaken early on in the course, since little background was required, and a longer project format was utilised so that students could return to the project and see direct applications of new concepts, such as autonomous vs. nonautonomous ordinary differential equations, slope fields, and Euler's method as they were introduced. The project prompt is provided as well as a detailed discussion of the motivation behind the questions. Finally, the pros and cons of requiring the students to submit a written lab report for the project are reflected upon and a sample rubric is provided.

Modelling roles of mathematics in physics has proved to be a difficult task, with previous models of the interplay between the two disciplines mainly focusing on mathematical modelling and problem solving. However, to convey a realistic view of physics as a field of science to our students, we need to do more than train them to become fluent in modelling and problem solving. In this article, we present a new characterisation of the roles mathematics plays in physics and physics education, taking as a premise that mathematics serves as a constitutive structure in physics analogous to language. In doing so, we aim to highlight how mathematics affects the way we conceptualise physical phenomena. To contextualise our characterisation, we examine some of the existing models and discuss aspects of the interplay between physics and mathematics that are missing in them. We then show how these aspects are incorporated in our characterisation in which mathematics serves as a foundation upon which physical theories are built, and on which we may build mathematical representations of physical information that in turn serve as a basis for further reasoning and modifications. Through reasoning processes mathematics also aids in generating new information and explanations. We have elucidated each of these roles with an example from the historical development of quantum physics. To conclude, we discuss how our new characterisation may aid the development of physics education and physics education research.

This study aimed to examine the quality of the open-access GeoGebra applets for function transformations by attending to the opportunity to learn function transformations afforded by them. Guided by the variation theory, this study conceptualized the opportunity to learn function transformations as the opportunity to discern critical features of function transformations. These critical features include function families in which function transformations are explored, representations of a parent function and its child function, and types and defining parameters of the transformations performed on the graph of a function. The results from the analysis show that the majority of existing GeoGebra applets use only one function family to explore a function transformation, of which quadratic and trigonometric functions are most prominent. The exploration of function translation is allowed in the largest number of applets followed by function dilation; function reflection over the x-axis, y-axis, and y = x; and function dilation. The functions in these applets are primarily represented symbolically and graphically and rarely have the defining parameters of transformations and corresponding points on the graphs of parent and child functions visible, which together suggest a graphical approach to function transformations. These results not only have implications for how to select existing GeoGebra applets for function transformations but also invite us to rethink how to design these applets that maximize students' opportunity to learn function transformations conceptually in dynamic mathematical environments.

This paper provides evidence on the effect of local prescription opioid use on academic achievement of 3rd-8th graders between 2009 and 2018. Using county fixed effects models, I find that when counties have higher levels of prescription opioid use, students score lower on standardized assessments two to three years later, with variation by student subgroups and magnitudes comparable to effective interventions. I find the largest magnitudes in counties with higher poverty rates and states with below-median state education spending. As test score effects predict adult outcomes, these findings point to economic and public health challenges when affected children become adults.

Background: Influential philosophers have suggested that interdisciplinarity is crucial for ecosystem management and scientific practice, and for education to democracy. However, a historical review of the rise of disciplines points at their compartmentalization in schools. An analysis of "core construct categories" of three disciplines, shows that this compartmentalization may decrease when dialogic argumentation is enacted. This background led us to launch an interdisciplinary program in schools. In previous publications, we identified multiple constraints in its implementation and listed design principles for affording interdisciplinary dialogic argumentation. Method: We adopt a "narrative approach" to analyze classroom talk, and ask whether and how interdisciplinary processes emerge in this talk. Findings: Students maintain dialogic argumentation around Interdisciplinary Social Dilemmas, but guidance is necessary for integrating knowledge from different disciplines. When the teacher is attentive to student's unarticulated references to disciplinary ideas, she may subtly guide the emergence of interdisciplinary dialogic argumentation. Often, the teacher misses those opportunities and declaims the integration of knowledge in a non-dialogic talk. Contribution: Dialogic Education is crucial for the success of interdisciplinary programs in schools, but the actual emergence of interdisciplinary processes depends on the handling of organizational and institutional constraints, on huge design efforts, and on subtle guidance.

Context: Dual-task (simultaneous cognitive–motor activities) assessments have been adapted into reliable and valid clinical concussion measures. However, abundant motor and cognitive variations leave researchers and clinicians uncertain about which combinations elicit the intended dual-task effect. Our objective was to examine differences between commonly employed dual-task motor and cognitive combinations among healthy, college-aged individuals. Design: Cross-sectional laboratory study. Methods: Twenty participants (age: 21.3 [2.4] y; height: 176.0 [9.1] cm; mass: 76.0 [16.4] kg; 20% with concussion history) completed 4 motor tasks (gait, tandem gait, single-leg balance, and tandem balance) under 5 cognitive conditions (single task, subtraction, month reversal, spelling backward, and visual Stroop) in a research laboratory. The motor performance outcomes were spatiotemporal variables for gait and tandem gait and center of pressure path length (in centimeters) for single-leg and tandem balance. Cognitive outcomes were response rate (responses/second) and cognitive accuracy. We used separate repeated-measures analyses of variance for each motor and cognitive outcome with post hoc Tukey t tests. Results: Gait velocity, gait stride length, and tandem gait velocity demonstrated significant cognitive–motor interactions (P's <.001) such that all dual-task conditions resulted in varyingly slower or shorter movement than single task. Conversely, single-leg balance (P =.627) and tandem balance (P =.434) center of pressure path length did not significantly differ among the dual-task cognitive conditions or relative to single task. Statistically significant cognitive–motor interactions were observed only for spelling backward accuracy (P =.004) and response rates for spelling backward, month reversal, and visual Stroop (P's <.001) such that worse accuracy, but faster response rates, occurred during motor tasks. Conclusions: Gait and tandem gait motor tasks accompanied with spelling backward or subtraction cognitive tasks demonstrated consistently strong dual-task effects and, therefore, may be the best suited for clinical and research use following concussion. [ABSTRACT FROM AUTHOR]

Purpose: To develop and evaluate a theory on the frequent observation that cyclists prefer cadences (RPMs) higher than those considered most economical at submaximal exercise intensities via modeling and simulation of its mathematical description. Methods: The theory combines the parabolic power-to-velocity (v) relationship, where v is defined by crank length, RPM-dependent ankle velocity, and gear ratio, RPM effects on the maximal lactate steady state (MLSS), and lactate-dependent carbohydrate oxidation (CHO). It was tested against recent experimental results of 12 healthy male recreational cyclists determining the v-dependent peak oxygen uptake (VO2PEAKv), MLSS (MLSSv), corresponding power output (PMLSSv), oxygen uptake at PMLSSv (VO2MLSSv), and CHOMLSSv-management at 100 versus 50 per minute, respectively. Maximum RPM (RPMMAX) attained at minimized pedal torque was measured. RPM-specific maximum sprint power output (PMAXv) was estimated at RPMs of 100 and 50, respectively. Results: Modeling identified that MLSSv and PMLSSv related to PMAXv (IPMLSSv) promote CHO and that VO2MLSSv related to VO2PEAKv inhibits CHO. It shows that cycling at higher RPM reduces IPMLSSv. It suggests that high cycling RPMs minimize differences in the reliance on CHO at MLSSv between athletes with high versus low RPMMAX. Conclusions: The present theory-guided modeling approach is exclusively based on data routinely measured in high-performance testing. It implies a higher performance reserve above IPMLSSv at higher RPM. Cyclists may prefer high cycling RPMs because they appear to minimize differences in the reliance on CHO at MLSSv between athletes with high versus low RPMMAX. [ABSTRACT FROM AUTHOR]

Biomechanics as a discipline is ideally placed to increase awareness and participation of girls and women in science, technology, engineering, and mathematics. A nationwide Biomechanics and Research Innovation Challenge (BRInC) centered on mentoring and role modeling was developed to engage high school girls (mentees) and early-mid-career women (mentors) in the field of biomechanics through the completion of a 100-day research and/or innovation project. This manuscript describes the development, implementation, and uptake of the inaugural BRInC program and synthesizes the research and innovation projects undertaken, providing a framework for adoption of this program within the global biomechanics community. Eighty-seven high school girls in years 9 and 10 (age range: 14–16 y) were mentored in teams (n = 17) by women in biomechanics (n = 24). Using a design thinking approach, teams generated solutions to biomechanics-based problem(s)/research question(s). Eight key reflections on program strengths, as well as areas for improvement and planned changes for future iterations of the BRInC program, are outlined. These key reflections highlight the innovation, impact, and scalability of the program; the importance of a program framework and effective communication tools; and implementation of strategies to sustain the program as well as the importance of diversity and building a sense of community. [ABSTRACT FROM AUTHOR]

Objectives: Fractal analysis is a numerical method that indicates the structural patterns and complexity of the trabecular bone on radiographs. The aim of this cross-sectional study was to evaluate the trabecular bone structure in systemically healthy patients and diabetes mellitus patients with periodontitis using fractal analysis. Method and materials: The study included 125 mandibular first molars of nonsmoker patients. The subjects were divided into five subgroups: diabetes mellitus patients with mild-moderate periodontitis, diabetes mellitus patients with advanced periodontitis, systemically healthy individuals with mild-moderate periodontitis, systemically healthy individuals with advanced periodontitis, and systemically healthy individuals with gingivitis (control group). Clinical periodontal parameters (pocket depth, bleeding on probing, clinical attachment loss, and bone loss) were recorded. Two specific sites located in the mesial-distal regions (n = 250) of the mandibular first molars were identified using periapical radiographs captured with a parallel technique. Fractal analysis values were calculated using the box-counting method. One-way analysis of variance (ANOVA), and Pearson correlation analysis were used forstatistical evaluation. Results: The highest fractal analysis values were observed in systemically healthy with gingivitis patients (mesial fractal analysis: 1.86 ± 0.01; distal fractal analysis: 1.85 ±0.01). Patients with periodontitis (mesial fractal analysis: 1.78 ±0.02; distal fractal analysis: 1.79 ± 0.01) exhibited lower fractal analysis values compared to the control group. There was no significant difference in mesial and distal fractal analysis values between all periodontitis groups. No correlation was found between age, sex, clinical attachment loss, bone loss, and fractal analysis (P>.05). Conclusions: Although fractal analysis values were lower in the periodontitis groups compared to the control group, fractal analysis did not demonstrate any periodontitis-associated changes of bone tra-beculationin diabetes at any stage of periodontitis. Furthermore, there was no significant association between fractal analysis values and age, sex, clinical attachment, and bone loss. [ABSTRACT FROM AUTHOR]

Purpose: To investigate the relationship between the structural parameters of trabecular bone obtained from CBCT imaging and the primary stability of dental implants. Materials and Methods: Sixty patients underwent implant placement followed by primary stability evaluation via measurement of the insertion torque (IT) and the implant stability quotient (ISQ). Gray values (GV) and the fractal dimension (FD) were also measured using pretreatment CBCT images. Results: FD values showed a positive and significant relationship with ISQ and IT values (P = .017 and P = .004, respectively). Additionally, there was a positive and significant correlation between GV and IT (P = .004) as well as between GV and ISQ (P = .010). FD and GV showed a considerable difference between the maxillary and mandibular jaws and were higher in the mandible. Only FD was significantly different between men and women and was higher in men. In the two age groups (older and younger than 45 years), only GV was considerably higher in people older than 45 (P < .05). Conclusions: Both fractal dimension and gray values obtained from CBCT are efficient methods for predicting the primary stability of the implant due to their relationship with ISQ and IT values. [ABSTRACT FROM AUTHOR]

Purpose: The aim of this study was to develop, implement, and evaluate a 16-lesson integrated physical education program focusing on Indigenous games: Education, Movement, and Understanding (EMU). Method: The study aligned with current physical education, English, and mathematics syllabi and involved 105 children (9–12 years) from two primary schools (Awabakal Country, Australia; 2020). Children participated in sixteen 45–60 min EMU lessons over 8 weeks, with feasibility and preliminary efficacy outcomes assessed via mixed methods. Results: EMU was delivered successfully by the research team, with excellent student and teacher evaluations (M = 4.36–5.0 across 20 items). Improvements resulted for children's cardiorespiratory fitness (d = 0.37, p =.001), enjoyment of sport (d = 0.27, p =.024), physical self-perceptions (d = 0.27, p =.043), and academic achievement (spelling d = 0.91, addition d = 0.40, subtraction d = 0.53, and division d = 0.68). No significant changes in well-being or multiplication scores resulted. Conclusion: Our results provide support for the feasibility and preliminary efficacy of EMU as a beneficial and enjoyable integrated primary school physical education program. [ABSTRACT FROM AUTHOR]