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Understanding the concepts related to real function is essential in learning mathematics. To determine how students understand these concepts, it is necessary to have an appropriate measurement tool. In this paper, we have created a web application using 32 items from conceptual understanding of real functions (CURF) item bank. We conducted a psychometric analysis using Rasch model on 207 first-year students. The analysis showed that CURF is a dependable and valid instrument for measuring students' CURF. The test is uni-dimensional; all items are consistent with the construct and have excellent item fit statistics. The results indicate that the items are independent of each other and unbiased towards the gender and high school background of the students.

The teachers' beliefs in ethnomathematics-based numeracy learning are a crucial element to be able to develop students' numeracy skills. The teachers' beliefs in developing students' numeracy skills through ethnomathematics-based numeracy learning is a teacher's personal view about certain practices that are considered correct, which include four dimensions. The first dimension is the teachers' beliefs about numeracy. The second dimension is teachers' beliefs about the role of ethnomathematics in learning numeracy. The third dimension is teachers' beliefs about ethnomathematics-based numeracy teaching. The fourth dimension is teachers' beliefs about ethnomathematics-based numeracy learning. This study aimed to investigate the characteristics of teachers' beliefs in developing students' numeracy skills through ethnomathematics-based numeracy learning. The teacher's response was acquired through the completion of a questionnaire. The findings indicated that most teachers believed fostering students' numeracy skills could be achieved by implementing ethnomathematics-based numeracy learning inside the semi-realisticmechanistic (SRM) categories. Further analysis reveals that more extended teaching experience may mean something other than that a teacher has a realistically oriented outlook. Teachers with teaching experience of fewer than five years (new teachers) and 5 to 10 years (junior teachers') have a semi-realisticmechanistic (SRM) view. Most teachers with more than 10 to 15 years (semi-senior-teachers) of teaching experience have a dominant realistic (DR) idea. In contrast, teachers with more than 15 years (senior teachers) of teaching experience have a semi-realistic-mechanistic (SRM) view and a dominant realistic (DR) view. Teachers' positive beliefs will likely improve students' numeracy skills in general and based on teaching experience in the dominant realistic (DR) and realistic (R) categories regarding ethnomathematics-based numeracy learning.

The present study examines the first-year engineering students' attitudes towards mathematics, their beliefs and self-efficacy about mathematics, as part of their affective performance, in relation to their mathematical academic performance before and after attending an introductory mathematics course. It aims to contribute on the ongoing discussion about the teaching of mathematics at the level of higher education in engineering programs. First-year engineering students completed a questionnaire and a test after their entrance at the university. Their mathematical performance was examined by using their results at the midterm and the final mathematical mark during AMAT111 course offered at the first semester of their studies. Results indicated that aspects of the affective domain were related with students' performance, while the predominant role belonged to their previous mathematical knowledge and skills (as learning outcome of the high school education), which undoubtedly need further enhancement. The belief about a formalistic perspective of mathematics and the lack of understanding of the implementation of the mathematical concepts on engineering problem solving situations were obstacles for them on recognizing the importance of attending mathematics courses as part of their engineering studies. Discussion concentrates on the following up steps, which have to be done at the level of higher education in order to face the initial difficulties, which have been identified.

The cognitive reflection test (CRT) assesses an individual's capacity to restrain impulsive and intuitive responses and to engage in critical reflection on mathematical problems. The literature indicates that several factors influence students' performance on CRT, including gender, age, and prior knowledge of mathematics. In this study, our objective was to investigate the correlation between CRT scores and students' achievements in both mathematics and physics. We conducted our research with a sample of 150 Italian high school students, and the findings revealed a positive predictive relationship between CRT scores and students' performance in both mathematics and physics. Furthermore, we employed an ordinal logistic regression to evaluate the impact of CRT scores, gender, and school level on students' achievements in mathematics and physics. The results showed that both CRT scores and school level had statistically significant effects on predicting these achievements. In contrast, gender emerged as a statistically significant factor only in predicting students' mathematics achievements.

The aim of this pilot study is to evaluate the relevance of the use of history in mathematics education. This paper presents an experiment carried out in France with sixth-grade students (n=108) in which an ancient number system is used, an approach that is commonly suggested in French sixth-grade textbooks but has previously been unassessed. Based on the data of a pretest and a post-test surrounding an activity on an ancient Chinese numeration system, a statistical analysis using Rasch modeling shows a specific added value of the history of mathematics for students with low abilities in mathematics. For these students, a significant increase in observed abilities of +0.67 logit in mean is measured with a large effect size (Cliff delta +0.52). This effect is then weighted by considering the regression to the mean (RTM) effect, leading to a value around +0.14 logit in mean and a negligible effect size (Cliff delta +0.10). So, this pilot study shows the important effect of RTM, which suggests a very strong rebalancing of students' results. In the last part of the paper, we discuss how RTM can nonetheless be positively interpreted in this specific context where students' disorientation is one of the purposes of history in mathematics education.

One of the main objectives of international large-scale assessments is to make comparisons between different countries, education policies, education systems, or subgroups. One of the main criteria for making comparisons between different groups is to ensure measurement invariance. The purpose of this study was to test the measurement invariance of the mathematics intrinsic motivation scale across 14 countries. For this purpose, the "students like learning mathematics" scale, which measures intrinsic motivation for mathematics, was included in the TIMSS 2019 cycle. The study sample consisted of a total of 152992 students, 70192 4th grade and 82800 8th grade students from 14 different countries participating in the TIMSS 2019 cycle. Measurement invariance was tested with Multi-Group Confirmatory Factor Analysis (MG-CFA) and Alignment Method. The mathematics intrinsic motivation scale provides only configural invariance according to MG-CFA at the 4th grade level, whereas the scale provides approximate invariance according to the alignment method. At the 8th grade level, the scale provides configural and metric invariance according to MG-CFA, whereas the scale provides approximate invariance according to the alignment method. The results indicate that the mathematics intrinsic motivation scale provides approximate measurement invariance at both grade levels and that comparisons can be made between the scores of the identified countries.

Purpose: Ethnomathematics are used in motifs by the Dayak Ngaju Tribe in Central Kalimantan. The motifs contain some Ethnomathematical objects and concepts for Geometry and values. Therefore, this study aimed to describe the motifs based on mathematical objects and concepts of Geometry and value viewed from ethnomathematics aspects. Methodology: This study used a qualitative approach with an ethnography method. The researchers collected information from documents and books. They conducted in-depth observations and interviews with the subjects regarding the culture of the Dayak Ngaju people who reside downstream of the Kahayan River in Central Kalimantan. The subjects were a Dayak Ngaju craftsman and a priest of the Hindu Kaharingan community. The motifs consist of "tingang," "dandang tingang," "jata," "batang garing," "tanduk muang," "buntut kakupu gajah," "taya" tree and "rambunan tambun." Findings: The motifs contain some mathematical objects and concepts. Mathematical objects are created as circles, "batang garing" and "jata" motifs, and a six-sided shape in the "tanduk muang" motif. The concept is the geometric transformations, namely the axis reflection in the mdandang tingang and tanduk muang motifs the axis reflection in the motifs of "tingang," "batang garing," "tanduk muang" and "taya" tree. The rotation on point (0,0) in the motifs of "buntut kakupu gajah" and "taya" tree, and the translation in the motif of "jata." Significance: The study provides some mathematical objects and concepts in the motifs of the Dayak Ngaju tribe in Central Kalimantan. Students learning those objects and concepts should be related to their culture, namely the motifs, and they should acquire the values in such learning. Ethnomathematics plays an important role among Dayak Ngaju people in understanding mathematics concepts such as Geometry and values.

To fully possess mathematical competence and to understand its relevance, importance and aesthetics, it is essential to be aware of aspects of mathematics not only as a school subject but also as a scientific discipline. In a systematic literature review, the theoretical characterization of compulsory school students' beliefs about mathematics as a discipline is investigated, as well as the empirical tendencies in the nature of their actual beliefs. Furthermore, the valuation of these beliefs is addressed. The 18 included studies demonstrate a clear pattern in applying a dualistic/relativistic spectrum when characterizing and analysing students' beliefs about mathematics as a discipline, with students generally possessing dualistic beliefs, which is in contrast to what is favourable to their learning.

The purpose of this research was to explain why many people do not like mathematics and find it difficult because it is difficult to understand or because a teacher they had did not give the appropriate weight. The methodology used in this research was the quantitative method. The sample was collected through electronic questionnaires involving sixty-three (63) participants from pedagogical departments. The following survey shows the main results of the research, more specifically, that negative emotions about mathematics are more prevalent. The three main elements that characterize the successful teaching approach of mathematics at school are the transmission of knowledge by the teacher, the approach of knowledge through play, and the selection of appropriate activities. While the two most appropriate ways of approaching mathematics in kindergarten are through play but also through investigation and discovery by the child based on the participants' answers.

Children with dyslexia frequently also struggle with math. However, studies of reading disability (RD) rarely assess math skill, and the neurocognitive mechanisms underlying co-occurring reading and math disability (RD+MD) are not clear. The current study aimed to identify behavioral and neurocognitive factors associated with co-occurring MD among 86 children with RD. Within this sample, 43% had co-occurring RD+MD and 22% demonstrated a possible vulnerability in math, while 35% had no math difficulties (RD-Only). We investigated whether RD-Only and RD+MD students differed behaviorally in their phonological awareness, reading skills, or executive functions, as well as in the brain mechanisms underlying word reading and visuospatial working memory using functional magnetic resonance imaging (fMRI). The RD+MD group did not differ from RD-Only on behavioral or brain measures of phonological awareness related to speech or print. However, the RD+MD group demonstrated significantly worse working memory and processing speed performance than the RD-Only group. The RD+MD group also exhibited reduced brain activations for visuospatial working memory relative to RD-Only. Exploratory brain-behavior correlations along a broad spectrum of math ability revealed that stronger math skills were associated with greater activation in bilateral visual cortex. These converging neuro-behavioral findings suggest that poor executive functions in general, including differences in visuospatial working memory, are specifically associated with co-occurring MD in the context of RD.

Formal teacher leader programs that develop, position, and reward teachers to work with peers to improve instruction are a growing reform effort in the United States, yet there are few published studies of their efficacy. In this paper, we examine the impacts of one district's teacher leadership program on students' annual state test performance. The program placed full-time instructional coaches and partly released English language arts (ELA) and mathematics content specialists in each of 11 district schools. To assess the program's impact, we examined five years of student-level state test data; two years before the adoption of the intervention and three years afterwards. Using an interrupted time series design, we examined trends in performance before and after the adoption of the intervention. Overall, there were no significant effects in ELA, and a small negative effect in mathematics. By contrast, in the stable sub-sample of students who were in the district for the five years examined in the study, there was a large significant positive effect in mathematics and large but non-significant positive effect in ELA. We conclude with a discussion the implications of these findings for research and policy.

The study involved 2,575 students selected through a combination of probability and non-probability sampling procedures. Explanatory sequential mixed methods design was used. Participants completed the FennemaSherman Mathematics Attitude Scales (FSMAS) to provide the quantitative data for the research. The qualitative data were gathered through interviews. The arithmetic mean from the survey data for each of the students was used to shortlist 140 students for focus group interviews. The findings revealed that some of the impetuses that drive the respondents' positive attitudes towards mathematics were mathematics as a compulsory subject, good teaching strategies by teachers, the utility of mathematics, career aspirations, and encouragement from parents, guardian or peers. The study recommended that stakeholders should encourage, enhance and promote these factors. Teachers, educators, and researchers are encouraged to dig deeper to unearth more of such factors.

This study aimed to explore preservice elementary teachers' use of a bar model as a heuristic for conceptualising relationships between quantities in situations involving ratio and percentages. As a part of a larger project, we focused on two preservice teachers, Maia and Jane, and investigated their solution paths in ratio and percentage problems and the role of the structural representations (i.e., bar model and percent line-bar model) in their solution paths. We analysed these focus participants' written solutions and their think-aloud process during interviews using three coding phases with a constructivist grounded theory approach. We observed that the problem text fed the construction of the structural representations that served to make sense of the quantities and the relationships among them. Furthermore, the structural representations enhanced Maia and Jane's mathematical insights about the problem situations. In addition, we observed that preservice teachers' solution paths were neither linear nor similar, which indicates a mathematical richness in learning. In those solution paths, the model construction played a role in guiding the mathematical operations of constructing and operating on a unit rate in the ratio problem and identifying and operating on a referent whole unit in the percentage problem. We interpreted that variety and nonlinearity in solution paths suggested mathematical richness in learning, the educational implications of which were further discussed.

The relation between prior knowledge and learning has been investigated in many studies. However, a recent meta-analysis showed that most of these studies suffered from serious methodological shortcomings, as they failed to account for knowledge growth over time, possible ceiling effects for learners with high prior knowledge, moderating effects of learning environments, and possible confounds between intelligence or traits that refer to intellectual investment and prior knowledge. The present study avoided these limitations. A total of 922 students were tested with progressively more difficult Rasch-scaled knowledge tests at four measurement points from Grades 5 to 7. The relation between prior knowledge and knowledge growth in six learning environments (i.e., mathematics, German, and English in regular and gifted classes) was investigated using multigroup latent growth curve models with and without controlling for students' intelligence and the intellectual investment trait of need for cognition. In regular classes, prior knowledge negatively predicted knowledge gains in all subjects. In gifted classes, prior knowledge negatively predicted knowledge gains only in German and English, and need for cognition positively predicted knowledge gains in mathematics but not in German or English. The results indicate that school instruction is designed to help all students reach the predefined learning goals and pass criterion-oriented tests. As a result, students with low prior knowledge tend to learn more than high prior knowledge students. More research is needed on how these processes are modulated by learning environments and are intertwined with students' intelligence and their intellectual investment.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.