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1.
The mathematics behind the design and use of bar codes is outlined. The paper makes the point that while recent technological developmens are being used to enhance the way mathematics is taught, there is another equally important aspect of new technology. This is the mathematics needed to develop the technology which could influence future mathematics curricula in schools and colleges. This aspect is explained by looking closely at the mathematics used in bar code design.  相似文献   

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This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.  相似文献   

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We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann‐distributed limit structure. We demonstrate how this setting encompasses arbitrary weighted assemblies of tree‐like combinatorial structures. As an application, we establish smooth growth along lattices for small block‐stable classes of graphs. Random graphs with n vertices from such classes are shown to form a giant connected component. The small fragments may converge toward different Poisson Boltzmann limit graphs, depending along which lattice we let n tend to infinity. Since proper addable minor‐closed classes of graphs belong to the more general family of small block‐stable classes, this recovers and generalizes results by McDiarmid (2009).  相似文献   

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Many studies (such as Pepin in Learners and pedagogy, Sage Publications, London, 1999; Kaiser in ZDM 34(6):241–257, 2002; Park and Leung in Mathematics education in different cultural traditions: a comparative study of East Asia and the West. The 13th ICMI Study, pp. 227–238, Springer, New York, 2006) have revealed that there is a strong dependence on cultural traditions in mathematics teaching in different countries. Education in Germany is influenced by the Central and North European Didaktik tradition (Westbury in Teaching as a reflective practice: the German Didaktik tradition, L. Erlbaum Associates, Mahwah, pp. 15–39, 2000), while that in East Asia is influenced by Confucian heritage culture. However, there have not been studies investigating the relationships between these two cultural traditions and their influences on teaching and learning. This study aims at filling this gap in knowledge. Some commonalities in the aims and beliefs in the underlying philosophies in education in traditional China and Germany were found and are presented in this paper. Specifically, the relationship between cultural traditions and the implemented mathematics curriculum was investigated, using Berlin and Hong Kong as examples. It was found that culture affects the implemented curriculum in a complicated way and that other factors such as the intended curriculum and textbooks may also influence the implemented curriculum.  相似文献   

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Birgit Pepin 《ZDM》2014,46(5):837-842
This article provides a commentary to the eight papers of this issue of ZDM entitled “Researching the enacted mathematics curriculum.” It is structured around three main questions concerning (1) the layers of the curriculum addressed in the eight papers; (2) an identification of the main theoretical framework used, and an appreciation of this as compared to another European framework; and (3) challenges for future research on the enacted mathematics curriculum. The author outlines her views derived from a particular European perspective.  相似文献   

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In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various aspects of coding theory. Many examples and problems are included.  相似文献   

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Conclusions  A lot of the mathematics of MER is hidden and not only from the public but even from the applied scientists working on the mission. As briefly sketched above, for the scientists, this could be disastrous in a worst-case scenario. The hiding of mathematics, both in our everyday life and within science itself, is a matter not often discussed in public —which in itself is a disaster, taking into account the consequences the hiding of mathematics might have for the public. We like to think that this article may help let in some light. Another question raised by our work is that of beliefs in mathematics. Only occasionally are the beliefs of mathematicians discussed. We found repeatedly that mathematical elements of MER are not actually considered to be mathematics among the applied scientists themselves, not on first hand anyway. Is this due to the fundamentally different views of what mathematics is between applied scientists (including engineers) and pure scientists of the 20th century? We do not know. Finally, we comment on the nature of the mathematics involved in MER. Because of the extreme nature of a Mars mission, one might expect “extreme” mathematics, mathematics developed for the sole purpose of this mission.  相似文献   

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This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination).  相似文献   

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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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To take its due place in the world of education, Turkey has been through serious reform initiatives in the curriculums of various school subjects since 2003. The new Turkish elementary school curriculum was prepared considering the research studies conducted in Turkey and in other countries, as well as the educational systems of developed countries and previous experiences with mathematics education in Turkey. This study attempts to provide a perspective on the nature of the instructional tasks in the new elementary school mathematics curriculum. In particular, our focus is to explore the level of cognitive demands (LCD) in the algebra tasks provided in the national elementary mathematics curriculum guidebook. This curriculum document is a major resource for administrators, stakeholders, textbook publishers and ultimately for teachers. For every learning objective, it provides sample tasks to be used in mathematics instructions. In this study, our purpose is to explore the LCD of each of these tasks by utilizing a framework developed by Smith and Stein (Math Teach Middle School 3:344–350, 1998). The framework classifies mathematical tasks according to the level of demands: lower-level and higher-level demands. While the lower-level demands are related to memorization and procedures without connections, the higher-level demands are related to procedures with connections and doing mathematics. The findings revealed that 60% of algebra tasks for each grade level required higher LCD and a great majority of the remaining tasks were at the level of procedures without connections. The findings of the study particularly inform curriculum developers about issues regarding the quality of the tasks given in the curriculum guide and provide possible suggestions to improve the implementation of the curriculum change process.  相似文献   

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The UK national curriculum in mathematics, through the shape and space programme of study, requires that all pupils engage in activities which lead to an understanding of transformation of the plane. This paper introduces Zeno, a package which offers vector operations and transformation primitives in addition to Logo turtle graphics‐like features. It runs on any IBM‐compatible (with CGA or better graphics) or Apple Macintosh personal computer. The paper demonstrates how the Zeno environment can enable pupils to ‘discover’ the central mathematical principles which underpin transformation of the plane.  相似文献   

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In part 1 [1] of this work we showed how modern mathematicalresearch could, with a suitably chosen problem, be includedin the first year curriculum of undergraduate mathematicians.With the use of Computer Algebra Systems, even the average undergraduatemathematician can aspire to discover interesting yet still unexplainedbehaviour in many areas of mathematics. Of course, interestingresults still need a true expert to furnish proofs. This articlecontinues the exploration of the so-called Buffon puzzle anddemonstrates how it can be made accessible to undergraduates.Part 1 dealt with material delivered in lectures 1–12.In part 2, we describe work that can be carried out in lectures13–24.  相似文献   

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This issue of ZDM focuses on research related to the enacted curriculum from various perspectives within the context of the US educational system. In this editorial, we describe the broad view of curriculum enactment taken in this issue, highlighting that we mean more than just how instruction plays out within a classroom. For instance, enactment can occur at a national level as educational goals are enacted into a set of national objectives or standards. Enactment can occur as goals or standards are embedded into written curriculum materials or textbooks, both in terms of teacher guides and materials for students. Enactment can occur as teachers make decisions about how to use their written curriculum materials. Finally, enactment can occur as teachers and students engage and interact with written materials during classroom instruction. We elaborate briefly on these views and then outline the structure of this ZDM issue.  相似文献   

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Berinderjeet Kaur 《ZDM》2014,46(5):829-836
The official curriculum for mathematics in Singapore schools is based on a framework that has mathematical problem solving as its primary goal. It is detailed and one may say that the gap between the designated curriculum and teacher intended curriculum is often very narrow. This is so as the main source of instructional materials is textbooks which are very closely aligned with the official national curriculum. There is a dearth of research on the enactment of the curriculum in Singapore schools, with the few research studies done so far appearing to cover only a narrow focus. The author’s view is that, even though only a few such studies have been published, schools have always been engaged in small-scale investigations, the findings of which are necessary to guide decisions on matters related to choice of textbooks and pedagogies for improved student learning. Considering all the published research and the investigative work undertaken by educators in Singapore, it may be said that the conceptual model proposed by Remillard and Heck is rigorous. In addition, the issues in this particular issue of ZDM offer educators, both classroom teachers and others, very good perspectives for research on the enactment of the school mathematics curriculum.  相似文献   

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Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. The validity of this metaphor is questioned and the case is made that engineers do in fact use mathematics as more than a set of passive tools— that mathematical models for phenomena depend critically on the settings in which they are used and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and the authors suggest that it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways.  相似文献   

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