Mathematical Questions Research Articles

An artificial intelligence application in mathematics education: Evaluating ChatGPT’s academic achievement in a mathematics exam

The aim of the research is to investigate the academic achievement of ChatGPT, an artificial intelligence based chatbot, in a national mathematics exam. For this purpose, 3.5 and 4 versions of ChatGPT were asked mathematics questions in a national exam. The method of the research is a case study. In the research, 3.5 and 4 versions of ChatGPT were used as data collection tools. The answers given by both versions of ChatGPT were analyzed separately by three researchers. As a result of the analysis of the data, it was found that ChatGPT-4 was more successful in the exam compared to ChatGPT-3,5 version, was better at understanding the questions asked, understood the instructions better and included more details in the question solution, and at the same time, both versions made common and different mistakes. According to the findings of the study, it was concluded that ChatGPT sometimes worked very well, sometimes only worked well and sometimes failed. In the light of the findings of the study, it can be suggested to use ChatGPT versions in mathematics education to obtain basic information and to get supervised help.

Fostering Interest and Critical Thinking in Mathematics Education: The Role of Integrated Evaluation Based on Linktree Platform

Based on a survey conducted by the United Nations Educational, Scientific, and Cultural Organization (UNESCO), the interest in learning among students in Indonesia is still relatively low, ranking 64th out of 120 countries. In 2007, the Global Institute reported that only 5% of students could solve high-level problem-solving tasks. This study aims to assess student responses, learning interests, and mathematical problem-solving skills following the implementation of Linktree. Linktree is an e-learning platform that offers ease in managing information despite being HTML-based. Moreover, it integrates seamlessly with various media, offers multiple tools, and presents customizable interfaces. The research methodology was quantitative, with a sample of 30 eighth-grade students from Junior high school. Data were collected through five mathematical problem-solving essay questions and questionnaires assessing student responses and learning interests post-Linktree usage. Findings revealed positive student responses towards Linktree, particularly in number patterns, with an average percentage of 84%, indicating excellent feedback. Post-Linktree usage, students exhibited an average percentage of 78% across four indicators of learning interest, classified as good. The students improved their mathematical problem-solving skills, with an average N-gain score of 0.64 and an N-gain percentage of 64.37%, categorized as moderately effective. Linktree's contribution to students' learning interest and mathematical problem-solving skills was significant, as evidenced by the hypothesis testing results, with a determination of 0.776 or 77.6% for learning interest and 0.629 or 62.9% for problem-solving skills. In conclusion, Linktree significantly contributes to students' learning interests and mathematical problem-solving skills

Quality Of Algebra Questions to Measure Mathematical Literacy Ability Using Partial Credit Model

<span lang="EN">Mathematical literacy skills require someone to understand, analyze, interpret, evaluate and synthesize knowledge obtained from the problems faced by modeling them into appropriate solutions in solving a problem effectively. The need to develop questions according to students' daily problems can familiarize students with mathematical literacy. The research developed mathematical literacy test questions on the theme of tobacco farming in the Puger Jember area to measure students' mathematical literacy abilities at the high school level. The research method used is Research and Development (R&D) using the Thiagarajan model which is modified into three stages, namely definition, planning and development. Field trial results were analyzed using Ministep software with Rasch modeling using the Partial Credit Model (PCM) method. The results obtained from the ten questions that were developed can be said to be fit, with the reliability of 139 interactions between students and the question items, the quality is still poor, 75 students' interactions between students and the question items are of good quality. The item reliability of the literacy questions developed was 0.80 in the first 75 samples, 0.95 in the next 75 samples and 0.89 in the last 64 samples, indicating that the questions developed were good and able to measure students' abilities well.</span>

The rhizomic tiles at Shooter’s Hill: an application of Truchet tiles

We discuss patterns formed by terracotta tiles found on a housing terrasse in London, UK and note their relationship to Truchet tiles. We consider some of the mathematical questions that arise when combining the tiles into 2 × 2 arrays and their use in the creation of woven strips. In particular, we determine equivalence classes of patterns, and using graph theory and combinatorics we provide results regarding the number of woven strips that meet particular criteria.

INVESTIGATING THE METACOGNITION CALIBRATIONS AND MATHEMATICAL METACOGNITION AWARENESS OF 8TH GRADE STUDENTS; SKILL-BASED MATHEMATICS QUESTIONS

The purpose of this study is to examine the metacognitive awareness of eighth-grade students in mathematics and their metacognitive calibrations in skill-based mathematics questions from various variables, and to determine the relationship between these factors. A relational survey design is used in the study. The sample of the research consists of 303 female students, 217 male students, totaling 520 students who are in the eighth grade. Data were collected using the "Mathematical Metacognition Awareness Scale (MMAS)," the "Skill-Based Mathematics Questions Test (SMQT)," and the "Self-Evaluation Scale (SES)." In the research, the Cronbach's alpha reliability coefficient of MMAS is found to be .881. The discriminability indices of SMQT are above .34, and the item difficulty indices range from .28 to .88. Descriptive statistics, independent groups t-test, related and unrelated groups ANOVA, and multiple correlation techniques were used in the analysis of the data. In the results of the research, it was observed that students' genders significantly differentiated their mathematical metacognition awareness and biases, but did not differentiate their accuracy significantly. The socio-economic levels (SEL) of students were found to significantly affect their mathematical metacognition awareness but did not differentiate their metacognitive calibrations. The students' mathematics grades were found to significantly differentiate their mathematical metacognition awareness and metacognitive calibrations. There was no significant relationship between students' mathematical metacognition awareness and metacognitive calibrations. Another finding obtained from the study is that students tend to be better calibrated in medium and difficult mathematics questions compared to easy questions, and in difficult and easy questions, they tend to be excessively confident compared to medium difficulty questions.

Modelling and analysis of cAMP-induced mixed-mode oscillations in cortical neurons: Critical roles of HCN and M-type potassium channels.

Cyclic AMP controls neuronal ion channel activity. For example hyperpolarization-activated cyclic nucleotide-gated (HCN) and M-type K+ channels are activated by cAMP. These effects have been suggested to be involved in astrocyte control of neuronal activity, for example, by controlling the action potential firing frequency. In cortical neurons, cAMP can induce mixed-mode oscillations (MMOs) consisting of small-amplitude, subthreshold oscillations separating complete action potentials, which lowers the firing frequency greatly. We extend a model of neuronal activity by including HCN and M channels, and show that it can reproduce a series of experimental results under various conditions involving and inferring with cAMP-induced activation of HCN and M channels. In particular, we find that the model can exhibit MMOs as found experimentally, and argue that both HCN and M channels are crucial for reproducing these patterns. To understand how M and HCN channels contribute to produce MMOs, we exploit the fact that the model is a three-time scale dynamical system with one fast, two slow, and two super-slow variables. We show that the MMO mechanism does not rely on the super-slow dynamics of HCN and M channel gating variables, since the model is able to produce MMOs even when HCN and M channel activity is kept constant. In other words, the cAMP-induced increase in the average activity of HCN and M channels allows MMOs to be produced by the slow-fast subsystem alone. We show that the slow-fast subsystem MMOs are due to a folded node singularity, a geometrical structure well known to be involved in the generation of MMOs in slow-fast systems. Besides raising new mathematical questions for multiple-timescale systems, our work is a starting point for future research on how cAMP signalling, for example resulting from interactions between neurons and glial cells, affects neuronal activity via HCN and M channels.

Seeing mathematical learning opportunities in preschool situations: the role of teacher disposition and type of picture book

Pre-school teachers’ competence to see and decide to use learning opportunities in informal play-based situations (i.e. situation-specific skills) is key for high-quality pre-school instruction. Current insights into pre-school teachers’ situation-specific skills and their association with underlying teacher disposition and instructional materials are limited. We aimed to complement existing findings by systematically analysing pre-service and in-service pre-school teachers’ situation-specific skills in association with their underlying disposition and the type of instructional material in the domain of early mathematics. We assessed 274 pre-service and in-service pre-school teachers’ mathematical content and pedagogical content knowledge (MCK, MPCK), beliefs and situation-specific skills, operationalised as the mathematical questions they formulate during simulated shared picture book reading activities. Logistic multilevel regression analyses revealed a complex interplay between pre-service and in-service pre-school teachers’ disposition, the type of instructional material and situation-specific skills, pointing to the need for future studies on the topic.

Math items about real-world content lower test-scores of students from families with low socioeconomic status

In many countries, standardized math tests are important for achieving academic success. Here, we examine whether content of items, the story that explains a mathematical question, biases performance of low-SES students. In a large-scale cohort study of Trends in International Mathematics and Science Studies (TIMSS)—including data from 58 countries from students in grades 4 and 8 (N = 5501,165)—we examine whether item content that is more likely related to challenges for low-SES students (money, food, social relationships) improves their performance, compared with their average math performance. Results show that low-SES students scored lower on items with this specific content than expected based on an individual’s average performance. The effect sizes are substantial: on average, the chance to answer correctly is 18% lower. From a hidden talents approach, these results are unexpected. However, they align with other theoretical frameworks such as scarcity mindset, providing new insights for fair testing.

Cultivating Students’ Agency by Infusing Number Talks with Notice and Wonder

ABSTRACT Instructional routines, like Number Talks and Notice and Wonder, engage students in doing and then talking about their mathematical thinking. Number Talk routines are short mathematical discussions where students mentally solve and share the strategies they used to make sense of the problem. In comparison, the Notice and Wonder routine asks students to reflect on a high-interest visual prompt with multiple entry points, share their noticings and wonderings, and then the teacher steers the discussion toward a mathematical question to explore further. But what happens when the Notice and Wonder routine is used in conjunction with a Number Talk? In this descriptive case study, we analyze whether and how this variation of a Number Talk provides a class of third-grade students opportunities to exercise agency. Findings from this study yielded two major themes: 1) agency is built when authority is shared during a mathematical discussion, and 2) Notice and Wonder is an instructional routine that supports sharing authority. We then discuss why this matters and next steps for research and practice.

Analysis Of Junior High School Students' Mathematical Creative Thinking Ability Reviewed By Gender

This research is motivated by the importance of creative mathematical thinking skills for students studying mathematics. This study aims to analyze students' mathematical creative thinking skills in terms of gender. This study used a qualitative descriptive method. The population in this study was 20 grade IX students of SMP Negeri 2 Cimahi who were used as a sample, consisting of 10 male students and 10 female students who were randomly selected. The instrument used in this study is to provide four mathematical creative thinking questions consisting of indicators of fluency, flexibility, originality, and elaboration. The data in this study were analyzed using the value of the percentage of students who had done mathematical creative thinking problems that had been given and then compared based on gender. The results of the research that has been conducted revealed that overall, the ability of female students to think creatively mathematically is valued higher than the ability of male students to think creatively mathematically. This can be seen in terms of the proportion of overall value or certain aspects. Regarding fluency, male students score higher than female students, while female students score higher on flexibility, originality, and elaboration. It can be concluded that gender can affect students' ability to creative mathematical thinking skills.

Exploring students' proportional reasoning in mathematical literacy problem solving: recognition of multiplicative relationship strategies

Introduction. A multiplicative relationship represents the association between two or more variables in the form of multiplication. For example, when one variable increases, the other variable also escalates proportionally. Accordingly, it is important for students to have the ability to identify the pattern of multiplicative relationships, describe them in the form of equations or comparisons, and apply them in different situations. This study describes the strategies used by students in recognizing multiplicative relationships, particularly in solving mathematical literacy problems containing proportional situations. Study participants and methods. The research was conducted in three junior high schools located in Malang, Indonesia, involving 191 ninth-grade students. They were asked to work on a mathematical literacy question, and then their answer sheets were corrected and grouped based on the developmental stage of proportional reasoning, particularly in recognizing multiplicative relationships. Furthermore, the subjects were interviewed in-depth concerning their experience in solving literacy problems in proportional situations. This study used a qualitative approach with a phenomenological research type. the subject's experience was investigated holistically, along with the appearing phenomenon. The garnered data were interpreted through continuous reflection and analysis for a deeper understanding. The results were then summarized. Results. In this study, two variations of strategies have been identified being used by students at the stage of recognizing multiplicative relationships in solving mathematical literacy problems, namely the multiple strategies and the pattern strategy. This finding serves as a valuable contribution to understanding students' strategies and behaviors in recognizing multiplicative relationships, which has not been revealed in previous studies. The main difference between these two strategy variations lies in the approach used in solving the problem. The multiples strategy emphasizes the conceptual linking of quantity values between objects, relying on the conceptual shifts that transpire as students navigate through their additive reasoning steps within the framework of multiplication. In this case, students need to comprehend various number concepts and number relationships, with frequent focus on multiplication as a form of repeated addition. On the other hand, pattern strategies rely on students' ability to match patterns, use the arrangement of numbers constituting the pattern, and relate them to other patterns in solving problems. Practical significance. The results of this study serve as a crucial reference for more effective and efficient mathematics learning formulation for improving students' proportional reasoning.

Development of E-Module Based on Mathematical Literacy Skill in Statistical Materials

This research aims to produce an E-Module with math literacy-based questions that are valid and practical for 10th-grade statistics in SMA Negeri 3 Padang. The type of research conducted is development research using the ADDIE development model. Data analysis techniques include interview analysis, E-Module validation analysis, and E-Module practicality analysis. The results of the research show that mathematics learning using the E-Module, which facilitates mathematical literacy questions, is both valid and practical. Based on the data analysis, it was found that the developed E-Module had a validity score of 92.31%, categorized as highly valid. The final practicality score for teachers was 85%, categorized as highly practical, and the final practicality score for students was 88.26%, also categorized as highly practical.

Investigating the Philosophical View of Teaching Circles Theorem

Circle theorem was seen as the most challenging mathematics topic most students’ in Ghana run away from. During the WASCE, most students run away from answering mathematics questions that are in line with circle theorem. Such challenge has drawn the attention of mathematics teachers and researchers in mathematics education to find out the factors that drives students from attempting circle theorem question and the appropriate approach that can be used to teacher and to solve questions in circle theorem. The study aimed to investigate the philosophical view of teaching circle theorem. The literature review was based on ontological view of circle theorem, axiological view of circle theorem, and epistemological view of circle theorem. The study concluded that, the three philological view of mathematics has a unique significant effect on teaching and learning circle theorem.

Analysis of Students' Mathematical Creative Thinking Ability in Solving Open-Ended Questions Based on Their Self-Concept

To find out students' mathematical creative thinking abilities, this can be done by giving students open-ended problems. The aim of this research is to describe students' mathematical creative thinking abilities in solving open-ended problems when viewed from their self-concept. This type of research is qualitative descriptive research. The subject selection technique used in this research was purposive sampling. The subjects of this research consisted of one student with a high self-concept category, one student with a medium self-concept category, and one student with a low self-concept. Data collection methods in this research include questionnaire methods and tests. And the data analysis techniques used include: analysis of mathematical self-concept questionnaires, analysis of open-ended mathematics questions. The research results show that students with a high self-concept category can fulfill all aspects of creative thinking abilities, including fluency, flexibility and originality, so that their mathematical creative thinking abilities are also high. In contrast to students with moderate self-concept, it was found that their creative thinking abilities were low and students with low self-concept actually had moderate mathematical creative thinking abilities. So it can be concluded that based on this research, it shows that students' self-concept does not always describe students' mathematical creative thinking abilities in solving open-ended problems.

Analysis of Junior High School Students' Errors in Solving Mathematical Literacy Problems based on Newman Procedure Viewed from Students’ Learning Styles

This study aimed (1) to determine students' mathematical literacy skills viewed from learning styles; (2) to know and describe students' mistakes in solving mathematical literacy questions based on Newman procedure viewed from students' learning styles; and (3) to know the causes of students' mistakes in solving mathematical literacy questions based on Newman procedures viewed from learning styles. This research was a qualitative research with a case study type and used a descriptive approach. The subjects of this study were 53 students of class VIII, 11 Public Junior High School, Tegal, Indonesia. The data were collected using questionnaires, tests, and interviews, which were then analysed. The results showed that: (1) the students' learning styles were visual, auditory, kinesthetic, and auditory-kinesthetic; (2) visual learning style students have the best mathematical literacy skills because they reach the lowest level 3 and the highest level 4, whereas kinesthetic learning style students made the most mistakes; and (3) the causes of students' errors in solving mathematical literacy questions viewed from their learning styles tend to be the same, i.e.: students do not master patterns and sequence material, and students felt rushed when working on the questions.

Preschool teachers’ mathematical questions during shared picture book reading

Preschool teachers’ mathematical questions during shared picture book reading

Pengembangan Media Pembelajaran Teka-Teki Matematika Untuk Meningkatkan Pemahaman Konsep Matematis Siswa Pada Materi Perbandingan

Mathematical puzzles are learning media based on Android applications that aim to improve students' understanding of mathematical concepts, especially in comparative material. The development of this application is based on the teacher's lack of innovation in making learning media. The purpose of this application is to make new innovations related to the development of learning media called Mathematical Puzzles which are valid, practical, and effective for increasing students' understanding of mathematical concepts in comparative material. This type of research is research and development (Reasearch and Development). The subjects of this study were students of class VII MTs Nahdlatul Ulama Tengguli Jepara. The development model applied is the development model in this study, namely ADDIE. The data collection techniques applied in this study were product validation questionnaires, teacher and student practicality response questionnaires, student mathematical ability test questions, and student motivation questionnaires. The data analysis applied was media expert and material expert tests, practicality tests through teacher and student response questionnaires, and effectiveness tests through classical tests and influence tests. The results of this study indicate that the learning media for math puzzles to improve understanding of mathematical concepts meets valid criteria with a validity value of 3.27, practical with a practicality value of 3.56, and is effective with a classical completeness test score of 80% and an effect test with influential results.

Mental Comparison of Students Learning Abacus-Arithmetic and Not Learning Abacus-Arithmetic on Mathematics Material

Students' mental mastery in elementary school mathematics lessons in Indonesia is weak, slow, inaccurate, and declining. Mastery problems among elementary school students who have studied mental abacus arithmetic were found to be low. This is an urgent matter to research because there is a gap between theory, expectations, and reality. The purpose of this research was to compare the ability to solve mathematical problems between students who studied abacus mental arithmetic and students who did not study abacus mental arithmetic. This research involved 70 students. Data collection techniques using instruments, the instruments used were the first-semester mathematics exam and mental arithmetic exam. Data analysis techniques using SPSS Version 25.0 statistics, namely the t-test, were used to compare the ability to solve mathematical problems between students who studied mental abacus-arithmetic and students who did not study mental abacus-arithmetic. Pearson correlation was used to determine the relationship between students' mental arithmetic learning achievement and their ability to solve mathematical problems. The results of the research showed that there was a significant difference (p<0.05) in learning achievement on symbolic mathematics questions and mental arithmetic achievement between students who studied mental abacus calculation and students who did not study mental abacus calculation. The minimum score of the group that studied mental abacus calculation was higher compared to the group that did not study mental abacus calculation. However, there was no significant difference (p<0.05) in mathematics learning achievement between students who studied mental abacus-arithmetic and students who did not study mental abacus-arithmetic.

The Effect of the PBL Model on Learning Outcomes Viewed from Mathematical Communication Ability of Students

Teachers as educators need to apply various learning models in order to optimize student learning outcomes. In addition, teachers need to concern to the mathematical communication skills possessed by students. The purpose of this research was to analyze the effect of Problem Based Learning (PBL) model on Mathematics Learning Outcomes in terms of students' mathematical communication skills. This research is a quantitative research using experimental methods and using a factorial experiment design. The sampling technique used is purposive sampling technique. The instruments used in this research were questions on the test of mathematical communication ability and test questions on learning outcomes in the form of descriptions. Statistical analysis used the Friedman two way ANOVA test. The results showed that there was an effect between learning models and mathematical communication skills on student learning outcomes. Students who receive PBL learning have an average learning outcome higher than students who receive conventional learning. In addition, students had high mathematical communication skills get the highest average learning outcomes compared.

Development of a Software Package for Computing Psychometric Properties of Multiple Choice Tests Using Norm-Referenced Approach.

This work is on the development of a software package for computing the psychometric properties of multiple choice tests using norm-referenced approach. Focus was on item indices which are difficulty, discrimination and distracter indices. There are no easily affordable statistical packages in the Nigerian market for the computation of these indices. Most studies involving them have always been done manually due non-availability of affordable statistical software. Hence, the researcher was motivated to embark on this investigation. Three research questions were formulated to guide this study. Analysis of the existing system was done on BILOG-MG statistics. This study deployed the following methodologies: mathematical, structured systems analysis and design methodology (SSADM), the object-oriented analysis and design methodology (OOADM) and prototyping. The design for the study was instrumentation. The population for the study was 225 students which consisted of all the JS3 students of 2016/2017 session in Port Harcourt, Rivers State. The researcher made use of two instruments for the study. The first was the Rivers State Basic Education Certificate Examination (BECE), 2017 multiple choice questions in Mathematics. The second was a group of system software: HTML, PHP, JavaScript and MySQL. The responses of the students were used to test the effectiveness and efficiency of the software package developed in this study. Data analysis was done first with manual computation and second with the software package that was developed. The manual computation took the researcher 180 hours while the electronic computation with the developed software took only six hours to complete. The findings from the results of the study showed that the developed software was accurate in computing the difficulty, discrimination and distactor indices of the test items and it has a very high rate of accuracy. The study recommended that the developed software should be used to compute the difficulty, distractor and discrimination indices of multiple choice tests.