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1.
How Students Attempt to Reduce Abstraction in the Learning of Mathematics and in the Learning of Computer Science 总被引：2，自引：2，他引：0
Orit Hazzan 《Computer Science Education》2013,23(2):95-122
This article focuses on ion and ways in which students cope with abstraction. The article has two goals: first, it illustrates how the theme of reducing abstraction (Hazzan, 1999) is useful for analyzing students' thinking about abstract concepts in mathematics and in computer science; second, it demonstrates how theories based on mathematics education research can be applied to analyzing students' understanding of computer science concepts. The main section of the article analyzes the understanding of concepts from four fields – abstract algebra, computability, data structures and differential equations – through the lens of reducing abstraction. The analysis shows that a wide range of cognitive phenomena can be explained by one theoretical framework. 相似文献
2.
Michael Otte 《Educational Studies in Mathematics》2007,66(2):243-255
History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is
concerned with questions of justification. Both play an essential role within the educational context. But there is a problem
because genuine historical studies necessitate ever greater particularity whereas mathematics and philosophy require generality
and abstraction. The paper offers some methodological reflections about these matters together with two case studies from
nineteenth century history of arithmetic and integration theory, respectively, which try to strike a balance between the directly
opposed requirements. 相似文献
3.
During the last two decades many researchers in mathematics and science education have studied students’ conceptions and ways of reasoning in mathematics and science. Most of this research is content‐specific. It was found that students hold alternative ideas that are not always compatible with those accepted in science. It was suggested that in the process of learning science or mathematics, students should restructure their specific conceptions to make them conform to currently accepted scientific ideas. In our work in mathematics and science education it became apparent that some of the alternative conceptions in science and mathematics are based on the same intuitive rules. We have so far identified two such rules: “More of A, more of B”, and “Subdivision processes can always be repeated”. The first rule is reflected in subjects’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.) in all tasks related to intensive quantities (density, temperature, concentration, etc.) and in all tasks related to infinite quantities. The second rule is observed in students’, preservice and inservice teachers’ responses to tasks related to successive division of material and geometrical objects and in seriation tasks. In this paper, we describe and discuss these rules and their relevance to science and mathematics education. 相似文献
4.
以《历学会通》为依据,探讨了薛凤祚的数学观。指出：明末清初,传教士传入的西学,使中国民间科学家薛凤祚认识到数学这一学科在自然科学以及社会科学中的地位和重要意义,形成了自己对数学的独特认识。薛凤祚＂无一事不本于数＂、＂明于求理＂和＂象数之学＂的数学观具有一定的科学性。薛凤祚的数学观对于清代数学发展起到一定的作用,对于当代数学发展也有一定的指导意义。 相似文献
5.
Giuliano Reis Richard Barwell 《International Journal of Science and Mathematics Education》2013,11(5):1067-1085
The day-to-day business of being a science or mathematics teacher involves the continuous assessment of students. This, in turn, is an inherently discursive process. The aim of the present study is to examine some of the specific discursive practices through which science and mathematics knowing is jointly produced through classroom interaction. In particular, we examine the coproduced nature of two students’ not knowing—one in an outdoor elementary school science lesson and the other in an elementary school mathematics lesson. Our analysis is based on ideas in discursive psychology and challenges conventional interpretations of students’ academic performance in school science and mathematics. 相似文献
6.
Howard Woodhouse 《Interchange》2012,43(1):1-23
In several of his works, Alfred North Whitehead (1861–1947) presents mathematics as a way of learning about general ideas that increase our understanding of the universe. The danger is that students get bogged down in its technical operations. He argues that mathematics should be an integral part of a new kind of liberal education, incorporating science, the humanities, and “technical education” (making things with one’s hands), thereby integrating “head-work and hand-work.” In order to appreciate the role mathematics plays in modern science, students should understand its diverse history which is capable of bringing abstract ideas to life. Moreover, mathematics can discern the alternating rhythms of repetition and difference in nature constituting the periodicity of life. Since these same rhythms are to be found in his theory of learning as growth, there appears to be a pattern linking Whitehead’s approach to mathematics and his educational philosophy. 相似文献
7.
奚小平 《湖北成人教育学院学报》2014,(4):64-65
高等数学是理工科院校的基础学科之一,作为一门重要学科,其具有高度的抽象性、广泛的应用性及严密的逻辑性等特点,因此,加强高等数学精品课程的建设,改善教学质量有着重要的现实意义。本文提出了高职院校建设高等数学精品课程的几点建议,并对未来发展需要面临的新课题进行了讨论。 相似文献
8.
Dr. Colin Gauld 《Research in Science Education》1991,21(1):133-140
The existence of similarities between the ideas of modern students and those of early scientists have led to suggestions about
how the history of science can be used to help students undergo similar transitions to those experienced by early generations
of scientists. In this paper attention is focused not only on these similarities but also on some crucial differences between
the processes and concepts or conceptual frameworks of these two groups of people. In the light of these similarities and
differences some of the implications for producing and using historical material in the science classroom are discussed.
Specializations: Physics education, concept development, history and philosophy of science and science teaching. 相似文献
9.
在数学教育中渗透人文教育,弘扬人文精神,是素质教育的要求,是我国新课程改革所规定的数学教育的目的,更是数学教育发展的必然。人文数学是数学与人文的结合,是用数学的精神、原则、思想和方法对学生进行文化陶冶和人格塑造,让数学教育在传授科学的同时起到提高人的文化素养和教化人格的作用。教育者可从创设特色人文课堂情境、引导学生自主学习、重视学生的个体差异三个方面实现人文教育在数学教学中的渗透,进而实现科学与人文在数学教学中有机的结合,进而促进学生人文素养的提升。 相似文献
10.
Katherine Chesnutt M. Gail Jones Elysa N. Corin Rebecca Hite Gina Childers Mariana P. Perez Emily Cayton Megan Ennes 《科学教学研究杂志》2019,56(3):302-321
This study examined the relationship between students' (N = 229) concepts of size and scale and students' achievement in science and mathematics over a 3-year period. Size and scale are considered one of the big ideas in science that permeates disparate science and mathematics content areas, yet little is known about the relationship between students' conceptualization of size and scale and students' achievement in science and mathematics. The study used a modified panel longitudinal design to follow the same class of students over a 3-year period. The goal was to explore whether understandings of size and scale are related to achievement in mathematics and science. Results indicated a strong positive significant relationship existed between students' understanding of size and scale and students' science achievement in grades 5 and 8. There was a positive significant relationship between students' concepts of size and scale and students' mathematics achievement in grades 5, 6, 7, and 8. An examination of the relationships is included as well as a discussion of the integration of crosscutting concepts into science and mathematics instruction as a way to support deep learning. 相似文献
11.
Science as inquiry and mathematics as problem solving are conjoined fraternal twins attached by their similarities but with distinct differences. Inquiry and problem solving are promoted in contemporary science and mathematics education reforms as a critical attribute of the nature of disciplines, teaching methods, and learning outcomes involving understandings, attitudes, and processes. The investigative and quantitative processes involved in scientific inquiry include seeking problems, identifying researchable questions, proposing hypotheses, designing fair tests, collecting and interpreting data as evidence for claims, constructing evidence-based arguments, and communicating knowledge claims. Within this empirical context, science and mathematics come together to solve problems with evidence, construct knowledge claims, communicate claims, and persuade others that the claims are valid and useful. This study examined the intersection of inquiry and problem solving and the use of mathematics in 26 extracurricular open science inquiries. The category and the appropriateness of the mathematical procedures revealed these students used measurement, numeracy skills of counting and calculation, and tables and graphs in their science inquiries. It was found that most measurements in the science inquiries were used appropriately, but there is room for improvement with other mathematical procedures that involve higher-level thinking skills, such as analyzing and calculating numerical data and interpreting graphs and tables. The findings imply that mathematics and science are connected in inquiry and should be extended to solve real-life problems and that instruction should emphasize comprehending and interpreting data. 相似文献
12.
There is a growing interest in the mathematics education community in the notion of abstraction and its significance in the learning of mathematics. Reducing abstraction is a theoretical framework that examines learners behavior in terms of coping with abstraction level. It refers to situations in which learners are unable to manipulate concepts presented in a given problem; therefore, they unconsciously reduce the level of abstraction of the concepts involved to make these concepts mentally accessible. This framework has been used for explaining students conception in different areas of undergraduate mathematics and computer science. This article extends the applicability scope of this framework from undergraduate mathematics to school mathematics. We draw on recently published research articles and exemplify how students behavior can be described in terms of various interpretations of reducing abstraction level. 相似文献
13.
邱浩 《南昌教育学院学报》2010,25(1)
随着科学技术的发展,尤其是计算机技术的发展,数学的应用愈来愈广泛。那么在大学里教数学,我们应该如何进行教学?笔者认为,作为数学老师,不仅要给学生介绍数学的重要成果和应用的方法,更重要的是介绍数学的思想,启发学生进行学习。 相似文献
14.
Force in modern classical mechanics is unique, both in terms of its logical character and the conceptual difficulties it causes. Force is well defined by a set of axioms that not only structures mechanics but science in general. Force is also the dominant theme in the ‘misconceptions’ literature and many philosophers and physicists alike have expressed puzzlement as to its nature. The central point of this article is that if we taught mechanics as the forum to discuss the nature of mechanics itself, then we would serve to better secure a learner’s understanding and appreciation of both science and mathematics. We will attempt to show that mechanics can provide the opportunity for students to enter this meta-discourse by engaging in Socratic discussion, entertaining thought experiments, comparisons made between force as defined within mechanics as a modern axiomatic system with Newton’s quantitative definition of force, how the concepts of force prior to Galileo and Newton can be used as a teaching aid with respect to student intuitive ideas and how mathematics was brought to bear on what is given empirically. Mechanics provides this opportunity and pedagogically may require it due to its axiomatic nature. 相似文献
15.
Stephanie J. Hathcock Daniel L. Dickerson Angela Eckhoff Petros Katsioloudis 《Research in Science Education》2015,45(5):727-748
Creativity can and should play a role in students’ science experiences. Beghetto (Roeper Review 29(4):265–270, 2007) suggested a framework for teachers to assist students in transforming their creative ideas into creative products. This framework involves taking time to listen to students’ ideas, helping them recognize the constraints of a task, and giving them multiple opportunities to think through and try their ideas. Ill-structured problems, such as those found in inquiry and engineering design activities, provide excellent opportunities for students to experience creative processing and express their creativity through product creation. These types of problems are typically challenging, but the use of appropriate questioning has been shown to assist students in solving problems. This multiple case study investigated the use of inquiry-based questioning as a means of supporting creativity within a design-based science, technology, engineering, and mathematics (STEM) activity. Findings suggest that groups facilitated by inquiry-based questioning strategies were better able to solve an ill-structured problem and achieved a more linear progression toward creative products than groups who were not facilitated by inquiry-based questions. 相似文献
16.
常天兴 《佳木斯教育学院学报》2012,(1):144-144
高等数学在教学过程中教学内容多,教学课时较少,理论性强,具有较高的抽象性。学生在学习过程中感到枯燥无味,很多学生认识不到学习数学的重要性。况且传统的数学教学中强调更多的是知识的传授,注重教给学生一套从定义、公理到定理、推论等逻辑体系,着力培养学生严谨的科学精神,忽略了数学应用能力和个性的培养,忽略了学习兴趣的激发,本文旨在为高等数学的教学提供参考帮助。 相似文献
17.
《老子》不是兵学著作,但包含着丰富的军事思想。《老子》与《孙子兵法》有着共同的时代背景,《老子》的产生要早于《孙子兵法》。孙子论兵多有与《老子》相通之处,《孙子兵法》在诸多方面受到《老子》的影响。 相似文献
18.
S. Selcen Guzey Tamara J. Moore Michael Harwell Mario Moreno 《Journal of Science Education and Technology》2016,25(4):550-560
In many countries around the world, there has been an increasing emphasis on improving science education. Recent reform efforts in the USA call for teachers to integrate scientific and engineering practices into science teaching; for example, science teachers are asked to provide learning experiences for students that apply crosscutting concepts (e.g., patterns, scale) and increase understanding of disciplinary core ideas (e.g., physical science, earth science). Engineering practices and engineering design are essential elements of this new vision of science teaching and learning. This paper presents a research study that evaluates the effects of an engineering design-based science curriculum on student learning and attitudes. Three middle school life science teachers and 275 seventh grade students participated in the study. Content assessments and attitude surveys were administered before and after the implementation of the curriculum unit. Statewide mathematics test proficiency scores were included in the data analysis as well. Results provide evidence of the positive effects of implementing the engineering design-based science unit on student attitudes and learning. 相似文献
19.
《老子》不是兵学著作,但包含着丰富的军事思想。《老子》与《孙子兵法》有着共同的时代背景,《老子》的产生要早于《孙子兵法》。孙子论兵多有与《老子》相通之处,《孙子兵法》在诸多方面受到《老子》的影响。 相似文献
20.
A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was developed, which was used in the teaching of mathematics in Austria at the beginning of the twentieth century and applied to different subjects ranging from simple operations in arithmetic to calculus. Besides the relevance of this method—also named the “Jacob method” after Josef Jacob who proposed it—to teaching practice, it could also be considered interesting in a wider context with reference to the mind-body problem. In particular, the importance that Jacob gives to “muscular activity” in the process of forming and elaborating mathematical concepts, derived from Mach, resounds in the current debate on embodied cognition, where cognitive processes are understood not as expressions of an abstract and merely computational mind but as based on our physicality as human beings, equipped not just with a brain but also a (whole) body. This model has been applied to mathematics in the “theory of embodied mathematics”, the objective of which is to study, with the methods and apparatus of embodied cognitive science, the cognitive mechanisms used in the human creation and conceptualisation of mathematics. The present article shows that the “Jacob method” may be considered a historical example of didactical application of analogous ideas. 相似文献