The relation between number line performance and mathematics outcomes: Two meta-analyses.

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be overestimated because general cognitive ability has not been fully controlled in prior studies. The first of two meta-analyses (162 studies, 33,101 participants) confirmed a relation between performance on whole number (r = 0.33) and fractions number (r = 0.41) lines and overall mathematics performance. These relations were generally consistent across content domains (e.g., algebra and computation) and other moderators. The second (71 studies, 14,543 participants) used meta-analytic structural equation modeling to confirm these relations while controlling general cognitive ability (defined by IQ and working memory measures) and, in one analysis, general mathematics competence. The relation between number line performance and general mathematics competence remained significant but reduced (ß = 0.13). Controlling general cognitive ability, whole number line performance consistently predicted competence with fractions but not performance on numeracy or computations measures. The results suggest an understanding of the magnitudes represented by whole numbers might be particularly important for students' fractions learning. RESEARCH HIGHLIGHTS: Two meta-analyses examined the link between the number line and mathematics performance. The first revealed significant relations across domains (e.g., algebra and computation). The second controlled for general cognitive ability and resulted in reduced but still significant relations. The relation between number line and fractions performance was stronger than relations to other domains.

Probing Our Built-in Calculator: A Systematic Narrative Review of Noninvasive Brain Stimulation Studies on Arithmetic Operation-Related Brain Areas.

This systematic review presented a comprehensive survey of studies that applied transcranial magnetic stimulation and transcranial electrical stimulation to parietal and nonparietal areas to examine the neural basis of symbolic arithmetic processing. All findings were compiled with regard to the three assumptions of the triple-code model (TCM) of number processing. Thirty-seven eligible manuscripts were identified for review (33 with healthy participants and 4 with patients). Their results are broadly consistent with the first assumption of the TCM that intraparietal sulcus both hold a magnitude code and engage in operations requiring numerical manipulations such as subtraction. However, largely heterogeneous results conflicted with the second assumption of the TCM that the left angular gyrus subserves arithmetic fact retrieval, such as the retrieval of rote-learned multiplication results. Support is also limited for the third assumption of the TCM, namely, that the posterior superior parietal lobule engages in spatial operations on the mental number line. Furthermore, results from the stimulation of brain areas outside of those postulated by the TCM show that the bilateral supramarginal gyrus is involved in online calculation and retrieval, the left temporal cortex in retrieval, and the bilateral dorsolateral prefrontal cortex and cerebellum in online calculation of cognitively demanding arithmetic problems. The overall results indicate that multiple cortical areas subserve arithmetic skills.

Efficacy of Learning Disorder Treatment for Reading or Mathematics Disorders: An Open Study.

Objectives: This study aimed to identify the effectiveness of treatment programs for children with reading (RD) or mathematics disorders (MD). Structured treatment programs were developed to improve phonological awareness and number sense among children and adolescents with RD or MD, respectively, and the effectiveness of the learning disorder treatment programs were evaluated. Methods: We used standardized, objective diagnostic, and evaluation tools not only to recruit participants with RD, MD, or comorbid attention deficit and hyperactivity disorder, but also to assess the effectiveness of the treatments regarding both improved core neurocognitive deficits of RD or MD and academic achievement. Forty children with RD or MD received one-on-one treatments from therapists. Results: In the RD group, treatment effects were observed in all subtests. In the word and paragraph reading tests, the accuracy rates and fluency improved. The results of the phonological working memory test, word-sound correspondence test, and rapid automatic naming tests also improved. In the MD group, the accuracy rate and fluency on the arithmetic test improved. An increase in the accuracy rate in the size and distance comparison tests and a decrease in the error rate in the estimation test were also observed. However, there were no improvements in reaction time in these subtests. Conclusion: Learning disorder treatment programs that focus on improving phonological awareness or number sense in children with RD or MD improved achievement, phonological awareness, and number sense.

Factors affecting success and failure in higher education mathematics: Students' and teachers' perspectives.

Background: Students from Bangladesh pursuing STEM education often encounter obstacles when tackling diverse mathematical problems within various educational settings. Frequently, they find themselves lacking the essential prerequisite knowledge and strong foundational skills necessary to engage with the teaching and learning resources utilized at the undergraduate level, resulting in a significant number of students needing to seek readmission annually. Objective: The objective of this study is to explore the determinants of academic achievement among university undergraduates majoring in mathematics in Bangladesh. Employing a mixed-method research approach, the study combines quantitative and qualitative data analysis to examine the viewpoints of both students and educators concerning these factors. The authors primarily emphasize classifying the factors that impact the efficacy of mathematics pedagogical methods. Methodology: The study is structured into three phases: i. An initial exploratory qualitative survey. ii. A quantitative triangulation survey. iii. Followed by explanatory semi-structured interviews. Findings: To begin, the initial qualitative survey identified significant factors that contribute to students' achievements and setbacks in mathematics. Subsequently, the quantitative analysis verified both similarities and distinctions in the perspectives of students and educators. Furthermore, the correlation coefficient analysis revealed that male students frequently exhibit inconsistency and a lack of enthusiasm for studying, resulting in subpar performance. Conversely, female students frequently cited challenges like the difficulty of connecting mathematical theories to real-world applications, heavy course loads, and limited resources as reasons for their academic difficulties. Lastly, insights from interviews with students highlighted their acknowledgment of inadequate study practices, excessive reliance on memorization, suboptimal teaching methods, low motivation, and external distractions as key factors leading to their struggles. They also recognized the importance of consistent practice, a solid comprehension of concepts, regular study routines, and effective learning strategies for successful mathematics education. In contrast, educators emphasized the significance of students having clear concepts, natural aptitude, motivation, and a sense of curiosity as pivotal elements for successful learning in mathematics. Conclusion: This conclusion suggests a new beginning in the realm of local mathematics pedagogy, achieved by scrutinizing teacher-student feedback about the factors influencing success and failure, considering the diverse individual and contextual variables at play. To foster mutual trust and understanding between students and teachers, it may be beneficial to engage in open discussions and interactions.

The impact of reading metacognitive strategies on mathematics learning efficiency and performance: An analysis using PISA 2018 data in China.

The current study employed latent profile analysis to examine the application patterns of students' reading metacognitive strategies using PISA 2018 data in China. Subsequently, it explored the differences in students' mathematics learning efficiency and performance. The results revealed that: (1) Six types of reading metacognitive strategies application patterns were identified: "Novice - indifferent," "Veteran - average," "Novice - low evaluating," "Veteran - skilled," "Novice - mixed," and "Novice - arbitrary." (2) The primary factors that affect the classification of reading metacognitive strategies application patterns were gender, and family economic, social, and cultural statuses (ESCS). (3) Mathematics learning time could positively predict performance overall, but the mathematics learning time of "Veteran - skilled" and "Novice - mixed" students had no significant correlation with their mathematics performance. The findings suggests that educators should not blindly increase students' mathematics learning time but instead provide appropriate guidance based on their mastery patterns of reading metacognitive strategies to enhance mathematics learning efficiency and performance.

The development of number line estimation in children at risk of mathematics learning difficulties: A longitudinal study.

Children with mathematics learning difficulties (MLD) show poorer performance on the number line task, but how performance on this task relates to other mathematical skills is unclear. This study examined the association between performance on the number line task and mathematical skills during the first 2 years of school for children at risk of MLD. Children (N = 100; Mage = 83.63 months) were assessed on four occasions on the number line task and other mathematical skills (math fluency, numerical operations, and mathematical reasoning). Estimation patterns were analyzed based on the representational shift and proportional judgment accounts separately. More consistent longitudinal trends and stronger evidence for differences in mathematical skills based on estimation patterns were found within the representational shift account. Latent growth curve models showed accuracy on the number line task as a predictor of growth in some mathematical skills assessed. We discuss impacts of methodological limitations on the study of estimation patterns.

Data on mathematics teacher educators' proficiency and willingness to use technology: A structural equation modelling analysis.

The role of Mathematics Teacher Educators (MTEs) in preparing future teachers to effectively integrate technology into their mathematics instruction is of paramount importance yet remains an underexplored domain. Technology has the potential to enhance the development of 21st-century skills, such as problem-solving and critical thinking, which are essential for students in the era of the fourth industrial revolution. However, the rapid evolution of technology and the emergence of new trends like data analytics, the Internet of Things, machine learning, cloud computing, and artificial intelligence present new challenges in the realm of mathematics teaching and learning. Consequently, MTEs need to equip prospective teachers with the knowledge and skills to harness technology in innovative ways within their future mathematics classrooms. This paper presents and describes data from a survey of 104 MTEs in Zambia. The study focuses on MTEs' proficiency, perceived usefulness, perceived ease of use, and willingness to incorporate technology in their classrooms. This data-driven article aims to unveil patterns and trends within the dataset, with the objective of offering insights rather than drawing definitive conclusions. The article also highlights the data collection process and outlines the procedure for assessing the measurement model of the hypothesised relationships among variables through structural equation modelling analysis. The data described in this article not only sheds light on the current landscape but also serves as a valuable resource for mathematics teacher training institutions and other stakeholders seeking to understand the requisites for MTEs to foster technological skills among prospective teachers of mathematics.

Developing a cognitive model of solid geometry based on Interpretive Structural Modeling method.

With the advancement of science and artificial intelligence, education is experiencing significant innovation. The adaptive learning system is emerging as a promising approach to achieving personalized learning. The cognitive model plays a crucial role as the fundamental rationale behind the adaptive learning system. Currently, there is no uniform and highly operational method for constructing cognitive models. This study adopts Interpretive Structural Modeling (ISM) as the foundational approach for constructing a cognitive model of solid geometry. Based on literature and expert opinions, 17 cognitive attributes of high school solid geometry were identified. Subsequently, a questionnaire survey involving 40 experts was conducted to establish the contextual relationships among these attributes. Applying the ISM method resulted in a seven-level model. This model was then revised based on expert opinions to create the final cognitive model, revealing three primary paths within the domain of high school solid geometry. This paper contends that the use of the ISM method for constructing cognitive models is effective and objective. The resulting cognitive model unveils the content structure of high school solid geometry, and provides an innovative perspective on the construction of cognitive models.

Quantifying nasal deformities using a novel mathematical method to complement preoperative assessment in rhinoplasty patients.

BACKGROUND: Rhinoplasty enhances facial symmetry and functionality. However, the accurate and reliable quantification of nasal defects pre-surgery remains an ongoing challenge. AIM: This study introduces a novel approach for defect quantification using 2D images and artificial intelligence, providing a tool for better preoperative planning and improved surgical outcomes. MATERIALS AND METHODS: A pre-trained AI model for facial landmark detection was utilised on a dataset of 250 images of male patients aged 18 to 24 who underwent rhinoplasty for cosmetic nasal deformity correction. The analysis concentrated on 36 different distances between the facial landmarks. These distances were normalised using min-max scaling to counter image size and quality variations. Post-normalisation, statistical parameters, including mean, median, and standard deviation, were calculated to identify and quantify nasal defects. RESULTS: The methodology was tested and validated using images from different ethnicities and regions, showing promising potential as a beneficial surgical aid. The normalised data produced reliable quantifications of nasal defects (average 76.2%), aiding in preoperative planning and improving surgical outcomes and patient satisfaction. APPLICATIONS: The developed method can be extended to other facial plastic surgeries. Furthermore, it can be used to create app-based software, assist medical education, and improve patient-doctor communication. CONCLUSION: This novel method for defect quantification in rhinoplasty using AI and image processing holds significant potential in improving surgical planning, outcomes, and patient satisfaction, marking an essential step in the fusion of AI and plastic surgery.

The Relationship Between Resilience, Interactive Distance, and College Students' Online Mathematics Learning Engagement: A Longitudinal Study.

Introduction: Resilience, a pivotal construct in positive psychology, remains incompletely understood in its facilitation of learners' online engagement. This study aims to investigate the relationship between resilience, transactional distance, and Online Mathematics Learning Engagement (OMLE) among first-year university students. Methods: Utilizing a cross-lagged path analysis approach, the study surveyed 612 first-year students. Multiple models were constructed and compared to explore the mutual predictive relationships between resilience, transactional distance, and OMLE. Results: Among the compared models, Model 4 demonstrated the best fit. The model revealed that: (1) resilience at Time 1 and Time 2 positively predicted transactional distance at Time 2 and Time 3; (2) transactional distance at Time 1 and Time 2 positively predicted OMLE at Time 2 and Time 3; (3) resilience at Time 1 significantly predicted OMLE at Time 3; and (4) transactional distance at Time 2 fully mediated the relationship between resilience at Time 1 and OMLE at Time 3. Furthermore, mediational model analysis confirmed that transactional distance played a mediating role in the longitudinal relationship between resilience and OMLE. Using a cross-lagged mediational model with 5000 bootstrap samples, the indirect effect of transactional distance on the relationship between resilience at Time 1 and OMLE at Time 3 was significant and remained stable over time. Discussion: The findings suggest that resilience, as a positive psychological resource, stimulates students to seek and utilize protective resources in online environments, leading to more active participation in interpersonal communication and classroom interactions. Additionally, resilience helps students overcome emotional and practical difficulties encountered in online learning, thereby enhancing their OMLE. These insights offer valuable implications for educators, highlighting the potential to improve students' online learning engagement by fostering their psychological resilience.

The inferior fronto-occipital fasciculus correlates with early precursors of mathematics and reading before the start of formal schooling.

Diffusion-weighted imaging studies in preschoolers have almost exclusively been done in the field of reading. As a result, virtually nothing is known about white matter tracts associated with individual differences in mathematics at this age. Studying the preschoolers' brain is crucial because it allows us to identify individual differences in brain anatomy without influences of formal mathematics and reading instruction. To fill this gap, we investigated for the first time before the start of formal school entry the associations between white matter tracts and precursors of mathematics and reading simultaneously. We also investigated whether these associations were specific to mathematics and to reading, or not. We focused on four bilateral white matter tracts (arcuate fasciculus (direct, anterior), inferior fronto-occipital fasciculus, inferior longitudinal fasciculus), which have been previously correlated with mathematical performance in older children and with reading performance in children of a similar age as the current study. Participants were 56 5-year-old children (Mage = 67 months; SD = 1.8), none of which received formal instruction. Our results showed an association between the bilateral inferior fronto-occipital fasciculus and precursors of mathematics (numerical ordering, numeral knowledge) and reading (phonological awareness, letter knowledge). Follow-up regression analyses revealed that the associations found with the inferior fronto-occipital fasciculus were neither specific to mathematics nor specific to reading. These findings suggest that, already before the start of formal schooling, the inferior fronto-occipital fasciculus might be related to the neural overlap between mathematics and reading. This overlap potentially reflects one of their many shared mechanisms, such as the reliance on phonological codes or the processing of visual symbols, and these mechanisms should be exploited in future studies.

A reciprocal association between interpersonal relationship quality and student's positive affect: A three-wave random intercept cross-lagged study in a Chinese primary mathematics learning context.

AIM: This study adopted a three-wave random intercept cross-lagged panel model to explore the longitudinal reciprocal relationships between (a) the teacher-student relationship (TSR) quality and (b) the parent-child relationship (PCR) quality and positive affect among Chinese primary school students. SAMPLES: Two primary school student samples, including 3505 and 2505 students, were tracked with their perceived relationship quality with math teachers and parents and their positive affect levels in mathematics learning over three academic years. RESULTS: The results demonstrated that more closeness with parents could significantly predict students' subsequent higher level of positive affect in mathematics learning. However, more closeness with their math teachers did not show significant prediction. Meanwhile, more conflict with math teachers and parents could significantly predict their subsequent lower degree of perceived positive affect in mathematics learning. That is, a reciprocal association lines in the PCR quality and positive affect, whereas only a unidirectional association exists between the TSR and positive affect. The predictions of the experienced positive affect on their perceived interpersonal relationships with math teachers and parents were stronger than those in the reverse association. CONCLUSIONS: This study identifies that while the effects of closeness with math teachers and parents on positive affect in students' math learning differ, conflict with math teachers and parents indeed harms students' experienced positive affect in math learning. More attention should also be paid to fostering positive affect in math learning.

The effect of music training on students' mathematics and physics development at middle schools in China: A longitudinal study.

As a descriptive-inferential study, this research aimed at revealing the relationship between music training and academic development with the Chinese middle school students' academic performance of mathematics and physics skills. The participants of this study consisted of the students from two different middle schools located at two cities in Shandong province, China. From each school 250 students were selected, and the statistics was used to analyze both the academic performance of the students and the data obtained from the scale designed by the authors. The research results show that the non-music students outperformed music students on both mathematics and physics development. In addition, music training did not contribute to the academic achievement independently but rather integrated with several factors like parents' education and out-of-school engagement. The findings suggest the positive influence on non-musical cognitive learning, and it has potential implications for the Chinese middle school education.

A Discrete Mathematics Approach for Understanding Risk Factors in Overactive Bladder Treatment.

Introduction Discrete mathematics, a branch of mathematics that includes graph theory, combinatorics, and logic, focuses on discrete mathematical structures. Its application in the medical field, particularly in analyzing patterns in patient data and optimizing treatment methods, is invaluable. This study, focusing on post-void residual (PVR) urine following overactive bladder (OAB) treatment, utilized discrete mathematics techniques to analyze PVR and its associated risk factors. Methods A retrospective study was conducted on 128 OAB patients who received intradetrusor onabotulinum toxin A injections between 2020 and 2022. Network graphs based on graph theory were used to analyze correlations between clinical variables, and clustering analysis was performed with PVR as the primary variable. Results The network graph analysis revealed that frailty, daytime frequency, and nocturia episodes were closely related to PVR. Clustering analysis with PVR as the primary variable divided the patients into three groups, suggesting that the group with particularly high frailty (Cluster 1) is at high risk for PVR. Moreover, significant differences in clinical indicators such as age, voiding efficiency, Overactive Bladder Symptom Score, and International Consultation on Incontinence Questionnaire-Short Form were observed in the remaining two clusters (Cluster 0 and 2). Conclusion This study demonstrates the effectiveness of discrete mathematics methods in identifying risk factors for PVR after OAB treatment and in distinguishing clinical subgroups based on patient characteristics. This approach could contribute to the formulation of individualized treatment strategies and the improvement of patient care quality. Further development and clinical application of this methodology are expected in future research.

Success-driven opinion formation determines social tensions.

Polarization is common in politics and public opinion. It is believed to be shaped by media as well as ideologies, and often incited by misinformation. However, little is known about the microscopic dynamics behind polarization and the resulting social tensions. By coupling opinion formation with the strategy selection in different social dilemmas, we reveal how success at an individual level transforms to global consensus or lack thereof. When defection carries with it the fear of punishment in the absence of greed, as in the stag-hunt game, opinion fragmentation is the smallest. Conversely, if defection promises a higher payoff and also evokes greed, like in the prisoner's dilemma and snowdrift game, consensus is more difficult to attain. Our research thus challenges the top-down narrative of social tensions, showing they might originate from fundamental principles at individual level, like the desire to prevail in pairwise evolutionary comparisons.