Difficulties In Solving Problems Research Articles

A two-stage bidirectional coevolution algorithm with reverse search for constrained multiobjective optimization

Abstract Constrained multiobjective optimization problems (CMOPs) are widespread in reality. The presence of constraints complicates the feasible region of the original problem and increases the difficulty of problem solving. There are not only feasible regions, but also large areas of infeasible regions in the objective space of CMOPs. Inspired by this, this paper proposes a bidirectional coevolution method with reverse search (BCRS) combined with a two-stage approach. In the first stage of evolution, constraints are ignored and the population is pushed toward promising regions. In the second stage, evolution is divided into two parts, i.e., the main population evolves toward the constrained Pareto front (CPF) within the feasible region, while the reverse population approaches the CPF from the infeasible region. Then a solution exchange strategy similar to weak cooperation is used between the two populations. The experimental results on benchmark functions and real-world problems show that the proposed algorithm exhibits superior or at least competitive performance compared to other state-of-the-art algorithms. It demonstrates BCRS is an effective algorithm for addressing CMOPs. Graphical Abstract

Low Frequency Hierarchical Cooperative Impulse Control for Gravitational Wave Detector Formation Keeping

Configuration stability is crucial for the detection accuracy of space-based gravitational wave (GW) detectors. This paper proposes a low-frequency hierarchical cooperative impulse control strategy and a high-fidelity orbit optimization method to achieve a formation of GW detectors with high detection performance. The control strategy employs a hierarchical structure to divide the configuration control into position and shape layers. In the upper layer, the position layer, a state transition tensor method is employed to analyze the sensitivity and feasible range of the formation center position on the configuration stability. In the lower layer, the shape layer, a novel consistency protocol cooperatively uses the states of all individuals in the formation to determine the control expectations. The constraint on formation position is relaxed to reduce the number of impulses, achieving a low-frequency impulse control. The optimization method, characterized by a careful selection of the optimization variables and a design of adaptive model continuation from a low-fidelity model to a high-fidelity model, is proposed to reduce the problem-solving difficulty. The proposed strategy and method are applied to the Laser Interferometer Space Antenna (LISA) mission, and the results demonstrate that the configuration stability is effectively enhanced with several low-frequency impulses.

A new method to solve the Reynolds equation including mass-conserving cavitation by physics informed neural networks (PINNs) with both soft and hard constraints

AbstractIn this work, a new method to solve the Reynolds equation including mass-conserving cavitation by using the physics informed neural networks (PINNs) is proposed. The complementarity relationship between the pressure and the void fraction is used. There are several difficulties in problem solving, and the solutions are provided. Firstly, the difficulty for considering the pressure inequality constraint by PINNs is solved by transferring it into one equality constraint without introducing error. While the void fraction inequality constraint is considered by using the hard constraint with the max-min function. Secondly, to avoid the fluctuation of the boundary value problems, the hard constraint method is also utilized to apply the boundary pressure values and the corresponding functions are provided. Lastly, for avoiding the trivial solution the limitation for the mean value of the void fraction is applied. The results are validated against existing data, and both the incompressible and compressible lubricant are considered. Good agreement can be found for both the domain and domain boundaries.

Efficacy of Individual Metacognitive Training in Patients with Schizophrenia: A Case Study

Background: Several cognitive biases may be involved in the pathogenesis and continuation of symptoms in schizophrenia. Metacognitive Training (MCT) is a treatment program that targets cognitive bias in schizophrenia. The current work aimed to evaluate the influence of MCT on schizophrenia using a single-subject design.
 Methods: Five patients with schizophrenia received metacognitive training. The treatments were done for at least four weeks, two sessions per week (number of sessions ranged from 8 to 18 sessions). The MCT consists of two sets of eight modules that target common cognitive biases and problem-solving difficulties in schizophrenia. Baseline assessment was performed using the Birchwood Insight Scale (BIS), the Positive and Negative Syndrome Scale (PANSS), the Psychotic Symptom Rating Scales (PSYRATS), the Global Assessment of Functioning (GAF), WHOQOL-BREF and the Peters et al, Delusions Inventory (PDI). The post intervention assessments included the afore-mentioned measures as well as treatment satisfaction. The follow-up assessments were conducted three and six months later. Data analysis was administered employing visual analysis diagrams, percentage of recovery and the Reliable Change Index (RCI).
 Results: MCT was associated with a reduction in positive and negative symptoms (up to 18.7, 100 and 100% on the PANSS, PSYRATS and PDI, respectively) in individuals with schizophrenia, and its effects diminish over time. Insight showed significant improvement, but it was mainly the insight into symptoms. In patients with low baseline score of Quality of Life (QOL), an improvement was reported. The GAF did not change significantly.
 Conclusion: MCT can be suggested as an adjunct therapy to decrease the symptoms of schizophrenia and improve the patients’ insight. Patients with more symptoms and lower levels of insight, performance and QOL seem to respond better to MCT. Randomized clinical trials are required.

Analisis kesulitan pemecahan masalah matematika berdasarkan teori Polya pada peserta didik kelas IV sekolah dasar

<p>This reseacrh aims at explaining and describing the difficulty of mathematics problem solving based on Polya theory to the 4<sup>th</sup> grade students of elementary school. This research is a qualitative descriptive research with a case study approach. Sampling was done with research subjects. Data collection was carried out using passive participatory observation techniques, in-depth interviews, and documentation studies. The technique to test validity data is using method triangulation and source triangulation. Data analysis uses the Creswell model technique The results of this study are the difficulties that occur in students in solving problems including: (1) understanding the concept of flat shapes when changed into word problems; (2) writing information that is known and asked about; (3) misconceptions about story problems; (4) determining the solution to the problem to be used; (5) problem-solving plans are not by the questions; (6) description of how to do things that are not systematic; (7) writing methods that do not use known, asked, answered, and conclusions; (8) completeness of problem-solving answers; (9) writing units of length and conclusions; (10) attention to the little things in detail that lead to errors.</p>

Cognitive and Emotional Well-Being of Preschool Children Before and During the COVID-19 Pandemic

The association between COVID-19 social disruption and young children's development is largely unknown. To examine associations of pandemic exposure with neurocognitive and socioemotional development at 24 and 54 months of age. This cross-sectional study evaluated associations between pandemic exposure vs nonexposure and developmental outcomes with covariate adjustment using data from the Ontario Birth Study collected between February 2018 and June 2022. Eligible participants were children aged 24 and 54 months. Data were analyzed from June to November 2022. COVID-19 pandemic exposure defined as assessment after March 11, 2020. Neurodevelopmental assessment using the ASQ-3 (Ages and Stages Questionnaire, Third Edition) and MCHAT-R (Modified Checklist for Autism in Toddlers, Revised) at 24 months of age, and neurocognitive and socioemotional assessment using the National Institutes of Health Toolbox at 54 months of age. A total of 718 children at age 24 months (mean [SD] age, 25.6 [1.7] months; 342 female [47.6%]; 461 White [64.2%]) and 703 at age 54 months (mean [SD] age, 55.4 [2.6] months; 331 female [47.1%]; 487 White [69.3%]) were included. At 24 months of age, 460 participants (232 female [50.4%]) were assessed during the pandemic (March 17, 2020, to May 17, 2022) and 258 (110 female [42.6%]) were assessed prepandemic (April 17, 2018, to March 10, 2020). At 54 months of age, 286 participants (129 female [45.1%]) were assessed from March 14, 2020, to June 6, 2022, and 417 (202 female [48.4%]) were assessed from February 8, 2018, to March 10, 2020. At 24 months of age, pandemic-exposed children had reduced risk of problem-solving difficulties using cutoff scores (odds ratio [OR], 0.33; 95% CI, 0.18-0.62; P = .005) and higher problem-solving (B, 3.93; 95% CI, 2.48 to 5.38; P < .001) compared with nonexposed children. In contrast, pandemic-exposed children had greater risk for personal-social difficulties using cutoff scores (OR, 1.67; 95% CI, 1.09-2.56; P = .02) and continuous scores (B, -1.70; 95% CI, -3.21 to -0.20; P = .02) compared with nonexposed children. At 54 months of age, pandemic-exposed children had higher receptive vocabulary (B, 3.16; 95% CI, 0.13 to 6.19; P = .04), visual memory (B, 5.95; 95% CI, 1.11 to 10.79; P = .02), and overall cognitive performance (B, 3.89; 95% CI, 0.73 to 7.04; P = .02) compared with nonexposed children, with no differences in socioemotional development. This cross-sectional study found both positive and negative associations between pandemic exposure and preschool children's cognitive and emotional well-being within a relatively socioeconomically advantaged sample.

The Effects of Visual Cueing on Students with and without Math Learning Difficulties in Online Problem Solving: Evidence from Eye Movement.

This study investigated the impact of visual cueing on attention guidance, deep-thinking promotion, and performance optimization in arithmetic word problem solving for students with mathematical learning difficulties (MLD). The participants included eight students with MLD and twenty students without MLD who attempted to solve mathematical word problems with and without visual cueing. Eye movements were recorded during the tasks. A repeated-measure design and nonparametric tests were applied to enhance the statistical power of the study. The data analysis results indicated that visual cueing effectively guided and sustained the attention of students with MLD, reducing their off-task duration. However, it showed limited influence in facilitating deep thinking and performance improvement for these students. There were no significant attention-guidance or performance-improvement effects observed in the problem-solving processes of students without MLD, who initially demonstrated better concentration levels and performance. The potential explanations for these findings are further discussed in this paper.

52 Stable Cognitive Impairment and Increased Psychiatric Symptoms in a Patient with Neuropathologically Progressive Fahr’s Disease After 2-Year Repeated Neuropsychological Assessment

Objective:Fahr’s disease is a rare genetic neurological disorder characterized by abnormal idiopathic calcification of the basal ganglia, typically with extrapyramidal symptoms, speech difficulty, behavioral disturbances, and progressive neurologic dysfunction. A small number of case reports have explored the neuropsychological profile of Fahr’s disease patients, and even fewer have followed the course of neuropsychological functioning over time.Participants and Methods:A 53-year-old Asian woman presented for a neuropsychological reevaluation (2021) after experiencing a recurrence of memory difficulties and mood changes. Relevant medical history was significant for systemic lupus erythematosus (SLE) and Fahr’s disease. Following an episode of acute confusion, the patient underwent a head CT (2019) which revealed extensive calcification throughout the cerebellum, central pons, and periventricular and subcortical white matter, suggestive of Fahr’s disease. Two months later, she underwent an initial neuropsychological evaluation (2019), which demonstrated prominent attention and processing speed deficits contributing to variably impaired new learning and memory along with spatial planning and problem-solving difficulties. The etiology of her cognitive deficits was determined to likely reflect metabolic and immune instability, consistent with her history of SLE and Fahr’s disease. An updated CT (2021) revealed increased calcification throughout the bilateral corona radiata, basal ganglia, cerebellar hemispheres, and midbrain, which was determined to be compatible with progressive Fahr’s disease.Results:The patient’s neurocognitive profile from current neuropsychological testing (2021) was marked by notable deficits in attention and processing speed, delayed memory, problem solving, visuospatial reasoning, and motor dexterity. Compared to her initial evaluation, her cognitive profile remained stable save for a slight decline in processing speed. The largest change was seen within the psychiatric domain. Self-reported depressive symptoms involving anhedonia, concentration difficulties, and anxiety symptoms involving nervousness and tension were more pronounced in her current evaluation. In addition, she endorsed an increase in apathy compared to her initial evaluation.Conclusions:The cognitive profile seen in this patient is consistent with the current literature relating to the clinical sequelae of Fahr’s disease in patients that eventually went on to develop dementia. Despite an increase in brain calcification seen on CT imaging over an 18-month interval, the patient’s neurocognitive profile remained relatively stable. An increase in psychiatric symptoms appeared to be the most prominent change over repeated neuropsychological assessment, which elucidates the heterogenous course of Fahr’s disease from a neuropsychological perspective. Further exploration of this disorder is warranted to better understand the clinical progression of symptoms over time.

Tantangan dalam Pembelajaran Berhitung di Kelas Awal dan Cara Mengatasinya

The low level of students' understanding in learning mathematics is caused by the assumption held by most students that mathematics is a difficult and boring subject. This diminishes students' motivation to learn, leading to the suggestion that mathematics is a subject to be avoided. This challenge serves as the foundation for the writing of this academic work. Through this research, it is hoped that we can identify the challenges in early math education, particularly in mathematics, and propose efforts to overcome difficulties in learning mathematics, especially in the third grade of Elementary School. This study is conducted using a qualitative method with a descriptive analysis approach. Data collection aims to adjust and obtain information about the factors that make it difficult for students to grasp mathematical concepts. The research results indicate that students' difficulties in learning mathematics consist of three components: difficulty in understanding concepts, difficulty in skills, and difficulty in problem-solving. The factors causing difficulties in learning mathematics originate from both internal and external factors. Based on these factors, efforts that can be made to reduce difficulties in learning mathematics include teaching math in an enjoyable way, using tangible learning media, increasing practice exercises, and establishing cooperation with students' parents.

Improving students’ performance and conceptual understanding of heat transfer using demonstration method

One of the physics topics difficult to understand among students at senior high schools (SHSs) is heat transfer. Various reasons have been advanced in an attempt to rationalize this difficulty. This study through an action research design was conducted to improve students’ performance and conceptual understanding of heat transfer at Oti Boateng Senior High School, Koforidua. The instruments used for the study were questionnaires, pre- and post-test. The study identified rote learning, inadequate understanding of concepts among others as the cause of difficulty in problem solving among students. The study revealed that although there are different methods of teaching, the efficacy of the demonstration method cannot be downplayed considering its role in improving students’ academic performance. The study concluded that for effective teaching and learning of heat transfer at SHS, it is important for teachers to employ the demonstration method in their teaching.

Verbal problem-solving in agenesis of the corpus callosum: Analysis using semantic similarity.

Previous studies demonstrated that individuals with agenesis of the corpus callosum (AgCC) experience difficulties in novel and complex problem-solving. The present study investigated verbal problem-solving, deductive reasoning, and semantic inference in AgCC. Capacity for semantic inference was tested in 25 individuals with AgCC and normal-range intelligence compared to 29 neurotypical controls. The Word Context Test (WCT) of Delis-Kaplan Executive Function System was used, employing a novel method of analysis (semantic similarity) to detect trial-by-trial progress toward a solution. With respect to the typical WCT scores, persons with AgCC had fewer total consecutive correct responses. In addition, semantic similarity to the correct word was significantly lower overall in persons with AgCC than in controls. These findings indicated that individuals with AgCC who have intelligence in the normal range are less able at the WCT taking all trials into account, although they often solve the problem eventually. This outcome is consistent with previous research indicating that callosal absence in AgCC results in a restricted imagination for possibilities, limiting their problem-solving and inferential capacities. The results also highlight the usefulness of semantic similarity as a means of scoring the WCT. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Analisis kesulitan peserta didik dalam menyelesaikan soal numerasi pecahan pada Asesmen Kompetensi Minimum di sekolah dasar

&lt;em&gt;The purpose of this study was to describe the implementation of the Minimum Competency Assessment, describe the difficulties of students in solving fraction numeracy problems on the Minimum Competency Assessment, and describe the efforts of Principals and Classroom Teachers in optimizing the Minimum Competency Assessment on numeracy. This research used descriptive qualitative research. The research subjects were the principal, grade V teacher, and grade V students. Data collection techniques were passive participation observation, interviews, and questionnaires. The data analysis technique used is Miles and Huberman interactive analysis which consists of data reduction, data presentation, verification, and conclusion drawing. Data validity testing techniques using triangulation techniques. The results of this study are Minimum Competency Assessment has been implemented well with a percentage of 83.1%. Second, students' difficulties in solving problems, namely: difficulties in concepts, difficulties in skills, and difficulties in problem solving. Second, the internal causal factors are attitude and motivation. Lack of variety and learning media, and family environment are external factors. Third, efforts made to reduce the difficulty of solving problems include using concrete learning materials, increasing practice problems, and working with parents.&lt;/em&gt;

Comparing Mental Effort, Difficulty, and Confidence Appraisals in Problem-Solving: A Metacognitive Perspective

It is well established in educational research that metacognitive monitoring of performance assessed by self-reports, for instance, asking students to report their confidence in provided answers, is based on heuristic cues rather than on actual success in the task. Subjective self-reports are also used in educational research on cognitive load, where they refer to the perceived amount of mental effort invested in or difficulty of each task item. In the present study, we examined the potential underlying bases and the predictive value of mental effort and difficulty appraisals compared to confidence appraisals by applying metacognitive concepts and paradigms. In three experiments, participants faced verbal logic problems or one of two non-verbal reasoning tasks. In a between-participants design, each task item was followed by either mental effort, difficulty, or confidence appraisals. We examined the associations between the various appraisals, response time, and success rates. Consistently across all experiments, we found that mental effort and difficulty appraisals were associated more strongly than confidence with response time. Further, while all appraisals were highly predictive of solving success, the strength of this association was stronger for difficulty and confidence appraisals (which were similar) than for mental effort appraisals. We conclude that mental effort and difficulty appraisals are prone to misleading cues like other metacognitive judgments and are based on unique underlying processes. These findings challenge the accepted notion that mental effort appraisals can serve as reliable reflections of cognitive load.

Using activity method to address students’ problem-solving difficulties in circle geometry

This action research sought to address the problem-solving difficulties of students in circle geometry problems using activity method of teaching and learning. The study in investigated students’ difficulties in solving circle geometry problems. It also found out how activity method of teaching and learning helped address the students’ difficulties of solving circle geometry problems. Finally, it established the extent to which the activity method of teaching and learning affected the performance of students in circle geometry. The accessible population was all form two students at Zion College in the Volta Region of Ghana. It numbered 499. The sample was general science 2B students. The sample size was 27 students made up of 10 girls and 17 boys. The instruments for data collection were pre- and post-test. The pre-test was conducted to establish the existence of the difficulties of students in solving circle geometry problems. After establishing the problems, activity method of teaching and learning was used as an intervention to remedy the situation. A post-test was administered to measure the improvement. The data was presented using tables and figures. Inferential statistics was also used to analyze the data. From the analysis, activity method help the students solve complex questions, which demand multiple circle theorems to solve. It was recommended that mathematics teachers should always use activity method of teaching and learning in teaching circle geometry.

Analisis Kesulitan Siswa Dalam Pembelajaran Matematika Pokok Bahasan Operasi Hitung Bilangan Bulat kelas V SD Negeri 021 Bangkinang

The purpose of this study is to determine where the location of difficulty and factors that cause difficulties in learning mathematics on the subject of integer count operation. Research subjects are taken that is class V which has the average value of mathematics still under Minimum Exhaustiveness Criteria (KKM). Data collection methods used were test method, observation method, interview method. The test method is used to obtain student completion data on the counting integer counting material in the form of essay 10 items. Observation method is used to determine the condition of subjects during the learning activities of mathematics and to know the factors that can affect the learning process of mathematics. And interview method is done to know clearly problem faced by student when study material counting integer. From the data of final analysis result, the percentage of students difficulties in skill 50% including enough category, difficulties in understanding the concept of 23.3% including less category and difficulty in problem solving by 20% including less category. So expect teachers in shaping the pattern of teaching mathematics is not solely shown in the students' skills in solving the problem. But more important is how to invite students to understand and understand and master the existing concepts well and correctly, so that students do not have difficulty in learning mathematics.

Design and development of critical thinking learning strategy in integral calculus

&lt;p&gt;Difficulty in understanding problem solving is due to the absence of critical thinking. Students lack knowledge in assessing critical thinking during problem solving. Hence, there is a need to study critical thinking infused through a learning strategy to enhance problem solving. Critical thinking (CThink) is a learning strategy designed which combines critical thinking and Integral Calculus. The development process of CThink combines the critical thinking process and questioning for critical thinking using the analysis, design, development, implementation, and evaluation (ADDIE) model. In the learning strategy, questions were applied based on CThink processes which consist of interpretation, analysis, inference, evaluation, explanation, and self-regulation. Besides, different questioning for CThink is presented based on the critical thinking process. CThink has achieved a content validity of 94.12% with a coefficient value of 0.94, and the value is above 70% or 0.70. Based on the result, the contents in the CThink are considered of good validity. From the calculation of the percentage from the expert given score, CThink has achieved the validity measurement for the language of 97.50% with a coefficient value of validity is 0.975, which is above 70 or 0.70. Based on the result, the activities and syllabus used in CThink achieved good validity measurements. The experts concluded that this CThink meets the content of Integral Calculus, in line with the level of polytechnic students, allowing students to think critically to solve problems as well as activities in CThink help to enhance student problem solving.&lt;/p&gt;

Low-Energy Transfer Design of Heliocentric Formation Using Lunar Swingby on the Example of LISA

Space-based gravitational wave (GW) detection at low frequencies is of great scientific significance and has received extensive attention in recent years. This work designs and optimizes the low-energy transfer of the heliocentric formation of GW detectors, which starts from a geosynchronous transfer orbit and targets an Earth-like orbit. Based on the example of the Laser Interferometer Space Antenna (LISA), the transfer is first designed in two-body dynamical models and then refined in simplified high-fidelity dynamical models that only consider the major orbital perturbations evaluated here. The main contributions of this work are to present an adaptive model continuation technique and to exploit the lunar swingby technique to reduce the problem-solving difficulty and velocity increment of orbital transfer, respectively. The adaptive model continuation technique fully reveals the effect of perturbations and rapidly iterates the solutions to the simplified models. The simulation results show that the lunar swingby does reduce the energy needed to escape the Earth’s sphere of influence. It is found that the gravitation of the Earth–Moon system has a significant contribution to reducing the velocity increment. The solution of low-energy transfer in the simplified models is that the duration is 360.6615 days and the total velocity increment is 0.8468 km/s.

Comparison of Mathematics Problem-Solving Abilities in Autistic and Non-autistic Children: the Influence of Cognitive Profile

This study examines relationships between mathematical problem-solving performance (in terms of strategies used and accuracy) and the main cognitive domains associated with mathematical learning (i.e. executive functions, verbal comprehension and social perception) of children with and without autism spectrum disorder (ASD and non-ASD resp.). The study involved 26 ASD and 26 non-ASD children without intellectual disabilities, between 6 and 12 years old, matched by sex, age and school (grade and classroom). The results show a higher percentage of ASD children with problem solving difficulties than non-ASD (57% vs. 23% resp.). Poor performing ASD children showed comparatively lower scores in inhibition, theory of mind and verbal comprehension. Implications for the design of mathematical interventions for ASD students are discussed.

The protective effects of dietary polyphenols on Alzheimer's disease

Alzheimer's disease (AD) is a progressive irreversible neurodegenerative disease in the hippocampus and cortex regions of the brain and is the most common cause of dementia in the elderly population among 40 million cases worldwide today, it is thought that this number will exceed up to 100 million by 2050. The disease is characterized by symptoms of memory loss, difficulty in speaking, decision making, learning, problem solving, and impaired perception of time and orientation. In its pathogenesis, the amyloid beta (Aβ) senile plaques accumulation in the extracellular synaptic spaces of the neurocortex, the formation of intracellular hyperphosphorylated tau protein deposition and neurofibrillary tangles (NFY) are important and triggered neurodegeneration mainly affects cognitive behavior and memory. Phenolic compounds are organic compounds containing a benzene ring to which one or more hydroxyl groups are attached. Studies have shown that regular consumption of polyphenols reduces the risk of developing neurodegenerative diseases. Studies have reported that polyphenols inhibit Aβ production and accumulation processes by interacting with different forms of amyloid structure. In this study, polyphenols and their therapeutic properties against AD will be discussed extensively.

Appealing to Creativity Through Solving and Posing Problems in Mathematics Class

Background: Creativity should be a key issue in mathematics learning. However, mathematics class rarely provides opportunities for students to experience it. Problem solving and posing can play a leading role in promoting creative thinking in mathematics. Objectives: This study aims to have an insight into 6 th -graders understanding of problem solving and posing, analyse their solving strategies, their ability to pose problems, and their difficulties when doing so. Design: Qualitative methods were used in a case study approach. An intervention of five sessions comprising five problem-solving and four problem-posing tasks was implemented in mathematics class. Setting and Participants: Participants were thirty 6 th -graders (11-12 year-olds) from a public supported school in Braga (Portugal). Data collection and analysis: Data collection used photographs, audio recordings, students’ written productions, and researcher field notes. Results: Students conceptualised strategies such as building schemas and tables, solving from the end to the beginning, making attempts, and reducing to a simpler problem. Students faced problem posing positively, creating problems adjusted to the requirements, with a wide variety of creative contexts. Students’ difficulties in problem solving rely on the interpretation of statements, recognition of previous similar problems, and mathematical communication; on problem posing, difficulties regarding the complexity of the formulated problems and a weak diversity of problems were identified. Conclusions: Problem solving and posing tasks can promote mathematical creativity and knowledge, therefore should be used more often in mathematics class, allowing the construction of solid mathematical skills and enthusiasm.