Mathematics Education Approach Research Articles

Mathematical understanding (hermeneutic aspects of educational activities)

The article discusses the issues of mathematical understanding as an educational practice of identifying the algorithmic meanings of mathematical (mathematized) educational texts. The hermeneutic orientation towards following the “guiding thread of language” (G.-G. Gadamer), as it is shown, cannot be narrowed to the attitude towards natural languages inherent in humanitarian educational practices. The “common place” of mathematical understanding in educational practices is: some of created languages (of scientific communication) being consolidated around the mathematical installation are not reducible to its sign universality or educational generalizations. But it often turns out to be outside the field of view of practicing teachers, in a didactically abstract position. The article substantiates the possibility of rehabilitating the hermeneutic attitude in mathematical education in connection with its development and strengthening in understanding the prerequisites for the algorithmic solution of mathematical problems (the need for additional information, non-standard solution techniques, transfer of educational goal setting to the area of interdisciplinary relationships or life experience, etc.). The author shows and comments on the effectiveness of the hermeneutic approach in mathematics education using examples of solving problems in algebra, geometry and in constructing mathematical models of various physical processes.

Understanding the onto-semiotic approach in mathematics education through the lens of the cultural historical activity theory

AbstractResearch in mathematics education can be understood as a system of activities addressing the basic and applied problems related to teaching and learning of mathematics. Such a system includes the activities of foundation, planning, implementation, evaluation of mathematics instruction, and teacher professional development, which are supported by different theories. This diversity of theories raises interest in their comparison, coordination, and possible integration. The paper aims to present a case of application of the Cultural Historical Activity Theory (CHAT), in its 3rd and 4th generation versions, to analyze the emergence of the Onto-semiotic Approach to mathematical knowledge and instruction as a theoretical framework that addresses the study of the five partial activities mentioned above. This use of the CHAT can be useful in studies on theory articulation by focusing not only on the subjects, the object, and the instruments but also on the community context, the ecological-normative environment in which these activities take place, and the dilemmas or contradictions between theories.

English Speaking Teaching Strategies Based on Natural Language Processing

The study of cognitive processes in English teaching methods from the perspective of HPM (History and Pedagogy of Mathematics) provides valuable insights into how students learn and understand the English language. Cognitive research in language learning focuses on the mental processes involved in acquiring, processing, and using language skills. By incorporating the principles of HPM, which examines the historical development and pedagogical approaches in mathematics education, researchers can draw parallels and apply similar methodologies to English language instruction. This paper constructed Bloom’s taxonomy Fuzzy Decision Support System (BTF-DSS). Bloom’s taxonomy provides information about the teacher’s understanding towards the teaching. Through BTF-DSS model offers teachers provides the knowledge and expertise for effective teaching with the fuzzy model. The BTF-DSS model uses the fuzzy logic decision support system for the appropriate significant teaching and learning experience. The simulation analysis of the BTF-DSS model expressed that the fuzzy model exhibits significant performance for the English teaching method in China through the HPM process.

신문 기사에 나타난 유아 수학에 대한 인식연구

Objectives In this study, the changes in interest and key words by period related to early childhood mathematics appeared in newspaper articles from January 1, 1990 to December 31, 2020 were examined.
 Methods For this purpose, 7,789 articles related to early childhood education were collected through ‘Big Kinds (www.bigKinds.or.kr)’. and 230 articles related to mathematics for earlychildhood were analyzed using buzz anal-ysis and topic modeling techniques.
 Results First, articles on early childhood education increased abou 13.7 times in the 3rd term compared to the 1st term, and articles related to early childhood mathematics increased 24 times in the 3rd term compared to the 1st term. As a result, it was confirmed that social interest in early childhood mathematics increased significantly. Secondly, the results of topic analysis by period: 1st period - ‘Early entry into elementary school’, ‘Establishment of early childhood public education’, 2nd period - ‘Early private education’, ‘Mathematics education approach’, 3rd period - ‘Mathematics and language’ ‘Relationship between mathematics’, ‘Mathematics education program’, and ‘Connectivity between mathematics and gifted education’ were selected as the main themes.
 Conclusions Through this, it was confirmed that social issues regarding early childhood mathematics changed by time, and there was a slight difference from social interest and research trends in academia.

Application of Embodied Learning in Middle School Mathematics Education

This paper explores the application of embodied learning as a pedagogical approach in mathematics education for middle school students. The main body of the paper is organized into three essential sections. Firstly, practical strategies for implementing embodied learning are discussed. These strategies encompass teaching through body movements, employing hands-on materials, and integrating technology such as virtual reality, augmented reality, and interactive manipulatives. Secondly, the challenges and limitations faced in the context of embodied learning are examined. These include the resistance of teachers lacking professional training, the scarcity of effective teaching resources, and limitations pertaining to interactivity and student participation. Lastly, the paper emphasizes the implementation of embodied learning in the middle school mathematics curriculum. Specifically, it highlights the integration of embodied learning into lesson plans and activities, considerations for effective classroom management and instruction, and the significance of providing professional development and support for teachers. Overall, this paper provides valuable insights into the potential benefits and considerations associated with the incorporation of embodied learning in middle school mathematics education. By presenting practical strategies, addressing challenges, and emphasizing the importance of proper implementation, the paper contributes to the existing body of knowledge on this innovative pedagogy.

Meta-Aggregation: Methodological Guidance and Lessons Learned on an Approach to Qualitative Synthesis for Mathematics Education Research

In this Research Commentary, we address a call to translate qualitative educational research into practice by highlighting the potential of the qualitative synthesis methodology, which thus far has had limited guidelines and exemplars in mathematics education research. We contribute methodological guidance on one qualitative synthesis approach, meta-aggregation, by sharing experiences and lessons learned from using this approach in mathematics education. We discuss how and why researchers can normalize the use of this synthesis approach to influence policies and practices in mathematics teaching and learning. By sharing our experiences and insights on meta-aggregation components, we aim to support and motivate future development and application of qualitative synthesis in mathematics education research.

Adversity quotient of Indonesian prospective mathematics teachers in solving geometry higher-order thinking skills problems

Comprehending and formulating strategies for geometry problems that require higher-order thinking skills (HOTS) is crucial in enhancing mathematics education. This study implements a qualitative case study approach to comprehend how prospective mathematics teachers with varying Adversity Quotients (AQ) solve geometry Higher-Order Thinking Skill (HOTS) problems. We selected 3 participants from 167 Indonesian prospective mathematics teachers to solve the three- and two-dimensional HOTS problems and were invited to an interview session. The three participants represent three types of participants: a climber student (high AQ), a camper student (medium AQ), and a quitter student (low AQ). Our findings show that each student had different responses to deal with the obstacles they faced while solving the problem. The climber student is more adept at solving problems than the camper and quitter students. In addition to identifying specific implications, this study offers a comprehensive understanding of AQ's significant role in solving mathematical problems. This knowledge serves as a concrete foundation for guiding the future advancement of curricula, assessment methods, and instructional approaches in mathematics education, particularly in the field of geometry. This research contributes to enhancing educational practices and policies on a broader scale.

A pedagogical reflection on the interplay between variation and invariant: Variational thinking

This commentary paper is a pedagogical reflection on the interplay between variation and invariant. It begins with a brief discussion on the concept of Unity of Opposites as an ancient philosophical theme. Ancient thinking systems regarded the variation and invariant pair as a Unity of Opposites. Next, the use of variation as a pedagogical approach in mathematics education is briefly examined under Marton's variational theory of learning, Gu's bianshi jiaoxue, and the related research done by the author in the context of Dynamic Geometry Environment (DGE). These lead to the formation of the concept of variational thinking, the main contribution of this paper, which is presented and explained. A DGE task design sequence example is presented to illustrate how variational thinking can be used to frame a process of geometrical reasoning and argumentation.

A Review of Pedagogical Approaches for Improved Engagement and Learning Outcomes in Mathematics

The traditional, lecture-based teaching approach in mathematics education has tended towards being a more standardized and passive learning environment, often failing to cater to diverse learning styles and needs. The consequence of this approach is the lack of engagement and understanding among students, a phenomenon prevalent in many classrooms worldwide. Indeed, student disengagement and a lack of critical thinking skills in mathematics are major concerns. Innovative pedagogical methodologies, such as Inquiry-Based Learning (IBL), Collaborative Learning, and the Flipped Classroom Model, have emerged as potential remedies to this issue. Still, their implementation faces challenges related to teacher preparation, technology dependence, and individual motivation. Despite these challenges, these methods have demonstrated significant potential to improve student outcomes. Evidence suggests IBL fosters critical thinking, collaborative learning enhances interpersonal skills, and the flipped classroom approach promotes personalized instruction and increased engagement. Improvements in student test scores ranging from 5% to 30% have been reported across different studies employing these innovative teaching methods. These methods have profound effects despite minimal funding. Combining these strategies, tailored to cater to diverse student needs, can create an effective and efficient learning environment. It can foster a deeper understanding and enjoyment of mathematics, thereby stimulating greater engagement and overall improved learning outcomes.

Peer Tutoring Learning Strategies in Mathematics Subjects: Systematic Literature Review

<p style="margin-left:-5pt; text-align:justify">The peer tutoring approach is a student-cantered teaching method in which students learn in pairs with teacher supervision. The study discussed in this paper is a systematic literature review related to the effectiveness of peer tutoring approaches which has been published within the last 5 years. A complete text analysis was conducted using 20 research papers stating the impact of the peer mentoring approach for this writing. Among the things obtained from previous studies are the variety of ways to implement peer tutoring approach, the impact on 3 aspects in students which are mathematical achievement, social skills and cognitive skills and the teaching theories used. The findings of the study indicate that most past studies used quantitative research methods with the concept of age peer approach. Then, constructivism theory was the most frequently applied with a sample of high school students. In conclusion, this systematic literature review shows that the peer tutoring approach in mathematics education has many benefits in various aspects and needs to be extended to improve the quality of education.</p>

On the relationship between school mathematics and university mathematics: a comparison of three approaches

This paper examines how different approaches in mathematics education conceptualise the relationship between school mathematics and university mathematics. The approaches considered here include: (a) Klein’s elementary mathematics from a higher standpoint; (b) Shulman’s transformation of disciplinary subject matter into subject matter for teaching; and (c) Chevallard’s didactic transposition of scholarly knowledge into knowledge to be taught. Similarities and contrasts between these three approaches are discussed in terms of how they frame the relationship between the academic discipline and the school subject, and to what extent they problematise the reliance and bias towards the academic discipline. The institutional position implicit in the three approaches is then examined in order to open up new ways of thinking about the relationship between school mathematics and university mathematics.

Comparison of Interdisciplinary Connections between Mathematic and other Subjects through Student-centred Approaches

In some European countries inquiry-based learning (IBL) has become popular in primary and secondary mathematics education, especially for science-connected content. On the other hand, problem-based learning (PBL) and project-based learning (PjBL) have a longer history in mathematics, science, technology, engineering (STEM) and in some other fields in higher education. After presenting the theoretical similarities and differences among these three interdisciplinary student-centred approaches, we review the use of them in mathematics education. We analyse a selection of n=112 high quality research articles about the use of IBL, PBL or PjBL in mathematics, and its interdisciplinary connection with other subjects, level of education, type of research method, research design and participants for each study. Based on these characteristics, we identify the differences between the approaches in mathematics education. Finally, detailed examination of a subsample of experimental studies, where effect size is or can be measured, describes differences in interdisciplinary connections between the target approaches and indicate what kind of studies are still missing in mathematics education.

PENGARUH PENDIDIKAN MATEMATIKA REALISTIK BERBANTU POWERPOINT INTERAKTIF DALAM MENINGKATKAN MOTIVASI DAN HASIL BELAJAR SISWA KELAS 1 SELAMA PEMBELAJARAN ONLINE DI SDK SAINT JOHN BEKASI

The emergency of Coronavirus disease in Indonesia makes the teaching and learning process should be held in an online learning setting. The existence of distance during the learning reduces the performance of students, especially the new enrolled students in grade 1 Saint John Christian elementary school. Therefore, this research aims to examine the Realistic Mathematics Education (RME) approach with interactive PowerPoint (iPP) media in improving students’ learning outcome and motivation during the online learning period. Classroom Action Research (CAR) is applied in order to analyze the effect of RME with iPP towards students’ performance in learning mathematics within two cycles. The participant is class 1-D Saint John Christian elementary school which consists of 22 students. Data were collected through assessment towards students’ learning outcome, and motivation matrix modeled by Keller to measure the learning motivation. Data in this research is analyzed using descriptive analysis. The final cycle showed that 91% of students successfully passed the passing grade and reached 360 points for the learning motivation. Meanwhile, the percentage target of students who would pass the test is only 80% and the target points of learning motivation is 320 points only. In conclusion, RME with iPP is able to improve student learning outcome, motivation as well as build interaction. The usage of RME with iPP in an online learning setting is recommended to increase students’ academic performances.

The inquirer, the sense maker, and the builder: Participant roles in an online working group designed to support inquiry-oriented instruction

In light of the expansion of student-centered instructional approaches in mathematics education and a brightening spotlight on instructional supports, we look to Inquiry Oriented Instruction (IOI) and explore instructors’ participation in an online working group designed to support the implementation of IOI. By coordinating the tenants IOI, the format and goals of the online working groups, and the analytic framing provided by the Instructional Triangle, three roles for the IOI professional development participants emerged: the sense maker, the inquirer, and the builder. This framing guided our study of participant role enactment in an online professional development setting. Here we detail two instructors’ approaches to IOI, the roles they played in in the online working group, and ultimately shed light on the intricacies of IOI and meaningful professional development engagement. Such findings support the growing bodies of research centered around IOI, corresponding professional development initiatives, and community formation in online professional development settings.

The Benefits of an Interdisciplinary Approach to Mathematics Education on Issues Around Computation in School.

We present arguments in favor of an interdisciplinary approach in mathematics education. As an instance, we briefly recall how cognitive neuropsychologists promoted intense finger gnosis acquisition, i.e., acquiring the ability to mentally represent one’s fingers, at an early age. Mathematics educators definitely recommended the development of finger gnosis but examined its limits. They also presented arguments in favor of developing flexible mental calculation as a goal of arithmetical instruction in elementary school. In this context we describe the training of “Zahlenblick” as a way to foster flexible mental calculation and connect it with concepts from the theory of metacognition. We illustrate how precisely this branch of metacognition demands further interdisciplinary research. In our analysis, “Zahlenblick” extends to acquiring an eye for proportions, beyond just whole numbers. We illustrate how useful it would be to better understand the neural underpinnings responsible for the advantages of so-called natural frequencies, compared with percentages or probabilities, and of icon arrays for representing them. Such natural frequencies are adequate formats for the early confrontation with decision-making under risk.

Effectiveness of Realistic Mathematical Education (RME) Approach Compared to Conventional Learning Models Elementary School Students

The learning approach that can be applied in learning mathematics is a realistic approach, because it has the advantage that it gives students a clearer understanding of the relationship between mathematics and everyday life and under the guidance of teachers students can solve their mathematical problems. The purpose of this study was to determine the effectiveness of RME compared to conventional learning models. This research is a quasi-experimental research. In this study, the population was the second semester students of class IV SD Negeri Pacitan District. In this study, the sample was part of the population taken using the Stratified Cluster Random Sampling technique, taking data from all public elementary schools in Pacitan District. The results before and after using the RME (Realistic Mathematical Education). Based on the results of the t-test analysis (paired sample t-test), it can be obtained that the t-count is greater than t table. Namely 12.078 > 1.68595 and Sig. (2 tailed) = 0.000 < 0.05, then Ho is rejected and Ha is accepted. So it can be concluded that there is an effect of the RME method on the development of mathematical reasoning abilities of elementary school students in the Pacitan district.

Learning Design of Set Material in 7th Grade using Demak Bintoro Traditional Market Context

The set is one of the important material for students. However, in reality many students still experience some difficulties in learning the set material, especially on the concept of set operations. So we need the right media and context in learning mathematics on set material. Therefore, this study aims to develop a learning trajectory using the traditional market of Demak Bintoro as a context in the learning process using the Indonesian Realistic Mathematics Education (PMRI) approach. The research method used is design research which consists of three stages, namely preliminary design, experimental design and retrospective analysis. The result of this research is the design of the learning trajectory of the set material using the traditional market of Demak Bintoro. This learning path consists of 4 activities, namely observing the interactive video of the Demak Bintoro traditional market to explain the meaning of sets, explaining about subset universes and describing Venn diagrams, explaining set operations on (slice and union) and solving contextual problems related to set operations. . The results of this study indicate that the use of the context of the Demak Bintoro traditional market can stimulate students' conceptual understanding of the set material. Furthermore, the results of this study are expected to be used as inspiration for exploring other local wisdom that can be used as a context in learning mathematics.
 Keywords: Group Operation, PMRI, Bintoro Traditional Market.

GEOMETRY LEARNING WITH INDONESIAN REALISTIC MATHEMATICS EDUCATION APPROACH

This research is based on the learning background that is still a teacher-centered dynamic while students are passive. The purpose of this research is to develop a teacher’s guideline in learning geometry with the Indonesian Realistic Mathematics Education (PMRI) approach that is valid, practical, and influential. This research is a development research (R&D) with the Tjeerd Plomp model. Field trial with an experimental design of one group pre-test and post-test time series, with a sample of 33 elementary school students in the city of Padang. The results showed that the PMRI teacher guidelines were valid, practical, and influential. In particular, there are significant differences in the geometry learning outcomes between before and after using this teacher guide. This is indicated by the results of the data analysis of the significant difference between post-test 1 and pre-test 1, post-test 2 and pre-test 2, as well as post-test 3 and pre-test 3 with a p-value of 0.001 < 0.05. Qualitatively, students can understand that a square is a rectangle whose all sides are the same length, and that a square and a rectangle had the characteristics of a parallelogram. In term of van Hiele's theory, students are at the stage of informal deductive thinking. Students can conclude the shapes and characteristics of flat shapes of triangles, squares, rectangles, and parallelograms. Elementary school teachers are advised in learning geometry to use the teacher’s guidelines that have been developed.Keywords: Learning, geometry, PMRI, van Hiele, primary school.

Constructive Learning Approach in Mathematics Education: Challenges and Possibilities

A constructive learning and instruction approach has been proposed as an alternative and latest scientific model, which is implicit in all behaviorist and some cognitive approaches to education. The major concern of this study is to analyze the theoretical views and challenges of the constructive learning approach in the mathematics classroom. This research is qualitative and does not use any primary data. The findings of the research are based on in-depth study and analysis of various articles, researches, books, and conference papers presented at various conferences published nationally and internationally as secondary data. The constructive learning approach encourages students to learn the information themselves, it helps students explore the knowledge themselves, it seeks to make students more aware, it develops more powerful thinking teaching and classroom environment, and it improves the students’ performance in various fields. Whereas the traditional learning approach has always been teacher-centered learning.

MƏKTƏBƏQƏDƏR YAŞLI UŞAQLARDA RİYAZİ TƏSƏVVÜRLƏRİN FORMALAŞMASI VƏ İNKİŞAFININ XÜSUSİYYƏTLƏRİ

The article deals with the actual problems of the formation of elementary mathematical representations in children. The paper shows that this approach in mathematics education based on action learning in conjunction with the natural motivation stemming from common sense is effective. Also, stimulating questions and classical famous problems are important motivating tools in mathematics, which are particularly beneficial in the framework of action learning. The analysis of psychological, pedagogical and methodological literature on the topic of research the author provides an experimental methodology for studying elementary mathematical representations, characterizes their features in young children. Key words: preschool children, mathematical representations, intellectual development of preschool children, mental education, features of development, elementary mathematical representations