Mathematical Reasoning Research Articles

Comparison Of Inquiry And Problem Solving Approaches Towards Improving Students' Mathematical Reasoning Ability And Self Confidence High School Students

The study aims to identify differences between improved mathematical reasoning skills of students taught with inquiry approaches and mathematics problem solving education approaches; to determine differences in improved self-confidence of teaching students with inquisition approaches, and in mathematically solving educational approaches. This research is categorized into quasy experimental research. This research is being carried out at one of the Higher Secondary Schools in Labuhan Batu regency in the academic year 2023/2024, with the timetable for the conduct of research coordinated according to the school's activities. The subject of this study is a total of 72 high school X-grade students. The results of this survey show that; there is a difference between improved mathematical reasoning skills of students with inquiry approaches and problem solving approaches; there are differences in improved self-confidence students with Inquiry and Problem Solving Approaches; There is a distinction between inquery and problem-solving mathematics education approaches to enhanced mathematic reasoning ability and self confidence

The Constructs of Students’ Logical Thinking in the Problems of Algebraic-Geometric Transformations

Logical thinking is a cognitive ability that plays a vital role in solving problems. The art of logical thinking is recognizing, selecting, and applying the appropriate reasoning to solve a problem. This study aimed to identify and investigate students’ logical thinking reasoning constructs when they face algebraic-geometric transformations. We used Kenexa tests to measure students’ mathematical logical thinking. The statistical sample size was 380 students from high schools in Tehran, Iran. We applied exploratory factor analysis to identify and examine appropriate indicators and latent factors of logical thinking. The results showed that an adequate number of suggested indicators could identify the reasoning dimensions of students’ mathematical logical thinking, and it can be used as a logical reasoning test in algebraic-geometric transformations. Moreover, the different performance of students in using reasoning strategies indicates that the content of textbooks and the teaching approach in the field of algebraic-geometric transformations should move in a direction that focuses on reasoning skills.

The Effect of Self-Efficacy and Learning Independence on Students Mathematical Reasoning Ability

The purpose of the research is to determine 1) Direct influence of self-efficacy on students' math reasoning ability 2) the Direct influence of learning independence on the ability of mathematical reasoning 3) the Direct influence of self-efficacy on student self-reliance 4). The indirect effect of self-efficacy on mathematical reasoning ability through student learning independence. This research used a survey method. The independent variables bound to this research are Self Efficacy (X1), Learning Independence (X2), and Mathematical Reasoning Ability (X3). The research method used surveys. The sample used is 100 students as a research sample by using a proportional random sampling technique from all students of class VII of National Junior High School in Bekasi City. The data were collected using math-reasoning test and self-efficacy questionnaire and learning independence. Hypothesis testing with path analysis (Path Analys). This study was conducted in January 2018. Based on the results of the hypothesis and data analysis concluded several things as follows (1) There is a direct influence of self-efficacy significant to the ability of mathematics reasoning of students of National Junior High School in Bekasi City. This is evidenced by the acquisition of tcount (4.615)> ttable (1.984). (2) There is a significant direct influence of learning independence to the students' math skills ability in National Junior High School in Bekasi City. This is evidenced by the acquisition of tcount (5.869)> ttable (1.984). (3) There is a direct influence of self-efficacy significantly to the independence of students studying National Junior High School in Bekasi City. This is evidenced by the acquisition of tcount (18,719) > ttable (1,984). (4) There is a significant indirect influence of self-efficacy of students to the ability of mathematical reasoning through the independence of students studying National Junior High School in Bekasi City. This is evidenced by the acquisition of tcount (6.4728) > ttable (1.984). The implications of this research are 1). To improve the ability of mathematical reasoning can be done by improving self-efficacy and student learning independence. 2) to improve learning independence is done by improving self-efficacy.

Reconstruction and normalization of LISA for spatial analysis.

The local indicators of spatial association (LISA) are important measures for spatial autocorrelation analysis. However, there is an inadvertent fault in the mathematical processes of deriving LISA in literature so that the local Moran and Geary indicators do not satisfy the second basic requirement for LISA: the sum of the local indicators is proportional to a global indicator. This paper aims at reconstructing the calculation formulae of the local Moran indexes and Geary coefficients through mathematical derivation and empirical evidence. Two sets of LISAs were clarified by new mathematical reasoning. One set of LISAs is based on non-normalized weights and non-centralized variable (MI1 and GC1), and the other set is based on row normalized weights and standardized variable (MI2 and GC2). The results show that the first set of LISAs satisfy the above-mentioned second requirement, but the second the set cannot. Then, the third set of LISA was proposed and can be treated as canonical forms (MI3 and GC3). This set of LISAs satisfies the second requirement. The observational data of city population and traffic mileage in Beijing-Tianjin-Hebei region of China were employed to verify the theoretical results. This study helps to clarify the misunderstandings about LISAs in the field of geospatial analysis.

Assessing Mathematical Deductive Reasoning Competence of Eighth-Grade Students from China

Assessing Mathematical Deductive Reasoning Competence of Eighth-Grade Students from China

Machine Learning and Information Theory Concepts towards an AI Mathematician

The current state of the art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities—which correspond to our intuition and habitual behaviors—but still lacks something important regarding system 2 abilities—which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example, by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.

Penerapan Pembelajaran Berbasis Masalah untuk Peningkatan Kemampuan Penalaran Matematis Siswa Kelas 8 SMP Al-Muhajirin Purwakarta

This research was aimed at analyzing the enhancement of students' mathematical reasoning abilities through problem-based learning. The experimental design was pre-post control group design. The research population was all junior high school student of SMP Al-Muhajirin Purwakarta. The research sample was taken randomly, was the class VIII C students as the experimental group who participated in instruction with problem-based learning and the other class VIII D as control group who participated in instruction with conventional learning. Data was collected through test and questionnaires. The statistical analysis used is the Gain test for the results of students' mathematical reasoning ability tests. The analysis of gain score showed that the enhancement of students’ abilities who participated in instruction with problem-based learning was better than those who participated in instruction with conventional learning. Problem-based learning in mathematics lessons shows a positive response which shows that students like the method used.

Natural Language Reasoning, A Survey

This survey paper proposes a clearer view of natural language reasoning in the field of Natural Language Processing (NLP), both conceptually and practically. Conceptually, we provide a distinct definition for natural language reasoning in NLP, based on both philosophy and NLP scenarios, discuss what types of tasks require reasoning, and introduce a taxonomy of reasoning. Practically, we conduct a comprehensive literature review on natural language reasoning in NLP, mainly covering classical logical reasoning, natural language inference, multi-hop question answering, and commonsense reasoning. The paper also identifies and views backward reasoning, a powerful paradigm for multi-step reasoning, and introduces defeasible reasoning as one of the most important future directions in natural language reasoning research. We focus on single-modality unstructured natural language text, excluding neuro-symbolic research and mathematical reasoning.

Bridging cognitive neuroscience and education: Insights from EEG recording during mathematical proof evaluation

BackgroundMuch of modern mathematics education prioritizes symbolic formalism even at the expense of non-symbolic intuition, we contextualize our study in the ongoing debates on the balance between symbolic and non-symbolic reasoning. We explore the dissociation of oscillatory dynamics between algebraic (symbolic) and geometric (non-symbolic) processing in advanced mathematical reasoning during a naturalistic design. MethodEmploying mobile EEG technology, we investigated students' beta and gamma wave patterns over frontal and parietal regions while they engaged with mathematical demonstrations in symbolic and non-symbolic formats within a tutor-student framework. We used extended, naturalistic stimuli to approximate an authentic educational setting. ConclusionOur findings reveal nuanced distinctions in neural processing, particularly in terms of gamma waves and activity in parietal regions. Furthermore, no clear overall format preference emerged from the neuroscientific perspective despite students rating symbolic demonstrations higher for understanding and familiarity.

The development of mathematical argumentation: A case study on two mathematics classrooms

Mathematical reasoning has been a critical concern in Turkey especially since the structure of the student selection examination for high schools changed six years ago. The ability to solve the questions in the new exam requires high level reasoning and argumentation skills. Schools, whether they are public or private, prepare 8th graders for this exam with intense educational programs. They frequently use skill-based questions–similar questions to the ones in the new exam, which require high level mathematical reasoning. This study indicates that students gain better mathematical reasoning skills in learning environments promoting collective discussion and argumentation. Hence, these questions need to be solved in these kinds of environments. In this study, two cases are analyzed to understand the argumentation process in classrooms in depth. Audiotapes of two 8<sup>th</sup> grade classrooms, one from a public school, another from a private school, are analyzed. The same teaching material–a worksheet including skill-based questions–is used in the classrooms. During analyzing, qualified argumentation pattern–a pattern including students’ claims and justifications/evaluations for those claims- is defined. Analysis of classroom audiotapes revealed that that there are significant differences between two classrooms’ argumentation structure and type of dialogues emerged in the classroom. In one classroom there is a more qualified argumentation process than in the other classroom. In addition, analysis of the type of the dialogues indicates that two classrooms have different types of dialogues. Overall, the study reveals that despite the differences, both classrooms mostly included teacher-individual interactions and they have little collective discussion.

Developing 21st century skills through PISA-based assessment-learning tasks

Relevance. Currently, the textbooks used in educational schools in Kazakhstan largely lack tasks that require decision-making under conditions of uncertainty. The relevance of this study lies in addressing a significant gap in the educational curriculum of the Republic of Kazakhstan. Purpose. The purpose of this study is to form and develop schoolchildren�s decision-making skills in conditions of uncertainty, and 21st century skills, by drawing up model assessment and learning tasks and assignments for them. Methodology. Diagnostic written work was carried out to identify the success of the developed method for constructing assessment and learning tasks, teaching schoolchildren to solve practice-oriented problems in the experimental (33 students) and control (32 students) classes. Results. Monitoring showed that out of 33 students from the experimental class 22% did not score points corresponding to the mandatory threshold level (13 out of 26 points), 72% achieved an average level of learning (from 14 to 21 points), 6% achieved a high level of learning (from 22 to 26 points). In the control class, 68% of schoolchildren did not reach the mandatory threshold level, 29% reached the average level, 3% reached a high level of development of practice-oriented knowledge. To establish the success of the developed methodology for constructing assessment and training tasks for practical problems, a survey was conducted among mathematics teachers (17 people). The survey results showed that this approach allowed all 17 teachers to successfully create assessment and teaching tasks for selected educational tasks from a mathematics textbook. Conclusions. Experimental studies confirm that teaching schoolchildren to solve practice-oriented problems and assessment tasks enhances their practice-oriented knowledge, including mathematical literacy, 21st-century thinking skills, and decision-making in uncertain conditions. Keywords: decision making; thinking skills; mathematical reasoning; exam

The Opportunities for Mathematical Reasoning Skills That Teachers Provide for Their Students in The Learning Environment

The acquisition of mathematical reasoning skills is directly related to the opportunities gained by the students in the learning environment. The complete lack or the rarity of such situations that support mathematical reasoning in the learning environment is an obstacle to conceptual learning. Therefore, it is important to investigate the extent to which different aspects of reasoning are encountered in teachers’ presentations and to convey the reflections of those from the learning environment. The objective of this study is to examine the opportunities for mathematical reasoning skills that teachers give to their students. A holistic case study design was used in the study process as a qualitative research approach. The study was carried out with two teachers working in public schools. Unstructured observations and video recordings conducted by the researchers were used to collect data, and content and descriptive analysis analyse the obtained data. When the teachers were evaluated regarding the opportunities for mathematical reasoning they provided in their classes, it was concluded that although these constitute a variety of opportunities, they present limited opportunities that could fully support mathematical reasoning. It is thought that offering limited opportunities in the learning environment may negatively affect students’ mathematical reasoning skills.

Random feedback alignment algorithms to train neural networks: why do they align?

Feedback alignment algorithms are an alternative to backpropagation to train neural networks, whereby some of the partial derivatives that are required to compute the gradient are replaced by random terms. This essentially transforms the update rule into a random walk in weight space. Surprisingly, learning still works with those algorithms, including training of deep neural networks. The performance of FA is generally attributed to an alignment of the update of the random walker with the true gradient—the eponymous gradient alignment—which drives an approximate gradient descent. The mechanism that leads to this alignment remains unclear, however. In this paper, we use mathematical reasoning and simulations to investigate gradient alignment. We observe that the feedback alignment update rule has fixed points, which correspond to extrema of the loss function. We show that gradient alignment is a stability criterion for those fixed points. It is only a necessary criterion for algorithm performance. Experimentally, we demonstrate that high levels of gradient alignment can lead to poor algorithm performance and that the alignment is not always driving the gradient descent.

PENGARUH STRATEGI WORKING BACKWARD DALAM PEMECAHAN MASALAH MATEMATIKA TERHADAP KEMAMPUAN PENALARAN SISWA SMP NEGERI KOTA JAMBI

Material mathematics and mathematical reasoning are two things that can not be separated, the material is understood through reasoning and mathematical reasoning to understand and learn the material drilled through mathematics. Working Backward strategy is a strategy that is closely associated with logical reasoning ability and verification. Working Backward strategy, students are required to analyze each step by using reasoning. This study used a quasi-experimental methods. This study aims to determine whether there are differences in the effect of the use of the Working Backward strategy in solving math problems on mathematical reasoning abilities of students. The experiment was conducted in Jambi City Junior High School. The population are 375 students, while the studied sample totaled 68 students consisting of 34 students in grade experiments and 34 students the control class. Sampling was done by using simple random sampling technique in class VII. Instruments in this study was a test in the form of mathematical reasoning abilities test description. The results showed that the average value of the experimental class of 74.92 and an average grade of 67.65 control. These results suggest that there are differences average value of the experimental class with the control class. So it can be concluded that the use of the Working Backward strategy in solving mathematical problems affect the ability of mathematical reasoning seventh grade students of SMP Negeri 11 Jambi. Keyword: Working Backward Strategy, Problem Solving, Reasoning Ability Mathematics

STUDY ON LITERACY NUMERACY TOWARDS STUDENTS’ LOGIC MATHEMATICS: A LITERATURE REVIEW

Numeracy literacy and mathematical logical thinking have a significant relationship in mathematics learning. Therefore, the study of this literacy examines the relationship between literacy, numeracy, and the development of students' logical thinking in the domain of mathematics education. This research aims to delineate the impact of numeracy literacy and logical thinking in shaping students' abilities to understand and apply logical principles in the context of mathematics, given the fundamental importance of literacy and numeracy skills. In this study, a literature review is employed to examine the relationship between literacy, numeracy, and logical thinking in the context of mathematics. The methodology used involves data collection, review processes, and in-depth analysis of scholarly articles sourced from Google Scholar, JSTOR, and PubMed. A total of 105 articles were analysed and categorized into the contexts of literacy, numeracy, and logical thinking in the context of mathematics. The research findings indicate the complexity of the interrelationship between literacy, numeracy, and logical thinking in mathematics education. This research contributes to offering insights into numeracy literacy and logical thinking for educators, researchers, and policymakers interested in enhancing the quality of mathematics education.

The Impact of Mathematical Reasoning and Critical Thinking Skills on Mathematical Literacy Skills

For learning mathematics, mathematical skills are needed, some of which are mathematical reasoning skills, mathematical critical thinking skill, and mathematical literacy skills. This research aims to obtain information regarding the impact of mathematical reasoning and critical thinking skills on mathematical literacy skills. This research used a quantitative approach using an associative method with a correlational technique. The sample of this research was comprised 51 students who took integral calculus course in the Department of Mathematics and Mathematics Education, Faculty of Mathematics and Science in Universitas Negeri Jakarta, which were collected randomly using simple random sampling. The statistical analysis used in this research was multiple regression analysis. The results of this research showed that: 1) There was a positive impact of mathematical reasoning on mathematical literacy. 2) There was a positive impact of mathematical critical thinking skill on mathematical literacy. 3) There was an impact of both mathematical reasoning skill and mathematical critical thinking skill together on mathematical literacy. Further research is needed related to the impact of mathematical reasoning and critical thinking skills on mathematical literacy skills reviewed from the student’s initial mathematical skill. Keywords: critical thinking skills, mathematical literacy skills, mathematical reasoning

Improving Mathematics Reasoning Ability of Junior High School Students Using the Learning Star with a Questions Model

This study examines the differences in increasing mathematical reasoning abilities using the Learning start with a question learning model and conventional learning. The research method is quantitative by way of experimental pretest-posttest control group design, which extends the one-group pretest-posttest design in two ways: a second group is added, called the comparison or control group; samples were placed randomly in each group of 83 people. The instrument used is an essay test; the questions are set in the form of mathematical reasoning abilities. Data were analyzed using inferential statistics with an independent sample t-test. The research results obtained are: The application of the LSQ learning model, most students, can solve mathematical reasoning questions correctly. The average score of students who follow the LSQ learning model is higher than the average value of students who take conventional learning; The results of the t-test explained that students who studied using the LSQ model and students who used conventional learning had significantly different improvements in their mathematical reasoning abilities. Students who learn to use the LSQ model increase their reasoning abilities more than the students who study using the conventional model. Keywords: junior high school, learning star with a questions model, mathematics reasoning ability, student

Deductive Reasoning and Mathematical Resilience in Complex Analysis

The pre-research data of mathematics prospective teachers in one of the universities in Bandung showed that the deductive reasoning ability in complex analysis was still not at good level. Beside the cognitive aspect, the affective aspect could be considered too in doing learning process, such as mathematical resilience. This study aims to analyze and identify the correlation between deductive reasoning and mathematical resilience in complex analysis. The research was conducted in one of the mathematics education departments of a university in Bandung. Correlation was the method used in this study. Mathematics prospective teachers were the sample of this research. This study concluded that mathematical deductive reasoning of prospective teachers was on a moderate level, the mathematical resilience of prospective teachers was on the positive category, and there was a significant correlation between deductive reasoning and the mathematical resilience of prospective teachers on a moderate level. Keywords: deduktif reasoning, matchematical resilience, complex analysis

Mathematical Reasoning Ability and Mathematics Self-efficacy in Gender Differences

Gender differences and aspects of self-efficacy are factors influencing the success of the mathematics learning process. This study aims to obtain an explanation of mathematical reasoning abilities based on gender differences in terms of mathematical self-efficacy. The sample of this research is a collection of scores of mathematical reasoning abilities, gender differences, and mathematical self-efficacy scores of XIth grade students from a high school in Bandung. The research sample consisted of 35 students, consisting of 19 male and 16 female students. The research instruments were tests of mathematical reasoning abilities (MRA), gender differences, and a mathematics self-efficacy (SEM) questionnaire. Data analysis was done using ANACOVA, with MRA in the form of interval scale, gender category scale, and SEM as covariate with interval scale. The results of the study were as follows: (1) there is a linear relationship between mathematical self-efficacy and mathematical reasoning ability; (2) there is no difference in students’ mathematical reasoning abilities based on gender differences. Furthermore, SEM students and gender differences have an influence on the MRA achieved by students. Keywords: gender differences, mathematical reasoning ability, mathematics self-efficacy

Understanding the Solution-Making Ability of Senior High School Students in Solving Photosynthesis Problems

This study further explains the errors made by senior high school students when trying to solve photosynthesis problems. The method used in this research is descriptive qualitative, involving a sample of four senior high school students. The study results will be discussed with Polya's problem-solving procedure, which includes understanding, planning, execution, and checking. Errors at the comprehension stage are in understanding the relationship between photons and photosynthetic light reactions and in drawing genealogies. Errors in the planning stage, in making wrong assumptions or inaccuracies in interpreting those derived from the understanding stage. In addition, this study found errors in identifying chemical reactions in photosynthesis and errors in mathematical reasoning competence. The conclusion of this study shows the failure in making photosynthesis problem-solving solutions due to the interaction between the problem-solving phase and the student's general competence.