Mathematical Difficulties Research Articles

Analysis of Bioheat Transfer with Thermoelastic Effect

The development of thermal therapy always requires more reasonable temperature distribution predictions. Controlling the amount of heating is a common practice within general thermal therapy operations. This paper used a modified three-phase lag (TPL) bioheat transfer equation to describe the behavior of heat conduction in tissue with thermoelastic effect. To explore the effect of thermal load, the tissue was subjected to a constant surface temperature and a pulsed surface heat flux, respectively. The modified TPL bioheat transfer equation involves mixed derivative terms and higher-order time derivatives of temperature. In analyzing such problems, there are mathematical difficulties. Therefore, the hybrid numerical scheme based on the Laplace transform and an improved discrete method was proposed to solve the present problem. The influence of thermoelastic parameters on the behavior of heat transfer in tissue has been investigated. The results depict the effect of thermal load on thermal response within heat transfer medium is obvious. The thermoelastic effect excites the thermal response oscillation, which is intensified for the reduction of material constant characteristic [Formula: see text] and phase lag [Formula: see text], in the heat conduction medium.

Considerations for Intensifying Word-Problem Interventions for Students With MD: A Qualitative Umbrella Review of Relevant Meta-Analyses.

Word problem-solving (WPS) poses a significant challenge for many students, particularly those with mathematics difficulties (MD), hindering their overall mathematical development. To improve WPS proficiency, providing individualized and intensive interventions is critical. This umbrella review examined 11 medium- to high-quality meta-analyses to identify intervention and participant characteristics, informed by the Taxonomy of Intervention Intensity (TII) framework, that consistently moderate WPS outcomes for students with MD. Our analysis identified four characteristics with consistent moderating effects: intervention model, number of treatment sessions, group size, and academic risk area. This result suggests that these variables are potential considerations when customizing and intensifying WPS interventions to maximize their effectiveness for students with MD. We discuss the implications of these findings for practice and research and acknowledge the limitations of our review.

A Scoping Review of Mathematics Interventions: Moderation Analyses of Initial Mathematics Skills

This scoping review describes mathematics intervention studies that include initial skill moderation analyses. Sixteen studies were included that focused on students with or at risk for mathematics difficulties (MD). The results revealed that mathematics intervention studies with initial skill moderation analyses focused on students in kindergarten through Grade 6 (no studies that met inclusion criteria were located for Grades 7–12). Studies focused more on whole number concepts and fractions than other areas of intervention (e.g., computation, word problem solving). Further, the studies were mostly conducted by two research teams, which potentially limits the generalizability of the findings. Overall, the review serves as a call to action for researchers to address important gaps in initial skill moderation analyses within mathematics intervention studies.

Pengembangan Integrasi Bangun Ruang Prisma Berbasis Etnomatika Terhadap Rumah Adat Joglo dengan Kemampuan Visualisasi Spacial pada Siswa Kelas V Sekolah Dasar

The background that prompted this research was the existence of factors in students' learning difficulties in understanding mathematics, especially in geometric material. The aim of the research is to determine the development stage and feasibility of integrating ethnomathematics-based prism spatial construction into Joglo traditional houses with spatial visualization abilities in fifth grade elementary school students. The research in this thesis uses Research and Development research using the ADDIE model. It can be concluded that the Omahku media based on ethnomathematics with visual spatial capabilities is a media that is suitable for use as a learning medium and of course can also be an alternative media used by teachers in mathematics lessons regarding spatial construction material. Based on the results of this research, the resulting learning media can provide suggestions that can be an alternative for teachers in learning, especially in building materials and can be combined with other learning resources.

Identifying Key Instructional Practices in Rational Number Interventions: A Systematic Review and Meta-Analysis

Impacts of rational number interventions among U.S. students in Grades 3 through 9 with mathematics difficulties are examined using a systematic review and meta-analysis. The primary goal of the meta-analysis was to identify instructional practices that are key drivers of student impacts. From approximately 1,200 published and unpublished study records, we identified 28 studies that met our inclusion criteria and coded the interventions for their instructional practices, intervention characteristics, and study design features. The random-effects mean effect size across all 28 studies (90 effect sizes) was 0.68 ( SE = 0.08, p < .001, 95% confidence interval [CI]: [0.51, 0.85]). The 95% prediction interval was −0.36 to 1.8. Using meta-regression techniques, we found the teaching of mathematical language ( β = 0.50) and the use of the number line ( β = 0.47) during intervention to be significantly associated with positive impacts when adjusted for controls. We discuss implications for intervention practice and study limitations along with the challenges of examining complex, multifaceted interventions.

Dimensional versus categorical approach: A comparative study of mathematical cognition

BackgroundResearchers have employed two distinct methods to understand the cognitive underpinnings of mathematical ability: categorical and dimensional. These two methods have different underlying assumptions. However, to the best of our knowledge, research to date has not empirically tested which method can better predict variance in mathematical ability. Method104 children from Indian public schools in the 3rd and 4th grades completed a mathematical ability test. For the categorical approach, participants were categorized into two groups: mathematical learning difficulty and high math achieving. For the dimensional approach, the data of all participants were considered. The cognitive abilities measured included approximate number system, working memory, inhibitory control, and spatial ability. ResultsMixed factorial ANOVA and hierarchical regressions revealed that the dimensional approach demonstrated better predictive power for mathematical ability than the categorical approach. ConclusionsThe dimensional approach offers a more comprehensive insight into mathematical cognition, enabling greater control over the predictors.

A Simplified Daily Fit Model to Reduce Costs and Nutrient Intake in Growing-Finishing Pigs.

Precision feeding is an excellent alternative to conventional phase feeding systems for growing-finishing pigs, especially with increasing feeding costs and environmental sustainability concerns. However, precision feeding strategies sometimes require advanced technologies such as electronic devices and the modernization of pig facilities. In addition to hardware implementation, precision feeding is frequently related to mathematical difficulties due to a lack of professionals trained in decision making. Therefore, this study compares a conventional phase feeding model (CON) and a daily fit model (DFM) with a simplified approach to the conscious use of nutrients for pig production. A simulation study was conducted using growth curves of barrow pigs, following three nutritional recommendations for conventional phase feeding. Once the nutrient requirements for CON were determined, these diets were used for the DFM by anticipating a proportional percentage of the next phase diet in the current diet. This simple adjustment does not impair the growth performance of pigs. However, in this study, the DFM showed promise during the growing-finishing phases to reduce pigs' costs and nutrient intakes, such as crude protein, lysine, and digestible phosphorus, up to 5.58, 7.11 and 9.13%, respectively. In conclusion, the DFM can effectively reduce costs, minimize environmental impact, and promote sustainable practices. Also, this industry-wide adoption of this simplified precision feeding strategy could play a vital role in swine farmers' challenges, fostering broader environmental benefits and improved resource efficiency.

Mathematical skills classification through primary education

By the end of primary school, children are expected to acquire a range of mathematical skills that progressively develop. This study aimed to gain insight into how a large number of numerical and geometrical measures are grouped and whether the structures shift or remain invariant along child’s development based on the data obtained from a sample of 1346 s to sixth grade children. On the basis of correlation analyses and exploratory factor analyses, we came up with an invariant four-factor structure for each grade. The four factors obtained were the following: (a) early and retrieval skills (subitizing, enumeration, number facts) (b) transcoding and ordinality skills, (c) numerical advanced skills and (d) visual-spatial advanced skills. Confirmatory factor analyses showed that the four-factor model fits well to the data (RMSEA < 0.06, CFI > 0.95, GFI > 0.93, SRMR < 0.05) at all grades. The associations between the mathematical measures were captured in each factor and the revealed invariant structure is discussed and compared with previous classification models of mathematical skills. Given that the difficulties in learning mathematics is currently being viewed as a continuum of academic abilities instead of a distinct problem, the underlying invariant four-factor structure can facilitate experts and educators to better understand how a broad area of mathematical skills are related across the primary education, in order to carry our comprehensive assessment of both the mathematical strengths and weaknesses of their students and to apply the appropriate customized teaching strategies.

Analisis Kesulitan Belajar Matematika Dalam Menyelesaikan Soal Materi Operasi Hitung Pecahan Pada Siswa Kelas V SD Negeri Morkepek

The purpose of this study was to determine the difficulty of learning mathematics and the factors that cause mathematics learning difficulties in solving problems of fraction counting operation material in fifth grade students of SD Negeri Morkepek. This research uses a method with a descriptive qualitative approach. This research uses data collection techniques with interview techniques and documentation. The results of this study are 1). Math learning difficulties in using facts, namely students have difficulty in translating fraction story problems into a form of solution according to symbols or fraction numbers correctly. 2). Math learning difficulties in using concepts, namely students are unable to master the prerequisite concepts of fraction calculation operation material regarding determining the KPK. 3). Difficulty in using principles, namely students have difficulty in connecting the concept of fractions into the right calculation relation. 4). Difficulty in using skills, namely students are unable to complete the problem solving according to the fraction calculation procedure.

Mathematics Learning Model for Children with Dyscalculia through Special Intervention

This research aimed to formulate a model of mathematical learning difficulties for children with dyscalculia to help children with dyscalculia overcome mathematics problems at school. This research is important to carry out considering that dyscalculia is a serious problem experienced by many students throughout the world. The SDTA model was built by analogizing the STIR model to non-communicable diseases. In this study, of 1247 students who conducted a series of tests (screening tests), there were 121 students, or 9.7% were initially identified as having dyscalculia. Furthermore, observations were carried out and confirmation was carried out with parents and teachers so that 119 students tested positive for dyscalculia. The research results showed that after intervention through treatment by the teacher, dyscalculia students experienced a very drastic decrease, especially in the material on recognizing and ordering numbers. Likewise, the results of model simulations on multiplication operation material illustrated the decline in students with dyscalculia. Specifically for division operations, the treatment process took relatively longer. Therefore, the simulation results in the SDTA model reflected students who are identified as having dyscalculia, along with planned intervention/ treatment, students could pass through the mathematics learning phase successfully.

Generalization to d-dimensions of a fermionic path integral for exact enumeration of polygons on hypercubic lattices

The generating function for polygons on the square lattice has been known for many decades and is closely related to the path integral formulation of a free fermion model. On the cubic and hypercubic lattices the generating function is still unknown and the problem remains open. It has been conjectured that the three-dimensional (3D) and higher dimensional problems are not solvable—or, to be more precise, that there are no differentiably finite (D-finite) solutions. In this context, very recently a Berezin integral of an exponentiated Grassmann action was found for the polygon generating function on the cubic lattice, making explicit the connection between 3D polygons and a model of interacting fermions. Here we address the problem of how to generalize the 3D result to higher dimensions. We derive a Grassmann representation in terms of a Berezin integral for the generating function of polygons on d-dimensional hypercubic lattices. On the one hand, this new result admittedly brings us no closer to the problem of finding an explicit analytic expression for the desired generating function for polygons. On the other hand, however, the significant advance reported here precisely quantifies the remarkable mathematical difficulty of finding the explicit generating function. Indeed, the non-quadratic functional form of the Grassmann action that we derive here provides a very clear picture of the formidable mathematical obstruction that would need to be overcome. Specifically, in d dimensions, the Grassmann action contains terms of degree 2(d-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2(d-1)$$\\end{document}, so the model describes interacting rather than free fermions. It is an open problem whether or not these models of interacting fermions can in principle be free fermionized through some still undiscovered algebraic method, but it is widely believed that this goal is mathematically impossible.

Executive performance and mathematic learning difficulties

Considering the association between Executive Functions (EF) and performance in mathematic, we aimed to analyse the low executive functions – which impact the individual’s personal, social, and educational functioning –, and their associations with this performance and sociodemographic aspects not already explored in students aged 8 to 12 years. One hundred and ten participants were evaluated using the MMSE, Coruja PROMAT, NEUPSILIN-INF, FDT and a Sociodemographic Questionnaire. Correlation and regression analysis indicated that low executive accomplishment influences performance in mathematics, especially considering working memory and cognitive flexibility. The variables gender, family income and parents’ age were not related to the presentation of low EF. In contrast, the sociodemographic aspects of school shift and parents’ education were shown to be related to executive performance, especially among public school students, revealing the importance of attention to these factors.

Bibliometric and Content Analyses of Dyscalculia Research

Dyscalculia is a math learning difficulty that many researchers have studied. A bibliometric and content analysis was conducted using the Web of Science database to provide a comprehensive overview of existing research on dyscalculia. The study aimed to identify key themes, prevailing research trends, potential knowledge gaps, and influential authors and articles in the field. The analysis focused on several research questions related to the distribution of articles and their citation data over the years, the types and numerical distribution of publications on dyscalculia, collaborative networks between authors, institutions, and countries/regions, topical research foci, prominent journals publishing articles on dyscalculia, top authors and countries researching dyscalculia, disciplines comprising the foundation of dyscalculia research, topics covered, the sample studied, and methods preferred in highly cited articles on dyscalculia. The co-occurrence analysis of the keywords revealed that dyscalculia, mathematical difficulties, dyslexia, and developmental dyscalculia were the most frequently cited terms. The top ten most cited articles were subjected to content analysis, revealing the types of research and methodologies. This study paves the way for future research and emphasizes the importance of interdisciplinary collaboration in understanding the nature and underlying causes of mathematics learning disabilities.

Motivation in learning mathematics among high school students in Ningbo, China

Motivation plays a crucial role in enhancing students' achievement in mathematics, as motivated students are more likely to engage actively with the subject. However, in China, there is a concerning trend of declining motivation among students toward mathematics, with many exhibiting avoidance behaviors. Despite Ningbo's significance as a major city in China, there is a lack of studies and surveys addressing students' motivation in mathematics learning. This study addresses this gap by employing a questionnaire based on Keller’s ARCS (Attention, Relevance, Confidence, Satisfaction) model, which has been proven effective in measuring students’ motivation. The survey, conducted among 384 high school students in Ningbo, China, aimed to assess their motivation levels in mathematics learning. Descriptive statistical analysis was performed using SPSS Statistics 29 to calculate the mean and percentage for each item. The results revealed that the motivation level among high school students in Ningbo is notably low. Two significant factors contributing to this low motivation were identified: students’ lack of confidence due to the perceived difficulty of mathematics and the belief that mathematics is not closely related to real life.

Using Assistive Technology to Differentiate and Accommodate Students with Special Needs Facing Learning Difficulties in Mathematics

This paper will discuss how assistive technology forms the basis of differentiation and support for students with special needs when conquering specific math learning difficulties. The Department of Special Education utilized a quantitative research design to collect data from 240 teachers through a structured, self-developed questionnaire. The use of simple random sampling maximized representative samples and minimized biases. We established the effects of AT in terms of differentiated instruction, increased student engagement, and an inclusive learning environment. Teachers estimated complex mathematical concepts using AT tools, such as virtual manipulatives and educational apps, as easier to understand and improve student confidence and participation levels. Overall, the findings indicate a need for continuous teacher training and resource allocation to effectively integrate these into a holistic classroom experience. The conclusion is that integrating assistive technology into education is a gateway to ensuring that every special need student receives quality learning in mathematics, thus equalizing access to education. Recommendations call for investment in professional development of the teachers, adequate resources for AT tools, and inculcation of AT provision in curriculum design. Further research should investigate the long-term effects of AT on students' achievement in other subjects.

Practices Used to Diagnose Hearing Impaired Students with Learning Difficulties in Mathematics

This study aimed to examine how teachers perceive the diagnostic practices used to identify mathematical learning difficulties among hearing-impaired students. This study adopted a quantitative research design, sampling 300 teachers using simple random sampling. We collected data using a self-developed questionnaire and analyzed the data using descriptive and inferential statistics in SPSS. The study highlights the importance of visual aids, non-verbal assessment, and teamwork between the audiologist and educator to identify hearing-impaired students. Teachers believe that we need to design more versatile tools in addition to norm-referenced tests. This underscores the shortcomings in the diagnostic tools. There was a lack of specialized diagnostic equipment for both hearing and learning disabilities, as reported during the observation. It also highlights the need for continuous practice improvement and excellent collaboration among all stakeholders. These findings contribute to the broader literature on inclusive education and underscore the necessity for innovation in diagnostic tools to support students with hearing impairments better. In this area, emerging technologies should be the focus of further research to improve diagnosis.

Evaluation of students’ performance in elective mathematics: The effect of high school students’ perceived difficulty of the subject

Perception has been attributed as a major cause of students' weakness in mathematics. Hence, this study evaluates its effect on student’s performance in the area of mathematics as an elective subject in some selected Senior High School (SHS) in Ghana. Mixed method research design that employed questionnaire with closed-ended and open-ended items were used in the collection of the data. Stratified sampling technique was used in selecting 300 students as sample for the study. Descriptive statistics and Multiple regression were used to analyse the quantitative data. Again, thematic analysis was used for the qualitative data. The findings showed that, SHS students perceived elective mathematics as a difficult subject. Nonetheless, they perceived the teacher-learner activities employed by their teachers in elective mathematics classroom as motivating. Further, they perceived as constructive, the teaching methods used by their elective mathematics teachers. In addition, the study revealed that students’ performance in elective mathematics was not significantly influenced by their perceived difficulty of elective mathematics, teacher motivation and teaching methods although the students expressed favourable dispositions towards these attributes. Thus, the need for Heads of High Schools, to do background check of students’ prior performance, interest and motivation in mathematics as a prerequisite condition for students to pursue elective mathematics is implied in this study. This could stem the tide in the students’ abysmal performance in elective mathematics. Implications for policy, practice and further research are discussed.

From developmental theory to effective training: long-term and transfer effects of promoting the quantity-to-number word linkage in first-graders at risk for mathematical difficulties.

The model of quantity-to-number word linkage (QNL model) identifies relevant milestones in the process of early numerical acquisition and describes a developmental sequence that can guide the fostering of foundational mathematical abilities in at-risk children. While there is substantial evidence for the predictive value of the quantity-number competencies (QNC) described by the model, evidence supporting the preventive potential of interventions targeting these QNC is so far largely restricted to short-term effects. Findings regarding their long-term preventive impact, especially in terms of transfer to mathematical school achievement, are still limited. This quasi-experimental study aimed to address this gap by evaluating the long-term transfer effects of an intervention program that is strictly derived from the QNL model of mathematical development [QNL training; in German "Mengen, zählen, Zahlen" (MZZ)]. We assessed the quantity-number competencies of 575 first-graders and identified 119 of them as being at risk for mathematical learning difficulties, who were then assigned to three experimental conditions. Sixty one children received 12 sessions of the QNL training, while 30 underwent training in inductive reasoning. Another 28 children served as a control group, receiving no specific intervention. Multi-level analyses confirmed both significant short-and long-term effects in the specifically trained quantity-number competencies as well as transfer effects on subsequent mathematical school achievement. In accordance with previous findings, transfer effects of the QNL training on mathematical school achievement were not yet evident immediately after the intervention but turned out to be significant after a delay of 6 months and remained stable even 15 months after training. Effect sizes ranged from d = 0.32 to d = 1.12. These findings both underscore the preventive potential of interventions that are strictly driven by developmental theory and, conversely, support the theoretical assumptions of the QNL model.

A Systematic Review of Mathematics Vocabulary Interventions for Students With or At-Risk for Mathematics Difficulty

This systematic review synthesizes the effects of mathematics vocabulary interventions on the mathematics outcomes of students with mathematics difficulty (MD) in Grades K through 12. We evaluated methodological rigor using three indicators: research design, implementation fidelity, and instruction in the counterfactual. Six peer-reviewed studies and three unpublished dissertations between 1990 and 2022 met inclusion criteria. Results showed mathematics vocabulary interventions improved students’ vocabulary knowledge, particularly when instruction was explicit with multiple opportunities to practice. Findings were less conclusive on whether improved mathematics vocabulary knowledge led to improved performance on related mathematics content. Results suggest mathematics vocabulary intervention is beneficial for higher-level mathematics reasoning, such as word-problem solving. The seven group design studies received an M rating of at least acceptable for methodological rigor, and one of two single-case studies met What Works Clearinghouse design standards without reservations. We highlight promising instructional practices implemented across studies that resulted in improved vocabulary outcomes.

Ethnomathematics Digital Student Worksheet Using the Problem Based Learning Model to Improve Creative Mathematical Thinking for Elementary School Students

Low creative mathematical thinking ability is caused by the difficulty of learning mathematics on the division of decimal numbers. Therefore, this research aims to develop digital ethnomathematics worksheets using the PBL model to build students' creative mathematical thinking skills on division of decimal numbers in class V elementary school. This type of research is development research with the ADDIE development model. The subjects of this research were 7 material experts and 2 learning media experts. The test subjects in this research and development were 8 students. Data collection techniques include observation, interviews, and questionnaires. The data collection instrument is a questionnaire sheet. The techniques used to analyze the data are qualitative and quantitative descriptive analysis. The research results, namely the assessment results given by learning material experts, were 84.29% so they were declared very good. The assessment results by learning media experts were 90.00% so they were declared very good. The assessment results by students obtained an overall average score of 81.52%, so it was very good. It was concluded that digital ethnomathematics worksheets using the PBL model were suitable for learning. This research implies that using digital ethnomathematics worksheets using models can improve students' creative thinking.