Mathematical Ability Research Articles

The cognitive gap in the mathematical thinking abilities of high school leavers for college: Are they ready?

After students spend approximately 12 years of formal math learning from high school, they bring a store of enormous “learned” mathematics factual knowledge to face the challenges and prepare for college/tertiary level learning. However, research has shown that early tertiary-level students struggle to learn college mathematics. The ability to think mathematically and use this learned factual knowledge (mathematical thinking) to solve higher-order thinking skills (HOTS) problems is essential to tertiary education. Thus, do these high school leavers have access to previously learned factual knowledge and use it effectively in solving these HOTS problems? This sequential research design study was conducted among 640 high school leavers who received an A in their national examination. In the first phase, the researchers investigated their mathematical thinking ability, followed by interviews with selected students on the difficulties and challenges they faced in solving the underlying problems. The findings showed that these students lack the ability to effectively use the previously learned factual knowledge from school mathematics to solve mathematical thinking problems. Secondly, they lack the habitual mind to check their answers after deriving a solution to a given problem. Thirdly, most rarely used heuristics to devise a strategy to solve fundamental math problems. Although the expectation of the school math curriculum over the last decade has been re-engineered towards “teaching students to think,” this expectation has yet to be fulfilled. Thus, university educators must do more to guarantee that high school leavers can deconstruct their mathematical knowledge and reconnect it with the underpinnings and linkages of college mathematics requirement.

Analysis of Mathematical Problem-Solving Ability in Terms of Multiple Intelligence, Cognitive Style and Learning Style of Junior High School Students

This study aims to describe: (1) the mathematical problem-solving ability of Sleman Regency's JHS students, (2) whether there is a difference in students' mathematical problem-solving ability in terms of multiple intelligence, (3) whether there is a difference in students' mathematical problem-solving ability in terms of cognitive style, (4) whether there is a difference in students' mathematical problem-solving ability in terms of learning style, and (5) whether there is an interaction between multiple intelligences, cognitive style and learning style. The research method used is a survey method with a quantitative approach. The research population is JHS students in the 2023/2024 school year in Sleman. The sample is 434 students, determined using a stratified proportional random sampling technique. The instruments used were a mathematical problem-solving ability test, a GEFT test, a multiple intelligence questionnaire, and a learning style questionnaire. The data analysis is descriptive statistics to determine students' mathematical problem-solving ability level and inferential statistics using a three-way ANOVA test to describe students' mathematical problem-solving ability's differences in terms of multiple intelligence, cognitive style and learning style, and to describe the interaction between multiple intelligences, cognitive style and learning style. The analysis showed that: (1) the mathematical problem-solving ability average score of Sleman's JHS students is 53.49 which is in the moderate category, (2) there is no difference in students' mathematical problem-solving ability in terms of multiple intelligence, (3) there is a difference in students' mathematical problem-solving ability in terms of cognitive style, (4) there is no difference in students' mathematical problem-solving ability in terms of learning style, and (5) there is no interaction between multiple intelligence, cognitive style and learning style of students.

Emergence of African Traditional Medicine: Understanding the Learning Process and Pedagogic Implications for Adolescents of the North West Region of Cameroon

This article examines the global debates about indigenous knowledge and Africa’s traditional medicine from the pedagogy perspective. This study investigated the emergence of African traditional medicine with keen attention on understanding the learning/apprenticeship process and deducing pedagogic implications for adolescents’ learners in the North west Region of Cameroon. Specifically, the paper examined the extent, traditional medicine influence the development of cognitive skills in adolescents. The development of cognitive skills in late adolescents is marked by social competence, decision making, and problem solving. A conceptual review of the major concepts was done. Theoretically, the article was anchored on the social learning theory of Bandura (1977). A convergent parallel mixed method research design was used. The sample of the study emerged through purposive and convenient sampling techniques. A pilot study was done with 10 participants. Interviews were conducted with 15 elders and a questionnaire for 150 adolescents drawn from 6 villages in Oku Subdivision, namely: Elak, Jikijem, Lui, Manchok, Keyon and Simonkoh. Quantitative data was entered using EpiData Version 3.1 (EpiData Association, Odense Denmark, 2008) and analysed using the Statistical Package for Social Sciences (SPSS) Standard version, Release 21.0 (IBM Inc. 2012). Interviews and focus group discussions were transcribed verbatim. Each interview or focus group was prepared as a single primary document and assigned for coding and analysis in Atlas.Ti 5.2 software (Atlas.ti Scientific Software Development GmbH, Berlin, Germany). Statistically the weight of traditional medicine = 80.3%; Traditional medicine (R=0.382; P=0.000);. These are marked by alertness, critical thinking, decision making, social competence, problem solving, imagination, mathematical abilities, etc. From the study it is recommended that indigenous practices be taught formally in schools and that indigenous medicines be studied more keenly and upgraded.

Cognitive, affective and sociological predictors of school performance in mathematics

Mathematics is a key school subject for some of the most lucrative and economically important careers. Low mathematics performance in school is associated with low psychometric intelligence, family socioeconomic status (SES), specific mathematical abilities, and high mathematics anxiety. We used a sample of Hungarian schoolchildren (N = 102, mean age = 12.3 years) to directly compare the predictive power of general intelligence, specific mathematical abilities measured by the Pedagogical Examination of Dyscalculia (DPV), mathematics anxiety, and socioeconomic status for mathematics grades. Mathematics grades correlated with IQ, specific mathematic ability, mathematics anxiety, and a composite measure of family SES. The WISC-IV showcased a manifest correlation of 0.62 and a latent correlation of 0.78 with the DPV and high manifest (r=-0.53) and latent (r=-0.59) correlations with mathematics anxiety. IQ alone accounted for 52% of the variance in mathematics grades. IQ, specific mathematical ability, family SES and mathematics anxiety jointly accounted for 56% of the variance in grades, with a non-significant contribution of specific mathematical ability and family SES over IQ and a marginal contribution of mathematics anxiety. Our results show that psychometric intelligence is the most important predictor of mathematics grades, while family SES and specific mathematical abilities are only associated with grades to the extent they reflect psychometric intelligence. The results, however, confirmed a small role of mathematics anxiety over intelligence in predicting grades.

Utilizing Decision-making Task: Students’ Mathematical Justification in Collaborative Problem Solving

Many studies reported the importance of mathematical justification in collaborative problem-solving (CPS). However, not all tasks could stimulate mathematical justification in CPS. This study explores the potential of a decision-making task in facilitating mathematical justification in CPS of a derivative topic. Two groups of 12 graders in Bandung, Indonesia solved a task. The group works were observed, recorded, and the written works were collected. The findings showed that the task encouraged the groups to focus on justifying mathematical claims. Both groups successfully solved the task, yet different mathematical justifications were observed. We discussed the possible roles of the task difficulty and groups’ mathematics ability in promoting mathematical justifications. Checking the effectiveness of the task on a larger sample was recommended for further studies.

Active Learning Strategies in Improving Middle School Students' Mathematical Abilities

Ability communication mathematics have role Which very important in learning mathematics. In mathematics ability Mathematical communication acts as a tool that students use in learning put forward idea Which they have For build knowledge the math. The low ability communication mathematical student influenced by many factors both internal and external. One of the research focuses This looks at external factors namely the learning strategy factor. To improve students' mathematical communication skills, then from teachers need to apply appropriate learning strategies. One strategy that can give chance to student role active in communicating knowledge is an Active Learning learning strategy type tutors peer.This research aims to determine the increase in students' mathematical communication skills after implementing the peer tutoring Active Learning strategy.Approach Which done in study This use approach quantitative. Approach quantitative is an approach based on interpretation of data in the form of numbers. Design study Which will used in study This is study quasi experimenter. On study This, type design Which used researcher that is design control group pretest-posttest design. The data collection technique used in this research is a test. The instruments used in this research are learning tools and test sheets.Based on the results of the research carried out, the conclusion is that the mathematical communication skills of students who apply the Active Learning learning strategy with the peer tutor type improve compared to expository learning.

Effective use of the tools of probability theory and mathematical statistics in solving the problems of the professional orientation of physicists and mathematicians: an interdisciplinary approach

ABSTRACT The use of methods of mathematical statistics for teaching students carries the task of determining mathematical abilities, formalizing the choice of a professional orientation and the potential choice of solutions. In higher education, the use of the mathematical apparatus allows students to form the ability to multiple choice and assess the conditions of the choice. These include not only the choice of training courses, but also the areas of knowledge in which each student can fulfil themself. For mathematicians, this is especially true, since in most cases mathematics is used to solve purely applied problems. The novelty of the study is determined by the fact that the methods and tools of probability theory cannot be applied exclusively on an individual level. To determine the effectiveness of the methods used, it is necessary to determine the possibilities of group application of the used methodological apparatus and identify areas of assistance to the student in choosing a professional orientation. In terms of the use of ubiquitous distance education, the authors demonstrate the possibility of group work with mathematical support through the use of clusters and network techniques, when each individual is the host of the training programme.

Integration of Multiple Intelligences Theory in Project-Based Learning, How It Impacts on Students' Critical Thinking and Mathematical Communication Skills?

In this study, we aim to assess the effectiveness of Project-Based Learning (PjBL) based on Multiple Intelligences (MI) theory on students' critical thinking and mathematical communication skills. This research is a quasi-experiment using non-equivalent (pre-test and post-test) control-group design. The population in this study were VIII grade students in a public junior high school in Yogyakarta and two sample classes were selected based on recommendations from teachers and had mathematical abilities that could be considered equal. The experimental class applied PjBL based on MI theory and the control class applied PjBL learning. Data collection was conducted using a test instrument in the form of description questions. This instrument is valid and reliable. Learning is said to be effective if: (1) the mean test score of critical thinking and communication skills is at least 70 (from a score range of 0-100); (2) the mean of post-test of critical thinking and communication skills is higher than the mean of pre-test; (3) the mean final score of students' critical thinking and mathematical communication skills in the experimental class is higher than the control class. Data analysis used one-sample t-test, paired-sample t-test, and T2 Hotteling test. The results of the study using the significance level α = 5% showed that (1) PjBL learning based on MI theory is effective in terms of students' critical thinking and mathematical communication skills; (2) PjBL based on MI theory learning is more effective than PjBL learning in terms of communication, but not more effective in terms of critical thinking skills. Although the data from the sample showed the acquisition of mean scores and the increase in the mean value of critical thinking learning in PjBL based on MI theory was better than PjBL learning in terms of critical thinking skill, but statistically both did not show a significant difference.

Correlation between Civil Engineering Student’s Performance in Mathematics and Academic Success

This research aims to examine the widely accepted paradigm that proficiency in mathematics significantly influences the academic success of Civil Engineering students. Using data from 119 students of the 2018 and 2019 cohorts at Universitas Mercu Buana, the study analyzes the correlation between their performance in Mathematics courses (Mathematics 1, 2, and 3) and their academic success, as measured by timely graduation and GPA. The data were processed using the Spearman correlation method, given its non-normal distribution as determined by Kolmogorov-Smirnov and Shapiro-Wilk tests. The results indicate a significant positive correlation (r = 0.313, p = 0.001) between mathematical performance and academic success, with students achieving higher mathematics scores more likely to graduate on time. These findings suggest that while mathematical ability is a critical factor in academic success, other elements such as motivation, teaching methods, and external support should also be considered in improving student outcomes.

Enhancing mathematical function understanding in university students: a comparative study of design thinking vs. traditional teaching methods

Mathematical education requires innovative didactic strategies to enhance the understanding and application of mathematical concepts, as traditional teaching methods often lack relevance. This methodology aims to develop a problem-solving scientific approach called design thinking as a strategy for learning mathematics functions. The study was applied to a sample of 138 students of biochemical, biological, and industrial engineering careers attending the first academic cycle at the Faculty of Natural and Exact Sciences of the Particular Technical University of Loja-Ecuador. The methodology uses a quasi-experimental design with a convenience sampling method. All participants were divided into a control group (C, D, K) and an experimental group (P, Q, R). Knowledge, skills, perceptions, and engagement were measured through pretest, posttest, workshop, rubric, project, and survey instruments. The pretest results indicate that both groups had similar knowledge of mathematical functions (pretest mean experimental group: 1.42/2 and mean control group: 1.55/2). Moreover, after applying design thinking strategy to the experimental group, variables questionnaire, project, and workshop show statistical differences (p < 0.001) between groups related to the traditional learning strategy, increasing the experimental group’s score in the project (posttest mean experimental group: 1.62/2 points, and mean control group: 1.65/2). The survey opinion indicates that 53.5% of the experimental group highlighted the project’s development as positively impacting their academic training. In conclusion, problem-solving design thinking using scientific projects as a mathematical function learning strategy contributes to improving the comprehension of polynomial functions and developing mathematical competencies, abilities, and skills to generate tangible solutions for real problems.

To promote the cultivation of mathematical thinking skills and strategies in games for the senior class of kindergarten children

With the advancement of quality education and an increase in research into preschool education, early childhood education is becoming more focused on individual physical and mental development, as well as the development of comprehensive quality education. Mathematical thinking ability represents a significant aspect of young children’s cognitive development. Given that young children’s brain development is not yet fixed, so their capacity for “plasticity” is considerable. The period between the ages of three and eight represents a critical phase in developing mathematical thinking ability in young children. Children undergo rapid growth in their mathematical understanding and reasoning abilities during this time. This paper will look at promoting the development of mathematical thinking and strategies in play for the senior class of kindergarten children, based on practice, in order to provide new strategies for preschool education. Through the research on the combination of games and mathematics education, we can provide better ideas and methods for the use of games in mathematics education, help the senior class of kindergarten children to develop their mathematical thinking skills, and help them to recognize, articulate, and generalize the quantitative relationships and spatial forms that exist in their daily lives so that they can be well-prepared for the next step of entering the primary school.

Students' Mathematical Connection Ability in Solving Block and Prism Problems viewed from Cognitive Style

Students' Mathematical Connection Ability in Solving Block and Prism Problems viewed from Cognitive Style

Dimensional versus categorical approach: A comparative study of mathematical cognition

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

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.