Identifying precondition configurations of mathematics anxiety among middle school students in China: using NCA and QCA approaches.

Introduction: Addressing mathematics anxiety is important to ensure that students achieve good academic performance and maintain their mental health during the critical middle school period. However, previous studies have focused on the separate effects of the preconditions for mathematics anxiety, ignoring the interaction of factors. Therefore, this study aims to identify the determinants of mathematics anxiety from the perspective of complex systems via necessary condition analysis (NCA) and qualitative comparative analysis (QCA). To the best of our knowledge, this is the first study to identify configurations of preconditions of mathematics anxiety among middle school students. Methods: A total of 183 middle school students aged 16 to 19 years (M age = 17.47, SD = 0.89) in China participated in this cross-sectional study. The outcome variable of the study is mathematics anxiety, and the condition variables include mathematics grade, parental support, learning motivation, learning planning, and learning interest. Results: The necessity condition analysis shows that not all the condition variables constitute the necessity condition of mathematics anxiety alone. Four paths for the influence of multiple condition variables on mathematics anxiety are identified via the configuration analysis. Notably, even students with high mathematics scores and learning interest still experience mathematics anxiety due to a lack of practical parental support and learning motivation. High levels of parental support can exacerbate the mathematics anxiety of students under two conditions: 1) a lack of learning motivation and learning plans, and 2) interest in learning but low mathematics scores and unclear learning plans. Discussion: This study highlights the need to consider the comprehensive impact of mathematics anxiety, and the findings will help educators and researchers identify the different characteristics of mathematics anxiety in student populations.

Discrete Mathematics in Dynamic Network Analysis: Long-Term Efficacy Evaluation of Fotona Laser Therapy for Overactive Bladder Syndrome Using Clustering-Based Patient Subgroup Identification.

Dynamic network analysis, a state-of-the-art application of discrete mathematics, offers unprecedented insight into complex, time-evolving clinical data. This technical report demonstrates the value of evaluating the long-term efficacy of Fotona laser therapy (Fotona d.o.o., Ljubljana, Slovenia) in overactive bladder (OAB) syndrome. We analyzed data from 101 female patients aged ≥60 years who underwent Fotona laser treatment, including Vaginal Erbium Laser (VEL) and Urethral Erbium Laser (UEL), between 2020 and 2022. OAB symptom scores (OABSS) were collected at baseline (T0) and at six, 12, 18, and 24 months post treatment. Network graphs were constructed, representing patients as nodes, and symptom similarities as edges. Clustering techniques identify patient subgroups, whereas principal component analysis reduces dimensionality. The dynamic evolution of patient clusters was visualized through changes in average degree centrality over time. This approach revealed three distinct patient clusters with unique treatment response patterns. The results showed a progressive reduction in OABSS, with the total score decreasing by 2.82 ± 3.03 at 24 months. Our method provides novel visualization and analysis of complex longitudinal clinical data, offering insights into personalized treatment strategies for OAB. This report presents one of the first applications of discrete mathematics and dynamic network analysis to evaluate the long-term outcomes of Fotona laser therapy for OAB and introduces an innovative perspective for clinical decision-making in urogynecology.

Mathematics and society reunited: The social aspects of Brouwer's intuitionism.

Brouwer's philosophy of mathematics is usually regarded as an intra-subjective, even solipsistic approach, an approach that also underlies his mathematical intuitionism, as he strived to create a mathematics that develops out of something inner and a-linguistic. Thus, points of connection between Brouwer's mathematical views and his views about and the social world seem improbable and are rarely mentioned in the literature. The current paper aims to challenge and change that. The paper employs a socially oriented prism to examine Brouwer's views on the construction, use, and practice of mathematics. It focuses on Brouwer's views on language, his social interactions, and the importance of group context as they appear in the significs dialogues. It does so by exploring the establishment and dissolution of the significs movement, focusing on Gerrit Mannoury's influence and relationship with Brouwer and analyzing several fragments from the significs dialogues while emphasizing the role Brouwer ascribed to groups in forming and sharing new ideas. The paper concludes by raising two questions that challenge common historical and philosophical readings of intuitionism.

A holistic framework to model student's cognitive process in mathematics education through fuzzy cognitive maps.

This study introduces a pioneering framework for modeling students' cognitive processes in mathematics education through Fuzzy Cognitive Maps (FCMs). By integrating key educational theories-Duval's Semiotic Representation Theory, Niss's Mathematical Competencies, Marton's Variation Theory, and the broad Engagement, Motivation, and Participation framework- the model offers a comprehensive and holistic understanding of students' cognitive landscapes. This research underscores the necessity of a multidimensional approach to capturing the intricate interplay of cognitive, affective, and behavioral factors in students' mathematical learning experiences. The novelty lies in its methodological innovation, employing FCMs to transcend traditional qualitative analyzes and facilitate quantitative insights into students' cognitive processes. This approach is particularly relevant in the current era dominated by digital learning environments and artificial intelligence, where real-time, automated analysis of student interactions is increasingly vital. The proposed FCM has been developed over the years with a data-driven approach; the concepts and relationships in it have been derived from the literature and refined by the author's experience in the field. Illustrated through case studies, the framework's utility is demonstrated in diverse contexts, highlighting how the quantitative data obtained are confirmed by qualitative approach: analyzing the impact of remote learning during the Covid-19 pandemic on student engagement and exploring Augmented Reality's role in enhancing mathematical conceptualization. These applications show the framework's adaptability and its potential to integrate new technologies in educational practices. However, the transition from qualitative to quantitative methodologies poses a challenge, given the prevalent use of qualitative approaches in mathematics education research. Additionally, the technological implementation of the FCM model in educational software presents practical hurdles, necessitating further development to ensure ease of integration and use in real-time educational settings. Future work will focus on bridging these methodological gaps and overcoming technological challenges to broaden the FCM model's applicability and enhance its contribution to advancing mathematics education.

A future classroom lab with active and gamified STEAM proposal for mathematics and science disciplines: Analyzing the effects on pre-service teacher's affective domain.

The recent emergence of innovative learning spaces, Future Classroom Lab (FCL), provides educators the use of physical learning spaces (to research, interact, exchange, develop, create, and present) and diverse technological tools to work according to active methodologies. Learners become more active in the learning process with the introduction of innovative learning environments that enable the application of interdisciplinary STEAM methodology and foster the development of 21st century competences. This study aims to uncover the probable link between application active and gamified STEAM educational interventions in the FCL and Pre-Service Teachers' (PSTs) affective domain. The findings obtained showed statistically significant variations and, therefore, positive effects on the PSTs' affective domain (self-efficacy, attitude, and emotion) after performing the intervention. The sample consisted of a total of 54 PSTs enrolled in the second year of Primary Education. Limited studies regarding the affective domain in the FCL were found, which restricted the comparison with prior research. This study has several implications, such as the introduction of innovative educational proposals to PSTs at the university level and, consequently, the implementation of similar interventions in elementary schools. This research intended to reveal how the different variables work as a support system for students' learning process in mathematics and science disciplines.

Executive functioning profiles and mathematical and reading achievement in Grades 2, 6, and 10.

Using a person-centered approach, we aimed to identify different executive functioning profiles to assess heterogeneity across individuals within the same school grade through latent profile analysis. A sample of 150 Grade 2 (7-8 years old), 150 Grade 6 (11-12 years old), and 150 Grade 10 (15-16 years old) children and adolescents were assessed on 11 different executive tasks representative of the three main executive functioning subcomponents (i.e., inhibition, cognitive flexibility, and working memory), fluid intelligence, processing speed, problem-solving, and reading comprehension. Three different executive functioning profiles of different patterns of interactions based on inhibition, cognitive flexibility, and working memory within and between grades were identified. Moreover, these profiles were differentially related to reading comprehension and mathematical achievement. Second, as expected, we did not find these profiles to be associated with sociodemographic variables such as chronological age or sex. Still, fluid intelligence and processing speed were differentially related to the different profiles at each grade. We also found that the executive functioning profiles interacted with each cognitive skill (i.e., fluid intelligence and processing speed) in predicting reading comprehension and math achievement. These findings provide valuable insights for developing preventive and intervention strategies in education.

Exploring the Impact of Math Anxiety and Task Difficulty on Pupil Dilation in Adults and Young Children.

We investigated the relations between self-reported math anxiety, task difficulty, and pupil dilation in adults and very young children during math tasks of varying difficulty levels. While task difficulty significantly influenced pupillary responses in both groups, the association between self-reported math anxiety and pupil dilation differed across age cohorts. The children exhibited resilience to the effects of math anxiety, hinting at additional influential factors such as formal math education experiences shaping their relations to mathematics and their impact on cognitive processes over time. Contrary to expectations, no significant association between self-reported math anxiety and pupil dilation during task anticipation was found in either group. In adults, math anxiety influenced pupil dilation exclusively during the initial phase of task processing indicating heightened cognitive load, but this influence diminished during sustained task processing. Theoretical implications emphasize the need for exploring individual differences, cognitive strategies, and the developmental trajectory of math anxiety in very young children.

Integrating vision and somatosensation does not improve the accuracy and response time when estimating area and perimeter of rectangles in primary school.

BACKGROUND: Problem-solving and learning in mathematics involves sensory perception and processing. Multisensory integration may contribute by enhancing sensory estimates. This study aims to assess if combining visual and somatosensory information improves elementary students' perimeter and area estimates. METHODS: 87 4th graders compared rectangles with respect to area or perimeter either solely using visual observation or additionally with somatosensory information. Three experiments targeted different task aspects. Statistical analyses tested success rates and response times. RESULTS: Contrary to expectations, adding somatosensory information did not boost success rates for area and perimeter comparison. Response time even increased with adding somatosensory information. Children's difficulty in accurately tracing figures negatively impacted the success rate of area comparisons. DISCUSSION: Results suggest visual observation alone suffices for accurately estimating and comparing area and perimeter of rectangles in 4th graders. IMPLICATIONS: Careful deliberation on the inclusion of somatosensory information in mathematical tasks concerning perimeter and area estimations of rectangles is recommended.

Brouwer and Hausdorff: On reassessing the foundations crisis.

Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this "foundations crisis" was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal Mathematische Annalen.

A meta-analysis of the relationship between metacognition and academic achievement in mathematics: From preschool to university.

Many studies have explored the relationship between metacognition and academic achievement in mathematics, but the results vary. In this study, meta-analysis was used to explore this relationship between metacognition and academic achievement in mathematics and influencing factors. According to the literature search, a total of 147 studies (1986-2024) and 338 independent samples met the inclusion criteria (n = 698,096). The results revealed metacognition was significantly positively correlated with academic achievement in mathematics, r = 0.32, 95 % CI [0.30, 0.34], Z = 28.49. Moreover, the moderating effects of age, domain, and culture were significant (p < 0.01). In conclusion, Metacognition is closely associated with academic achievement in mathematics but also that age, domain, and culture have a considerable impact on their relationship. More specifically, the degree of correlation between metacognition and academic achievement in mathematics was on the rise from preschool to high school, while it was lower in college. Compared with general field metacognition, mathematical metacognition is more closely linked to mathematics academic achievement. Lastly, compared with British and American countries, Chinese metacognition was more closely related to academic achievement in mathematics.

Non-local interaction in discrete Ricci curvature-induced biological aggregation.

We investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods. We find that even a single effective topological neighbour suffices for significant order in a system with non-local topological interactions. We also explore topological information flow patterns and clustering dynamics using Hodge spectral entropy and mean Forman-Ricci curvature.

Uncovering mathematics teachers' instructional anticipations in a digital one-to-one environment: A modified UTAUT study.

More and more digital technologies are being integrated into school learning, and one strategy by policymakers to reinforce this trend is employing digital one-to-one approaches. For digital technologies to be fruitfully integrated into school-based learning scenarios, teachers and their anticipations are key. In our study, we want to explore how internal, external and technological factors affect the instructional anticipations of mathematics teachers in a digital one-to-one educational environment. Therefore, we employed a modified model of the Unified Theory of Acceptance and Use of Technology. Through our structural equation study, in which data from more than 900 mathematics teachers were analyzed, we identified that especially technological and external factors can predict mathematics teachers' instructional anticipations. Findings from our study could be particularly relevant for educational policymakers, informing them about the importance of factors or interventions related to educational technology implementation.

Quantitative evaluation of a theoretical-conceptual model based on affective and socio-behavioral dimensions to explain the academic performance of mathematics students.

Objective: There is evidence that suggests that affective dimensions, personality traits, as well as students' cooperative interpersonal interactions, are an important element in the students learning process. In this work we propose a theoretical model, based on evidence, that shows the direct and indirect relationships between these factors and academic performance in mathematics courses, in undergraduate and school students. Methods: To understand the type of relationships between these variables, the PANAS psychometric test of positive and negative affect, the BIG FIVE personality test and the economic decision game DUPLES GAME were applied. The study sample was 130 students between 17 and 22 years of age from undergraduate and school (M ± SD = 20.1 ± 3.99). Results: From a path analysis, statistically significant relationships were found, for example, a direct relationship between neuroticism and positive affect, which in turn is related to academic performance. We also found a direct relationship between neuroticism and negative affect, extraversion and positive affect. This allows us to propose that some of the independent variables of the model directly and indirectly influence the academic performance of students in the subject of mathematics. Conclusion: Positive affect and negative affect directly affect academic performance in mathematics, neuroticism has a direct impact on negative affect and extraversion direct impact on positive affect. Consequently, there are direct and indirect relationships between personality traits and affective dimensions, which affect the academic performance of mathematics students.

Habituation as optimal filtering.

Habituation, the reduction of responding to repetitive stimuli, is often conceptualized as a kind of attentional filter, amplifying salient signals at the expense of non-salient signals. No prior account has explicitly formalized filtering principles that can explain the major characteristics of habituation. In this paper, a simple probabilistic model is developed which permits analysis of the optimal filtering problem. This model exhibits the major characteristics of habituation, while also shedding light on other, relatively neglected, characteristics. These results demonstrate that habituation can be understood as a form of optimal filtering.

Math Abilities Among Children with Neurodevelopmental Difficulties: Understanding Cognitive Factors and Evaluating a Pilot Intervention.

Math development in children relies on several underlying cognitive functions, including executive functions (EF), working memory (WM), and visual-motor abilities, such as visual-motor integration (VMI). Understanding how these cognitive factors contribute to children's math performance is critical to supporting math learning and long-term math success. The present quasi-experimental waitlist control study (N = 28) aimed to (a) examine the unique contributions of EF, WM, and VMI to math abilities among children ages 5-8 years old with neurodevelopmental difficulties; (b) determine whether a math intervention (the Mathematics Interactive Learning Experience; MILE) that supports these cognitive processes was effective when modified to be delivered to small groups in a school setting, and (c) examine whether any participant characteristics, such as age or IQ, were correlated with post-intervention math score changes. At baseline, participants' math scores were significantly below the normative mean in all math content areas (ps < .01). EF, WM, and VMI were highly correlated with math ability; however, verbal WM was the only unique predictor of math ability in regressions analysis. Compared to a waitlist control group, children in the immediate MILE intervention group achieved significantly greater math gains overall. When all children who ultimately completed the intervention were considered together, significant improvement was observed in more than half of math content areas. Furthermore, at the individual level, 85.7% of participants showed reliable change in at least one math content area. Implications for supporting math learning in children with neurodevelopmental difficulties are discussed.

Counting on Change: Conquering Challenges in Teaching Pharmaceutical Calculations.

All pharmacists are expected to accurately perform pharmaceutical calculations to ensure patient safety. In recent years, there have been trends in declining performance on the North American Pharmacist Licensure Examination related to calculations. Understanding the cause of this decline and determining methods to correct underlying issues could benefit pharmacy administration, faculty, students, and patients. The aims of this commentary are to present the factors impacting the students' pharmaceutical calculations abilities, discuss the consequences of declining math skills, and provide a call to action for scholarship of teaching and learning pertaining to calculations, as well as increased administrative support to rectify this challenge.