Field Of Mathematics Education Research Articles

Effects of Dynamic Geometry Software on Students’ Geometric Thinking Regarding Probability of Giftedness in Mathematics

Gifted students have potential to improve countries and this potential can be revealed and developed in schools where they spend most of their times with other regular students. However, these classrooms have some limitations for them; hence, they need some differentiated activities. Usage of dynamic geometry in mathematics lessons could be an opportunity to provide differentiated activities. Therefore, the aim of this study is to explore effects of mathematics lessons integrated with dynamic geometry activities on students' van Hiele geometric thinking levels controlling their probability for mathematical giftedness. Participants of the study were fifty-three fifth graders from a private school in Marmaris, Turkey. These students were grouped in terms of their probability of mathematical giftedness. Seven dynamic geometry activities about properties of line segments, triangles and quadrilaterals were developed and implemented in classrooms with tablets. Van Hiele geometric thinking level test was administered to the participants as pre-test and post-test. Results showed that dynamic geometry activities help students to move from geometric thinking level about recognizing shapes with visual clues to higher level about geometrical properties of shapes, namely relationship among shapes and their properties. Moreover, interaction between their probability for mathematical giftedness and improvements in geometric thinking levels were found. This study may contribute both to the gifted education and mathematics education fields by exploring the improvements in geometric thinking level and differentiated opportunities for gifted students. As a suggestion, a more comprehensive experimental study with larger samples so as to obtain generalize the findings could be conducted as a further study.

Primitive Model of Partitive Division: A Replication of the Fischbein et al. Study

Abstract We present a replication study of one of the most renowned seminal works in the field of mathematics education, i.e., the Fischbein et al. (1985) study on implicit models of multiplication and division in solving word problems. The original instrument was administered to a sample of 902 grade 7 students, proposing some methodological variations. The discussion focuses on four items involving partitive division of integer numbers, and results are compared to the original study: the main results of the original study are confirmed, but we contribute further with considerations on the statistical significance of differences observed in item difficulty. Finally, through our new methodological approach, we broaden the results of the original study by analysing students’ behaviour on the basis of their general arithmetical problem-solving ability. Students with medium-level ability are more influenced by the primitive model than those with lower ability.

Literature review on networking of theories developed in mathematics education context

The research aim is made a literature review on research focused on networking of theories developed in mathematics education field with several mathematical concepts. On the other hand, to illustrate what a networking of theories consists of, a synthesis of an articulation between the extended theory of connections (ETC) and the onto-semiotic approach (OSA) was presented using the study of the mathematical connections built by a university student on the derivative concept as an example. A qualitative study was developed in two stages: (1) Three phases were followed: search for information in various search engines and databases (ERIC, Google Scholar, etc.), organization and analysis of the documentation, finding works on articulation of theories focused on various mathematical concepts such as derivative. (2) A synthesis of the theoretical articulation ETC-OSA is presented, emphasizing the analysis of an episode over the derivative. It is concluded that the research reviewed on the articulation of theories about a certain phenomenon or teaching of content represents an important contribution to improving its understanding. In addition, this research provides a theoretical input or detailed panorama of background organized chronologically so that the community interested in this research line can use it for future studies.

2022 Founder’s Lecture: Current Research Trends in Mathematics Learning that Guide Us for the Future

ABSTRACT Mathematics teaching and learning are critical aspects of education that impact our world. There are implications for the mathematics education research community that should push us to have critical conversations about our research and how it informs mathematics education. I present a brief overview of research in mathematics education through the lens of Investigations in Mathematics Learning, the official journal of the Research Council on Mathematics Learning, using issues from 2017-2021. Included are findings from qualitative analyses and ideas calling on the mathematics education community to consider that provide a positioning for mathematics education researchers (MERs). I challenge us to consider multiple questions with regard to our research: What does it add to the field of mathematics education? How does it contribute to broadening and deepening our understandings? How does it inform practice to further effective equitable teaching and learning of mathematics? Are we being inclusive? Are we a leading voice in mathematics education research and are we being effective curators and stewards of this work? As MERs, as a field, as professional organizations, what could and should we do? We have a unique opportunity at this juncture to work together to inform and impact mathematics learning in profound ways.

A Systematic Review of Studies on Teacher Noticing in the Field of Mathematics Education in Turkey

Bu çalışmanın amacı, Türkiye’de 2000-2021 yılları arasında matematik eğitiminde öğretmenin fark etme becerisi konusunda yayımlanan lisansüstü tezlerin ve makalelerin sistematik incelemesini yapmaktır. Bu kapsamda ULAKBİM TR-Dizin, YÖK Ulusal Tez Merkezi, DergiPark, Google Akademik veri tabanları kullanılarak literatür taraması yapılmıştır. Literatür taraması sonucunda Türkiye’de matematik eğitimi alanında öğretmenin fark etme becerisi ile ilgili yayımlanan 36 çalışmaya (17 makale, 9 doktora tezi ve 10 yüksek lisans tezi) ulaşılmıştır. Veriler yayın sınıflama formu kullanılarak kodlanmış ve tematik içerik yöntemi ile analiz edilmiştir. Bu çalışmanın sonuçları Türkiye’de öğretmenin fark etme becerisi ile ilgili çalışmaların 2017 yılından itibaren artış gösterdiğini, daha çok makale türünden çalışmanın yapıldığını, çalışmaların daha çok nitel araştırma yöntemi ile yürütüldüğünü, durum çalışması ve eylem araştırma deseninin tercih edildiğini göstermiştir. Üstelik çalışmaların daha çok küçük örneklem grupları ile matematik öğretmen adayları ve öğretmenler ile yürütüldüğü tespit edilmiştir. Veri toplama aracı olarak daha çok video kaydı, görüşme, gözlem, yansıtma raporu ve öğrenci çalışma kağıtlarının kullanıldığı, içerik ve doküman analiz tekniğinin daha çok tercih edildiği ortaya çıkmıştır. Fark etme becerisi çalışmalarında çoğunlukla birden çok matematik konusunun ele alındığı, bununla birlikte geometri ve ölçme, cebir ve kesirler konusunun ele alındığı tespit edilmiştir. Çalışmaların daha çok öğretmen ve öğretmen adaylarının fark etme becerisi düzeylerinin belirlenmesine odaklandığı, bunun yanında video-kulüp, ders imecesi ve fakülte-okul işbirliği uygulamalarının fark etme becerisi üzerine etkisi incelenmiştir. Fark etme becerisi için daha çok araştırmacılar tarafından oluşturulan analiz çerçevesi kullanılmış, bununla birlikte van Es (2011), van Es ve Shein (2008) ve Jacops ve diğerlerinin (2010) analiz çerçevesi de tercih edilmiştir. Bu çalışma, öğretmenin fark etmesi konusunda karma ve nicel araştırma yöntemlerine dayalı araştırmalara ihtiyaç olduğunu göstermiştir.

Realistic Mathematics Education: A Bibliometric Analysis

The aim of the study is to conduct a bibliometrical analysis on the published articles related to RME. Accordingly, Scopus database was scanned using the keywords “realistic mathematics education” or “realistic mathematic education” or “realistic maths” or “realistic mathematical education” and a total number of 1190 articles published on RME between 1986 and 2021 were obtained and anayzed bibliometrically. The data gathered was then analyzed utilizing “biblioshiny”, which is a web interface app in the bibliometric R-Studio program package. The analyses were conducted in order to find out the sample of the articles’ annual distributions; their 3-D area chart; the list of the journals that published the highest number of related articles; the authors and their institutions; source clusters obtained through Bradford’s Law, the scientific productivity of the authors by years and their citation burst scores; the scientific productivity of the countries; the word cloud and word tree patterns of these articles; co-word analysis of the concepts, the collaboration networks of the authors and the conceptual structure mapping. The findings obtained as a result of the conducted analyses indicate that there has been an increase in the interest in RME research after 2016 and the journal with the highest number of published articles on RME is Journal on Mathematics Education. Also, the authors with the highest numbers of publications are Z. Zulkardi, S. Suparman and R. I. I. Putri, respectively, while Utrecht University has the highest number of publications on the topic. The countries with the highest rates of productivity in terms of publications on RME are found to be the USA, Indonesia, and the Netherlands, respectively. In addition, the most frequently used keyword by the researchers is found to be “realistic mathematics education”, while “mathematics” is the most frequently utilized word in the titles of the analyzed articles. The overall findings of the study point out the need for further studies on RME as realistic mathematics education is considered to be a significant method in finding solutions to the problems in the field of mathematics education. Further theoretical contributions are also thought to be crucial as they could provide fundamental references for future research.

Digital educational technologies and resources in teaching geometry using the example of dynamic environment GeoGebra

The organization of the educational process, characterized by high performance, requires providing students with an opportunity to acquire deep subject knowledge, including mathematics. Digital technologies and resources are a tool aimed at optimizing the learning process. This paper discusses basic concepts and definitions from the field of digitalization and mathematical education. The author lists the features of the organization of the educational process using the GeoGebra dynamic environment, theoretical and practical aspects of the use of the environment in solving planimetric problems both in the classroom and in the homework of students. The characteristic of the methodological and technical stages of the development of the worksheet is given. The content of the work contains an example of a task in the format of a worksheet. The program of the electronic educational module Animation Mathematics developed by the author is analyzed, aimed at achieving the main educational results by students of the 8th grade in the section Similarity of triangles. The approbation of the results of the study was carried out on the basis of school in Orenburg and showed that the use of GeoGebra in teaching geometry expands the prospects for pedagogical activity, optimizes the work of teachers and leads to an increase in the effectiveness of training.

SPATIAL SENSE ABILITY INSTRUMENT FOR PRIMARY SCHOOL STUDENTS

This research is motivated by the importance of spatial sense skills possessed by elementary school students. The research aims to develop an instrument of spatial sense ability suitable for elementary school students. The indicators developed in the preparation of questions include: 1) classifying real objects into 3D form (building space); 2) investigating, exploring, and describing geometry in nature and the real world; 3) exploring the directional relationship of objects in space; 4) analyzing the nature of 3D shapes and interpreting 3D shapes into 2D forms. Research and Development was chosen as the method of this research. A total of 33 grade VI students of SDN 1 Nagri Kidul, Purwakarta Regency, West Java Province, were the samples in this study. The sample was selected by purposive sampling. The instrument used is an essay test consisting of seven questions regarding the geometry of cubes and blocks. The expert (Professor in the field of mathematics education) validated the seven questions that had been prepared. Expert considerations are used as the basis for the improvement of the compiled questions. Then the questions that have been corrected are tested on the research sample. The results of the trial were calculated for validity, reliability, difficulty index, and discriminatory power. Of the seven questions compiled, six were declared valid, reliable, and had high discriminatory power, and the level of difficulty of the questions consisted of medium and difficult. Thus, 6 of the seven items developed can be used by teachers or researchers as an instrument to measure the spatial sense abilities of elementary school students, primarily fifth-grade students.

Intelligent tutoring systems for word problem solving in COVID-19 days: could they have been (part of) the solution?

The COVID-19 pandemic led to the lockdown of schools in many countries, forcing teachers and students to carry out educational activities remotely. In the case of mathematics, developing remote instruction based on both synchronous and asynchronous technological solutions has proven to be an extremely complex challenge. Specifically, this was the case in topics such as word problem solving, as this domain requires intensive supervision and feedback from the teacher. In this piece of research, we present an evaluation of how technology is employed in the teaching of mathematics, with particular relevance to learning during the pandemic. For that purpose, we conducted a systematic review, revealing the almost complete absence of experiments in which the use of technology is not mediated by the teacher. These results reflect a pessimistic vision within the field of mathematics education about the possibilities of learning when the student uses technology autonomously. Bringing good outcomes out of a bad situation, the pandemic crisis may represent a turning point from which to start directing the research gaze towards technological environments such as those mediated by artificial intelligence. As an example, we provide a study illustrating to what extent intelligent tutoring systems can be cost-effective compared to one-to-one human tutoring and mathematic learning-oriented solutions for intensive supervision in the teaching of word problem solving, especially appropriate for remote settings. Despite the potential of these technologies, the experience also showed that student socioeconomic level was a determining factor in the participation rate with an intelligent tutoring system, regardless of whether or not the administration guaranteed students' access to technological resources during the COVID-19 situation.

Marginalized within the margins: Supporting mathematics meaning making among students with learning disabilities

Students with learning disabilities are often excluded from conversations about high-quality mathematics instruction as well as conversations about equitable mathematics instruction. As such, they may not be provided many opportunities to engage in mathematics with teachers who implement practices that the field of mathematics education would consider “high-quality” or “equitable”. In this paper, we examine how three students with learning differences participate in instruction that demonstrates aspects of high quality and equitable mathematics instruction. Our findings outline practices that appeared to support increased opportunities for students to demonstrate their own reasoning and sense making in mathematics. Contributions of this work include illuminations of specific pedagogical moves that may support students identified as having learning disabilities to engage in more student-centered, conceptually-oriented mathematics.

Interpretation and Use Statements for Instruments in Mathematics Education

This Research Commentary addresses the need for an instrument abstract—termed an Interpretation and Use Statement (IUS)—to be included when mathematics educators present instruments for use by others in journal articles and other communication venues (e.g., websites and administration manuals). We begin with presenting the need for IUSs, including the importance of a focus on interpretation and use. We then propose a set of elements—identified by a group of mathematics education researchers, instrument developers, and psychometricians—to be included in the IUS. We describe the development process, the recommended elements for inclusion, and two example IUSs. Last, we present why IUSs have the potential to benefit end users and the field of mathematics education.

Competence and autonomous motivation as motivational predictors of college students’ mathematics achievement: from the perspective of self-determination theory

BackgroundApplied Calculus courses serve hundreds of thousands of undergraduates as quantitative preparation and gatekeepers across diverse fields of study. The current study investigated how motivational factors are associated with students’ learning outcomes in Applied Calculus courses from the perspective of self-determination theory—a sound comprehensive motivation theory that has been supported by considerable research in psychology and education. In order to have a nuanced understanding of students’ motivation and learning in Applied Calculus courses, we used three different types of learning measures to investigate students’ mathematics achievement, including course grades, a standardized knowledge exam, and students’ perceived knowledge transferability.ResultsWe tested the relationships between motivational factors and learning outcomes with a multi-semester sample of 3226 undergraduates from 188 Applied Calculus classrooms. To increase the precision of our analysis, we controlled for three demographic variables that are suggested to be relevant to mathematics achievement: gender, minority group status, and socioeconomic status. With a series of multilevel modeling analyses, the results reveal that: (1) competence satisfaction predicts college students’ mathematics achievement over and above the satisfaction of needs for autonomy and relatedness; and (2) autonomous motivation is a more powerful predictor of college students’ mathematics achievement than controlled motivation and amotivation. These findings are consistent across different types of learning outcomes.ConclusionsSelf-determination theory provides an effective framework for understanding college students’ motivation and learning in Applied Calculus courses. This study extends self-determination theory in the field of mathematics education and contributes to the dialogue on advancing undergraduate science, technology, engineering, and mathematics (STEM) education by providing evidence to understand how motivational factors are associated with students’ learning outcomes in undergraduate mathematics courses.

Application of ROC Curve Analysis for Predicting Students’ Passing Grade in a Course Based on Prerequisite Grades

Determining prerequisite requirements is vital for successful curriculum development and student on-schedule completion of the course of study. This study adapts the Receiver Operating Characteristic (ROC) curve analysis to determine a threshold grade in a prerequisite course necessary for passing the next course in a sequence. This method was tested on a dataset of Calculus 1 and Calculus 2 grades of 164 undergraduate students majoring in mathematics at a private university in Kazakhstan. The results showed that while the currently used practice of setting prerequisite grade requirements is accurately identifying successful completions of Calculus 2, the ROC method is more accurate in identifying possible failures in Calculus 2. The findings also indicate that prior completion of Calculus 1 is positively associated with success in a Calculus 2 course. Thus, this study contributes to the field of mathematics education by providing a new data-driven methodology for determining the optimal threshold grade for mathematics prerequisite courses.

Power relations and the negotiation of meanings in a Community of Practice in the field of Mathematics Education

This article aims to identify and analyze power relations in the negotiation of meanings in a Community of Practice, called the “Observatório da Educação Matemática” da Bahia (OEM-BA), formed by academics from the university and teachers of Basic Education, who came together to produce educational math curriculum materials. The research carried out was of a qualitative nature and the data were produced through observations of the activities carried out by OEM-BA. To support the analysis, we used Etienne Wenger's Social Theory of Learning and Basil Bernstein's Theory of Codes. By analyzing the data, we identify power relations between academic and non-academic discourses, as well as interdisciplinary and interdisciplinary discourses. This happened when members negotiated meanings relative to teaching and learning content operations with whole numbers and quantities directly and inversely proportional. The results of this research gave visibility to variations in the principles and hierarchies underlying the meeting between academics and scholars.

Self-Regulated Learning dan Motivasi Belajar dalam Pembelajaran Matematika Secara Online: Systematic Literature Review

This research aims to explore and create synthesis about Self-Regulated Learning (SRL) and learning motivation in online learning. There is some research related to SRL and learning motivation as well as its impact on students' academic achievement in math learning. The search for relevant data base was conducted in a study published from 2015 to 2021 that examined SRL and learning motivation, especially in the field of mathematics education. The search strategy is done systematically by reviewing articles that have been published on the databases OF ERIC, Scopus, PubMed, Science Direct, and Google Scholar. Based on the results of a systematic review of the literature, it was produced that SRL and motivation learning are important predictors in online math learning. In addition, SRL and learning motivation have a positive and significant influence on students' academic achievement. As for efforts to improve SRL and student learning motivation in learning can be done by applying learning that can help students develop positive values and realistic expectations for success in mathematics

Improving the Trigonometric Functions Learning Concept with Dynamic Mathematics Software

Since the 21st century, the new model of Internet+Education has gradually penetrated into the field of mathematics education and has become a hot topic in the current research on mathematics education, and education informatization has become the main development trend. Therefore, the purpose of this research is to help students and teachers how to use Hawgent dynamic mathematics software to help students learn trigonometric functions and help teachers practice trigonometric functions. The research method used is the research and development (R&D) method and this research was done at Chongqing Zhongxian Senior Middle School for the period month of July to August 2021. The model has adaptive guiding principles that can help researchers develop ICT based learning media in the five stages of analysis, design, development, implementation, and evaluation. This research is based on the Hawgent dynamic mathematics software to design a trigonometric function integrable ware design model, dynamically presenting the concept of trigonometric function and its image and properties, and then use integrable ware to assist the teaching of trigonometric functions, and verify it through experimental teaching. The results show that the learning of trigonometric functions assisted by Hawgent dynamic integrable ware design can help improve students' understanding and interest in trigonometric functions. In the future, other researchers can study the influence of information technology on the teaching of mathematical formulas, theorems, and mathematical problem solving, and explore SEM models of influencing factors.

PERANAN STATISTIKA DALAM PENELITIAN PENDIDIKAN MATEMATIKA

Research is an activity to obtain a solution to a problem or phenomenon that occurs through scientific steps. To understand research, researchers must first understand what statistics are. Statistics is a science that studies the methods of collecting, processing, interpreting and drawing conclusions from the data collected or obtained. Therefore, statistics is said to be one of the sciences that is indispensable in research, not least in the field of mathematics education because statistics are used to identify and describe the relationships obtained from the data that has been collected and then processed to obtain a conclusion. The role of statistics has been seen from before the research was carried out, the research took place until the processing of research results.

The role of teacher actions for students’ productive interaction solving a linear function problem

Many studies in mathematics education have emphasized the importance of attending to students’ interactions, particularly, their mathematical reasoning when collaborating on solving problems. However, the question of how teachers can facilitate students’ productive interactions for learning mathematics, is still a challenging one. This case study aims to provide detailed insights into opportunities and limitations related to teachers’ actions for the productivity of students’ interactional patterns solving a linear function problem together. Four student-pairs in the first year of upper secondary school (11th grade) serve as a background on students’ interactional patterns, which in this study focused on three interactional aspects: collaborative processes, mathematical reasoning, and exercised agency. The student-pairs’ three teachers provide insights on teacher actions observed as different funneling and focusing actions, which elucidated opportunities and limitations in several situations influencing the productivity of students’ interactional patterns. The study used purposive sampling in selecting the particular school and three teachers, which were chosen based on acquaintances and willingness to participate in the study. The students’ interaction when solving the mathematical problem and the teachers’ interaction with the pairs were video recorded and observed by the researchers. The analysis method was a deductive analytical strategy, where specific events of interactions were identified, based on the three interactional aspects combined with teacher actions. Coding schemes on students’ interactions were used, as well as on teacher actions. The findings indicate that teachers’ actions and questions influenced students’ interactions, but mainly their reasoning, and particularly the primary agent’s reasoning. Moreover, students who were engaged in interactional patterns called bi-directional and one-directional did not change their ways of interacting after a teacher interaction. Thus, the teachers’ actions did not impact students’ collaborative processes and agencies in the same way as their reasoning. This study adds to the field of mathematics education by illuminating the importance of teachers being aware of students’ roles when they work together, for facilitating a productive interaction for both students in dyads. The study highlights the importance of further research on teacher actions and teacher awareness for facilitating collaborative situations of bi-directional interactions for students’ shared understanding of mathematical concepts and ideas.

Evolution in the Field of Mathematics Education: Its People, its Products, and its Directions

Reflections on the Field of Mathematics Education

Reflections on the Field of Mathematics Education Introduction

Reflections on the Field of Mathematics Education