Differences In Mathematical Ability Research Articles

Problems and Solutions in Vertical Addition of Adults Mental Disorders

This study discusses the problems of adult students (30-40 years old) with mental disabilities in vertical addition learning and proposes several tailored solutions. Through the specific analysis of three students that participated in the study, the difficulties in the process of their mathematical operation ability acquisition are found, such as being influenced by others, and forgetting to carry numbers. In response to these problems, concrete measures have been taken, such as improving students’ self-confidence, using auxiliary tools, and concretizing mathematical concepts. Through the implementation of these measures, a noticeable difference in mathematical ability was achieved. The research summarized some teaching experiences, including the rational use of tools, and attention to students’ psychology and behavior norms.

Developmental Dyscalculia in Relation to Individual Differences in Mathematical Abilities.

There is still much debate about the exact nature and frequency of developmental dyscalculia, and about how it should be defined. This article examines several key questions in turn: Is developmental dyscalculia a distinct disorder, or should it be seen as the lower end of a continuum-or possibly more than one continuum-of numerical ability? Do individuals with developmental dyscalculia show atypical brain structure or function? Does the study of acquired dyscalculia have anything to teach us about developmental dyscalculia? In studying dyscalculia, should we look less at arithmetical ability as a single entity, and more at separable components of arithmetical ability? How heterogeneous is developmental dyscalculia, and how important is it to study individual profiles? To what extent is developmental dyscalculia influenced by domain-specific versus domain-general abilities? The conclusion is that, though a significant amount has been discovered through existing research, and though this has some important implications for screening and diagnosis of dyscalculia, there is much more research that still needs to be conducted if we are to answer all of these questions fully. In particular, the study of developmental dyscalculia must be more integrated with the study of individual differences in mathematics in the population as a whole.

Upaya Melawan Stereotip dengan Membangun Minat Matematika Menggunakan Strategi Inovatif Untuk Anak Sekolah Dasar Di SD Negeri 05 Pemulutan

Gender stereotypes in mathematics education have long been a concern in the field of education. Although empirical evidence shows that there are no inherent differences in mathematical abilities between boys and girls, these stereotypes persist in culture and society. The impact is particularly significant, especially on elementary school children, who tend to have low interest and confidence in mathematics. However, innovative strategies such as the Problem Solving approach can address these stereotypes and help build strong interest and skills in mathematics. Through observation and evaluation, it was found that the implementation of innovative strategies has a significant positive impact on students' interest and achievement in mathematics. Therefore, continuous efforts to combat stereotypes, foster interest in mathematics, and implement innovative strategies are crucial in creating a supportive learning environment that advances students' mathematical abilities

A Comparative Study of Secondary School Mathematics Teaching Materials from the Perspective of Reasoning--Taking "Pythagorean Theorem" as an Example

Education has always been a hot topic of discussion. From the results of junior high school mathematics assessments in recent years, there are differences in mathematical abilities between Eastern Europe and Europe and America. Since reasoning is crucial to understanding mathematics, we compare the "Pythagorean Theorem" in textbooks from China, the United States, and Singapore, examining the theorem's different types of reasoning and how it relates to previously acquired knowledge. The reasoning categories proposed by Shi Ningzhong, Harel, and Sowder serve as the fundamental basis for categorizing the varieties of reasoning in this research. The introduction of proofs for the hook and Pythagorean theorem is investigated for each edition of the textbook, and concerning the deductive reasoning ability, the People's Education Press edition (PEP) and Zhejiang Education edition (ZJE) editions are in the first tier, followed by Singaporean textbooks and American textbooks. In terms of the correlation between the Pythagorean theorem and what has been learned, the ZJE involves the most points of correlation. Finally, we discuss the implications of these results for teachers' explanations of the Pythagorean theorem: teachers can briefly introduce the geometric deductive proof process of the Pythagorean theorem to stimulate students' interest in learning mathematics.

PENERAPAN MODEL PEMBELAJARAN STUDENT TEAM ACHIEVEMENT DIVISION UNTUK MENINGKATKAN KEMAMPUAN MATEMATIS

Mathematics learning is designed to achieve the objective of mathematics learning, that is to stimulate students to grow their mathematical abilities. However, the activities of teaching-learning have been applying the conventional learning method, in which the teacher has full control of learning so that students' mathematical abilities are classified as low. The learning model that is applied to the solution to improve students' mathematical abilities is Student Team Achievement Division (STAD). This research involved VIII classes of SMP Negeri 50 Jakarta, which are VIII-B and VIII-D classes using a Quasi-Experimental Design. Data collection was based on a pretest, posttest, and gain data by statistical test through the Mann-Whitney U test by the calculation of the program SPSS 26 because the data is not a normal distribution and not homogeneous so that it is obtained that: (1) There is a difference in mathematical ability between students who apply STAD and Expository learning models. The average posttest score of mathematical ability between students with the STAD learning model treatment is superior to the Expository learning model, that is 66,64 and 15,78. (2) There is a difference in improving mathematical ability between students who apply the STAD and Expository learning models. The average gain score of mathematical ability between students who apply the STAD learning model is superior to the Expository learning model, that is 64,56 and 13,08.

The relationship of metacognitive abilities of students with ADHD with their mathematical competence with the use of ICT’s

Metacognition is the ability of learners to take necessary steps to plan suitable strategies for solving the problems they face, to evaluate consequences and outcomes and to modify the approach as needed, based on the use of their prior knowledge. Students are aware of the learning process and know how they learn is important in terms of both controlling their previous learning and building their new learning on the previous ones. Knowing which cognitive factors underlie individual differences in mathematical abilities is the key to gaining further insight into children’s mathematical development. In this article are conceptualized children with ADHD (Attention Deficit Hyperactivity Disorder) who experience difficulty in managing attention in school and make a thorough study which is focused on how metacognition helps ADHD-learners to successfully achieve a personal goal by choosing the right cognitive Information and Communication Technologies (ICT) tools for this purpose. This article, therefore, discusses the object of explaining the relationship and impact of metacognitive awareness on student's academic achievement, especially on their mathematical competence and makes the appropriate connections with the contemporary necessary technological equipment for educational use, in a way that students who receive metacognition-based education do enjoy learning and this method is sustainable

CONCEPT MAPPING: A WAY FOR INVESTIGATING STUDENTS’ MATHEMATICAL UNDERSTANDING

Understanding the concept is one of the main goals in learning mathematics. Teachers as the main pillar in the implementation of learning can use various ways and methods to analyze the extent to which students understand the mathematical concepts being taught. One way that can be used by teachers to observe students' understanding is through a concept map. This study was a qualitative study with the purpose of describing students' understanding on mathematical concepts by using a concept map. The subjects of this study were three students who were selected based on differences in mathematical ability. Students were asked to develop a concept map according to their understanding of the material on mathematical functions. The results show that concept maps can show the level of students' understanding on mathematical concepts based on the number of relationships formed (map complexity). Students with high mathematical abilities can form a fairly complex concept map by showing the relationship of each given concept. On the other hand, students with low mathematical abilities have not been able to show the relationship between the concepts given yet. Keywords: Understanding, Mathematical Concepts, Concept Maps

Analysis of Student Thinking Ability in the Topic of Probability: A Descriptive Study of Gender and Math Ability

The probability is very closely related to everyday life that includes a probabilistic situation. This situation contains an element of uncertainty when someone is thinking about a problem that has various possibilities or consists of a part of luck, then that person is thinking probabilistically. The purpose of this study is to analyze the mathematical probability thinking skills of senior high school students in the response aspect with gender and mathematical abilities. This type of research is a qualitative descriptive study based on five stages, namely (1) natural design, (2) descriptive data, (3) attention, (4) data processing, and (5) the main focus of research. The research was conducted at Senior High School in Jayapura, Indonesia. The research subjects were students of class XI Science. The research instrument consisted of mathematical ability test sheets, probability problem-solving tasks, interviews. The results of the investigation show that the profile of male students' probabilistic thinking on mathematical abilities in solving probability problems includes providing statistical responses in solving probability. Issue is related to the sample space (representatives formation) because it uses a combination to calculate the number of members of the sample space by providing the right reasons. Meanwhile, for women, the profile of probabilistic thinking is using several strategies in solving probability problems related to the sample space (representatives formation). Based on the investigation of the results shows that there are differences in mathematical ability between male and female students probability of problem-solving.

Neurobiological origins of individual differences in mathematical ability.

Mathematical ability is heritable and related to several genes expressing proteins in the brain. It is unknown, however, which intermediate neural phenotypes could explain how these genes relate to mathematical ability. Here, we examined genetic effects on cerebral cortical volume of 3–6-year-old children without mathematical training to predict mathematical ability in school at 7–9 years of age. To this end, we followed an exploration sample (n = 101) and an independent replication sample (n = 77). We found that ROBO1, a gene known to regulate prenatal growth of cerebral cortical layers, is associated with the volume of the right parietal cortex, a key region for quantity representation. Individual volume differences in this region predicted up to a fifth of the behavioral variance in mathematical ability. Our findings indicate that a fundamental genetic component of the quantity processing system is rooted in the early development of the parietal cortex.

Students’ Mental Construction in Cube and Cuboid Concepts Based on Mathematical Ability Differences

Understanding of cube and cuboid concepts is one of the essential goals of solid geometry learning. Most studies of students’ understanding of these concepts have posited a gap between the students’ surface area and volume conceptions of its and students’ understanding. The study aims to describe the students’ mental constructions in APOS (Action, Process, Object, and Schema) theory framework. This study used analysis of students as subject to three junior high school students who have differences in mathematical abilities with a qualitative approach. Data were collected by the task sheet and interview. The result of this study evidences that subject who has high mathematical ability could solve problems about cube and cuboid concepts correctly in the action stage. In the process and object stage, subject could provide detailed explanations of how steps to assess the surface area and volume of cube and cuboid. She compared two shapes with different sizes of cube and cuboid. In the schema stage, she made systematic understanding related to the concepts of surface area and volume of cube and cuboid. The subject who has medium mathematical ability explained her mental construction in action and process stage well, despite the error in the process stage. Next stage, she had compared two different shapes of cube and cuboid to found their ratio. The last stage, she had not completed her explanation. The subject has low mathematical ability could solve the problems about cube and cuboid concepts. At the process, object, and schema stage, she had not completed its indicators to show cube and cuboid concepts.

Redesign and validation of a computer programming course using Inductive Teaching Method.

Inductive Teaching Method (ITM) promotes effective learning in technological education (Felder & Silverman, 1988). Students prefer ITM more as it makes the subject easily understandable (Goltermann, 2011). The ITM motivates the students to actively participate in class activities and therefore could be considered a better approach to teach computer programming. There has been little research on implementing ITM in computer science courses despite its potential to improve effective learning. In this research, an existing computer programming lab course is taught using a traditional Deductive Teaching Method (DTM). The course is redesigned and taught by adopting the ITM instead. Furthermore, a comprehensive plan has been devised to deliver the course content in computer labs. The course was evaluated in an experiment consisting of 81 undergraduate students. The students in the Experimental Group (EG) (N = 45) were taught using the redesigned ITM course, whereas the students in the Control Group (CG) (N = 36) were taught using the DTM course. The performance of both groups was compared in terms of the marks obtained by them. A pre-test conducted to compare pre-course mathematical and analytical abilities showed that CG was better in analytical reasoning with no significant differences in mathematical abilities. Three post-tests were used to evaluate the groups theoretical and practical competence in programming and showed EG improved performance with large, medium, and small effect sizes as compared to CG. The results of this research could help computer programming educators to implement inductive strategies that could improve the learning of the computer programming.

Numeracy skills in child synaesthetes: Evidence from grapheme-colour synaesthesia

Grapheme-colour synaesthesia is a neurological trait that causes lifelong colour associations for letter and numbers. Synaesthesia studies have demonstrated differences between synaesthetes and non-synaesthetes in ways that extend beyond synaesthesia itself (e.g., differences in their cognition, personality, and creativity). This research has focused almost exclusively on adult synaesthetes, and little is known about the profiles of synaesthetic children. By and large, findings suggest advantages for synaesthetes (e.g., Chun & Hupé, 2016; Havlik, Carmichael, & Simner, 2015; Rothen, Meier, & Ward, 2012; Rouw & Scholte, 2016; Simner & Bain, 2018) although differences in mathematical ability are unclear: some research indicates advantages (e.g., Green & Goswami, 2008) whilst others suggest difficulties (e.g., Rich et al., 2005). In the current study, we tested numerical cognition in a large group of children with grapheme-colour synaesthesia. Synaesthetes with coloured numbers showed advantages over their peers in their sense of numerosity, but not in their curriculum mathematics ability. We discuss how our findings speak to models for synaesthesia, to methodologies for assessing number cognition (e.g., dot numerosity tasks), and to the wider educational practice of using coloured number-tools in schools (e.g., Numicon; Oxford University Press, 2018).

Are preschoolers who spontaneously create patterns better in mathematics?

Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children's ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. The present study aimed to explore 4- to 5-year olds' Spontaneous Focusing On Patterns (SFOP) and its association with their patterning and mathematical ability. Participants were 378 children (Mage =4years 10months; 191 boys) from 17 preschools. Spontaneous Focusing On Patterns was measured with a construction task in which children had to build a tower with 15 blocks of three different colours. The constructions of the children were grouped into three categories (i.e., pattern, random, and sorting). We additionally administered tasks assessing their patterning ability, mathematical ability, spatial ability, and visuospatial working memory. When building a tower, 37% of the preschoolers spontaneously created a pattern, 49% made a random construction, and 14% sorted the blocks per colour. Preschoolers who spontaneously created a pattern had better patterning and mathematical ability than children in the random group. Group differences in patterning ability and spatial skills accounted for the difference in mathematical ability. The current data suggest that children's spontaneous attention to patterns is an important component of their mathematical ability. Children's spontaneous pattern constructions may provide opportunities to discuss and practice patterns in preschool settings or at home, but more research is required to further analyse the role of SFOP in early mathematical development.

Sex Differences in 32,347 Jordanian 4th Graders on the National Exam of Mathematics

Abstract. Sex differences in mathematical ability were examined in a nation-wide sample of 32,346 Jordanian 4th graders (age 9–10 year) on a 40-item mathematics test. Overall, boys were found to perform slightly worse ( d = −0.12) but had slightly more variation in scores ( SD = 1.02 and SD = 0.98 for boys and girls, respectively). However, when results were disaggregated by school type, single-sex versus coed (i.e., coeducational), boys were found to perform better than girls in coed schools ( d = 0.27) but worse across single-sex schools ( d = −0.37). Two-parameter item response theory analysis showed that item difficulty was similar across sexes in the full sample. Item loadings exhibited substantial departure from measurement invariance with respect to boys and girls at single-sex schools, though. For boys and girls at coed schools, both the item difficulty and item loading correlations were highly similar, evincing that measurement invariance largely held in this case. Partially consistent with findings from other countries, a correlation between item difficulty and male advantage was observed, r = .57, such that the relative male advantage increased with increased item difficulty. Complicating interpretation, this association did not replicate within coed schools. Item content, Bloom’s cognitive taxonomy category, and item position showed no relation to sex differences.

Analysis of mathematical ability based on gender

The purpose of the study was to analyze the mathematical abilities of students of mathematics education regarding gender and personality. Mathematical abilities include the ability to explore, speculate and logical reasons for solving routine and non-routine problems. While gender is a cultural concept that is used to identify differences regarding roles, behaviours and others between male and female that develop in a society based on social engineering. This study is descriptive research. The subjects of this study were 38 students of mathematics education department of Universitas Halu Oleo, consisting of ten male and 28 female. Based on gender tests, it will be classified into four types: masculine male, feminist male, masculine female, and feminine female. Based on the results of the analysis through a mathematical ability test, it can be concluded that there are differences in mathematical abilities based on gender.

Karakteristik Metakognisi Mahasiswa Dalam Menyelesaikan Masalah Matematika Berdasarkan Langkah-Langkah Polya Dan De Corte

This research describes the student metacognition profile Tadris Department of Mathematics State Islamic Institute Tulungagung based differences in mathematical ability that is highly capable student, medium, and low. Collecting data in this exploratory study done by solving mathematical problem solving and in-depth interviews. To get the process used metacognitive interview leads to the question steps to resolve the matter by the steps Polya and De Corte. Results of a study of college students show that students are capable of moderate or low it did not do a good metakognisis process in the last three stages of problem-solving by step Polya and De Corte. Students with moderate and low level of capability are only looking do metakognisis at the stage of understanding the problem, whereas high-ability students perform well metacognitive processes.

Cognition, emotion, and arithmetic in primary school: A cross-cultural investigation.

The study investigated cross‐cultural differences in variability and average performance in arithmetic, mathematical reasoning, symbolic and non‐symbolic magnitude processing, intelligence, spatial ability, and mathematical anxiety in 890 6‐ to 9‐year‐old children from the United Kingdom, Russia, and China. Cross‐cultural differences explained 28% of the variance in arithmetic and 17.3% of the variance in mathematical reasoning, with Chinese children outperforming the other two groups. No cross‐cultural differences were observed for spatial ability and mathematical anxiety. In all samples, symbolic magnitude processing and mathematical reasoning were independently related to early arithmetic. Other factors, such as non‐symbolic magnitude processing, mental rotation, intelligence, and mathematical anxiety, produced differential patterns across the populations. The results are discussed in relation to potential influences of parental practice, school readiness, and linguistic factors on individual differences in early mathematics. Statement of contribution What is already known on this subject? Cross‐cultural differences in mathematical ability are present in preschool children.Similar mechanisms of mathematical development operate in preschool children from the United Kingdom, Russia, and China.Tasks that require understanding of numbers are best predictors of arithmetic in preschool children. What does this study add? Cross‐cultural differences in mathematical ability become greater with age/years of formal education.Similar mechanisms of mathematical development operate in early primary school children from the United Kingdom, Russia, and China.Symbolic number magnitude and mathematical reasoning are the main predictors of arithmetic in all three populations.

Mathematical (Dis)abilities Within the Opportunity-Propensity Model: The Choice of Math Test Matters.

This study examined individual differences in mathematics learning by combining antecedent (A), opportunity (O), and propensity (P) indicators within the Opportunity-Propensity Model. Although there is already some evidence for this model based on secondary datasets, there currently is no primary data available that simultaneously takes into account A, O, and P factors in children with and without Mathematical Learning Disabilities (MLD). Therefore, the mathematical abilities of 114 school-aged children (grade 3 till 6) with and without MLD were analyzed and combined with information retrieved from standardized tests and questionnaires. Results indicated significant differences in personality, motivation, temperament, subjective well-being, self-esteem, self-perceived competence, and parental aspirations when comparing children with and without MLD. In addition, A, O, and P factors were found to underlie mathematical abilities and disabilities. For the A factors, parental aspirations explained about half of the variance in fact retrieval speed in children without MLD, and SES was especially involved in the prediction of procedural accuracy in general. Teachers’ experience contributed as O factor and explained about 6% of the variance in mathematical abilities. P indicators explained between 52 and 69% of the variance, with especially intelligence as overall significant predictor. Indirect effects pointed towards the interrelatedness of the predictors and the value of including A, O, and P indicators in a comprehensive model. The role parental aspirations played in fact retrieval speed was partially mediated through the self-perceived competence of the children, whereas the effect of SES on procedural accuracy was partially mediated through intelligence in children of both groups and through working memory capacity in children with MLD. Moreover, in line with the componential structure of mathematics, our findings were dependent on the math task used. Different A, O, and P indicators seemed to be important for fact retrieval speed compared to procedural accuracy. Also, mathematical development type (MLD or typical development) mattered since some A, O, and P factors were predictive for MLD only and the other way around. Practical implications of these findings and recommendations for future research on MLD and on individual differences in mathematical abilities are provided.

Student’s thinking process in solving word problems in geometry

This research aims to find out the thinking process of seventh grade of Junior High School in solve word problem solving of geometry. This research was descriptive qualitative research. The subject of the research was selected based on sex and differences in mathematical ability. Data collection was done based on student’s work test, interview, and observation. The result of the research showed that there was no difference of thinking process between male and female with high mathematical ability, and there were differences of thinking process between male and female with moderate and low mathematical ability. Also, it was found that male with moderate mathematical ability took a long time in the step of making problem solving plans. While female with moderate mathematical ability took a long time in the step of understanding the problems. The importance of knowing the thinking process of students in solving word problem solving were that the teacher knows the difficulties faced by students and to minimize the occurrence of the same error in problem solving. Teacher could prepare the right learning strategies which more appropriate with student’s thinking process.

MATHEMATICAL ABILITIES AND EDUCATIONAL STRATEGIES FOR CHILDREN WITH AUTISM SPECTRUM DISORDER

The exploration of mathematical abilities in children with Autism Spectrum Disorder (ASD) reveals a diverse and complex landscape, highlighting both strengths and challenges. Structured mathematics education plays a vital role in the cognitive development of these children by offering tailored, predictable methods that address their unique learning needs. King, Lemons, and Davidson (2016) stress the importance of evidence-based practices to help students with disabilities meet rigorous mathematical standards. Their review underscores the necessity of targeted interventions, particularly for students with co-occurring intellectual disabilities. Iuculano et al. (2014) further explore the cognitive strengths of children with ASD in mathematics, revealing that these individuals often employ sophisticated problem-solving strategies, despite differences in brain activation patterns compared to their typically developing peers. This suggests that specialized educational approaches could leverage these strengths effectively. Oswald et al. (2016) address the spectrum of mathematical achievement within ASD, from mathematical disabilities to giftedness, and the influence of cognitive and clinical factors such as test anxiety and perceptual reasoning. Their findings emphasize the need for interventions that consider individual differences in mathematical ability. Chiang and Lin (2007) and Titeca, Roeyers, and Desoete (2017) highlight the variability in mathematical skills among children with Asperger Syndrome (AS) and high-functioning autism (HFA), showing that while some have average abilities, others may exhibit significant weaknesses or exceptional skills. Early numerical competencies were found to be similar between children with ASD and typically developing peers, suggesting that early educational strategies should focus on foundational skills. Wei et al. (2015) examine longitudinal growth and achievement profiles, identifying distinct categories such as hyperlexia and hypercalculia, and noting how socioeconomic factors impact mathematical development. These studies collectively advocate for a nuanced understanding of ASD and suggest that tailored, evidence-based educational strategies are crucial for supporting the diverse needs of students with autism.