Longitudinal predictors of conceptual understanding of arithmetic principles

This study starts from the low ability of reasoning and understanding of the math concepts students with the root of the problems caused by the use of teachers teaching model less relevant and very limited use of learning media. The study aims to determine: (1) whether the application of Bruner's theory with the help of concept maps can enhance students 'mathematical reasoning, (2) whether the application of Bruner's theory with the help of concept maps can enhance students' understanding of concepts, and (3) describe the activity levels of students in the application of theory Bruner with the help of concept maps. This research a classroom action research. Subjects in this study were students of class XI SMA 20 field totaling 40 people. Object of study is the increase in students' mathematical reasoning and understanding through learning to use Bruner's theory with the help of a concept map on the subject of Opportunity. The results of the data analysis an average score of 72.2 mastery of prerequisite. From the results of the study concluded that the application of mathematics learning using Bruner's theory with the help of concept maps can enhance students 'reasoning and understanding of mathematics, and their lessons take place either by reviewing the observations of students' activities. Based on this conclusion it is expected that the findings of this study can be used as a reference for the improvement of reasoning and understanding of math concepts students

Although verbal and numerical abilities have a well-established interaction, the impact of phonological processing on numeric abilities remains elusive. The aim of this study is to investigate the role of phonemic awareness in number processing and to explore its association with other functions such as working memory and magnitude processing. One hundred seventy-two children in 2nd grade to 4th grade were evaluated in terms of their intelligence, number transcoding, phonemic awareness, verbal and visuospatial working memory and number sense (non-symbolic magnitude comparison) performance. All of the children had normal intelligence. Among these measurements of magnitude processing, working memory and phonemic awareness, only the last was retained in regression and path models predicting transcoding ability. Phonemic awareness mediated the influence of verbal working memory on number transcoding. The evidence suggests that phonemic awareness significantly affects number transcoding. Such an association is robust and should be considered in cognitive models of both dyslexia and dyscalculia.

ABSTRACT: This article presents a study that aimed to identify general and specific cognitive skills as predictors of arithmetic achievement. Through a quantitative analysis, we evaluated 127 students in the 3rd and 4th grades on the following skills: working memory, phonemic awareness, reading comprehension, number transcoding, number line estimation, and quantitative reasoning. We assessed these cognitive skills in two moments, at the beginning and the end of the school year. In this second moment, we also assessed the students' arithmetic achievement. The results specifically indicated a direct influence of number transcoding, quantitative reasoning, and phonemic awareness on arithmetic performance. In addition, the findings showed that number transcoding is a mediator in the relation between quantitative reasoning and phonemic awareness with arithmetic performance. Thus, we emphasize the importance of general and specific skills for students' arithmetic performance. Furthermore, we highlight the prioritization of teaching based on the understanding of the number system and the relations between amounts (quantitative reasoning) for arithmetic learning, as well as for preventing future mathematical difficulties.

This study investigates the effect of the Quantum Learning model integrated with STEM Education on students' mathematical reasoning and conceptual understanding, with a focus on gender differences. The research employed a quasi-experimental design with Randomized Block Design involving 50 students of MTs SA Nurul Qona'ah in the academic year 2023/2024, divided into experimental and control groups. The experimental group received instruction through Quantum Learning integrated with STEM, while the control group followed conventional teaching methods. Data were collected using validated essay-type tests measuring higher-order thinking skills. The results showed that students taught with the integrated model achieved significantly higher scores in both mathematical reasoning and conceptual understanding compared to those taught conventionally. Furthermore, male students outperformed female students in mathematical reasoning, while no significant gender difference was found in conceptual understanding. The model also proved effective for both male and female students individually, with male students generally showing greater gains in reasoning and female students demonstrating better conceptual understanding in conventional settings. These findings suggest that integrating Quantum Learning with STEM creates a meaningful and equitable learning environment that supports higher-order thinking and addresses gender-specific learning needs. The implications of this research highlight the importance of adaptive, student-centered instruction supported by schools, and the need for continued teacher innovation in implementing interdisciplinary, project-based mathematics education.

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 contributionWhat 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.

Visuospatial working memory (WM) capacity is highly correlated with mathematical reasoning abilities and can predict future development of arithmetical performance. Activity in the intraparietal sulcus (IPS) during visuospatial WM tasks correlates with interindividual differences in WM capacity. This region has also been implicated in numerical representation, and its structure and activity reflect arithmetical performance impairments (e.g., dyscalculia). We collected behavioral (N = 246) and neuroimaging data (N = 46) in a longitudinal sample to test whether IPS activity during a visuospatial WM task could provide more information than psychological testing alone and predict arithmetical performance 2 years later in healthy participants aged 6-16 years. Nonverbal reasoning and verbal and visuospatial WM measures were found to be independent predictors of arithmetical outcome. In addition, WM activation in the left IPS predicted arithmetical outcome independently of behavioral measures. A logistic model including both behavioral and imaging data showed improved sensitivity by correctly classifying more than twice as many children as poor arithmetical performers after 2 years than a model with behavioral measures only. These results demonstrate that neuroimaging data can provide useful information in addition to behavioral assessments and be used to improve the identification of individuals at risk of future low academic performance.

Literature is well-stocked with studies confirming that an instructional approach, self-efficacy, and mathematical reasoning skills are critical for enhancing students’ conceptual understanding and achievement in mathematics. However, there has been little emphasis on establishing whether being able to reason mathematically depends only on the instructional approach or students’ self-efficacy beliefs about mathematics also play a hidden role. A quasi-experimental study involving 301 grade 11 students from six public secondary schools in one district was carried out to investigate the mediating effect of self-efficacy on the relationship between instruction and students’ mathematical reasoning. Participants of the study were selected using the cluster random sampling method. Data were collected before and after the intervention via a mathematical reasoning test and a mathematics self-efficacy beliefs questionnaire. A Parallel Multiple Mediator Model in SPSS using the PROCESS custom dialogue version 3.4 was employed for data analysis. Findings suggest that mathematics self-efficacy and task-specific self-efficacy beliefs collectively and significantly mediate the effect of the instructional approach on students’ mathematical reasoning. The Student Teams-Achievement Division (STAD) was found to be an effective approach for enhancing students’ mathematical reasoning alongside self-efficacy beliefs. These findings provide evidence on the need to select an instructional approach that does not only focus on developing students’ cognitive abilities such as mathematical reasoning but also fosters students’ affective attributes such as maths self-efficacy beliefs.

The ability of students’ conceptual understanding and inductive reasoning in mathematics learning needs to be considered, because conceptual understanding can organize and consolidate mathematical thinking, as well as reasoning will gain meaningful knowledge for students. This can be done through learning by using generative approach. This research is a correlational research to know the correlation between the ability of conceptual understanding and inductive reasoning of VII grade students at SMP Negeri 3 Cugenang-Cianjur in 2009/2010 Academic Year on triangle and quadrilateral materials, using generative approach. Based on the results of correlation analysis, it was obtained rxy = 0.618 in moderate correlation, and it can be concluded that there is a positive correlation between the ability ofstudents’ conceptual understanding and inductive reasoning.

This article discusses the application of Realistic Mathematics Education approaches against the ability of mathematical reasoning and understanding of the students. The purpose of this research is to 1) know the comparison the ability between students who learn to use Realistic mathematics education approach with scientific approach, 2) know the comparative ability of reasoning mathematically between students who learn to use Realistic mathematics education approach with scientific approach, 3) know the difference between the understanding of mathematical concepts and reasoning of students. Data collection techniques was in the form of test result data post test as the learning outcomes of students. The data analysis used t test with two samples and test the correlation with significance level 0.05. As for the results of the analysis of the data shows that the 1) the ability of understanding the concept of students who use Realistic mathematics education approach better than students who use scientific approach, 2) mathematical reasoning ability of students using Realistic mathematics education approach better than students who use scientific approach, 3) there is a connection between the understanding of mathematical concepts and reasoning of students.

Does the Content of Mothers' Verbal Stimulation Explain Differences in Children's Development of Verbal and Nonverbal Cognitive Skills?

<p>This research was conducted in order to know the influence of the anxiety of learning and students' understanding of mathematical concepts penanalaran mathematical abilities of students. The hypothesis of this study include: 1) There is a significant direct effect on the ability of anxiety learn mathematical reasoning. 2) There is significant direct influence students' understanding of mathematical concepts of mathematical reasoning abilities. 3) There is a significant direct effect of anxiety learn to understanding math concepts students. 4) There is a significant indirect effect on the ability of anxiety learn mathematical reasoning through the understanding of math concepts students. The method used in this research is survey method. Affordable population is class VIII students of academic year 2014/2015 a private SMP in Depok. A large sample of 80 students, with a sampling technique used was multistage sampling, taken four private schools. Research instrument used is questionnaire anxiety to learn as much as 25 statement, test understanding of mathematical concepts as much as 23 multiple choice questions, tests of mathematical reasoning ability in the form of an essay as much as 10 questions, which te; ah tested its validity. Analysis of data using path analysis. Hypothesis testing results show that: 1) There is a direct effect not significant anxiety study on the ability of mathematical reasoning, 2) There is a direct effect of significant understanding of the mathematical concept of the ability of mathematical reasoning, 3) There is a direct effect not significant anxiety learn to understanding of mathematical concepts , 4) There is the indirect effect which is not significant anxiety on the ability to learn mathematical reasoning.</p><p> <strong>Keywords</strong>: anxiety of learning , mathematical concepts , mathematical reasoning</p>

Although GeoGebra applets are widely used in technology-based mathematics learning, their implementation still faces limitations in optimally supporting students’ visualization and mathematical reasoning. This study aims to analyze their utilization, challenges, and impact on students’ mathematical thinking. A Systematic Literature Review (SLR) was conducted using the Publish or Perish (PoP) application by retrieving articles from Google Scholar and Scopus published between 2020 and 2025, based on predefined inclusion criteria. The review followed the PRISMA framework. Out of 263 identified articles, 20 studies were selected for in-depth analysis. The findings reveal that GeoGebra applets are predominantly implemented in higher education and junior high school contexts, particularly in geometry topics that require strong visual representation. The use of GeoGebra applets contributes positively to students’ conceptual understanding, visualization ability, mathematical reasoning, and higher-order thinking skills (HOTS), especially when integrated with interactive and student-centered learning approaches. However, several challenges remain, including limited technological facilities, varying levels of teacher competence, insufficient student readiness, and the tendency to emphasize technical features over conceptual reasoning. Therefore, this study underscores the importance of designing pedagogical strategies that integrate GeoGebra applets with structured learning activities to explicitly foster students’ mathematical reasoning rather than merely serving as visualization tools.

The purpose of this study is to determine the relationship and influence of understanding mathematical concepts with mathematical reasoning in learning matrix on grade XI of senior high school. In this study the survey method was conducted using random sampling. The scores were obtained from the 54 students' understanding and mathematical reasoning tests. Based on SPSS calculations 20. Correlation coefficient between the understanding of mathematical concepts with mathematical reasoning is 0.695, meaning a strong relationship. The significance value is 0,000 <0,005 which means that it is significant. The regression equation is = -0,989 + 9,71 , if there is no concept understanding then mathematical reasoning is negative. The regression coefficient X value of 9.71 states that each addition of one value to the understanding of mathematical concepts will increase mathematical reasoning by 9.71. From the data and analysis above, it is shown that there is a significant relationship between understanding concepts and students' mathematical reasoning on the matrix material, indicated by the correlation coefficient of 0.695, which means a strong relationship, sig. 0,000 <0.005 that means significant.

What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.

What are the cognitive mechanisms supporting non-symbolic and symbolic order processing? Preliminary evidence suggests that non-symbolic and symbolic order processing are partly distinct constructs. The precise mechanisms supporting these skills, however, are still unclear. Moreover, predictive patterns may undergo dynamic developmental changes during the first years of formal schooling. This study investigates the contribution of theoretically relevant constructs (non-symbolic and symbolic magnitude comparison, counting and storage and manipulation components of verbal and visuo-spatial working memory) to performance and developmental change in non-symbolic and symbolic numerical order processing. We followed 157 children longitudinally from Grade 1 to 3. In the order judgement tasks, children decided whether or not triplets of dots or digits were arranged in numerically ascending order. Non-symbolic magnitude comparison and visuo-spatial manipulation were significant predictors of initial performance in both non-symbolic and symbolic ordering. In line with our expectations, counting skills contributed additional variance to the prediction of symbolic, but not of non-symbolic ordering. Developmental change in ordering performance from Grade 1 to 2 was predicted by symbolic comparison skills and visuo-spatial manipulation. None of the predictors explained variance in developmental change from Grade 2 to 3. Taken together, the present results provide robust evidence for a general involvement of pair-wise magnitude comparison and visuo-spatial manipulation in numerical ordering, irrespective of the number format. Importantly, counting-based mechanisms appear to be a unique predictor of symbolic ordering. We thus conclude that there is only a partial overlap of the cognitive mechanisms underlying non-symbolic and symbolic order processing.