Aspects Of Mathematics Education Research Articles

Meta-Synthesis of Effective Practices and Outcomes in the Use of Manipulatives for Teaching Mathematics

Use of manipulatives in mathematics classes has yielded compelling evidence of their value in improving several aspects of mathematics education. This report endeavored to gain a clearer picture of their benefits by using a meta-synthesis technique by integrating findings from 12 previous qualitative or mixed methods studies. They were evaluated using the Critical Appraisal Skills Programme and summarized using a PRISMA diagram. Content analysis identified five main (5) themes: (1) activation of classroom engagement and participation, (2) building of confidence and motivation, (3) enhancement of mathematical proficiency, (4) availability and accessibility of varied resources as manipulative, and (5) teachers’ competency and careful planning. A meta-theme that emerged was Optimizing Mathematics Learning with Effective Classroom Resources through Manipulatives. Thematic study revealed that strategically integrating manipulatives into classroom instruction has a favorable influence on student engagement, confidence, motivation, and mathematical ability. By incorporating manipulatives into mathematics instruction, educators may create inclusive, engaging, and dynamic learning environments that encourage deeper conceptual comprehension.

Sociocultural aspects of mathematics education and curricula review

Sociocultural aspects of mathematics education and curricula review

Mathematics Teachers' Challenges in Implementing Reasoning and Proof Assessment: A Case of Indonesian Teachers

The assessment in mathematics proof and reasoning is one of the crucial aspects of mathematics education. It aims to elicit the development and the level of students' mathematics ability. Nevertheless, several challenges arise from implementing proof and reasoning assessment. This study investigated the challenges experienced by the high school teachers in implementing assessment in proof and reasoning. The study sample comprises three groups with different teaching experiences consisting of ten mathematics teachers in each group. The data were collected through a questionnaire, a depth interview, and a focus group discussion. Bogdan and Biklen's qualitative descriptive analysis is used to analyses the obtained data to elicit a particular theme. The significant challenges included dealing with the implementation of reasoning and proof evaluation. The results indicate that (1) in developing item tests, teacher faced challenges in arranging test framework, determining the suitable mathematics topics, and developing scoring framework; (2) during the test implementation, the teachers have difficulties on the time allocation issue; (3) in analyzing of the assessment result, the teachers inadequately describe the students' mathematical reasoning and proof ability. A collaboration involving mathematics teacher's organization with mathematics education experts is needed to counter the challenges. In detail, this collaboration should focus on the assessment of mathematical reasoning and proof implementation.

Awareness about and Implementation of Research Findings on Mathematics Education among Teachers in Selected Schools in Ibadan, Nigeria

This study attempted to establish the level of awareness about and implementation of research findings in some aspects of Mathematics Education. Two validated instruments (on teachers’ awareness about and their use of research findings) were used to collect data from 132 mathematics teachers who had been purposively selected from a random sample of 34 secondary schools in Ibadan metropolis. The findings were that Mathematics teachers are moderately aware of research findings on Mathematics education. There were significant differences between teachers’ qualifications in Mathematics and use of research findings on Mathematics testing. Motivation of Mathematics teachers to explore new strategies of teaching and to implement them in their classroom practice is recommended .

旧制中等工業学校における数学教育の実相 ―「学科課程表」を中心とする検討から ―

旧制中等工業学校における数学教育の実相 ―「学科課程表」を中心とする検討から ―

Intercultural Aspects of Mathematics Education

Intercultural Aspects of Mathematics Education

Balance between foundations and creativity: features of Korean mathematics education

We are very pleased to write this introductory paper to the special issue of ZDM that provides readers with a glimpse of mathematics education in Korea. In July 2012 (7th–15th), the 12th International Congress on Mathematical Education (ICME-12) takes place at COEX in the center of Seoul, Korea. The ICME is the most important congress in the mathematics education community. It is held once every 4 years under the auspices of the International Commission of Mathematical Instruction (ICMI). The impetus for having this special issue during ICME-12 arose from the scarcity of literature on Korean mathematics education despite Korean students’ high achievement on international comparison studies. Korean students have consistently performed well in recent international assessments of mathematics achievement such as the Trends in International Mathematics and Science Study (TIMSS), the OECD Program for International Student Assessment (PISA), and the International Mathematics Olympiad. In addition, a recent study titled Mathematics Teaching in the 21st Century (MT21) compared prospective teachers’ knowledge and beliefs about teaching and learning in six participant countries, reporting that Korean prospective secondary mathematics teachers were better prepared than those in other countries (Schmidt et al., 2007; Schmidt, Blomeke, Tatto, 2011). Despite such outstanding performances of Korean students and prospective teachers, very little literature is available on factors that contribute toward it. In addition relatively little is also written about mathematics education in Korea. Many scholars, particularly in the West, are curious about Korea’s excellence in teacher quality and student achievement (e.g. Akiba, LeTendre, & Scribner, 2007; Kang & Hong, 2008). There are, however, a relatively small set of systematic studies that examine various aspects of Korean mathematics education substantively and carefully (Kwon, Park, & Park, 2011). Further, some studies on Asian education have even mistakenly assumed that mathematics education in Korea is almost the same as that in other East Asian countries (e.g., Leung, 2011). Considering teaching and learning as cultural practices (e.g., Alexander, 2000; Fernandez & Yoshida, 2004; Ma, 1999; Stigler & Hiebert, 1999), this could mislead readers to ignore the uniqueness of mathematics education in Korea. As a historical–cultural construct, educational practice of mathematics is situated in a specific cultural context of South Korean society, where there are a range of unique cognitive and normative assumptions around the functions and purposes of education, the kinds of knowledge pursued in school and society, the roles taken by teachers and students. Thus, this special issue not only overviews major aspects of Korean mathematics education, it also addresses the historical and cultural foundations of Korean mathematics education in order to foster an understanding of its practices. This issue, a thematic collection of studies, consists of nine papers that present and discuss emerging issues and challenges of Korean mathematics education with respect to various aspects of mathematics education such as curriculum, teaching practices, student learning, textbooks, assessment, and teacher education. It makes an important contribution by Korean mathematics educators to the international community. O. N. Kwon (&) S. J. Cho Department of Mathematics Education, College of Education, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul 151-748, Korea e-mail: onkwon@snu.ac.kr

A changing trajectory of proof learning in the geometry inquiry classroom

The purpose of this study is to explore how students changes through learning to construct mathematical proofs in an inquiry-based middle school geometry class in Korea. Although proof has long been considered as one of the most important aspects of mathematics education, it is well-known that it is one of the most difficult areas of school mathematics for students. The geometry inquiry classroom (GIC) is an experimental class designed to teach geometry, especially focusing on teaching proof, based on students’ own inquiry. Based on a 2-year participant observation in the GIC, this study was conducted to address the following research question: how has students’ practice of mathematical proof been changed through their participation in the GIC? The in-depth analysis of the classroom discourse identified three stages through which the students’ practice of mathematical proof was transformed in the GIC: ‘emergent understanding of proof’, ‘proof learning as a goal-oriented activity’, ‘experiencing proof as the practice of mathematics’. The study found that as learning evolved through these stages, so the mathematics teacher’s role shifted from being an instructor to a mediator of communication. Most importantly, this research showed that the GIC has created a learning environment where students develop their competence in constructing meaningful mathematical proof and grow to be ‘a human who proves’, ultimately ‘a person who playfully engages with mathematics’.

Educação matemática: propostas e desafios

Neste artigo, discutimos alguns aspectos da educação matemática, vista como uma região de inquérito, e mostramos os laços que esse campo estabelece tanto com a matemática quanto com a educação e outras áreas. Buscamos também ilustrar por meio de um exemplo relacionado à pesquisa sobre educação matemática a distância – como a matemática se transforma quando diferentes mídias passam a integrar processos de produção de conhecimento. Finalmente, são tecidas considerações sobre como pesquisa e reflexões geram novos projetos de pesquisa.

Aspectos sociales y culturales de la educación matemática

This paper deals with two fields of research which have contributed to revise the teaching of Mathematics over the last decade: those concerned with social and cultural aspects of Mathematics education.

Computational Fluency, Algorithms, and Mathematical Proficiency: One Mathematician's Perspective

In recent years, few aspects of mathematics education have been as much discussed and debated as the notions of computational fluency and algorithms. A National Research Council report, Adding It Up: Helping Children Learn Mathematics (Kilpatrick, Swafford, and Findell 2001), offers an image of what it means to have skill with mathematics, or mathematical proficiency. This concept is helpful for moving beyond these debates. Mathematical proficiency includes five components: conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition (Kilpatrick, Swafford, and Findell 2001, p. 116). That these components are not separate but fundamentally intertwined is important to note. This article illustrates some of the ways in which the goal of computational fluency and an appreciation of mathematical algorithms are related to this larger concept of mathematical proficiency.

Lebendiges Mathematiklernen:

Subject-Centred Interaction (TZI) offers a holistic understanding of learning and teaching situations and, therefore, it yields a convincing, complex conception for accessing central aspects of mathematics education. In this paper, we present how this perspective can be used for teacher education as well as for restructuring the landscape of mathematics education research and its central questions. Emphasis is put on the relation between mathematics and individuals.

The keyskills agenda: exploring implications for mathematics

As part of a broader research objective concerned with identifying the range of employer defined skill profiles that characterize workplace performance, this paper examines skill contexts for Application of Number, one of six UK defined Key Skills similar to Australian defined Key Competencies. Following the construction of questionnaires, grounded in the Analytic Hierarchy Process, applications of the instrument in both the UK and in Australia produced a ratio scale of priorities within the Key Skills area. This enabled a specification of the relative balance between classical competencies, e.g. facility with pen and paper calculations and emerging competencies demanded by the effective use of ICT. Relevance to workplace learning, including the transition from school to employment, and related aspects of mathematics education are discussed. Among the research outcomes is that spreadsheets are assuming a pre-eminent position and that this is an overriding priority for each defined activity and at each job level.

Problematising mathematics education research

In his introduction to the International Handbook on Mathematics Education, Bishop (1996) commented that the 36 chapters of the Handbook provide "glimpses into the future in many important aspects of mathematics education/' and collectively, "constitute a blueprint for mathematics education in the 21st century" (p. 4). I have a similar conviction about the articles published in the Mathematics Education Research Journal. Although the word "conviction" may sound emotional, and perhaps even extreme in this context, unless articles published in MER], and other similar international mathematics education research outlets, are thought of as sources from which new directions for the future can be conjectured, then mathematics educators are in danger of looking back complacently at their past achievements, of not reflecting sufficiently on past impediments, and of not using the results of research to achieve improvement. In other words, we need to be forward looking, consciously seeking to learn from the past while at the same time grasping the nettle of future possibilities invited by the results and directions of research. At present there is no shortage of published reports of quality mathematics education investigations, ~nd of high-quality syntheses of research findings (see, for example, the reviews in Grouws, 1992). But what is the purpose of such publications if they do not inspire reflection and action which enables many more learners, around the world, to learn mathematics well? Reflection, I believe, should be a key to the planning, conduct, and interpretation of all mathematics education research. But to talk solely of reflection about data gathered, or about the mode of analysis, or about the methodology adopted, would be to trivialise the whole process of reflection. For unless we are able to stand back from our immediate small worlds of research-including the pressure to produce research output-and reflect on and problematise the criteria for proposing and evaluating mathematics education research, then it is almost impossible to look forward in the true sense of the word.

Cognitive Effects of Self-Referencing

The role of self-referencing was investigated in a 5-term linear ordering task (A > B > C > D > E) designed to simulate certain aspects of mathematics education. College students read brief stories containing linear ordering information, then answered pair-wise comparison questions (e.g., A > B?). Two major factors were manipulated: the inclusion of a "You" term (Self-referencing), and the position of the "You" term (Position) in the linear ordering. Three separate experiments yielded consistent results. Beneficial effects of self-referencing were found for test questions that themselves involved self-referencing, but not for test questions that did not involve self-referencing. Also, locating the "You" term at various positions in the linear ordering resulted in different levels of performance and different types of serial position curves. Students appeared to use "self" as an anchor in organizing information, and the further away the self-anchor was from the endpoints, the worse performance became. Educational implications of these findings were discussed.

The second iteration: 1991 Presidential address

It has been my good fortune in life to have been able to work with inspiring and generous people. When I was writing this address, I found myself thinking particularly of one, Geoffrey Matthews, to whom I still often turn when I need reminding of the funnier aspects of mathematics education. I have vivid memories of his elation, 15 years ago, when he was first approached to be President-Elect of the Mathematical Association. Being a stickler for punctuality, he went straight home and wrote his Presidential Address , more than one year in advance of its delivery. In contrast I started on this address just 10 days ago, and have had to amend it twice since, because of announcements of radical shifts in government policy. Even the title, chosen five months ago, may be out of date for reason which I will explain later.

More about mathematical paradoxes in preservice teacher education

This is a third report on a naturalistic study in Israel of the role mathematical paradoxes can play in the preservice education of high school mathematics teachers. The study examined the potential of paradoxes as a vehicle for: (a) sharpening student-teachers' mathematical concepts; and (b) raising their pedagogical awareness of the constructive role of fallacious reasoning in the development of mathematical knowledge. Course material development and data collection procedures are described. Results obtained through written responses and class-video-tapes are analyzed and discussed. The findings indicate that the model of dealing with paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions, and constructive learning. Generalizations are discussed.

Preservice education of math teachers using paradoxes

This is a report on a naturalistic study of the role mathematical paradoxes can play in the preservice education of high school mathematics teachers. The study examined the potential of paradoxes as a vehicle for: (a) sharpening student-teachers' mathematical concepts; (b) raising their pedagogical awareness of the constructive role of fallacious reasoning in the development of mathematical knowledge. Course material development and data collection procedures are described. Results obtained in parts of the study through written responses and class-videotapes are analyzed and discussed. The findings indicate that the model of dealing with paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions and constructive learning.

One Point of View: Reclaiming School Mathematics

The framers of the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) call for a radical “design change” in all aspects of mathematics education. They believe that “evaluation is a tool for implementing the Standards and effecting change systematically” (p. 189). They warn, however, that “without changes in how mathematics is assessed, the vision of the mathematics curriculum described in the standards will not be implemented in classrooms, regardless of how texts or local curricula change” (p. 252).

Aspects of mathematics education in some third world universities

Information on principal aspects of the present state of mathematics education in 18 third world universities is presented. The principal tool used in collecting the information was a questionnaire which was widely distributed. Analysis of the information reveals important variations and similarities in the programs and structures of responding institutions. Some weaknesses are identified.