Mathematical Ability Research Articles

Empowering Discovery Learning and Direct Instruction with Computer-Assisted to Enhance Mathematical Performance

In the current educational context, the low academic performance of students in mathematics indicates the need for the implementation of more effective teaching methods to support the understanding of complex concepts. The effectiveness of learning can be enhanced through computer-assisted instruction, particularly in discovery learning (DL-CA) and direct instruction (DI-CA) utilizing web-based media. This study employs a quantitative approach with statistical analysis to examine the significant impact of these teaching methods on students' mathematical performance. Discovery learning and direct instruction were applied to two groups studying numerical methods, focusing on the topic of nonlinear equation solutions using the bisection method, with each group consisting of 33 students. The statistical test results indicated that there was no significant difference in mathematical performance between the DL-CA and DI-CA groups; both methods showed comparable effectiveness. However, both methods had a significant effect on the N-Gain of the learning outcomes in both groups. The improvement in mathematical performance for the DL-CA group was better than that for the DI-CA group, with more students showing high improvement (11 students) compared to the DI-CA group (1 student). Additionally, in the low improvement category, the DL-CA group had fewer students (2 students) than the DI-CA group (8 students). This suggests that both discovery learning and direct instruction have almost equivalent reliability in achieving students' mathematical abilities, but DL-CA is more effective in enhancing performance compared to DI-CA.

Fostering Inclusivity: A Critical Emancipatory Approach to Dyscalculia in Primary School Mathematics

This research endeavoured to revolutionise primary school mathematics education by implementing an active learning approach tailored to addressing dyscalculia. The study used a critical emancipatory framework as the theoretical foundation, and participatory action research as the chosen methodology. The researcher employed purposive sampling to select two mathematics teachers, one school-based teacher, a district education psychologist, two learners displaying dyscalculia symptoms, and two parents. The research collaboratively engaged participants to identify challenges, crafting interventions, and reflecting on outcomes through the lens of the critical emancipatory framework and participatory action research,. The researcher assessed the effectiveness of the active learning strategy to enhance students’ mathematical abilities, self-efficacy, and attitudes toward mathematics. Critical discourse analysis shed light on the potential of active learning strategies to improve mathematical learning outcomes and create a supportive learning atmosphere. The results indicated that the implemented active learning strategy offers effective pedagogical practices for learners with dyscalculia by influencing positive changes in their attitude towards mathematics and the learning environment. The participating teachers gained insights into understanding the behaviour of learners with dyscalculia and the role of active learning in intervention strategies. The study’s findings can guide educators, policymakers, and researcher in developing inclusive mathematics instruction for diverse learners in primary school classrooms.

The Impact of Cooperative Learning Activities using the Team-Assisted Individualization (TAI) Technique Combined with Activity-Based Learning on Problem-Solving Abilities and Mathematical Connections Abilities in the Subject of Congruence

The Impact of Cooperative Learning Activities using the Team-Assisted Individualization (TAI) Technique Combined with Activity-Based Learning on Problem-Solving Abilities and Mathematical Connections Abilities in the Subject of Congruence

Secondary school learners’ academic achievement in mathematics through a practical instruction teaching approach in the Kigezi and Ankole regions of Uganda

Addressing the challenge of subpar mathematics achievement levels in secondary education has gained global attention. Due to teachers’ inability to teach mathematics without real objects to explain it in real life, learners take the subject as very abstract, hence the poor academic achievement in national examinations. This qualitative case study investigates the impact of practical instruction on the mathematics achievement of secondary school students in Uganda. The research involved interviews with sixteen teachers from selected secondary schools in the Kigezi and Ankole regions to gain insights into their perspectives on the utilization and advantages of practical instruction in mathematics. Thematic analysis was employed to analyze the data. Regarding assessment strategies, the study found that there is a need to incorporate alternative assessment methods that can effectively assess the range of learners’ mathematics abilities. The study’s findings highlight that teachers view practical instruction as a valuable approach that enhances students' mathematics achievement by involving them in hands-on experience with real objects and learner-centered activities. Based on these results, the study recommends the widespread adoption of practical instruction as a means to elevate the quality of mathematics education in Uganda, ultimately addressing the prevalent challenges in mathematics achievement at the secondary school level.

Development of a Cognitive Assessment Checklist for First-Grade Mathematics: Utilizing Hierarchical Cognitive Diagnostic Modeling in Elementary Education

This study aimed to address the need for a comprehensive assessment tool to evaluate the mathematical abilities of first-grade students through cognitive diagnostic assessment (CDA). The primary challenge involved in this endeavor was to delineate the specific cognitive skills and sub-skills pertinent to first-grade mathematics (FG-M) and to determine the most suitable model for assessment. Employing a mixed-methods approach, the research identified nine cognitive attributes essential for FG-M and developed a Q-matrix delineating the relationship between these attributes. A preliminary version of the FG-M checklist comprising 74 items was formulated. Subsequently, the assessment tool was administered to 1018 first-grade students, with their teachers utilizing the FG-M checklist for evaluation. Results indicated a commendable accuracy in classifying the nine cognitive attributes, ranging from 0.68 to 0.92, with an average accuracy of 0.76. Furthermore, the validity of the scores was corroborated by a substantial correlation (r = 0.78) between scores from the FG-M checklist and the arithmetic subtest of the Wechsler Intelligence Scale for Children, Fourth Edition (WISC-IV). Overall, the study concluded that the scores from the FG-M checklist are reliable for assessing the mathematical skills of first-grade students. The findings underscored the students’ proficiency in fundamental mathematical concepts such as cardinality, addition, subtraction, weight, and statistics. However, areas of weakness were identified in concepts related to multiplication, time, symmetry, and geometry. This research contributes significantly to the advancement of CDA in educational contexts, providing educators with a valuable tool for identifying students’ strengths and weaknesses in mathematical cognition.

Fostering Self-efficacy: Understanding South African Grade 9 Students’ Confidence in their Mathematics Abilities

In poor-performing, resource-constrained education systems, such as South Africa, solutions to improve academic achievement have tended to focus on resources and cognitive factors. An area that requires more attention is the importance of non-cognitive, psychosocial factors and their relationship with academic performance. These factors are strongly associated with behaviour, playing a role in either facilitating or impeding the learning process. Understanding attitudes is therefore critical in interpreting achievement results with a view to improving them. This article used data from the 2019 Trends in International Mathematics and Science Study administered to 20,829 South African students in Grade 9 to investigate the confidence these students have in their mathematics ability (their self-efficacy) and the relationship with achievement. Linear regression analysis was employed to determine: (1) the relationship between Grade 9 students’ self-efficacy and mathematics achievement in South Africa; and (2) the contextual factors that were associated with the mathematics self-efficacy of the students. The results indicate a positive correlation between students’ self-efficacy and their performance in mathematics. In addition, good teaching practices and parental involvement in school activities were associated with higher levels of students’ mathematics self-efficacy. Being female was associated with lower levels of self-efficacy. These findings have important implications for shaping educational policy and practice in the resource constrained context of South Africa, to enhance students’ self-efficacy and performance in mathematics.

Exploring the influence of the DRD2 gene on mathematical ability: perspectives of gene association and gene-environment interaction

Mathematical ability is influenced by genes and environment. This study focused on the effect of DRD2, a candidate gene for working memory, on mathematical ability. The results in child participants revealed associations between the DRD2 gene and mathematical ability. It was found that individual’s mathematical ability was influenced by Single Nucleotide Polymorphisms (SNPs) in DRD2, both in the form of haplotypes and in the way of interaction with parental education. These findings suggest that dopaminergic genes are linked to mathematical ability. This study provides evidence for the genetic basis of mathematical ability and offers guidance for personalized intervention in mathematical education.

Професійна спрямованість математичної підготовки студентів технічних спеціальностей у контексті фундаменталізації освітнього процесу

The article examines the peculiarities of mathematical training of future technical specialists in the context of fundamentalization of the educational process. The study of the definitions of fundamentalization, mathematical preparation was carried out, the main characteristic features of mathematical preparation, proposed by the researchers of the problem of mathematical preparation, were singled out. An analysis of the work of scientists dedicated to the selected research problem was carried out. It has been established that the mathematical training of future technical specialists is a dialectical combination of formed mathematical skills and abilities for their applied application and the direct process of forming these skills. The fundamentalization of mathematical training is considered to be the concept of improving mathematical training, in which basic mathematical invariants are selected for their further application in professional activities. To implement the approach of professional orientation of mathematical training of students of technical specialties, it is recommended to take into account the peculiarities of the construction of the course of higher mathematics and courses of special disciplines in order to enable the integration of educational material, as well as the organization of the educational process in higher education institutions. Based on the analysis of educational programs for students of various specialties of the Vinnytsia National Technical University, a conclusion was made about the difference in program results in mathematics for students of the same lecture stream. On the basis of which it is proposed to unify tasks of professional content. Examples of professional tasks from the "Theory of Probability" section are given.

Формирование элементарных математических представлений у детей с ограниченными возможностями здоровья (с нарушением зрения)

The aim of this study is to improve the math skills of preschool children (5-7 years old) with visual impairment. In this context, it is expected that the target behavior of children with visual impairment will be changed through the creation of a specialized educational space that promotes the formation of mathematical abilities, arithmetic skills, creativity, ability to plan and organize their activities. The research group consists of 48 preschool children (5-7 years old) with visual impairments. The study was conducted in the fall of the 2023-2024 school year. During the study, the preschoolers received eight weeks of training to improve math skills. The study found that numeracy and math skills in preschool children with visual impairments had a positive effect on cognitive development, fine motor skills, and motivation to learn.

Factors Influencing Mathematical Ability of Grade 6 Pupils

It is crucial for educators and policymakers to comprehend the elements influencing sixth-grade children’s mathematics abilities if they are to successfully support students in their learning process. In this premise, this study analyzed the extent of factors influencing the mathematical ability of Grade 6 learners in one elementary school in Bacolod City Division during the school year 2022-2023. The variables included in this study are sex, parent’s education, and family income. To determine the extent of factors influencing the student’s mathematical ability, the following areas are considered: learners’ motivation, parental support, teachers’ instructional skills, and learning resources. Data for this descriptive study was collected from 101 Grade 6 pupils- respondents using a self-made survey questionnaire that has passed the rigorous tests of validity and reliability. Results show that most respondents are female, and parents are at the elementary and high school level only, with Php 12,000.00 and above as the Family Income. The extent of factors influencing the mathematical ability of grade 6 learners according to learners’ motivation and Parental support and when group according to variables shows moderate extent except for parent’s highest educational attainment in of learner’s motivation that shows great extent while in teacher’s instructional skills, and learning resources and when group according to variables shows great extent. Also, results show that there is no significant difference among all areas. To foster students’ mathematical proficiency and interest, this paper calls for teachers to offer varied exercises and activities, for parents to engage children in math tasks at home, maintain communication through regular meetings and group chats, and teachers should continuously enhance instructional skills, ensure access to organized learning resources, and provide ample time and supplementary materials for concept mastery. Keywords: Education, mathematical ability, parental support, teachers’ competence, Bacolod City, Negros Occidental, Philippines.

Kemampuan Literasi Matematis Ditinjau dari Motivasi Belajar pada Siswa Kelas XI SMA Negeri 2 Padang Panjang

This research is motivated by the fact that the number of students who have low mathematical literacy skills is caused by various factors. One of the factors that affects mathematical literacy ability is learning motivation. This study aims to determine the ability of mathematical literacy when viewed from the learning motivation of students. This type of research is quantitative descriptive. The sample in this study is grade XI students of SMA Negeri 2 Padang Panjang. The sample selection technique in this study uses the Stratified random sampling technique where the sample is selected based on strata. The instrument used in this study is test questions in the form of essays to see students' mathematical literacy skills. Data analysis was carried out descriptively on all research data. The results showed that the average mathematical literacy ability was 50 which was classified as low. If viewed from high learning motivation is classified as medium with an average score of 69, when viewed from medium learning motivation has low mathematical literacy skills with an average score of 56 and mathematical literacy ability reviewed from low learning motivation is classified as low in the low category with an average score of 25

Implementasi Pembelajaran Matematika Realistik dalam Menganalisis Kemampuan Penalaran Matematis Siswa pada Materi Satuan Debit

This study aims to (1) describe the learning of unit debit with PMR approach and (2) describe the reasoning ability of grade V students on unit debit material. This research was conducted at SDK Lamawalang on April 20, 2024. The subjects in this study were fifth grade students of SDK Lamawalang. The type of research used is descriptive qualitative research, where researchers describe learning practices using PMR models and students' mathematical reasoning abilities after the learning process. Data analysis techniques used include data collection, data reduction, data presentation, and verification/conclusion. The results showed that, (1) the steps of learning unit debit material with PMR model are: (a) understanding contextual problems, (b) solving problems, (c) comparing and discussing answers, (e) drawing conclusions, (2) based on indicators of mathematical reasoning ability, (a) making conjectures, (b) performing mathematical manipulations, (c) compiling evidence, providing reasons/evidence for the correctness of the solution, and (d) drawing conclusions from a statement, obtained for problem I, 20 students can achieve 1-4 indicators of mathematical reasoning, 1 student can achieve 1-3 indicators of mathematical reasoning. For problem 2, 18 students can achieve 1-4 indicators of mathematical reasoning, while 3 students can achieve 1-2 indicators of mathematical reasoning.

Impact of gist intervention on automated system interpretability and user decision making.

As they become more common, automated systems are also becoming increasingly opaque, challenging their users' abilities to explain and interpret their outputs. In this study, we test the predictions of fuzzy-trace theory-a leading theory of how people interpret quantitative information-on user decision making after interacting with an online decision aid. We recruited a sample of 205 online crowdworkers and asked them to use a system that was designed to detect URLs that were part of coordinated misinformation campaigns. We examined how user endorsements of system interpretability covaried with performance on this coordinated misinformation detection task and found that subjects who endorsed system interpretability displayed enhanced discernment. This interpretability was, in turn, associated with both objective mathematical ability and mathematical self-confidence. Beyond these individual differences, we evaluated the impact of a theoretically motivated intervention that was designed to promote sensemaking of system output. Participants provided with a "gist" version of system output, expressing the bottom-line meaning of that output, were better able to identify URLs that might have been part of a coordinated misinformation campaign, compared to users given the same information presented as verbatim quantitative metrics. This work highlights the importance of enabling users to grasp the essential, gist meaning of the information they receive from automated systems, which benefits users regardless of individual differences.

The Effectiveness of Missouri Mathematics Project Learning Models for Improving Students’ Mathematical Connection Ability on Junior High School

Mathematical connection ability is one of the high level abilities but is still classified as low because students' understanding of the conceptual material given by the teacher, there are still students going through steps in working on the problems given, such as describing a symbol, in completing mathematical concepts, therefore This research aims to examine the effectiveness of using the Missouri Mathematics Project Learning Model carried out at MTs Ibnu Sina Jl. Tegal Overtime No. 105, Pamekaran, District. Soreang, Bandung Regency, West Java 4091, by taking a sample of 60 students consisting of control and experimental classes. The research method used in this action was the experimental method. Based on the results of descriptive analysis of students' mathematical ability data before being given treatment, it showed the highest score was 70, the lowest score was 55 and the average score was 61. Meanwhile, the results of descriptive analysis of students' mathematical ability data after being given The treatment showed the highest score of 70, the lowest score of 55 and the average score of 61. Those given the treatment showed the highest score of 87, the lowest score of 69, and the average score of 77.83. So the average mathematical connection ability of students after being given treatment is higher than the students' mathematical ability before being given treatment.

The Effect of Habits of Mindo n Junior High School Students’ Mathematics Communication Ability

This research aims to determine the effect of habits of mind on junior high school students' mathematical communication skills on triangles and quadrilaterals. Habits of Mind is defined as a habit of thinking that is carried out as an intelligent behavior pattern when faced with a problem whose solution isn’t easily known so that productive action occurs. The problem in this research is motivated by its importance habits of mind in learning mathematics and improving students' mathematical abilities. The method used in this research is method ex post facto. The population in this study were all class VIII students in one of Junior High Schools in Karawang Regency. The sample in this study was 42 students using the technique purposive sampling. The instrument used in this research is a test, namely mathematical communication skills which consists of 5 (five) description questions. Apart from that, it also uses non-test instruments in the form of questionnaires habits of mind which consists of 30 statements. Data analysis was carried out using simple linear regression techniques. The research results obtained a linear regression equation Y = -25.065 + 1.345X. The magnitude of the correlation coefficient r2 = 0.848 and coefficient of determination = 84.8%. This shows that there is habits of mind had an influence on students' mathematical communication skills of 84.8%, while 15.6% was influenced by other factors not measured in this research.

Analyzing Student’s Mathematical Critical Thinking Ability of Concept Newman’s Error Analysis Review from Habits of Mind

This study aims to analyze and describe the mistakes made by students in completing mathematical critical thinking skills in terms of habits of mind (HOM) with three categories, namely limited, developing, and proficient. The review was also analyzed from the factors that led to the occurrence of errors based on error analysis according to Newman. This research uses qualitative research methods. The data collection techniques used are questionnaires, tests, and interviews. The instruments used are HOM questionnaires and mathematical critical thinking ability tests. The selection of the study subject was carried out purposively with the consideration that the subject had a HOM category. A total of 25 students who filled out the HOM scale and mathematical critical thinking ability test, 3 students were selected to be interviewed based on the HOM category classification. The data analysis techniques used in this study are data reduction, data presentation, and drawing conclusions. Based on the results of the study, students with limited HOM were only able to solve questions up to indicator 1 because they made mistakes in reading and process skills. Students with HOM develop, only able to solve problems up to indicator 2 due to Comprehension and transpormation errors. Students with proficient HOM, are able to solve questions up to indicator 3 because they make mistakes in the skill and encoding process.

The Implementation of Geogebra-Assisted Discovery Learning Approach Towards Mathematical Communication Ability of Vocational Students

Mathematicals communication ability is one of essential mathematical abilities that every person, who learns mathematics, needs to have. However, many facts found in many studies has shown us that students’ achievements on this ability are still low. Factors that may cause it spread from teacher factors, tools, approaches, learning media to students themselves. To overcome these issues, many efforts are made to select and implement learning approaches that can improve students' mathematical communication ability as well as their activities in instructional process. Thus, the purpose of this study is to examine whether the implementation of GeoGebra-assisted discovery learning approach is effective in improving vocational school students' mathematicals communication ability or not. This quasi experimental research design involved 60 students of Gema Karya Bahana Vocational School as samples. The samples were divided into two groups in which 30 students of Accounting-1 class as the experimental group and 30 students of Accounting-2 as the control group. The data collected through a description test consisted of 3 questions on a linear program. The data collected through the test, both in pre-test and post-test, then analyzed using inferential statistics. The results of this analysis showed that the implementation of the discovery Learning approach assisted by GeoGebra was effective in improving vocational school students' mathematicals communication ability. Thus, the discovery learning approach assisted by GeoGebra can be implemented on instructional processes as one of instructional approach alternatives.

Analyzing Junior High School Students’ Mathematical Communication Ability and Self Esteem using Discovery Learning Model

Mathematical reasoning, mathematical communication, mathematical problem solving, conceptual understanding, mathematical understanding, creative thinking and critical thinking are part of the mathematical abilities that students must have. One of the goals of learning mathematics according to NCTM is learning to communicate (mathematical communication). Mathematical communication skills in mathematics learning really need to be developed. This type of research design uses a quasi-experimental research design, namely pretest and post-test with non-equivalent control group design . The research used research subjects into two groups, namely the experimental group and the control group. The subjects of this research were students of class VII I MTs As-Sa'adah Padahanten Majalengka, numbering 64 people. Subjects were selected based on experimental class VIII A, 32 people and control class VIIIB, 32 people. Walkthroughs, questionnaires, and tests are techniques used in data collection. Data processing analysis was carried out qualitatively and quantitatively. The results of this research are that there is a difference in the effectiveness of the Discovery Learning model learning approach with the ordinary (conventional) learning model in terms of the aspects of mathematical communication skills and self-esteem of MTs in statistics material. The implications of the Discovery Learning learning model in this research are that it makes it easy for students to remember the lessons learned, integrate self concept according to their initial abilities, focus, be creative in exploratory projects, and the effect of knowledge transfer on learning outcomes can last a long time.

Computational Thinking Readiness Level of First-Year Students of Mathematics Education

The main objective of this study was to measure the level of computational thinking readiness in prospective first-year mathematics education students. In addition, this study also aims to identify factors that influence their level of readiness towards computational thinking. This research is qualitative and descriptive in nature. This study describes first-year mathematics education students' mathematical computational thinking ability based on the theory of mathematical computational thinking. This study was conducted on first-year mathematics education students in the academic year 2023/2024. There were 16 first-year mathematics education students, all of whom were taken as samples in this study, to obtain more in-depth information about the computational thinking ability of first-year mathematics education students for further research development. The instruments used to collect data on first-year mathematics education students' mathematical computational thinking ability are (1) a mathematical computational thinking ability test and (2) an interview. The data obtained were calculated using statistical tests, and the results will be explained in depth. The mean score of the first-year mathematics education student's computational thinking ability test was 59.68, indicating that students generally have a fairly good level of computational thinking ability.

The Students’ Problem-Solving Abilities in Mathematics and English at the Secondary School Level

The Students’ Problem-Solving Abilities in Mathematics and English at the Secondary School Level