Mathematical Reasoning Research Articles

The relationship between executive functions and mathematics achievements in early-grade elementary students

ABSTRACT Mathematics, along with reading and writing, is a core academic subject in the school curriculum. The development of mathematical skills is influenced by various cognitive factors, with executive functions (EF) playing a central role. EF, which encompasses working memory, inhibitory control, and cognitive flexibility, is critical for supporting complex cognitive processes required for problem-solving and mathematical reasoning. Research consistently shows that children with stronger EF tend to achieve better academic outcomes, including in mathematics. The goal of the present study was to examine the relationships between the global EF and its three core components – working memory, inhibitory control, and cognitive flexibility – and their impact on mathematics achievement. The sample for this study consisted of 180 children, aged 8–11 years (mean age: 9.6, SD: 1.0 year; 83 girls, 97 boys). EF was assessed using the Yellow-Red test, while mathematics achievement was evaluated based on teachers’ evaluations of the child’s mathematics performance. The results indicated a statistically significant effect of global EF and its three components on mathematics achievement. Given the potential malleability of EFs, we conclude with recommendations for strategies to enhance EF development at an early school age.

Didactic Innovation in Mathematics Using Technologies

The continuous progress of society requires all the actors to be dynamic and constantly updated, both in terms of monitoring as well as in the need to adapt. Regarding education, no matter how updated we are in relation to the contents, didactic strategies, and technological resources, we are still inevitably forced to adapt to new paradigms, leading us to reformulate traditional teaching methods. In this context, the contribution of e-learning platforms emerges, where teachers and students have at their disposal new means of empowering the teaching and learning process, since these platforms can be defined as a virtual teaching support environment. Currently, our students, in general, have many difficulties in problem-solving and mathematical reasoning, which often reflects in the performance of very simple tasks, with a growing disinterest towards Mathematics. It is also possible to argue that our students' "poor preparation" is a contributing factor in their failure (many did not attend Mathematics in Secondary Education and/or have not studied for several years, as is the case of those who entered through special contingents, as the “aged 23 and over”). In order to promote a distinct, alternative and supportive pathway that may help to solve this issue, a project on the Moodle learning management system (LMS) platform has been developed with the goal of assisting students in their study and the development of their skills in a way that is directly related to the curricular units (CU) in the scientific field of Mathematics, in an online learning environment. To increase students’ engagement into their learning process in a collaborative environment, a flipped model was employed into a Financial Mathematics/Financial Calculus Course (FCC). This paper's primary goal is to examine the effects of implementing the flipped classroom paradigm on students' performance, learning, and classroom instruction. The results from employing this approach have indicated a beneficial effect on the overall academic progress of students.

Mathematical reasoning in elementary grade classrooms in India: what is there and what is missing?

Mathematical reasoning in elementary grade classrooms in India: what is there and what is missing?

<span>Enhancing student's mathematical competency in learning the graph and properties of the sine function by Google Sheets app on smartphone</span>

This study explores the integration of the Google Sheets app on smartphones to enhance students' mathematical competency in understanding the graph and properties of the sine function. The paper was an exploratory study involving 32 11th-grade students. The teaching intervention was structured into four phases: familiarizing with the Google Sheets app, creating the sine function value table, sketching the function graph, and analyzing the graph to deduce the sine function's properties. Data were collected through worksheets and audio -video recordings of group work, focusing on manifestations of mathematical competencies. The findings indicate that students completed the tasks and demonstrated significant competencies in mathematical reasoning and using digital tools. Students were able to identify and solve mathematical problems, utilize Google Sheets effectively, and use logical reasoning to enhance their understanding of the sine function. The study concludes that integrating Google Sheets into mathematics education not only aids in visualizing and comprehending mathematical concepts but also promotes interactive and collaborative learning environments, ultimately fostering a deeper understanding and proficiency in mathematics.

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.

Integrating the Treisman Model and Math Circles Improves Student Performance in Introduction to Advanced Mathematics

We describe a lecture-free problem-solving Mathematical Communication and Reasoning (MCR) course that helps students succeed in the Introduction to Advanced Mathematics course. The MCR course integrates elements from Uri Treisman's Emerging Scholars workshop model and Math Circles. In it students solve challenging problems and form a supportive cohort. Analysis of course grades of students identified for intervention in the Introduction to Advanced Mathematics course showed significant improvement. The number of non-passing grades (F through C−) decreased by more than 50%, while the number of desirable grades (B− through A) increased by more than 50%. We offer insights from our experience for readers interested in developing such a course at other institutions.

The Effect of Google Classroom-Assisted Realistic Mathematics Education Approach on Students’ Mathematical Reasoning Ability

Mathematical reasoning is an important aspect, but there are still many students who are weak when it comes to mathematical reasoning. Factors that affect the level of mathematical reasoning of low students, including: a) students easily forget the material taught; b) the student has no idea in completing it; c) students are not careful in understanding the problems in the problem; d) students do not understand which formula will be used in solving the problem; e) Students do not understand the concept of the material. This research aims to determine whether or not there is an influence of the approach realistic mathematics education helpgoogle classroomon mathematical reasoning abilities. Quantitative Approach method used in this researchpre-experimental design with one group pretest posttest design. The research subject is the experimental class. Data collection was carried out with pretest and posttest data on the mathematical reasoning abilities of grade 7 students at one of the junior high schools in Purwasari district, kabupaten Karawarang. Data analysis techniques in this study that is analyze the scores of pretest and posttest results students by t-test for 2 dependent samples (Paired Sample T-Test) done with the help of IBM SPSS 21 software. The research results show that there is value of sig 0,000 < 0,05 which means a positive influence approach realistic rathematic education help google classroomon ability students' mathematical reasoning. Based on the result, we can be concluded that there is a positive influence of the approach realistic mathematic education help google classroomon students mathematical reasoning abilities. The learning process uses an approach realistic mathematic education help google classroom can be used as an alternative learning to improve students mathematical reasoning abilities.

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.

Games in Mathematics Education: Trends and Methodological Approaches in the Context of the Congress of European Research in Mathematics Education (CERME) Review

This study aimed to examine the studies on digital games presented in The Congress of European Research in Mathematics Education (CERME) using a systematic analysis approach in terms of research method, data collection tool, and how they define digital games. Sixteen studies related to games were selected from the proceedings. The findings of the research revealed that the number of studies on games has increased in recent years, and the interest of the mathematics education community in this subject has gradually increased. It was seen that qualitative research approaches were used in most of these studies. As a data collection tool, a semi-structured or clinical interview form was mainly used. To reach more comprehensive results, it is necessary to give importance to quantitative research approaches and even to prefer the use of both approaches together. It was indicated that the tendency towards mathematical reasoning and puzzle games has continued predominantly in recent years. Although it was seen that the number of studies on digital games has increased in the last five years, only six studies in total were presented at the CERME. Moreover, three digital games developed by using the tools in the context of dynamic geometry environments were found. Another significant finding was that most of these studies did not define games. Only a few studies that defined the game considered the game as a tool used to acquire a mathematical concept or knowledge. Based on the findings, it can be argued that digital games are not among the interests of the mathematics education community. Finally, it was observed that mathematical theorems and approaches were central to the studies reviewed. Games were generally defined as tools within these studies. Therefore, future research should particularly consider fundamental game features such as game mechanics to create more integrated research environments with mathematics education.

Metaphorical Thinking Intervention in Learning and Its Impact on Mathematical Reasoning Ability

Dalam beberapa tahun terakhir, penelitian tentang intervensi Metaphorical Thinking (MT) dalam pendidikan matematika semakin mendapat perhatian. Namun, penelitian terbatas telah meneliti bagaimana intervensi MT, ketika diintegrasikan dengan model pembelajaran yang menantang, dapat meningkatkan Kemampuan Penalaran Matematis (MRA) siswa. Untuk mengatasi kesenjangan ini, penelitian kuasi-eksperimental dengan menggunakan desain kelompok kontrol posttest-only dilakukan terhadap 50 siswa di SMP Widya Bhakti Ruteng, NTT, Indonesia. Penelitian ini bertujuan untuk menganalisis pengaruh intervensi MT dalam lingkungan Pembelajaran Berbasis Masalah (PBL) terhadap MRA. Data dikumpulkan melalui tes PMA yang terdiri dari lima soal, dan hasilnya dianalisis menggunakan uji t setelah melakukan analisis prasyarat. Temuannya menunjukkan bahwa siswa yang menerima intervensi MT dikombinasikan dengan PBL menunjukkan MRA yang jauh lebih tinggi dibandingkan dengan mereka yang tidak menerima intervensi MT. Hasil ini menggarisbawahi potensi manfaat dari mengintegrasikan intervensi MT dengan pendekatan pedagogi menantang lainnya. In recent years, research on Metaphorical Thinking (MT) interventions in mathematics education has gained increasing attention. However, limited studies have examined how MT interventions, when integrated with challenging instructional models, can enhance students' Mathematical Reasoning Ability (MRA). To address this gap, a quasi-experimental study utilizing a posttest-only control group design was conducted with 50 students at SMP Widya Bhakti Ruteng, NTT, Indonesia. The study aimed to analyze the effects of MT interventions in a Problem-Based Learning (PBL) environment on MRA. Data were collected through a PMA test consisting of five questions, and the results were analyzed using a t-test after performing a prerequisite analysis. The findings revealed that students who received MT interventions combined with PBL demonstrated significantly higher MRA compared to those who did not receive MT interventions. These results underscore the potential benefits of integrating MT interventions with other challenging pedagogical approaches.

Which Variables Better Predict Phonemic Awareness of First Grade Primary School Students?

The purpose of the research was to discover which variables better predict phonemic awareness. Socioeconomic status (SES), quality of parent-child interaction (PCI), screen time (DST), visual-spatial ability (VSA), and mathematical reasoning (MR) were included as independent variables in the model, while phonemic awareness (PA) was the dependent (outcome) variable. The research was designed as correlational research. A total of 556 first grade primary school students were recruited into the research sample upon approval by their parents. In the analytic procedures, supervised machine learning was adopted and data were analyzed through classification and regression trees (CART) by using rprart, rpart.plot, tidyverse, dplyr, ggplot2, and corrplot packages in R. Results of data analysis indicate that MR, PCI, and VSA can predict PA, while SES and DST are not predictors. Findings of the research were discussed along with intelligence theories and practical implications were noted for teachers and researchers.

Digital educational resources in the development of mathematical logical thinking in middle school students

This article "Digital Educational Resources in the development of mathematical logical thinking in high school students" arises from the scientific problem: how do digital educational resources contribute in the development of mathematical logical thinking? The main objective is to analyze the importance of the contribution of digital educational resources in the development of mathematical logical thinking in high school students of the following educational institutions: Mariscal Sucre, Coronel Olmedo Alfaro and José María Velasco Ibarra. The research is descriptive with a mixed approach; for the development of the research techniques and instruments were used, where interviews and surveys were recorded, in addition, the difficulties presented by students in the development of mathematical logical thinking were detected, therefore, as an alternative solution to the problem, the guide of digital educational resources for strengthening skills in the subject of mathematics is presented.

Exploring the Primary School Teachers’ Reasoning and Individuals with Limited Education When Solving False Proportionality Problems

In this study employing a qualitative approach, we explore and compare the mathematical reasoning of active primary school teachers and individuals with limited education when tackling problems involving false proportionality and lack of authenticity. The research is justified by the importance of understanding how these issues are addressed in various educational groups and how teaching strategies in this area can be enhanced. An individual questionnaire containing five problems was administered to five participants in each group. The results indicate that teachers tend to more frequently succumb to the illusion of linearity, incorrectly applying linear relationships to non-proportional problems compared to individuals with lower educational attainment. This suggests a greater influence of algorithmic approaches and clauses of the didactic contract on their mathematical reasoning. This tendency could be attributed to a greater exposure to algorithmic approaches during the formative stages, as well as certain clauses in the experimental contract. Conversely, individuals with limited education approached problems with greater flexibility, linking their responses to everyday experiences. The study concludes that it is imperative to implement educational strategies aimed at overcoming limitations such as the illusion of linearity and fostering meaningful problem-solving skills from the early stages. It is recommended to developteacher training programs that promote a more contextualized and flexible approach to mathematics teaching, as well as the include contextualized and meaningful problems in the school curriculum.

Optimalisasi Kemampuan Penalaran Matematis melalui Metode Mind Mapping

Increasingly rapid global developments raise complex problems that require effective and innovative solutions. Mathematical reasoning is the key to solving the problem. But on the other hand, learning in schools is still a lot of conventional learning and the development of the students' mathematical reasoning skills is not optimal. The aim of this study was to explore the effectiveness of using mind map-based learning methods that were judged to be effective in developing mathematical reasoning skills. With a qualitative approach to literature studies, research results were obtained which showed that the method of mind mapping had a significant influence on the mathematical reasoning ability of the students. Library study sources are derived from previous research that had the same focus of study. Library reviews are used to analyze several studies related to the use of mind mapping-based learning methods and their influence on mathematical reasoning capabilities. This research is expected to provide an understanding of the importance of developing mathematical reasoning skills to form intelligent and critical generations

Security, QoS and energy aware optimization of cloud-edge data centers using game theory and homomorphic encryption: Modeling and formal verification

Privacy and efficient data processing are crucial research areas in the field of outsourcing computing. Thus, the contribution of the paper is twofold. First of all, we develop a secure offloading technique that can process data while preserving privacy. Although RSA and Paillier cryptosystems are highly beneficial for mathematical operations on basic encrypted data due to their homomorphic properties, images are processed using permutation-ordered binary (POB) and Shamir's secret sharing (SSS). Second, a non-cooperative game theory model was formulated to examine the interactions between service providers, characterizing each edge as an M/M/1 system with an infinite queue. Through formal verification using rigorous mathematical reasoning, the suggested strategies for task offloading and resource allocation are shown to be effective in terms of security, quality of service (QoS), and energy consumption. The best-response dynamics approach is used to calculate the final strategy for each participant and assess how fairly resources are allocated. Finally, the potential of our approach is demonstrated numerically, revealing a faster convergence towards attaining Nash equilibrium in a duopoly cloud-edge data center market, granted that the necessary and sufficient conditions are met.

Ground rules for talk – the use of conversation rules to increase productivity in mathematical conversations in the early years

ABSTRACT In recent years, social aspects of teaching and learning have gained increased recognition, prompting researchers to focus on conversations and language in mathematics classrooms. While prior studies have highlighted the importance of conversations in primary school teaching, a gap remains in understanding how they influence mathematics teaching and learning, especially among younger children (Muhonen et al. 2016; Patterson 2018). To address this gap, this study explores the implementation of ground rules for talk in two first-grade classrooms in Norway (ages 5–6 years). This educational design research study investigated the impact of conversation rules on enhancing mathematical reasoning and promoting productive communication in primary school. Findings indicate that implementing ground rules for talk can foster productivity by encouraging pupils to inquire about others’ reasoning and share their perspectives to foster a respectful discourse. However, it also emphasises the importance of teachers being mindful of their language to foster reasoning effectively.

The Relationship of Mathematical Reasoning to Mathematics Achievement and Academic Excellence

This study aimed to investigate the relationship between mathematical reasoning and achievement in mathematics, and extend this to its correlation as a higher cognitive ability with various academic subjects in general, particularly across different levels of academic performance efficiency. The study employed a descriptive correlational approach with a sample of 106 twelfth-grade secondary school students. The sample was divided into three groups based on academic performance efficiency. The study sought to answer the following questions(1)What is the extent and direction of the correlation between mathematical reasoning as a higher cognitive qualitative ability, and achievement in mathematics as educational content? (2)To what extent does the extent and direction of this correlation vary between mathematical reasoning variables and achievement in mathematics across different levels of academic performance in this subject? (3)What is the extent and direction of the correlation between mathematical reasoning and achievement in different academic courses?(4)To what extent do the extent and direction of correlation relationships vary between mathematical reasoning variables and different academic courses across varying levels of academic performance in these courses? Naturally, these questions were addressed by verifying the validity of the following scientific hypotheses:Hypothesis1There is a strong correlation between mathematical reasoning (as a higher cognitive ability) and achievement in mathematics, as presented to fourth-grade secondary school students. Hypothesis2: The correlation between mathematical reasoning and achievement in mathematics varies in strength and weakness across different levels of academic performance efficiency in this subject.Hypothesis3:There is a strong correlation between the variable of mathematical reasoning and various academic subjects in general. However, the correlation is stronger between this ability and scientific subjects compared to subjects with linguistic or humanistic nature.Hypothesis4:The extent of correlation relationships (both strong and weak) between mathematical reasoning and different academic courses varies across different levels of academic achievement efficiency in general. The results of this study revealed the validation of all these hypotheses except for the third hypothesis, which was partially validated.The most significant findings from this study have highlighted a set of important indicators that shed light on the nature of non-cognitive factors behind academic excellence in general and specifically in mathematics, as presented in our context previously.

IMPLEMENTASI MODEL PROBLEM BASED LEARNING UNTUK MENINGKATKAN KEMAMPUAN PENALARAN MATEMATIS PADA MATERI LINGKARAN KELAS VIII

The purpose of this class action research is to define the implementation of the problem based learning model to improve the mathematical reasoning ability of the students of the eighth grade Fatimah Azzahra SMP IT Izzudin Palembang 2023/2024 on circular material. Execution of research using two cycles, each cycle has steps namely planning, action, observation, and reflection. Data collection on this study uses observation, and testing. The research was carried out with the participation of 17 students of the eighth grade at Izzudin Palembang IT High School. The aim of this study is to apply the learning model of problem based learning with the aim of improving the ability of mathematical reasoning of students. Students experience improvement in every aspect. The increase in the percentage of students' scores in mathematical reasoning skills during the first cycle reached 61.91%, while in the second cycle increased by 84.03%. The implementation of this study uses the pre-cycle phase by giving pre-test questions so that students reached the percent of 43.13% and in the post-test phase students achieved 80.84% so that it can be concluded that each indicator of mathematic reasoning ability students experienced a good improvement.

The Development of Canva-Assisted Scientific Approach Pythagoras Teaching Materials to Improve Students’ Mathematical Reasoning Ability on Junior High School

This research was conducted to determine the development, feasibility, effectiveness, and difficulties in the development of teaching materials on the Pythagorean Theorem using a scientific approach assisted by Canva to enhance the mathematical reasoning abilities of junior high school students. This research was conducted at SMP PGRI 10 Bandung using the Research and Development (R&D) method based on the 4D stages. The research subjects included 33 students from class IX F for limited trials, 27 students from class VIII B, and 29 students from class VIII D for extensive trials. The research instruments used in this study included interviews in the preliminary learning, student responses to the teaching materials, expert validation sheets, and 6 items of reasoning ability test questions. The material used in this research was the Pythagorean Theorem. Student reasoning ability test data were analyzed using Microsoft Excel calculations. The research results indicate that: 1) the development process of the 4D method teaching materials, including a) Define (Definition); b) Design; c) Develop; and Disseminate, have been successfully implemented according to the plan; 2) the validator calculation results obtained a percentage of 86.21%, categorized as "very valid and do not need revision"; 3) the student reasoning ability test results prove that the teaching materials are reasonably effective; 4) significant difficulties include students' lack of understanding of the material, low activity, and a lack of supportive learning facilities.

Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures

AbstractSpecial tasks for pre-service teachers (PSTs) in university mathematics courses (“interface tasks”) are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and skills in a professionally relevant way. In this paper, we analyze answers that PSTs have created to an interface task on symmetry. The PSTs were asked to clarify a student’s question from a mathematical perspective and then give a suitable elementarized answer. We situate these two steps theoretically and reconstruct the mathematical reasoning in PSTs' answers. Through qualitative content analysis, we examined how PSTs justify figures' symmetries from a university mathematics perspective and when responding to the fictitious student. The scenario of a student questioning the existence of 100° rotationally symmetrical figures elicited rich and varied responses, proving suitable for an interface task. We compared PSTs' reasoning related to mathematical clarification with the reasoning related to elementarization. In many cases, this revealed a productive use of course content. An interesting result is that there is no uniform picture as to whether the arguments are more detailed in the mathematical clarification or in the elementarization.