scholarly journals Teaching Units as the Integrating Core of Mathematics Education

2020 ◽  
pp. 25-36
Author(s):  
Erich Christian Wittmann
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Mathematics Teaching ◽  
Teaching Practice ◽  
Empirical Studies ◽  
Interdisciplinary Field ◽  
The Status ◽  
Psychology Pedagogy ◽  
Didactics Of Mathematics

AbstractHow to integrate mathematics, psychology, pedagogy and practical teaching within the didactics of mathematics in order to get unified specific theories and conceptions of mathematics teaching? This problem—relevant for theoretical and empirical studies in mathematics education as well as for teacher training—is considered in the present paper. The author suggests an approach which is based on teaching units (Unterrichtsbeispiele). Suitable teaching units incorporate mathematical, pedagogical, psychological and practical aspects in a natural way and therefore they are a unique tool for integration. It is the aim of the present paper to describe an approach to bridging the often deplored gap between didactics of mathematics teaching on one hand and teaching practice, mathematics, psychology, and pedagogy on the other hand. In doing so I relate the various aspects of mathematics education to one another. My interest is equally directed to teacher training and to the methodology of research in mathematics education. The structure of the paper is as follows. First I would like to make reference to and characterize an earlier discussion on the status and role of mathematics education; secondly, I will talk about problems of integration which naturally arise when mathematics education is viewed as an interdisciplinary field of study. The fourth and essential section will show how to tackle these problems by means of teaching units. The present approach is based on a certain conception of mathematics teaching which is necessary for appreciating Sect. 4. This conception is therefore explained in Sect. 3.

scholarly journals Mathematics Education as a ‘Design Science’

2020 ◽  
pp. 77-93
Author(s):  
Erich Christian Wittmann
Keyword(s):  
Mathematics Education ◽  
Design Science ◽  
Schools Of Education ◽  
Thinking Aloud ◽  
The Status ◽  
German Speaking ◽  
Nature Of Mathematics ◽  
Psychology Pedagogy ◽  
Didactics Of Mathematics

AbstractMathematics education (didactics of mathematics) cannot grow without close relationships to mathematics, psychology, pedagogy and other areas. However, there is the risk that by adopting standards, methods and research contexts from other well-established disciplines, the applied nature of mathematics education may be undermined. In order to preserve the specific status and the relative autonomy of mathematics education, the suggestion to conceive of mathematics education as a “design science” is made. In a paper presented to the twenty second Annual Meeting of German mathematics educators in 1988 Heinrich Bauersfeld presented some views on the perspectives and prospects of mathematics education. It was his intention to stimulate a critical reflection’among the members of the community’ on what they do and what they could and should do in the future (Bauersfeld 1988). The early seventies have witnessed a vivid programmatic discussion on the role and nature of mathematics education in the German speaking part of Europe (cf., the papers by Bigalke, Griesel, Wittmann, Freudenthal, Otte, Dress and Tietz in the special issue 74/3 of the Zentralblatt für Didaktik der Mathematik as well as Krygowska 1972). Since then the status of mathematics education has not been considered on a larger scale despite the contributions by Bigalke (1985) and Winter (1986). So the time is overdue for redefining the basic orientation for research; therefore, Bauersfeld’s talk could hardly have been more appropriate. In recent years the interest in a better understanding of the nature and role of mathematics education has also grown considerably at the international level as indicated, for example, by the ICMI-study on ‘What is research in mathematics education and what are its results?’ launched in 1992 (cf., Balacheff et al. 1992). The following considerations are intended both as a critical analysis of the present situation and an attempt to capture the specificity of mathematics education. Like Bauersfeld, the author presents them ‘in full subjectivity and in a concise way’ as a kind of ‘thinking aloud about our profession’. (The present paper concentrates on the didactics of mathematics although the line of argument pertains equally to the didactics of other subjects and also to education in general (cf., Clifford and Guthrie 1988, a detailed study on the identity crisis of the Schools of Education at the leading American universities).)

Activating Assessment Alternatives in Mathematics

1992 ◽  
Vol 39 (6) ◽  
pp. 24-29 ◽  
Author(s):  
David J. Clarke
Keyword(s):  
Mathematics Education ◽  
Mathematics Teaching ◽  
Teaching Practice ◽  
Mathematics Curriculum ◽  
Teaching Program ◽  
Evaluation Standards ◽  
Pencil And Paper ◽  
And Mathematics ◽  
Assessment Strategies

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 1, 2) emphasizes the role of evaluation “in gathering information on which teachers can base their subsequent instruction.” This strong sense of assessment's informing instructional practice is also evident in the materials arising from the Australian Mathematics Curriculum and Teaching Program (Clarke 1989: Lovitt and Clarke 1988, 1989). Both projects offer their respective mathematics-education communities a set of goal much broader than those traditionally conceived for mathematics instruction. The adoption of these goals by mathematics teachers and school systems demands the use of new assessment strategies if the restructuring of the mathematics curriculum and mathematics-teaching practice is to be effected. Mathematics education must not restrict itself to those goals that can be assessed only through conventional pencil-and-paper methods.

Mathematics Textbook as an Object of Research/Matematički udžbenik kao predmet istraživanja

2014 ◽  
Vol 16 ◽  
Author(s):  
Dubravka Glasnović Gracin
Keyword(s):  
Mathematics Education ◽  
Mathematical Knowledge ◽  
Empirical Studies ◽  
Mathematics Textbooks ◽  
Mathematics Textbook ◽  
Mathematics Book

AbstractA mathematics textbook can be described as an officially authorized and pedagogically designed mathematics book written to provide mathematical knowledge to students. This description suggests the authority of the textbook - because it has been authorized by an administrative source and because it deals with authorized knowledge. This paper provides an overview of research on mathematics textbooks. The emphasis is on questions concerning the extent to which and how textbooks are used in mathematics education in Croatia and in the world.Research results show that mathematics textbooks are widely used in mathematics education worldwide. This finding points to the need for research on the content and structure of textbooks. Such studies are combined with the associated results on how textbooks are used in the classroom and which methods teachers apply in using textbooks in mathematics education. The results of the empirical studies show that teachers use textbooks for lesson preparation and pupils use mathematics textbooks for exercises to a great extent. These results imply that such an important role of textbooks in mathematics education deserves additional attention, with the goal of understanding and improving mathematics education.Key words: mathematics education; overview; research on textbook---SažetakMatematički udžbenik može se opisati kao službeno autorizirana i pedagoki osmiljena matematička knjiga napisana s ciljem da učenicima ponudi matematičke sadržaje. Taj opis sugerira autoritet udžbenika jer ga je autorizirao administrativni izvor i jer sadrži autorizirano znanje. Ovaj članak daje pregled istraživanja matematičkih udžbenika, a naglasak je na pitanjima u kojoj mjeri i kako se udžbenici koriste u nastavi matematike u Hrvatskoj i u svijetu.Rezultati raznih istraživanja pokazuju da se udžbenici u velikoj mjeri koriste u nastavi matematike irom svijeta. Taj nalaz ukazuje na potrebu za istraživanjem sadržaja i strukture matematičkih udžbenika. Uz to, prikazani su rezultati istraživanja o tome na koji se način udžbenici koriste u razredu i koje metode nastavnici prakticiraju prilikom upotrebe udžbenika na nastavi. Rezultati empirijskih studija pokazuju da nastavnici udžbenike većinom koriste za pripremu nastavnog sata, a učenici udžbenike koriste u najvećoj mjeri za vježbanje. Ti rezultati ukazuju na to da tako važna uloga udžbenika u matematičkom obrazovanju zaslužuje dodatnu pažnju s ciljem razumijevanja i poboljanja nastave matematike.Ključne riječi: istraživanje udžbenika; nastava matematike; pregled.

scholarly journals HISTORY OF MATHEMATICS EDUCATION IN PRIMARY SCHOOL AND IN TEACHER TRAINING IN BRAZIL

2020 ◽  
Vol 24 ◽  
Author(s):  
Wagner Rodrigues Valente ◽  
Maria Célia Leme da Silva
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Primary School ◽  
Mathematics Teaching ◽  
History Of Mathematics ◽  
Theoretical Hypothesis ◽  
Disciplinary Field ◽  
History Of ◽  
The 19Th Century ◽  
The Relationship

Abstract This article discusses results from research developed on the transformations in mathematics teaching in primary school and the mathematics in teacher training from the 19th century to the mid-20th century in Brazil. We have analyzed the understanding of the relationship between the mathematical disciplinary field and pedagogy in order to confirm the theoretical hypothesis that the interactions between the two fields produce mathematics of different natures, which are interconnected.

History of mathematics, mathematical histories, storytelling in Hungarian mathematics education

2019 ◽  
pp. 137-148
Author(s):  
Katalin Gosztonyi
Keyword(s):  
Mathematics Education ◽  
Historical Perspective ◽  
Teaching Practice ◽  
History Of Mathematics ◽  
Guided Discovery ◽  
Mathematics History ◽  
History Of ◽  
Nature Of Mathematics ◽  
Written Sources

History of mathematics is rarely used in Hungarian mathematics education, and even more rarely goes beyond anecdotic mentions of history. In this paper I will argue that despite of this phenomenon, a historical perspective on mathematics, in a more general way, plays a crucial role in a specific Hungarian tradition of mathematics education, called felfedeztető matematikaoktatás (“teaching mathematics by guided discovery”). I will revisit the epistemological background of this approach, analyse the role of history in this view on the nature of mathematics and its teaching, and illustrate the analysis by some examples from written sources and nowadays teaching practice. Classification: A30, D20, D40. Keywords: History of mathematics, history in mathematics education, guided discovery in mathematics education.

scholarly journals O ensino da matemática em meio à tecnologia: desafio aos programas de formação de professores

2015 ◽  
Vol 4 (2) ◽  
Author(s):  
Marcelo Máximo Purificação ◽  
Teresa Pessoa
Keyword(s):  
Mathematics Education ◽  
Teacher Training ◽  
Social Space ◽  
Teaching Practice ◽  
Educational Process ◽  
Math Teachers ◽  
Use Of Technology ◽  
De Se ◽  
Technological Educational ◽  
Society Today

Resumo: É fato que a tecnologia se faz presente em todas as camadas da sociedade atual. A escola, como espaço social marcado pela diversidade, não mais consegue deter a tecnologia trazida pelos estudantes e a sua fácil acessibilidade. Daí a necessidade de se pensar o processo educacional de modo a integrar a educação matemática à tecnologia. O presente artigo faz uma análise de alguns aspectos importantes sobre o desafio dos programas de formação de professores de matemática frente às inovações tecnológicas. Metodologicamente foi realizada uma análise documental, através da qual se buscou conhecer esses desafios. Para isso, foi importante conhecer os componentes tecnológicos, educacionais e profissionais, mostrando as relações dialéticas estabelecidas por eles e buscando compreender como as mesmas se aplicam na formação do perfil docente que estamos a formar. Concluiu-se que com uso da tecnologia o professor se familiariza com ela, e que seu domínio pode levá-lo a ter um novo olhar sobre ela, procuramos investigar se o uso de tecnologia pode auxiliar na produção de mudanças na prática pedagógica. Palavras-chave: Educação Matemática. Formação de Professor. Ensino e Tecnologia.   TEACHING MATH AMIDST THE TECHNOLOGY: THE CHALLENGE PROGRAMS TEACHER TRAINING Abstract: It is true that technology is present in all layers of society today. The school, as a social space marked by diversity, is no longer able to stop the technology brought by students and their easy accessibility. So, it’s important to think about  the educational process in order to integrate mathematics education technology. Methodologically it carried out a document analysis, through which it sought to meet these challenges. This article analyzes some important aspects of the challenge of math teachers programs besides all the technological innovations. So, it is important to know the technological, educational and professional components, showing the dialectical relationships established by these matters and how they apply in the training of teaching profile that we are forming. It is concluded that with the use of technology teacher becomes familiar with it, and that your domain can cause him to take a fresh look about it, we investigate the use of technology can help in producing changes in teaching practice. Keywords: Mathematics education. Teacher training. Education and Technology. 

scholarly journals The Role of Theory in L2 Empirical Research on Language Complexity, Accuracy and Fluency

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Yanina Tsupa
Keyword(s):  
Empirical Research ◽  
Empirical Studies ◽  
Review Of Literature ◽  
Linguistic Complexity ◽  
Language Complexity ◽  
The Status ◽  
Lexical Complexity

This forum attempts to uncover the role played by theory in three empirical studies. To that end, in the sections that follow, I will begin with the review of literature on language complexity, accuracy, and fluency. Next, I will report on metric indices employed in the studies to measure the phenomenon of linguistic complexity and the results pertaining to grammatical and lexical complexity. Then I proceed with describing the status of theory in empirical research and the challenges research on CAF faces. The closing presents the discussion on how theory impacted the design of the empirical studies sampled for this paper.

scholarly journals How to Strengthen Mathematics Teaching in College Education

2019 ◽  
Vol 3 (2) ◽  
pp. 117
Author(s):  
Jiayou Song
Keyword(s):  
Higher Education ◽  
Mathematics Education ◽  
21St Century ◽  
Mathematics Teaching ◽  
Modern Science ◽  
College Education ◽  
Colleges And Universities ◽  
Vital Role ◽  
Teaching Process

<p>The 21st century is an era of the coexistence of opportunities and challenges. Domestic higher education and modern science and technology have obtained unprecedented development, making people more clearly understand the vital role of mathematics, which is both pressure and power for college mathematics teaching. In addition, due attention should be taken on the problems in mathematics teaching. This paper dwells on the problems and opportunities of mathematics education in colleges and universities, hoping to find and solve the root causes of problems in the teaching process from three aspects of teachers, schools and students, so as to improve the quality and efficiency of mathematics teaching.</p>

scholarly journals Collective Teaching Experiments: Organizing a Systemic Cooperation Between Reflective Researchers and Reflective Teachers in Mathematics Education

2020 ◽  
pp. 239-248
Author(s):  
Erich Christian Wittmann
Keyword(s):  
Mathematics Education ◽  
Learning Environments ◽  
Mathematics Teaching ◽  
Empirical Studies ◽  
Empirical Information ◽  
Reflective Teachers ◽  
Empirical Foundation ◽  
Teaching Experiments

AbstractThe success of any substantial innovation in mathematics teaching depends crucially on the ability and readiness of teachers to make sense of this innovation and to transform it effectively and creatively to their context. This refers not only to the design and the implementation of learning environments but also to their empirical foundation. Empirical studies conducted in the usual style are not the only option for supporting the design empirically. Another option consists of uncovering the empirical information that is inherent in mathematics by means of structure-genetic didactical analyses. In this chapter, a third option is proposed as particularly suited to bridge the gap between didactical theories and practice: collective teaching experiments.

Sign in / Sign up

Export Citation Format

Share Document