Mathematical Ideas Research Articles

Products From Building an Engineering Model for Stem Education Activity

The aim of this study is to examine whether the purpose of the Engineering Model Eliciting Activities (EngMEAs) are to be used as a tool to bridge engineering and school mathematics in the transition to STEM education. To this end, researchers have developed "Traffic Lights Problem", which has an interdisciplinary nature, working with mathematics teacher. This problem was applied to two groups of 3 and 4 students studying in the 7th grade in a city center in the eastern region of Turkey in the 2017-2018 academic year. In the process of solving the problem, the students used mathematics, science, technology and engineering knowledge in an integrated structure and introduced their own mathematical and scientific ideas and supported these ideas with in-group discussions and presented different models (products). The models of the students were different from each other because of students’ first exposure to such a process, different way of thoughts in the groups and inherent complexity of the modelling problems. In the light of the findings, it was concluded that the traffic lights modeling problem had an interdisciplinary nature, and this problem may have an important function for STEM education.

EKSPLORASI ETNOMATEMATIKA DALAM TRADISI PERNIKAHAN ADAT DAYAK KEBAHAN DI KECAMATAN BELIMBING KABUPATEN MELAWI

<em><span lang="EN-US">There is a relationship between cultural activities and education; this education applies to all subjects, one of which is mathematics. The relationship between mathematics and culture is called ethnomathematics. One of the cultural activities that has a relationship with mathematics is the traditional wedding tradition. Traditional wedding traditions are often carried out every year, and many people are interested in attending and witnessing the traditional wedding tradition taking place. Unbeknownst to the public, they have witnessed some mathematical activity. Many people still think that mathematics is something foreign and difficult, even though they just don't realize that so far every activity they have done has mathematics in it. In order to raise awareness of the role of mathematics in everyday life, a study of ethnomathematical activities and mathematical ideas embedded in the Dayak Kebahan traditional wedding ritual has been conducted. This study employed an ethnographic approach and a qualitative research methodology. by observing and interviewing two people as research subjects to get research results that are in accordance with the existing problem formulation. The results of the research show that there are ethnomathematical activities and mathematical concepts in the traditional Dayak Kebahan wedding tradition.</span></em>

Why Mathematics at the High School Level Evolved to Include Linguistics

This article foregrounds the fundamental role that language can play in communicating mathematical ideas and contexts. The findings from this article contribute to an understanding of different ways textbook series with particular orientations make opportunities available for students to develop forms of agency and autonomy during classroom learning. The article also contributes methodology for analyzing mathematical texts of different genres.

Exploration of Prospective Mathematics Teachers’ Mathematical Connections When Solving the Integral Calculus Problems Based on Prior Knowledge

<p style="text-align:justify">Mathematical connection ability is very important to be mastered by prospective mathematics teacher students as competency to teach in secondary schools. However, the facts show that there are still many students who have weak mathematical connection abilities. This qualitative descriptive study aimed to explore how the process, and product of the mathematical connection made by prospective mathematics teacher students when solving the integral calculus problems based on their prior knowledge. The research subjects were 58 students who were prospective high school mathematics teachers at the University of Jember, Indonesia. Data were collected using documentation, questionnaire, test, and interview methods. After the test results of all subjects were analyzed, six students were interviewed. To find the match between the results of the written test and the results of the interview, a triangulation method was carried out. Data analysis used descriptive qualitative analysis with steps of data categorization, data presentation, interpretation, and making conclusions. The results show that the research subjects have connected and used mathematical ideas in the form of procedures, facts, concepts/principles, and representations in solving integral calculus problems. Students with high prior knowledge abilities can make better mathematical connections than students with moderate and low prior abilities. From these results, it is recommended that lecturers need to improve students' prior knowledge and train the students more intensely to solve integral calculus problems so all students can develop their mathematical connection abilities into very strong categories.</p>

Developing Awareness Around Language Practices in the Elementary Bilingual Mathematics Classroom

This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-onone interview and of the circulating portion of a mathematics class from a secondgrade classroom. We use these examples to foreground instructional practices, forresearchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal manipulation to a more academically ample discussion of perspectives that investigate critically both mathematical concepts and their modes of transmission, which involve language practices, that are crucial for educating bilingual children.

Student Mathematical Communication in Online Discussion in Introduction to Geometry Course using Edmodo

Mathematical communication is an important part in learning mathematics. Mathematical communication is a way for students to express mathematical ideas either orally, in writing, pictures, diagrams, using objects, presenting in algebraic form, or using mathematical symbols. Through mathematical communication, students can convey ideas and clarify understanding and knowledge during the mathematics learning process. Mathematical communication skills are important because in learning mathematics, the use of notation, symbols, formulas and terms is a determining factor in problem solving. Due to the pandemic, learning activities are carried out online through Edmodo. This may bring changes to students' mathematical communication when doing a discussion. For this reason, this research aims to describe students' mathematical communication during discussion session in the Introduction to Geometry course through Edmodo. This research is a qualitative descriptive research. The subjects of this research were 35 students of first semester mathematics education who were taking the Introduction to Geometry course. The results showed that in doing a discussion, the students used written, visual, and symbolic mathematical communication. In expressing their opinion, students can also use more than one type of mathematical communication. In addition, the opinions expressed in the discussion were at various cognitive levels.

Can Mathematical Modelling Be Taught and Learned in Primary Mathematics Classrooms: A Systematic Review of Empirical Studies

STEM education has been promoted in schools worldwide to cultivate students’ 21st-century skills. Mathematical modelling is a valuable method for developing STEM education. However, in this respect, more attention is given to secondary level or above compared with kindergarten or primary level. Teaching mathematics at the primary level is closely related to authentic problems, which is a crucial characteristic of mathematical modelling activities. After screening 239 publications from various databases, we reviewed 10 empirical studies on mathematical modelling at the primary level. In this systematic review, we analysed the following three aspects: (1) the use of professional development intervention methods/strategies to enhance the intervention effects and the competencies of primary teachers to utilize mathematical modelling; (2) the effects of mathematical modelling on primary students and methods of improving their mathematical modelling skills; and (3) methods used to assess the modelling skills of primary school teachers and students. The results indicate that professional development interventions can enhance the teaching quality of mathematical modelling. The components of the interventions should include an introduction to the pedagogy of mathematical modelling, clarifying the role of the teacher and the student in mathematical modelling activities. Through mathematical modelling, students can generate mathematical ideas, explore mathematical theorems independently, develop critical thinking, and improve their metacognitive and communicative skills. The competency of mathematical modelling is often determined using formative assessments of teachers and students. Because limitations still exist in conducting primary-level modelling activities, schools should utilise more standardised assessment methods, provide universal teacher training, and grant more opportunities for primary school students to participate in mathematical modelling activities. The lack of research on cross-cultural contexts should draw the attention of future research.

MOODLE-BASED LEARNING MEDIA DEVELOPMENT OF FLEX MODEL IN IMPROVING MATHEMATICAL HARD SKILLS OF HIGH SCHOOL STUDENTS

The development of the flex media model looks like the beginning of the problems in the classroom, especially in the new normal. Students experience difficulties when given math problems. Students are less able to solve these problems, especially in understanding justifying mathematical ideas and arithmetic skills, and are less interested and enthusiastic when learning. This study aimed to develop a Moodle-based flex model learning media to improve students' mathematical hard skills with three-dimensional material. The study was used to research and develop the four-D model. The instruments used included validation, questionnaires, pre, and post-test questions, small-scale trials of 10 students, and large-scale trials with a purposive sampling technique of 30 class XII students. Data collection techniques include (1) validation questionnaires of media and material experts, (2) practicality questionnaires (student responses), and (3) pre-posttest questions. Material and media expert validator test with very decent results. The results of the student response questionnaire were reasonably practical regarding statements related to the practicality of the Moodle-based flex model media. The N-gain average score indicated a "moderate" improvement category. Based on the study results, the developed media meets valid, practical, and effective criteria for improving students' hard skills

Autism spectrum disorder and shared creativity in mathematics: breaking the stigma of limitation in order to bring out potentialities

It was analyzed how the processes involved in shared creativity in mathematics of an 11-year-old student with Autism Spectrum Disorder take place in interactions with peers at the same age. This study aimed to understand how subjects with this condition can generate mathematical ideas when doing collective work, helping peers and getting their help. Based on a qualitative approach, a math creativity test was used as a data collection instrument, and students were invited to respond to it and come up with open problems. Interviews and interactions were recorded, transcribed and, later, treated by using content analysis. Seventeen initial categories were found in which the creative production process occurred in the reality studied, and they were grouped into 4 intermediate categories: a) Personal traits, b) Favorable traits to shared creativity in mathematics, c) Production of ideas, d) Improvement of peers’ ideas. In turn, these were allocated to final categories: a) How an autistic person collaborates in the production of ideas, and b) How an autistic person receives collaboration in the production of ideas. Based on the findings, it was concluded that the performance of the autistic student, with his particular conditions, made the mathematical idea sharing process a phenomenon with many possibilities.

Transforming dis-embodied mathematical representations into embodied representations, and vice versa: a two-way mechanism for understanding mathematics

Since formal mathematics is discussed in terms of abstract symbols, many students face difficulties to acquire a clear understanding of mathematical concepts and ideas. Transforming abstract or dis-embodied representations of mathematical concepts and ideas into embodied representations is a strategy to make mathematics more tangible and understandable. This representational transformation allows us to actively employ our sensorimotor resources in the process of mathematical understanding. However, a one-way transformation of dis-embodied mathematical representations into embodied representations cannot always be the best strategy to understand mathematics. In order to omit or suppress contextually irrelevant information, we may need to transform an embodied representation into the dis-embodied representation. In other words, a dynamic mechanism in which the individual shifts between the two types of representational transformation could be the best way to acquire a better understanding of mathematical concepts/ideas and solve mathematical problems.

ANALISIS KEMAMPUAN KOMUNIKASI MATEMATIS DITINJAU DARI MOTIVASI BELAJAR MATEMATIKA PADA SISWA KELAS VIII D SMP N. 2 CAMPALAGIAN

This study is descriptively qualitative and aims to analyze the ability of mathematical communication related to the motivation to study mathematics in class VIII D of SMP Negeri2 Campalagian. Of the 29 students who completed the diagnostic test, 6 showed high levels of mathematical communication skills, 9 showed moderate mathematical communication skills, and 12 showed low levels of mathematical communication skills. rice field. It was reduced from 29 students to 6 students, with talking subjects each covering the mathematical communication skills of low, middle and high level students. In this study, mathematical communication skills tests and interviews were used to obtain the desired results. The results of this study only met 3-4 indicators of mathematical communication, but intermediate level mathematical communication skills, the ability to connect jasmani mathematical ideas, students who failed to meet everyday events. It was the ability of. Express using mathematical symbols when presenting ideas. Achieve high level communication skills, ability to explain math sentences, ideas, everyday situations, math relationships with sentences and photos: Students who meet all the indicators of math communication adjusbility.

The Implementation of Realistic Mathematics Learning in School (Phenomenological Study at State Junior High School 1 Manokwari)

This research method is a phenomenological study to describe the implementation of realistic mathematics learning in State Junior High School 1 Manokwari and to test the construction of mathematics teachers' perceptions of the meaning of realistic mathematics learning. This study uses observation, interview, and recording techniques to explore perceptions and implementations of realistic mathematics learning. The results showed that mathematics teachers at State Junior High School 1 Manokwari carried out realistic mathematics learning in a different way of perception. There is a tendency to apply the principles of realistic mathematics learning, using contextual questions that students can see, experience, or imagine to implement realistic mathematics learning in the classroom. In addition, another tendency is that teachers do not understand the concept of realistic mathematics learning, as evidenced by the lack of use of demonstration methods as motivational triggers in realizing students' mathematical ideas and concepts. Mathematics teachers need to be aware of themselves as facilitators of student learning because they build formal knowledge in a holistic and sustainable manner. This research shows that perception has a strong influence on certain decisions or actions.

Students’ problem-solving ability in solving algebra tasks using the context of Palembang

This descriptive research aimed to know students' problem-solving ability in arithmetic operations on algebra forms through an Indonesian realistic mathematics education, namely Pendidikan Matematika Realistik Indonesia (PMRI), approach in secondary school number 17 Palembang. The learning process, material, and assessment used were principles and characteristics of PMRI. The data collection technique was done by two students' activities and the written test to measure students' problem-solving abilities. The written test, which referred to the indicators of problem-solving ability, was given after the learning process. This study's findings indicate that Palembang's context helps students comprehend algebraic arithmetic operations. The principles and characteristics of PMRI play an essential role in enhancing students' problem-solving skills. To conclude, students develop and solve problems by modeling based on their mathematical ideas. In addition, students must be able to develop problem-solving strategies in which they employ a variety of procedures.

The Role of Interactive Features within a Mathematics Storybook in Interpreting a Conflict and Conflict Resolution: The Case of Three Fifth Graders

Students often experience cognitive conflicts when trying to interpret negative numbers’ order and values because they do not correspond to their prior whole number knowledge. One way to trigger students’ cognitive conflicts and support their conflict resolution meaningfully is through stories. Thus, I used a temperature-related mathematics storybook—Temperature Turmoil—to highlight the cognitive conflict students often experience because of relying on the integers’ absolute value and introduce conflict resolution (i.e., integers have both absolute value and directed value). By incorporating interactive features, I used a multiple-case approach to describe three fifth graders’ cognitive conflict and conflict resolution experiences. Harry, Lola, and Claire were engaged in control, interactive language, and interactive visual version of the storybook, respectively. I analyzed their responses to integer order and value questions on the pretest, session tests, and posttest as well as retellings to characterize the extent of their conflict and conflict resolution. All three benefited from the storybook with Lola making the most growth and using the mathematical language in her retellings more often. Harry, more accurately than others, described the mathematical ideas of the storybook in his retellings. Claire did not make large progress because of misinterpreting the language used in the integer values questions. This paper provides implications for how to make use of students’ common conflicts to facilitate their learning, which adds to the current understanding of using cognitive conflict as a teaching strategy. Further, the findings contribute to underdeveloped research on the benefits and limitations of interactive mathematics storybooks.

Mathematical Communication Skills in Terms of Student Learning Motivation on ARCS Model with Immediate Feedback

This research objective is to describe mathematical communicarion skill through ARCS- IF Model based on learners motivation. Type of this research is Mixed Method with concurrent embedded designs. This research population was Eight grader of SMP Maarif Kyai Gading Demak 2020/ 2021. Result of this research showed that ARCS- IF learning is effective in learners mathematical communication skill. Result of learners description with high learners motivation categories were able to complete mathematical communication skill with the indicator ability to express mathematical idea to write and convey them visually. Ability in stating idea or situation of problem into mathematical models (pictures, graphs, diagrams, tables and equations), ability to use right formulas in solving problems, students with motivation categories students are being able to complete communication skills mathematical with indicators Motivation learners were Ability to express mathematical ideas in writing and express them visually, Ability to use right formula to solve problems, students with low motivation categories were able to complete mathematical communication skills with Low Motivation indicators Ability to express mathematical idea to write and convey them visually.

REALISTIC MATHEMATIC EDUCATION ON HIGHER-ORDER THINKING SKILL MATHEMATICS OF STUDENTS

The literature on the effect of the Realistic Mathematics Education (RME) approach on high-order thinking skills (HOTS) students is massive. There is a diversity of research results. So a systematic and comprehensive review is needed to justify and describe its effect, which includes problem-solving, critical, creative, and reasoning abilities. This research used a systematic literature review (SLR) technique to search the Semantic Scholar, ERIC, Google Scholar database, and direct URLs from 2013 to 2022, yielding 49 studies that matched the inclusion criteria. Every paper was recorded and then categorized for analysis based on the title, education level, year of publication, sample size, and kind of HOTS. The findings indicated that RME positively impacted students' HOTS when learning activities were applied with student-centered, contextual problems, and the teacher was the facilitator. Working together in small groups allowed students to carry out individual exploration activities, reconstruct concepts from their own experiences, and connect these concepts to the mathematical ideas studied. RME thus becomes appropriate for use in achieving learning's aims and urgency, particularly in raising students' mathematical HOTS. The study's findings also offer information on the trends and heterogeneity of research into applying RME on mathematical HOTS in Indonesia. It is thus anticipated that it will serve as a recommendation and a focus for further study.

The efficacy of a four-stage learning model incorporating ACODESA method and mind map in fostering students’ mathematical communication skills: A data report

Learning mathematics equips students with the necessary competencies, and mathematical communication abilities allow them to discuss and exchange mathematical ideas with others. Correspondingly, research is needed into ways to help students develop these skills. These data were collected from 87 students in grade 10 at An Nhon Tay High School in the Cu Chi neighborhood of Ho Chi Minh City, Vietnam. These students took part in a quasi-experimental study whose goal was to determine how a four-step learning model that included activities using the ACODESA method and mind maps affected the student’s ability to communicate mathematically. In the experimental group, students were taught using the learning mentioned above model, while those in the control group received traditional instruction. To determine the efficacy of this teaching strategy, a quasi-experiment that included a pre-test, a treatment, and a post-test was designed and carried out. The student’s development in mathematical and linguistic activities was evaluated using both quantitative and qualitative analyses of the data that was gathered. Data gathered may shed light on how effective the learning model is in helping high school students enhance their mathematical communication skills. Also, the pre-test and post-test items from the supplementary data files can be a starting point for creating new learning tasks to evaluate students’ mathematical communication abilities.

Coding Dancing Figural Animations: Mathematical Meaning-Making Through Transitions Within and Beyond a Digital Resource

We investigate three 8th-grade students’ mathematical meanings developed in the context of using linked representations to generate animations of figural models tuned in musical rhythm in “MaLT2,” a programmable Turtle Geometry in 3D resource affording dynamic manipulation of variable values. We adopted a modified version of the UDGS (Using, Discriminating, Generalizing, Synthesizing) model, introduced by Hoyles and Noss in 1987, in order to frame and analyze students’ mathematical meaning-making process involving setting out goals; posing conjectures; using mathematical ideas to test them; and exploring, generalizing, and expanding these ideas. This dynamic process was contextualized and connected to a flow of two different types of transitions: (1) transitions within the different representations of MaLT2 and (2) transitions beyond MaLT2, among the representational contexts of the digital microworld, artistic ideas, and abstract mathematics. In our analysis, we use this theoretical concept to trace the kind of mathematical meanings connected to multidisciplinary notions embedded in dance and music, such as synchronicity, symmetry, periodicity, and harmony, emerging from this learning context. We also look into the way these mathematical meanings were gradually evolved from being implicitly integrated in digital and artistic ideas to being reflected on and generalized.

Using mathematical ideas from carpet and carpet-weavers as a context for designing mathematics tasks

In this study, the mathematics of carpet will be introduced by presenting the lifestyle of two expert carpet-weavers from Kerman, Iran, who work for many years in carpet-weaving activities through an explanation of carpet weavers’ culture. This explanation reveals that carpet weavers can do mathematics and solve related real-world problems without academic education in mathematics according to their needs through practical activities. The main purpose of this study is to investigate the mathematical ideas in the art of carpet weavers, and the ethnography approach is used as a methodological framework. Our findings showed that there are many mathematical concepts in the carpet weaving process, such as mirror axes, parallel and diagonal lines, geometric shapes, ratio, and measurement which can be used as context for developing enrich and meaningful mathematical tasks.

ENHANCING THE PROBLEM-SOLVING AND CRITICAL THINKING SKILLS OF STUDENTS USING THE MATHEMATICAL INVESTIGATION APPROACH

The interest in understanding what is involved in doing mathematical investigations brought together several researchers and classroom teachers. In this paper, the proponent decided to set up a project to experiment with tasks involving students exploring and investigating mathematical ideas, concepts, and processes. The work includes producing, experimenting, and evaluating such tasks and studying the competencies needed for using them successfully in the mathematics classroom. This study aimed to describe the attitude and performance of the students when exposed to investigative tasks. It is also driven to compare the performance of the control and experimental groups in relation to the implementation of the intervention and to see whether their attitude towards math investigation matters in the students' problem-solving and critical thinking skills. 
 The findings showed that on the attitudes, the experimental group has a very favorable attitude toward the process of doing the investigation in spite of its complexity particularly in giving proof. The data obtained claimed that the control group did meet the expectations for both tests while the experimental post-test presented a very satisfactory performance indicating that their exposure to investigations taught them to explore and provide absolute mathematical reasoning. A significant difference was found in the performance of the two groups making the experimental group better than the control group as reaffirmed in the effect size of large. Further, students’ attitudes on the implementation of math investigation are described as a predictor of successful problem solving and improving the critical thinking skills of the students.