Mathematical Problem-Posing Research: Revisiting Some Answered and Unanswered Questions

The investigations have been concerned with mathematics programs from the kindergarten through the graduate school. A first goal of many studies has been the production of sample course materials; the implications for and effect on teacher education are far-reaching. The academic and professional training of teachers must take into account the changing mathematics curriculum. All the groups preparing and trying out new materials have recognized the related teacher-education problems, and almost all have carried on investigations specifically concerned with teacher education. Jones (1960) emphasized implications of research in mathematics for teacher education in a paper before the American Association of Colleges for Teacher Education. Some 20 separate studies in mathematics curriculum were under way during the review period. The School Mathematics Study Group (SMSG) of mathematicians and teachers in all parts of the country, which has an advisory committee appointed by the presidents of the three major national mathematical societies, has offered its co-operation to all independently operating centers of activity and is in a position to take advantage of the good work of the other groups. A major concern of the SMSG is teacher education. Another kind of investigation which has equally far-reaching implications for teacher education is the growing interest of psychologists in learning theory as related to mathematics. This research is best exemplified by the work of Bruner (1960). Research in mathematics and science is often classified as basic or applied. Duncan and Frymier (1960) made this distinction for research in teacher education. This review, more concerned with applied research, reviews studies peculiar to mathematics-teacher education rather than studies which have implications for teacher education generally. Moreover, a greater proportion of the former is clearly applied, particularly the investigations of course content. Research dealing with the way children learn mathematics, since it has important implications for other fields, may come to be classified as basic.

Differentes recherches ont etabli l'influence des enseignants sur la qualite de l'apprentissage des enfants. La question est de savoir ce qui rend un enseignant plus performant qu'un autre. Quatre indicateurs, etudies par les AA., peuvent etre utilises dans ce but : les acquisitions pedagogiques des enseignants, leurs participations dans les programmes d'etudes, leurs connaissances des matieres enseignees et leurs strategies pedagogiques

This chapter synthesizes the current state of knowledge in problem-posing research and suggests questions and directions for future study. We discuss ten questions representing rich areas for problem-posing research: (a) Why is problem posing important in school mathematics? (b) Are teachers and students capable of posing important mathematical problems? (c) Can students and teachers be effectively trained to pose high-quality problems? (d) What do we know about the cognitive processes of problem posing? (e) How are problem-posing skills related to problem-solving skills? (f) Is it feasible to use problem posing as a measure of creativity and mathematical learning outcomes? (g) How are problem-posing activities included in mathematics curricula? (h) What does a classroom look like when students engage in problem-posing activities? (i) How can technology be used in problem-posing activities? (j) What do we know about the impact of engaging in problem-posing activities on student outcomes?

Vladimir Igorevich Arnold

In this paper, a model is outlined for integrating research activities with undergraduates within the mathematics curriculum. Introducing a sequence of courses designed to engage students in research projects has brought about a change in the mathematical culture of students. The history and challenges associated with the creation of this program are discussed, indicating the positive outcomes it has had on student learning. Also discussed is the shift in departmental thoughts on student capabilities. Specific examples of student work are cited.

Early childhood education is a critical stage in individual development. At an early age, children have the ability to absorb knowledge quickly, including in mathematics. The aim of this study was to identify trends and patterns of mathematics research in early childhood using bibliometric analysis. The data was obtained from the Scopus database which has been refined with 4 stages (identification, screening, eligibility, and inclusion). The results showed that the peak of publications related to mathematics research in early childhood occurred in 2022. 2017 was the year with the most influential publications. Journal “Early Childhood Education Indexed Journal Scopus with the highest quartile score (Q1) is the most popular place for publication of previous research related to this field. The United States is the most influential country in this field because both the number of publications and the number of citations are the highest than any other country. As for three focus study related study mathematics in children age early on the Scopus database from 1988-2023 namely, 1) mathematics, human, learning and gender; 2) early childhood, professional development, and teachers; 3) mathematics learning, early childhood, curriculum, and achievement.

In 1985 the International Commission on Mathematical Instruction (ICMI) convened a meeting in France of mathematicians, computer scientists, and mathematics educators from around the world to discuss the impact of “informatics” (the common European term for computer science) on mathematics—specifically, on mathematical research, on the mathematical curriculum, and on mathematical pedagogy.

In 1985 the International Commission on Mathematical Instruction (ICMI) convened a meeting in France of mathematicians, computer scientists, and mathematics educators from around the world to discuss the impact of “informatics” (the common European term for computer science) on mathematics—specifically, on mathematical research, on the mathematical curriculum, and on mathematical pedagogy.

Since 1989, with the publication of Curriculum and Evaluation Standards for Mathematics by the National Council of Teachers of Mathematics, standards have been at the forefront of the education reform movement in the United States. The mathematics standards, which were revised in 2000, have been joined by standards in many subjects, including the National Research Council's National Science Education Standards published in 1996 and the Standards for Technical Literacy issued by the International Technology Education Association in 2000. There is no doubt that standards have begun to influence the education system. The question remains, however, what the nature of that influence is and, most importantly, whether standards truly improve student learning. To answer those questions, one must begin to examine the ways in which components of the system have been influenced by the standards. Investigating the Influence of Standards provides a framework to guide the design, conduct, and interpretation of research regarding the influences of nationally promulgated standards in mathematics, science, and technology education on student learning. Researchers and consumers of research such as teachers, teacher educators, and administrators will find the framework useful as they work toward developing an understanding of the influence of standards.

Introduction. The relevance of the research on the formation and assessment of the level of development of competencies in the mathematical educational field is due to the fact that the subject competence of the participant of the Olympiad predetermines his victory in the competition. And the Mathematical Olympiad, as a form of education, has potential not only for the formation, development, but also for determining the level of mathematical competence of its participants. The research problem is to justify the didactic potential of the mathematical Olympiad as a tool for determining the level of mathematical competence of school students. Aim of the study: to theoretically substantiate, develop and specify the content, indicators of mathematical competence of mathematical Olympiad participants Methodology and research methods. The methodological basis of the study is determined by: the activity and competence-based approaches to teaching; a retrospective analysis of psychological and pedagogical studies affecting the formation and development of key and subject competencies of schoolchildren; an analysis of the content of mathematical Olympiads; an analysis of the results of Kyrgyz Republic schoolchildren in international mathematical Olympiads; the study and generalization of the experience of juries of Olympiads. Results. The subject Olympiad forms a competence-based educational environment in which the levels of formation of key and subject competencies of its participants are most fully displayed. The competence-based approach to training in the Olympiad environment is characterized by the formulation of objectives from the point of view of the activity approach to the formed competence. Subject competence is leading in determining the quality of the student’s Olympiad activity. The mathematical Olympiad is one of the effective forms of both the formation and development, and the determination of the level of mathematical competence of its participants. The introduction of presented system for preparing schoolchildren for mathematical Olympiads, using model’s formation of mathematical, informational competencies in the experimental group, led to an increase in students' knowledge of the theory and practice of solving Olympiad problems in mathematics by 12,95%; the qualitative indicator of knowledge of the school curriculum in mathematics increased by 15,25%. The index of absolute indicators in the experimental groups in the theory of Olympiad mathematics was 53,12%, in the methods of solving Olympiad problems – 55,38%. In control groups, these indicators were 41,23% and 42,36%, respectively. The qualitative indicator of exam results of schoolchildren of the Olympic reserve turned out to be 19% higher. The results of the questionnaire survey participants of the Olympiads confirm the expediency of using technology for the development of critical thinking, the project method of teaching, ICT in the process of preparing for the Olympiads, contributing to the emergence of motivation to study an extracurricular course in mathematics in 68% of students, 42% of students showed a desire to participate in the Olympiads. The results obtained confirm our conclusions that the development of the mathematical competence of the participants of the Olympiads is successfully realized only in a situation of continuous Olympiad activity.

This paper looks at the evolution of ideas on the role of proof in mathematics education from 1980 to 2020, examining in particular the contributions of both theoretical and empirical research to the teaching of mathematical proof. In so doing, it describes some of the major epistemological themes that emerged in the last forty years, primarily in the philosophy of mathematics and in mathematical education, and informed both the mathematics curriculum and research in mathematics education. The paper also discusses selected research studies that shed light on the opportunities and limitations students face when they engage in proof. Finally, it describes briefly a number of developments in proof technology and the potential of automated theorem provers for enhancing the teaching of proof.

Henry O. Pollak is Director of the Mathematics and Statistics Research Center of Bell Laboratories. He is responsible for research on the mathematics of physics and networks, communication theory, discrete systems, statistics and data analysis. As Director, he administers a remarkable group of highly skilled mathematicians who not only create beautiful mathematics but who are remarkably adept at drawing inspiration from and linking mathematics to real-world applications. Pollak is a strong advocate of incorporating applications into the mathematics curriculum at all levels of education. For more than a quarter century, he has worked very hard to improve mathematics instruction. Despite his heavy adminis? trative responsibilities at Bell Laboratories, he has found time to serve professional mathematics associations in this country and overseas. Most recently, he was Chairman of the Fourth International Congress on Mathematical Education and President of the Mathematical Association of America.

PREFACEThe 2nd International Conference on Mathematics and Science Education (ICOMSE) 2018 on Malang, 28 – 29 August 2018, is an annual conference oganized by Faculty of Mathematics and Natural Science, Universitas Negeri Malang, Indonesia. ICOMSE 2018 provides a platform to researches, experts and practitioners from academia, governments, NGOs, and research institutes to meet and share research interests and knowledge as well as to enhance understanding of the relationship between knowledge and research. This is in line with this year theme “Innovative Research in Mathematics and Science Education for The 21st Century”. The scope of the conference covers mathematics education, science education, biology eduaction, physics education, and chemistry education.We would like to express our gratitude to the keynote speakers and all authors of contributed papers for participating excellently and eagerly. We are also very grateful to the expert reviewers who provided their valuable time for giving constructive comments and suggestions to the authors. We would like to extend our thanks for the tireless efforts shown by the organizers and faculty members of Faculty of Mathematics and Natural Science, Universitas Negeri Malang.Our sincere gratitude also goes to the IOP Publishing editors and managers for their helpful cooperation during the preparation of the proceedings.

Kindergarteners need access to blocks as thinking tools to develop, model, test, and articulate their mathematical ideas. In the current educational landscape, resources such as blocks are being pushed to the side and being replaced by procedural worksheets and academic “seat time” in order to address standards. Mathematics research provides a solid basis for advocating for hands on resources to explore geometry and number concepts. Through the use of blocks in standards based mathematical tasks, students have the opportunity to develop important mathematical concepts and reasoning strategies. Kindergarten teachers’ instructional actions can be grounded in history, research, personal wisdom, and professional knowledge regarding what is appropriate and meaningful for their students in learning mathematics with thinking tools such as blocks.

This volume focuses on research related to mathematics curriculum. But rather than focusing on results of research, it focuses on lessons learned about conducting research on curriculum, whether about design and development, analysis of curriculum in the form of official standards or textbook instantiations, teacher intentions related to curriculum implementation, or actual classroom enactment. For scholars interested in curriculum research, the volume offers lessons about conducting curriculum research that have been learned by others engaged in such work, including frameworks, tools, and techniques, as well as challenges and issues faced, with solutions to address them. Sharing lessons from authors of different countries strengthens the broader mathematics research community and provides insights that can help researchers make important strides forward in research on mathematics curriculum.