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1.
This article explores the following question: What does it mean to enact curriculum? In order to do so, it offers a conceptualization of the enacted curriculum and situates it within a curriculum policy, design, and enactment system. The system depicts the formal and operational domains in which curricular aims and objectives are developed and curriculum plans formulated and enacted. The authors situate the enacted mathematics curriculum in the operational part of the system and define it as the interactions between teachers and students around mathematical tasks of a lesson and collection of lessons, but argue that understanding what it means to enact curriculum involves examining the many places within the system that curricular elements are translated and transformed. The authors describe each of the articles in this special issue with respect to the framework.  相似文献   

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This paper discusses issues related to the potential adoption of inquiry-based learning (IBL) projects in mathematics in the United States. To explain the challenges faced in making a place for IBL in the mathematics curriculum, we describe the historical demands of working with a diverse, highly distributed educational system (that is, a system that does not have a central educational decision-making agency with the authority to mandate nation-wide changes), the impact of high-stakes tests to either open or limit the potential for curricular changes, and the changing context in the United States owing to the emergence of the Common Core State Standards in Mathematics (CCSS-M) and nationwide high-stakes assessments designed to be consistent with the CCSS-M. We identify a number of dimensions along which there would be challenges for the implementation of IBL in US school mathematics, including: perceived societal needs; schooling traditions; the specific framing of CCSS-M goals pertaining to problem solving, communicating and reasoning, and modeling and data analysis; and the readiness of the US teaching force to implement IBL. We then consider the issue of scaling up interventions such as IBL, and the politics involved therein.  相似文献   

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This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.  相似文献   

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A rational discussion of the use of Computer algebra systems (CAS) in mathematics teaching in general education needs an explicit image of (general) mathematics education, an explication of global perspectives and goals on mathematics teaching focusing on general education (chapter 1). The conception of general education according to the «ability of communication with experts» described in chapter 2 can be such an orientation for analysing, considering, classifying and assessing the didactical possibilities of using CAS. CAS are materialised mathematics allowing for more or less exhaustive outsourcing of operative (also symbolically) knowledge and skills to the machine. This frees up space of time as well as mental space for the development of those competences being in our view relevant for general mathematics education. In chapter 3 the idea of outsourcing and the role of CAS for it is discussed more detailed as well as consequences being possible for the CAS-supported teaching of mathematics. Beyond, CAS can be didactically used and reflected as a model of communication between (mathematical) experts and lay-persons (chapter 4). Chapter 5 outlines some research perspectives.  相似文献   

5.
According to previous studies, inquiry-based mathematics teaching enhances learning. However, teachers need support in implementing this type of teaching. In this study, a high school teacher was given a short preplanned inquiry-based mathematics teaching unit that included activities with GeoGebra. The teacher was interviewed after every lesson to explore her reflections after teaching. I analyzed how the teacher described the differences between her regular teaching style and the teaching unit and the pros and cons of the teaching unit. The teacher reflected on the roles of the teacher and students, depth of students’ knowledge, her stance toward the teaching unit, constraints for using this type of teaching approach, and challenges in guiding the students. The results give insights to what kind of reflections on technology-enriched inquiry-based mathematics teaching it is possible to initiate with short preplanned teaching units.  相似文献   

6.
This study addresses aspects that should be considered in every investigation concerning the reality of the subject being investigated, which in turn provide the basis for the procedures adopted to carry out the research. It speaks about the analysis of the procedures chosen to carry out the research. It is assumed that this care should be taken by the researcher at the moment the research procedures are being defined and made explicit. It is argued that the consonance between the ontological and epistemological dimensions of “what” and “how” to investigate the subject of investigation confers a degree of confidence to the research findings. The search for that confidence transcends analyses based only on calculations and explanations of methodological procedures, regardless of how well founded they are. This study addresses mathematics education specifically, adopting a phenomenological perspective. It is focused on the constitution of mathematical idealities and of mathematics as a science under the perspective of the Husserlian phenomenological conception of reality and knowledge. Characteristics of a phenomenological pedagogy are presented, which is carried out through work that is always intentional, with the educator taking account of what occurs with himself/herself, with the life world of the school, and with the student. The student is seen as a person and as being with others, his/her classmates, and the theme is addressed in the context of the field of inquiry under focus, with the teacher and with his/her “surroundings”.  相似文献   

7.
Stephen Lerman 《ZDM》2013,45(4):623-631
Whilst research on the teaching of mathematics and the preparation of teachers of mathematics has been of major concern in our field for some decades, one can see a proliferation of such studies and of theories in relation to that work in recent years. This article is a reaction to the other papers in this special issue but I attempt, at the same time, to offer a different perspective. I examine first the theories of learning that are either explicitly or implicitly presented, noting the need for such theories in relation to teacher learning, separating them into: socio-cultural theories; Piagetian theory; and learning from practice. I go on to discuss the role of social and individual perspectives in authors’ approach. In the final section I consider the nature of the knowledge labelled as mathematical knowledge for teaching (MKT). I suggest that there is an implied telos about ‘good teaching’ in much of our research and that perhaps the challenge is to study what happens in practice and offer multiple stories of that practice in the spirit of “wild profusion” (Lather in Getting lost: Feminist efforts towards a double(d) science. SUNY Press, New York, 2007).  相似文献   

8.
The role of metacognition in mathematics education is analyzed based on theoretical and empirical work from the last four decades. Starting with an overview on different definitions, conceptualizations and models of metacognition in general, the role of metacognition in education, particularly in mathematics education, is discussed. The article emphasizes the importance of metacognition in mathematics education, summarizing empirical evidence on the relationships between various aspects of metacognition and mathematics performance. As a main result of correlational studies, it can be shown that the impact of declarative metacognition on mathematics performance is substantial (sharing about 15–20% of common variance). Moreover, numerous intervention studies have demonstrated that “normal” learners as well as those with especially low mathematics performance do benefit substantially from metacognitive instruction procedures.  相似文献   

9.
Luis Moreno-Armella 《ZDM》2014,46(4):621-633
There is a problem that goes through the history of calculus: the tension between the intuitive and the formal. Calculus continues to be taught as if it were natural to introduce the study of change and accumulation by means of the formalized ideas and concepts known as the mathematics of ε and δ. It is frequently considered as a failure that “students still seem to conceptualize limits via the imagination of motion.” These kinds of assertions show the tension, the rift created by traditional education between students’ intuitions and a misdirected formalization. In fact, I believe that the internal connections of the intuition of change and accumulation are not correctly translated into that arithmetical approach of ε and δ. There are other routes to formalization which cohere with these intuitions, and those are the ones discussed in this paper. My departing point is epistemic and once this discussion is put forward, I produce a narrative of classroom work, giving a special place to local conceptual organizations.  相似文献   

10.
This article covers a project conducted by the Freudenthal Institute from August 1991 to September 1994 entitled “The graphics calculator in mathematics education.” The theory of realistic mathematics education was taken as the point of departure for formulating the hypotheses. The developmental research design was used. Observation of the students' behavior during the experimental lessons supports the premise that the graphics calculator can stimulate the use of realistic contexts, the exploratory and dynamic approach to mathematics, a more integrated view of mathematics, and a more flexible behavior in problem solving.  相似文献   

11.
Karl Josef Fuchs 《ZDM》2003,35(1):20-23
The paper gives an overview of the increasing influence of Computer Algebra Systems in Mathematics Education. On one hand the new aims when teaching this new media will be shown. On the other hand examples will illustrate the principles behind the contents chosen for the lectures. Basic ideas of mathematics and computerscience will appear just as well as basic concepts of Mathematics Education.  相似文献   

12.
Werner Blum 《ZDM》2014,46(4):697-698
This article pays tribute to the German mathematics educator Arnold Kirsch (1922–2013), especially for his contributions to calculus education. The main aim of his work was to make mathematics accessible to learners so that they are able to genuinely understand the subject.  相似文献   

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This paper describes the broad lines of the development of mathematics education in Brazil since 1500, emphasizing the development of secondary mathematics education. We divide this history into seven major periods, based on the political and cultural development of Brazilian society, and stress the characteristics of each period.  相似文献   

17.
In summer 2006 the University of Education in Weingarten, Germany, and East China Normal University, Shanghai, performed a semi-virtual seminar with mathematics students on “Mathematics and Architecture”. The goal was the joint development of teaching materials for German or Chinese school, based on different buildings such as “Nanpu Bridge”, or the “Eiffel Tower”. The purpose of the seminar was to provide a learning environment for students supported by using information and communication technology (ICT) to understand how the hidden mathematics in buildings should be related to school mathematics; to experience the multicultural potential of the international language “Mathematics”; to develop “media competence” while communicating with others and using technologies in mathematics education; and to recognize the differences in teaching mathematics between the two cultures. In this paper we will present our ideas, experiences and results from the seminar.  相似文献   

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The participation of students in processes of collective argumentation is seen as a fundamental condition for enabling mathematics learning in classroom settings. Using data from a finished research project on argumentation in primary mathematics classrooms it will be shown, that in elementary education these processes are of a narrative character.  相似文献   

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