Mathematical Difficulties Research Articles

What Components of Working Memory Are Impaired in Children with Reading and/or Mathematics Difficulties?

Both reading difficulties (RD) and mathematics difficulties (MD) are common neurodevelopmental disorders. The co-occurrence of RD and MD, known as comorbid RDMD, is estimated to range between 21% and 45% of children with learning disabilities. Deficits in working memory have been reported in both RD and MD groups, as well as among comorbid RDMD. However, previous comorbidity studies have only examined the role of some components of working memory, and they do not strictly match their groups on relevant reading and mathematics tasks. Thus, the purpose of this study is to examine the nature of working memory deficits in comorbid RDMD after matching groups based on reading and mathematics tasks. We assessed four groups of children (RD [n = 21, Mage = 10.96 years], MD [n = 24, Mage = 11.04 years], comorbid RDMD [n = 26, Mage = 10.90 years], and chronological-age controls [n = 27, Mage = 10.96 years]) on measures of the phonological loop (word span and digit span forward tasks), central executive (complex word and digit span), and updating tasks (word and digit 2-back). The results of ANCOVA (covarying for gender and non-verbal IQ) showed first that the RD and RDMD groups performed significantly worse than the MD and control groups in both measures of the phonological loop. For the central executive and updating tasks, we found an effect based on stimulus type. For word-related tasks, the RD and comorbid RDMD groups performed worse than the MD and control groups, and for number-related tasks, the MD and comorbid RDMD groups performed worse than the RD and control groups. Taken together, our findings provide support for the correlated liability model of comorbidity, which indicates that working memory deficits experienced by the RDMD group are an additive combination of deficits observed in the RD and MD groups, suggesting that working memory tasks used to examine underlying deficits in reading and/or mathematics difficulties may dictate whether or not significant group differences are found.

Effects of Principled Digitalized Interactive Components on Geometry Computer-Based Assessment in High Schoolers With Learning Difficulties in Mathematics: A Preliminary Investigation

This study investigated the effectiveness of four Digitalized Interactive Components (DICs) designed based on cognitive principles to accommodate individual differences among students with learning difficulties in geometry during computer-based assessments. The four DICs were annotations (allowing students to make notes on the screen), pop-up glossary (providing definitions of math terms upon clicking), signaling (displaying corresponding visual information upon clicking verbal information), and rotation (allowing students to rotate shapes). Sixteen high school students with mathematics difficulties participated in the study and were tested with and without the principled DICs. The findings indicate that the principled DICs statistically significantly improved students’ accuracy on the majority of tested problems and increased the average duration engaged in solving geometry problems. Analysis of video data revealed that the pop-up glossary was the most frequently used DIC, followed by signaling, while annotation was the least used.

Asymptotic behavior of a system of two coupled queues when the content of one queue is very high

We consider a system of two parallel discrete-time single-server queues, queue 1 and queue 2. The service time of any customer in either queue is equal to 1 time slot. Arrivals during consecutive slots occur independently from slot to slot. However, the arrival streams into both queues are possibly mutually interdependent, i.e., during any slot, the numbers of arrivals in queue 1 and queue 2 need not be statistically independent. Their joint probability generating function (pgf) A(x, y) fully characterizes the queueing model. As a consequence of the possible intra-slot correlation in the arrival process, the numbers of customers present (“system contents”) in queues 1 and 2, at any given slot boundary, are not necessarily independent either. In a previous paper, we have already discussed the mathematical difficulty of computing their steady-state joint pgf U(z_1,z_2); explicit closed-form results can only be obtained for specific choices of A(x, y). In this paper, we therefore look at the problem from an other angle. Specifically, we study the (asymptotic) conditional steady-state behavior of the system under the condition that the content of queue 1 is (temporarily) very high (goes to infinity). For ease of terminology, we refer to the system as the “asymptotic system” in these circumstances. We prove that the asymptotic system is nearly identical to the original (unconditional) system, but with a modified joint arrival pgf A^*(x,y) that can be computed explicitly from A(x, y). This fundamental result allows us to determine the stability condition of queue 2 in the asymptotic system, and explicitly compute the classical queueing performance metrics of queue 2, such as the pgf, the moments and the approximate tail distribution of its system content, when this condition is fulfilled. It also leads to accurate approximative closed-form expressions for the joint tail distribution of the system contents in both queues, in the original (unconditional) system. We extensively illustrate our methodology by means of various specific (popular) choices of A(x, y). In some examples, where an explicit solution for U(z_1,z_2) or for the (approximative) joint tail distribution is known, we retrieve the known results easily. In other cases, new results are found for arrival pgfs A(x, y) for which no explicit results were known until now.

Development of a Fraction Vocabulary Measure

Developing mathematics proficiency requires an understanding of mathematics vocabulary. Although previous research has developed several measures of mathematics vocabulary at different grade levels, no study focused solely on fraction vocabularies. We developed and tested a measure of fraction vocabulary for students in Grade 4 to determine the internal consistency and difficulty level of such a measure. Analysis indicated the measure demonstrated high internal consistency. Students, on average, answered less than one-third of fraction vocabularies correctly. We also detected performance differences between students with and without mathematics difficulty and dual-language learners and their peers.

POWER SPECTRAL ANALYSIS OF VARYING COMPLEXITY TASKS USING EEGLAB

Analysis of the effects of increasing degrees of complexity on students’ brains is the primary topic of this research. Therefore, this study aims to use Electroencephalography (EEG) to determine the task’s difficulty level. This research examined assertions of broad mathematical and logical difficulty that can be addressed with the “C programming language.” The EEGLAB software has been used to analyze brain waves’ power spectrums while solving problem statements of different degrees of complexity. Most significantly, we discovered that as problem statements get more complicated, the strength of the Alpha, Beta, and Theta bands rises. Input features for machine learning classifiers have included descriptive statistical metrics such as mean, standard deviation, skewness, and kurtosis. Specifically, we have compared and analyzed the efficacy of four ML classifiers: Logistic Regression, Neural Network, Decision Tree, and Support Vector Machine. To classify EEG data into “easy” and “hard” categories for C programming problem statements, the DT classifier has been found to perform better with a 69.23% accuracy. The results of this research can be used to generate test questions for open-book exams, and higher-order laboratory experiments.

Development of <i>algebrameter</i> for remediating junior secondary school students’ learning difficulties in mathematics

The purpose of the study was to develop mathematical instructional card game titled <i>algebrameter</i> and determine its efficacy in remediating junior secondary school (JSS) students’ learning difficulties in algebra and geometry. The study employed research and development design. A sample of 120 JSS II students drawn from a population of 4800 JSS II students in Nsukka Education Zone, using multi-stage sampling procedure participated in the study. Algebra and geometry achievement test (AGAT) comprised 30 multiple choice questions developed by the researchers was used for data collection. The internal consistence of AGAT was determined using Kuder-Richardson formula 20 (KR-20) formula, which yielded α value of 0.82. Research questions were answered using mean and standard deviation while the hypothesis was tested using analysis of covariance. The results of this study revealed that students who were exposed to <i>algebrameter</i> significantly performed better than students who were not exposed to <i>algebrameter</i> package.

Correlation Analysis of Anxiety and Mathematical Self-Efficacy on Problem Solving Ability Class XI IPA SMAN 2 Rumbiojaya

Solving math problems is important in learning mathematics. In fact, there are still many students who do not like mathematics. This is due, among other things, to the difficulty of understanding mathematics. These difficulties have an impact on student learning outcomes. Student learning outcomes can be optimal if students believe in their abilities. Confidence that students lack can cause anxiety. Anxiety is considered as one of the inhibiting factors in solving math problems. This is what prompted the researcher to conduct a study entitled "Analysis of Mathematical Anxiety and Mathematical Self-Efficacy on the Mathematical Problem Solving Ability of Class XI IPA Students of SMAN 2 Rumbio Jaya. This study aims to determine whether or not the influence of mathematical anxiety and mathematical self-efficacy of students together on problem-solving abilities. The benefit of research for researchers is as an exercise in carrying out scientific research and for teachers is knowing things that affect problem-solving abilities. This research is a type of quantitative descriptive research using frequency distribution and correlation analysis techniques. The population in the study was students of class XI IPA SMAN 2 Rumbio Jaya. The sample selection used a purposive sampling technique. Data collection instruments use questionnaires and tests. Questionnaires were used to obtain data about students' mathematical anxiety and mathematical self-efficacy while tests were used to obtain data about problem solving abilities. The results of the study show that mathematical anxiety and mathematical efficacy are related to problem solving abilities with a coefficient of determination of 0.078% and 21.25%

A meta-analysis on the effectiveness of strategies and programs used to address the mathematics learning difficulties

The present study aimed to obtain an empirical evidence about the effectiveness of strategies and programs used to address mathematical learning difficulties through studies published in some Arab periodicals and through adopting the meta-analysis method. Furthermore, the study investigated whether the efficacy of these strategies and programs differ according to the independent variables and educational stage in the selected studies. A systematic search of experimental and quasi-experimental studies published between 2012 and 2022 was conducted. 47 studies from a total of 154 studies met the study selection criterion. The results revealed that the average standard effect size (ES) for all studies included in the meta-analysis was 3.19, with a huge ES. The results also showed no difference in the efficiency of strategies and programs in the selected studies according to the independent variables and the educational stage.

ANALISIS FAKTOR INTERNAL KESULITAN BELAJAR MATEMATIKA KELAS V DI SEKOLAH DASAR QUR’AN AL- MUWAFFAQ KABUPATEN TANGERANG

Learning mathematics is one of the subjects that students are less interested in. One of the reasons is that mathematics is a subject that is difficult to understand or understand. The low interest of students in learning mathematics causes low student learning scores in mathematics. This study aims to determine the factors that cause learning difficulties in fifth grade students. The method used in this research is descriptive qualitative using data collection techniques in the form of kuesioner interviews. and documentation. Checking the validity of the data using triangulation. Data is analyzed through the steps of data collection, data reduction, data presentation, and drawing conclusions. The subjects in this study were students and teachers of class V with a total of 16 respondents, namely teachers of class V and students of class V. Based on the results of the study it was found that there were factors of learning difficulties in mathematics that caused low student learning scores.

The Effect of the Joyful Learning Method on the Third-Grade Students' Learning Outcomes in Mathematics

Students who have learning difficulty in mathematics learning subjects indicate unsatisfactory learning results and incomplete scores with KKM. The quantitative research method is a research method that is based on positive philosophy used to study the research instruments, and the data analysis is quantitative or statistical in order to test the hypotheses that have been set. The research method used is an experimental research method. The students' mathematics learning outcomes before being given treatment obtained an average value of 50.80. The result of the normality test was 0.128. Hence, it can be concluded that the pretest learning outcomes are normally distributed. The students’ mathematics learning outcomes after being given treatment obtained an average score of 72.69. The normality test result was 0.117. Hence, it can be concluded that the post-test learning outcomes are normally distributed. It can be proven that a correlation coefficient value of 0.846 is in the powerful interference category. The results of the T-test to find out whether the hypothesis is accepted or rejected are seen from the tcount 9,118 ≥ ttable 1,692, which means that there is an effect of Joyful Learning on students’ learning outcomes. Thus, Ha was accepted and Ho was rejected.

Meningkatkan Pemahaman Anak-anak Mengenai Perkalian dan Pembagian dalam Pelajaran Matematika

Mathematics is one of the fields of study taught in schools. Both elementary schools, junior high schools and public high schools. In Mathematics Lesson there are various kinds of material presented, starting from Multiplication, Addition, Division, Subtraction, Trigonometry, and much more. Learning Mathematics at school is expected that all students can know numbers and be able to count, because in the real world and work in mathematics it is very important so that there are no such things as Number Illiteracy and Calculation Stuttering. But who would have thought that there were many children who still did not understand mathematics, one of them was the children at the Panti Asuhan Solaya (PASO), the children complained that they did not understand Mathematics material, namely Multiplication and Division. the interesting subject of Mathematics and the difficulty of Mathematics. In this complaint, children need motivation to be enthusiastic and learn mathematics while playing so that children do not get bored in learning. And to overcome these problems optimally, Mini Project Practicum 2 was carried out, where the project used the Group Work Intervention method which consisted of several stages, namely Assessment, Planning, Intervention, Monitoring, Evaluation, and Termination. The implementation of the intervention method is expected to have a good impact on children.

Preterm children born below 33-35 weeks of gestation have an increased risk of mathematical difficulties.

To investigate the association between gestational age (GA) and grade point averages by domains of language and mathematics at the end of lower secondary education. A nationwide register-based study including all Danish children born in 1992-1997 who completed lower secondary education. Grades were evaluated by GA. Domain-specific differences in grades were investigated, and academic profiles were made. The study population comprised 319 796 children. For language, only minor differences in grades were observed. The grades in mathematics ranged from 7.02 (95% confidence interval [CI]: 7.00-7.04) at GA = 40 weeks to 5.86 (95% CI: 5.61-6.11) at GA <28 weeks. Grade differences showed lower grades in mathematics, compared to language, below GA 33-35 weeks. The academic profile of mathematical difficulties was more prevalent among GA <32 weeks. Average/high grades within both domains represented the predominant academic profile, constituting 68.8% at GA 39-41 weeks and 56.6% at GA <28 weeks. Only in mathematics decreasing GA was associated with lower grades. Increased mathematical difficulties were found below GA 33-35 weeks. The academic profile of mathematical difficulties was more prevalent among GA <32 weeks. However, the absolute differences in grades were small, and the predominant academic profile was average/high grades within both domains across all GA.

The analytic solution of interfacial concentration with observed rejection ratio during dead-end membrane filtration

In this study, we revisit the fundamentals of constant–flux dead–end filtration, develop an analytical solution of the interfacial concentration ϕmτRo as a function of dimensionless time τ and observed rejection Ro, and compare the solution with previous work developed for constant intrinsic rejection, Ri. The excessive concentration, ϕmτRo−1, consists of three nonlinear terms of τ and reaches 4Roτ in an asymptotic limit of τ>1/2. We apply the Robin (mixed) and Dirichlet boundary conditions on the membrane surface and at a far feed–entrance, respectively. The mathematical difficulties for the inverse Laplace transform are resolved using a linear combination of the Laplace transform of error and complementary error functions and applying the convolution theorem. We analytically obtain the unsteady variation of the interfacial concentration after the pressure release using the global mass balance and numerically calculate the required time to reduce the interfacial concentration to a specific limit. More importantly, a relationship between observed and intrinsic rejection ratios is found, such as, Ro≃Ri, and verified using experimental data from the literature.

New Analytical Solutions for Elastoplastic Buckling of Non-Lévy‐Type Rectangular Plates

Analytical solutions for elastoplastic buckling of plates play a crucial role in providing benchmark results and facilitating fast structural analyses for preliminary designs. However, the analytical solutions for elastoplastic buckling of plates remain incomplete due to the inherent mathematical difficulties associated with higher-order partial differential equations and material nonlinearity. Consequently, the existing analytical solutions for rectangular plates are only applicable to those with Lévy‐type boundary conditions. To address the limitation, this study extends a novel symplectic superposition method to obtain new analytical elastoplastic buckling solutions of non-Lévy‐type rectangular plates, where both the incremental theory (IT) and deformation theory (DT) are adopted. Comprehensive benchmark elastoplastic buckling loads are presented and validated by the modified differential quadrature method. The plastic buckling paradox is explicitly observed, which highlights a significant disparity between the IT and DT in predicting buckling loads for relatively thick plates. Furthermore, our analysis reveals that the DT provides an optimal load ratio for buckling resistance, while no such finding is observed with the IT. The stability criterion curves are plotted using the elastic theory and plastic theories (IT and DT) to further reveal the importance of incorporating the effect of plasticity as well as to provide a useful guideline for the relevant analyses and designs.

THE INVESTIGATION OF CULTURE-INTEGRATED MATHEMATICS REMEDIAL MODULES ON INDIGENOUS STUDENTS’ LEARNING OUTCOME

The purpose of this study was to use activity theory to analyze the mathematics difficulties of indigenous low-achieving students, to develop culturally integrated mathematics remedial modules to solve this difficulty and test the student's learning outcomes. This research applied the case study method and invited twelve grade 4-5 Truku indigenous students as the participants. The research tools used for analysis included a teacher-student interview outline, an indigenous culture integration mathematics remedial teaching module, classroom videos, and reflection logs. The results showed that the difficulties of indigenous low-achieving students were among the tools, community, rule, and division of labor by activity theory analysis, which caused them to produce contradictory emotions towards mathematics. In the second stage, the study team developed an indigenous culture integrated into the mathematics remedial module to solve the difficulties. After teaching, 70% of the indigenous low-achieving students improved their math performance. The cultural dual-guidance teaching strategy expanded the indigenous students' ability to use multiple representations to solve problems, promoted confidence to present their solving method, and showed the ability to contribute to the group.

Analisis Faktor Kesulitan Belajar Matematika Siswa Pada Materi Penyajian Data Di MIS TPI Sei Bamban Kec. Batang Serangan Kab. Langkat

This study aims to describe students' difficulties in learning mathematics in mathematics subject data presentation material in class V MIS TPI SEI BAMBAN. The goal is: 1.To find out the difficulties experienced by students in learning mathematics in the material for presenting data at MIS TPI SEI BAMBAN, 2.To find out the factors that cause students to have difficulty learning mathematics in the material for presenting data at MIS TPI SEI BAMBAN 3.For find what efforts were made in overcoming students' learning difficulties in Mathematics in the Data Presentation material at MIS TPI SEI BAMBAN Kec. Batang Serangan Kab. Langkat. This study used qualitative research methods. The techniques used to collect data are observation, interviews, and documentation. The conclusion from the results of this study namely : 1.Types of learning difficulties experienced by students, namely difficulties in understanding formulas, multiplication, division and in data presentation material, namely in line charts. 2.Then the factors that cause student learning difficulties consist of internal factors and external factors. Internal factors include attitudes in students and external factors, namely factors from outside the student's self. 3.Efforts made by the teacher, namely motivating students, learning in a fun way and increasing practice questions.

Analysis of Student Difficulties in Learning Mathematics in Class VIII Students at SMP Negeri 2 Hiliduho Academic Year 2021/2022

Learning difficulties are one of the external factors (from outside themselves) of students that have been identified as resulting in low student achievement in mathematics. These learning difficulties can be caused by many factors. This research aims to: (1) analyze students' difficulties in learning mathematics. (2) describe the student's mathematics learning difficulties in mathematics learning. This research was carried out at SMP Negeri 2 Hiliduho. This research is qualitative research with a descriptive approach. The results of data analysis show that: (1) in mathematics learning in Class VIII of SMP Negeri 2 Hiliduho, 69% of 23 students had difficulty learning mathematics. (2) Difficulty learning mathematics is caused by difficulty understanding concepts, difficulty finding the correct solution or formula to solve problems, students' lack of ability in operating numbers and students being unable to write answers correctly.

PENERAPAN TEKNIK SCAFFOLDING DALAM MENGURANGI MATHEMATICS ANXIETY SISWA PADA MATERI PELUANG

One of the difficulties in learning mathematics is anxiety. The level of anxiety can be seen from the students' responses in solving math problems. The process of minimizing these conditions in order to obtain better learning outcomes requires learning techniques that are in accordance with students' cognitive abilities. The learning technique that corresponds to this is the scaffolding technique. This study aims to analyze the factors that cause learning difficulties in mathematics in terms of math anxiety in the opportunity material for class X SMAN 2 Seunuddon and the results of applying scaffolding techniques to overcome the level of anxiety. The research approach is in the form of a qualitative descriptive type. X-2 grade students' research subjects. Data collection techniques used observation, tests, questionnaires, and interviews which were then analyzed using reduction, presentation and conclusion of data. Based on the test results, it was found that the difficulty of learning facts, concepts, operations and principles was 58%, 50%, 58% and 75%, respectively. Through interviews, it was found that the factors that caused students to experience learning difficulties were: difficulties in understanding the opportunity material, there were physical disturbances to students, lack of interest in studying mathematics, lack of self-motivation, teachers were less interesting in presenting material, lack of motivation from parents and inadequate facilities. Next, the scaffolding technique of the environmental provisions type was carried out. The test results after the technique was carried out found difficulty learning facts, concepts, operations and principles of 8%, 8%, 8% and 41%, respectively. Thus it was concluded that the use of scaffolding techniques of the environmental provisions type provided a significant reduction in students' difficulties caused by anxiety in working on word problems on probability material.

PEDAGOGICKÁ DIAGNOSTIKA OBTÍŽÍ V MATEMATICE U ŽÁKŮ ZÁKLADNÍCH ŠKOL

This paper focuses on the pedagogical assessment of primary school pupils' mathematical abilities and skills. The present study includes pupils taught by conventional methods and pupils taught by the so-called Hejny method based on the constructivist approach. Using standardized diagnostic methods, children nominated by teachers as having difficulties in mathematics were compared in terms of their performance in mathematics and non-verbal intellectual abilities with a control group of pupils without identified difficulties. The results showed significant differences in favor of the control group, especially for children taught within a constructivist approach.

General dispersion relations for resistive wall modes in tokamaks

The dispersion relation for the resistive wall modes (RWMs) is derived without the use of the trial function bHF proposed in S. W. Haney and J. P. Freidberg [Phys. Fluids B 1, 1637 (1989)] for the magnetic perturbation b outside the plasma. Another difference from the Haney–Freidberg (HF) approach is the incorporation of non-ideal effects in the plasma description. These enter the final result through the energy functional and affect the external solution for b through the boundary conditions only. This allows to perform the derivations in a general form without constraints on the dissipation mechanisms in the plasma. Then, the main mathematical difficulties are related to the description of the energy flow outside the plasma. This part of the task is presented with details allowing easy comparisons with the reference HF case. Being universally applicable, the resulting dispersion relation covers the existing variants, including those based on the so-called kinetic approaches. It shows that, because of its integral nature, the same predictions can be expected from various models for the plasma. Another conclusion is that, with a non-ideal contribution, just one or two free parameters would be enough to get agreement with experimental data on the plasma stability boundary. This, however, does not guarantee that the same choice of the fitting coefficients will be similarly efficient on other devices. The proposed relations provide a unified approach to the problem of plasma stability against RWMs.