Mathematical Thinking Research Articles

Interactive Learning: Unpacking the Influence of Computer Simulations on Students’ Mathematical Modeling Processes

Mathematical modeling and use of technology have been recognized as powerful vehicles for advancing mathematical thinking. The use of technology to aid students to gain understanding about real-world mathematical problems has long been a subject of inquiry. Using the extended Blum’s modeling cycle as the theoretical framework, this study explores how computer simulations influence fifth-grade students’ mathematical modeling processes. We investigated interpretations and perceptions of students regarding a situation model, and how these interpretations and perceptions changed as a result of exposure to the simulation. Observing students as they worked with three interactive computer simulations during task-based interviews, we found that animated graphics of the simulations helped the participants to visualize the problem and learn about the effect of different variables and their interactions on the outcomes of the simulations. Students explored simulation environments, ran simulations to observe outcomes of specific settings, and formed conjectures to describe the effect of simulation variables on the outcomes. Analyzing participants’ activities and movements along the extended Blum modeling cycle, we propose a three-stage learning model composed of “exploration and discovery”, “structured inquiry”, and “synthesizing”.

Balance Board Math: Exploring the Sense of Balance as a Basis for Functions and Graphing and Number Line Concepts

Can math concepts be experienced through the sensory modality of balance? Balance Board Math (BBM) is a set of pedagogical math activities designed to instantiate mathematical concepts through stimulation to the vestibular sense: an organ in the inner ear that detects our bodily balance and orientation. BBM establishes the different ways children spontaneously rock and move as the basis for inclusively exploring mathematical concepts together across diverse sensory profiles. I describe two activity sets where students explore focal concepts by shifting their balance on rockable balance boards: “the Balance Number Line,” using analog materials to foster understandings of the number line and negative numbers, and “Balance Graphing,” using sensors and a digital display to foster exploration of functions and graphing concepts, including the parameters of trigonometric functions and function addition. I outline proposed ways that engaging with concepts through balance-activating movement can change learners’ mathematical thinking and learning.

Lateral Thinking Ability Through Challenge-based Learning with Sparkol Videoscribe

Online learning during the Covid-19 pandemic was very interesting to observe because learning can be done anytime and anywhere. However, Covid-19 has an impact on the learning process in schools and students’ thinking abilities. The purpose of this paper is to analyze the differences in the improvement of mathematical lateral thinking skills between students who received challenge-based learning through sparkol videoscribe and those learning through WhatsApp. The research method used was a quasi-experimental, non-equivalent control group design. The sample was randomly selected from four parallel high school classes in the city of Bandung, namely class X 1 who learned through videoscribe sparkol and class X 3 who studied via WhatsApp. The instrument used is a test of mathematical lateral thinking ability and a test of prior mathematical knowledge. Data analysis was done using two-way ANOVA. Findings: A difference was observed in the achievement of mathematical lateral thinking skills between students who carry out learning through sparkol videoscribe better than those learning through WhatsApp based on prior knowledge of mathematics in the smart, medium, and low categories. Challenge-based learning sparkol videoscribe makes it easier for students to understand the material, the construction process, interaction, and reflection, thereby increasing the ability to think mathematically, laterally.
 Keywords: lateral thinking ability, challenge-based learning, sparkot videoscibe

Development of Motion Graphics Video Based on CPA Approach to Enhance Elementary Students' Mathematical Creative Thinking Ability

It is important to develop the creative thinking ability of elementary school students so they can tackle the challenges of today’s world. This skill can be enhanced through learning activities at school, particularly in subjects like mathematics. This study aimed to create motion graphics video teaching materials based on the CPA approach to help improve students’ creative thinking abilities. The 4-D model was used to develop these materials, which involves defining, designing, developing, and disseminating the materials. The experts used teaching materials assessment sheets and test items to evaluate the effectiveness of the materials. The results showed that mathematics teaching materials using motion graphics video teaching based on the CPA approach were successful in improving students’ creative thinking skills. These teaching materials can be used in elementary mathematics education and for further research purposes.
 Keywords: CPA approach, mathematical creative thinking ability, motion graphics video.

Research on Integrated Teaching of Mathematical Units from the Perspective of HPM

In recent years, unit holistic teaching has been continuously focused on as an effective way to implement core competencies. This teaching method takes a global perspective, organizes teaching content from a unit perspective with systematic thinking, and emphasizes the improvement of students' basic abilities and the development of core competencies. At the same time, teaching based on the history of mathematics is highly valued, HPM (History and Pedagogy of Mathematics) entered the mathematics classroom teaching. HPM teaching can transform science oriented mathematics into education oriented mathematics, thereby maximizing the educational value of the history of mathematics. HPM teaching coincides with unit teaching. This article conducts in-depth research on the overall teaching of mathematical units, sorts out the development of mathematical history, explores the historical background of mathematical knowledge, calculates the evolution process, and effectively integrates mathematical history resources into unit teaching design. The introduction of M-perspective can effectively enrich the content of mathematics teaching, enhance students' interest in learning, deepen their cognitive depth, and help cultivate students' innovative thinking ability in mathematics. Explore the overall teaching implementation strategy of mathematical units, propose corresponding teaching suggestions, and provide reference for mathematics educators.

Exploring transdisciplinary, technology-assisted, and architectural modelling STEAM practices through a cultural lens

In this paper, we propose novel transdisciplinary STEAM practices to enable students and teachers to model architecture using technology. Architectural modelling can foster students’ mathematical knowledge and computational thinking while connecting them to other disciplines such as culture and history. Our study focuses on enabling architectural, cultural, and historical diversity in educational practices. Moreover, the study tries to foster participants’ modelling skills and innovative technology use as augmented reality and 3D printing. Thus, this paper will describe three case studies from Austria, Libya, and Indonesia and how these STEAM practices were used in different ways to allow participants to express their diversities through modelling diverse architectural constructions cross-culturally. We followed a qualitative data analysis approach for the participants’ interviews, questionnaires and artefacts including architectural modelling, disciplines connections and lesson plans. The data analysis resulted in emerging themes emphasizing STEAM practices’ possibilities to connect architecture to culture and history and highlighting the participants’ cultural diversities in each of the three case studies.

Analysis Error Student in Solving Problem Logarithm Based on the Kastolan Procedure

Mathematics is very important in teaching students to have and apply mathematical thinking patterns in everyday life and become a reference for studying various other branches of science. One of the mathematics materials is logarithms, where students often make mistakes when solving these problems, so it can indicate how far students have mastered the logarithm material chosen for this research because logarithms have properties that students must understand. So, this research aims to analyze the errors made by students when solving logarithm problems using the Kastolan procedure. Subject in this study, nine students from class X IT SMKS, Darel Hikmah Pekanbaru. The research instrument used a 5-item logarithmic description test instrument. The data analysis techniques are data reduction, data presentation, and conclusion. Based on the research data results, it was concluded that students made conceptual errors, namely the inability to apply the concept of the properties used. Procedural errors were when students were unable to solve the problem until they got the final solution, and technical errors occurred because they made mistakes in calculations to produce answers wrong.

Pengembangan LKPD Matematika dengan Pendekatan Contextual Teaching and Learning Pada Kelas V SD

This research began by finding that students lack mathematical problem-solving, critical thinking, and curiosity skills, due to their difficulty applying mathematical principles in real-world situations. They have difficulty applying what they have learned in real life, thus limiting their ability to solve math difficulties. Learner Worksheets (LKPD) are not designed to allow learners to actively develop their own understanding. The purpose of this study is to develop authentic, practical, and successful LKPD using CTL (Contextual Teaching and Learning) approach to increase students' participation in problem solving in grade V elementary school. This research follows Plomp's development paradigm, which consists of three stages: initial investigation, prototype development, and assessment. The result of this research is a validated, practical, and effective mathematics LKPD with CTL method to be used in grade V elementary school

The Improvement of Students' Mathematical Critical Thinking Skills and Learning Motivation Through Contextual Teaching and Learning

This research aims to investigate the improvement of students' critical thinking skills and learning motivation using a problem-solving approach through Contextual Teaching and Learning (CTL) in the topic of statistics with the assistance of GeoGebra. This study employs a pre-experimental research design with a one-group pretest-posttest approach. The sample consists of one eighth-grade class in a public junior high school in Yogyakarta. Data collection techniques include pretests and posttests to measure students' critical thinking skills and a questionnaire to assess students' learning motivation. The paired sample t-test is utilized for data analysis. The results reveal an improvement in critical thinking skills, with an average pretest score of 49.33 and a posttest score of 85.00. Students' learning motivation also increased, with an average pretest score of 73.60 and a posttest score of 88.87. The t-test result shows a significance value of 0.000 < 0.05, indicating the rejection of the null hypothesis. This implies that there is a significant influence on students' critical thinking skills using a problem-solving approach through Contextual Teaching and Learning in the statistics subject, resulting in an enhancement of students' critical thinking skills

Analysis of Critical Mathematical Thinking Skills in Level 1 Cadets of Surabaya Maritime

Analysis of Critical Mathematical Thinking Skills in Level 1 Cadets of Surabaya Maritime

PENERAPAN PEMBELAJARAN INKUIRI DALAM MENINGKATKAN KEMAMPUAN BERPIKIR KRITIS MATEMATIS SISWA SMK

The research aims to be able to find out the applications of inquiry learning using exponential material which can improve the mathematical critical thinking skills of vocational school level students in Bekasi Regency. This research approach uses descriptive methods of analysis in testing and observing the improvement of the ability to think critically mathematically of learners, test instruments are used in the form of questions on students' mathematical critical thinking skills on exponent material. The results showed a percentage score of 100% for six students classified as "very critical"; 80% percentage for six students who fall into the critical category; 60% percentage for six students who fall into the less critical category; and a 40% rate for four students who fall into the non-critical category. It can be concluded that the inquiry-based learning model used to improve students' critical thinking is successful.

Using Mathematical Thinking in Solving Trigonometric Problems within Mason’s Cognitive Framework

The paper focuses on the synergy between mathematical thinking and solving trigonometric problems within Mason’s cognitive framework. It presents and analyzes concepts related to mathematical thinking, especially Mason’s definition of the thinking process into three stages: input, impact, and evaluation. Applying this framework to solving trigonometric equations, the paper illustrates how mathematical thinking can help approach problems in an organized and rigorous manner, while opening opportunities for creativity and exploration. Discussing mathematical thinking, the paper defines it as a creative process involving prediction, induction, interpretation, description, abstraction, and reasoning. Aligned with Mason’s definition of mathematical thinking, the paper describes how this thinking aids students in understanding complex structures and solving problems quickly and flexibly.

Improving Students' Creative Thinking Ability by Applying Project Based Learning in Mathematics Learning

This study aims to explore the impact of implementing Project Based Learning (PJBL) in improving students' creative thinking skills in mathematics learning at upper secondary schools. The research method used was a pre-test post-test control group experimental research design, which involved two groups of students: an experimental group that applied PJBL and a control group that received mathematics learning with conventional methods. The research instruments used were creative thinking ability test, observation, and interview. The results showed that students who engaged in mathematics learning with PJBL experienced a significant improvement in their creative thinking ability compared to students who followed conventional learning. In addition, interviews with students and teachers also showed that PPA provided a more interesting and relevant learning experience for students, and enabled the development of creative thinking skills effectively. These findings provide strong support for the use of PPA as an effective learning strategy in improving students' creative thinking ability in mathematics learning in the school environment.

Kategori Kemampuan Berpikir Kreatif Siswa dalam Menyelesaikan Soal Bunga Tunggal dan Majemuk

The research was conducted to categorize and describe the creative thinking ability of students of SMK Ma'wattaibin Banjarejo Pagelaran in solving mathematical problems on single flower and compound flower materials. The research involved 13 students of grade X with different abilities in the even semester because according to the material, single flower and compound flower were taught. The research method used was qualitative-descriptive. Written tests and interviews were used for data collection. Students were given a written test with 2 questions containing indicators of creative thinking skills. The results of the students' answers were analyzed based on indicators of creative thinking ability and then categorized based on the level of creative thinking ability (TKBK). The indicators of creative thinking ability used are fluency, flexibility and novelty. There are five levels of TKBK, including TKBK level 0 (not creative), level 1 (less creative), level 2 (moderately creative), level 3 (creative) and level 4 (very creative). Data analysis techniques include data reduction, data presentation and inference. Triangulation techniques were also used in this study. The results showed that there were 38% students in the uncreative category, 47% students in the less creative category, 15% students in the moderately creative category and no students in the creative and highly creative categories. Students at the uncreative level cannot fulfill any of the indicators of creative thinking ability. Students in the less creative level can only fulfill the fluency indicator according to their abilities. Students at the moderately creative level can only fulfill the flexibility indicator according to their abilities. Teachers need to train different mathematical problems that have different answers for students. This research is limited to categorizing and describing students' creative thinking skills, as further research can be carried out in relation to strategies to improve students' mathematical creative thinking skills.

Teaching Mathematics to Students with Hearing Loss Using Instructional Materials

Submission of an article implies that the work described has not been published previously except in Teaching mathematics to students with hearing loss requires special attention and care. Using materials in mathematics education is crucial in helping students concretize abstract concepts and relationships, create schemas related to the taught subject, understand the content, apply it, and develop mathematical thinking in a broader context. In mathematics classes for students with hearing loss, teachers often struggle to find ready-made materials suitable for the instructional content and the language, cognitive, and readiness levels of students with hearing loss. Teachers themselves need to prepare instructional materials for students with hearing loss. This study aims to identify and explain the types and characteristics of materials prepared and used by teachers in mathematics classes for 6th-grade students with hearing loss, and to highlight the contributions of these materials to the mathematics teaching process. Research data were collected through materials used in mathematics instruction, lesson plans and evaluations, the researcher's diary, and video recordings of lessons. The collected data were analyzed by using the content analysis method. As a result of the research, support and resources have been provided to teachers and instructional programs to create and use mathematics lesson materials suitable for students with hearing loss.

Emergence of Mathematical Thinking in a Community of Older Adults

Emergence of Mathematical Thinking in a Community of Older Adults

Mathematical Thinking and Problem Solving Performance: The Mediating Role of Hope

The purpose of the present study is to provide a mediation model by exploring the relationships among mathematical thinking, hope and problem solving performance in mathematics. The participants of the present study were composed of 311 preservice mathematics teachers. In this mixed method research, these preservice mathematics teachers were conducted to the scales of Dispositional Hope and Mathematical Thinking, and Problem Solving Test. Based on the quantitative data analysis, it was observed that statistically significant relationships among the variables of hope, mathematical thinking and problem solving performance. The quantitative data collected through these instruments were also analyzed by mediation analysis techniques. The qualitative data gathered through semi-structured interviews were analyzed by content analysis technique. These data encouraged the findings acquired from quantitative data analysis. The qualitative findings confirmed the findings of the mediator role of hope. The qualitative findings encouraged the relationships among the variables and the role of mediator.

A long-term shift to include students’ first language in the mathematics teaching practice: socialization events and learning opportunities

The notion of multilingual students’ first language has been advocated as a resource in mathematics learning for some time. However, few studies have investigated how implementing students’ L1 in the teaching practice impacts multilingual students’ mathematics learning opportunities. Based on a 9-month-long ethnographic study conducted in Iran, we investigate what a long-term shift from mathematics teaching in the language of instruction (Persian) to mathematics teaching that includes students’ first language (Turkish) may mean in terms of learning opportunities. In language positive classrooms, students’ socialization into mathematics and language includes using students’ first languages and paying explicit attention to different aspects of language use in mathematics. Among other things, socialization events provide possibilities to share explanations of mathematical thinking. The results of this study suggest that using students’ first languages may reinforce other language positive socialization events and provide mathematics learning opportunities during individual assignment activities. Furthermore, the results suggest that the conceived value of mathematics education in the local communities changed with the introduction of students’ L1 in the teaching practice. Consequently, this study indicates that using students’ first languages in mathematics classrooms may be a key issue in multilingual contexts.

Learning Achievement of Class-1 Learners in Foundational Literacy and Numeracy

On the curricular side, there is an increased focus on foundational literacy and numeracy. The specific focus generally is on reading, writing, speaking, counting, arithmetic, and mathematical thinking. It is highly focused throughout the preparatory and middle school curriculum, with a robust system of continuous formative/adaptive assessment to track the performance of the learners. Specific hours daily and regular events over the year-on activities involving these subjects will be dedicated to encourage and enthuse students. Teacher education and the early grade curriculum is on the ways to be redesigned to have a renewed emphasis on foundational literacy and numeracy. It is observed that in early years learners like to play, paint, sing, dance and question. If we encourage this likeness of the children through the play-based activities, the academic performance of the learners is increased. They love play together and work together. Our school activities must be accompanied by these activities to engross Foundational Literacy and Numeracy. In this research, the findings pertaining to the achievement of Class I learners in Language, Mathematics revealed that the early grade have performed very poor .The cause may be that students are not exposed different types of activities. time on task and continuous and comprehensive assessment may be one of the causes. However, the result coincides with the result found by the previous researchers on these areas .The researcher has done the comparative discussion among boys and girls students and found that in some competencies boys have done better and in some competencies, girls have done better.

Student Creativity in Developing Interactive Multimedia Using Kodular for Junior High School Mathematics Learning

This research is qualitative research that aimed to investigate the results of the development of learning media by students to improve school students' creative performance and students' creative thinking using the Kodular application. This study focuses on the problem of the lack of learning media at the junior high school level which is used as a means of independent learning for students at home. The subject was a class of The Department of Mathematics Education. The research subjects were 41 students in the department of mathematics education. data were taken using observation and documentation techniques that were adapted to mathematical creative thinking indicators. Interactive multimedia developed by students in the form of mathematical material presented in text form, containing equations, screenshots of graphics from the Desmos application, and video explanations of the material. Furthermore, practice questions and post-tests are presented using the help of Google Form, Quizziz, and Liveworksheets so that users get a direct response to the answers to the questions so that they meet the interactive characteristics of the learning media. The results obtained are 41 students are able to develop interactive multimedia that is run through an android application in junior high school mathematics learning. Creative thinking skills are achieved by using the dimensions of fluency, flexibility, and originality. This is achieved from media development carried out by students The creative performance of students reaches the usefulness dimension but has not been able to reach the novelty of the interactive multimedia that has been developed.