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1.
Savas Basturk 《Educational studies》2010,36(3):283-298
The aim of this study is to investigate students’ conceptions about proof in mathematics and mathematics teaching. A five‐point Likert‐type questionnaire was administered in order to gather data. The sample of the study included 33 first‐year secondary school mathematics students (at the same time student teachers). The data collected were analysed and interpreted using the methods of qualitative and quantitative analysis. The results have revealed that the students think that mathematical proof has an important place in mathematics and mathematics education. The students’ studying methods for exams based on imitative reasoning which can be described as a type of reasoning built on copying proof, for example, by looking at a textbook or course notes proof or through remembering a proof algorithm. Moreover, they addressed to the differences between mathematics taught in high school and university as the main cause of their difficulties in proof and proving. 相似文献
2.
Takeshi Miyakawa 《Educational Studies in Mathematics》2017,94(1):37-54
This paper reports the results of an international comparative study on the nature of proof to be taught in geometry. Proofs in French and Japanese lower secondary schools were explored by analyzing curricular documents: mathematics textbooks and national curricula. Analyses on the three aspects of proof—statement, proof, and theory—suggested by the notion of Mathematical Theorem showed differences in these aspects and also differences in the three functions of proof—justification, systematization, and communication—that are seemingly commonly performed in these countries. The results of analyses imply two major elements that form the nature of proof: (a) the nature of the geometrical theory that is chosen to teach and (b) the principal function of proof related to that theory. This paper suggests alternative approaches to teach proof and proving and shows that these approaches are deeply related to the way geometry is taught. 相似文献
3.
Although studies on students’ difficulties in producing mathematical proofs have been carried out in different countries,
few research workers have focussed their attention on the identification of mathematical proof schemes in university students.
This information is potentially useful for secondary school teachers and university lecturers. In this article, we study mathematical
proof schemes of students starting their studies at the University of Córdoba (Spain) and we relate these schemes to the meanings
of mathematical proof in different institutional contexts: daily life, experimental sciences, professional mathematics, logic
and foundations of mathematics. The main conclusion of our research is the difficulty of the deductive mathematical proof
for these students. Moreover, we suggest that the different institutional meanings of proof might help to explain this difficulty.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
Kazutoshi Aso 《Community College Journal of Research & Practice》2013,37(5-6):355-360
In general, students in school learn mathematical concepts by words. Some mathematical concepts, however, are difficult to understand by words. This is especially true of some of the more complicated concepts in mathematics taught in higher education. For students who are studying to become engineers, it is very important to understand mathematics intuitively. Ways must be found for them to learn mathematics that will promote intuitive understanding. We often find that a figure helps us understand mathematical concepts and provides important clues for solving problems. A figure may serve as a concrete expression of an abstract mathematical concept; it is a visual image of the mathematical concept. A visual image is a figure with no words but its title. The aim of this article is to introduce some visual images that are effective in mathematical education. 相似文献
5.
Gabriel J. Stylianides 《International Journal of Science and Mathematics Education》2008,6(1):191-215
Despite widespread agreement that proof should be central to all students’ mathematical experiences, many students demonstrate poor ability with it. The curriculum
can play an important role in enhancing students’ proof capabilities: teachers’ decisions about what to implement in their
classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused
on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials
offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that
can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the
proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an
analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed. 相似文献
6.
Amal Hussain Alajmi 《Journal of Mathematics Teacher Education》2009,12(4):263-283
Computational estimation has not yet established a place in the Kuwaiti national curriculum. An attempt was made to include
it during the early 1990s, but it was dropped by the Kuwaiti Ministry of Education because of the difficulties teachers had
teaching it. In an effort to provide guidance for reintroducing the concept into the curriculum, this study reports on mathematics
teachers’ understanding of the meaning of computational estimation and their views about its significance in the elementary
and middle school curricula in Kuwait. Data gathered from 59 elementary and middle schools teachers in Kuwait revealed that
more than 60% of teachers equate computational estimation with rounding. While two-thirds of the teachers viewed computational
estimation to be an important skill for daily life; only one-fifth (20%) saw it as important in mathematics education. More
than half of the teachers either disagreed with the idea of teaching computational estimation or only wanted to teach it in
limited situations. Most were concerned about the difficulty of learning computational estimation or feared that teaching
computational estimation would cause problems with students’ development of standard algorithms for determining an exact answer.
These findings reveal the challenge that mathematics educators face in introducing computational estimation into the mathematics
curriculum. In order for computational estimation to be taught in elementary and middle school classrooms, teachers need to
understand the concept and its value in education. Teacher education needs to focus on helping teachers better understand
the concept of computational estimation and appreciate its value for instruction. 相似文献
7.
Yvette Solomon 《Educational Studies in Mathematics》2006,61(3):373-393
The ability to handle proof is the focus of a number of well-documented complaints regarding students' difficulties in encountering
degree-level mathematics. However, in addition to observing that proof is currently marginalised in the UK pre-university
mathematics curriculum with a consequent skills deficit for the new undergraduate mathematics student, we need to look more
closely at the nature of the gap between expert practice and the student experience in order to gain a full explanation. The
paper presents a discussion of first-year undergraduate students' personal epistemologies of mathematics and mathematics learning
with illustrative examples from 12 student interviews. Their perceptions of the mathematics community of practice and their
own position in it with respect to its values, assumptions and norms support the view that undergraduate interactions with
proof are more completely understood as a function of institutional practices which foreground particular epistemological
frameworks while obscuring others. It is argued that enabling students to access the academic proof procedure in the transition
from pre-university to undergraduate mathematics is a question of fostering an epistemic fluency which allows them to recognise
and engage in the process of creating and validating mathematical knowledge. 相似文献
8.
Gila Hanna 《Educational Studies in Mathematics》2000,44(1-2):5-23
This paper explores the role of proof in mathematics education and providesjustification for its importance in the curriculum. It also discusses threeapplications of dynamic geometry software – heuristics, exploration andvisualization – as valuable tools in the teaching of proof and as potentialchallenges to the importance of proof. Finally, it introduces the four papers in this issue that present empirical research on the use of dynamicgeometry software. 相似文献
9.
Helen R. Stiff-Williams 《Clearing house (Menasha, Wis.)》2013,86(4):115-120
This article challenges policymakers, school leaders, and teachers to implement wide-scale and systematic teaching of character education in every classroom. In support of the idea that student character development should be a priority in all classes, I explain that youth need “decision-filters” to negotiate life's challenges. Further, the article illustrates how character education can be taught through various courses. Several state-level academic standards are analyzed to (1) identify cognitive instructional emphases and (2) determine relevant affective teachings for character instruction. As I explain, the teaching of character education can be integrated naturally with and taught alongside any state's standards-based curriculum. Rather than adding a new course to an already overloaded school curriculum, character education should be integrated with other subject areas and routinely taught through all classes and by all teachers. 相似文献
10.
Aeneas Rooch Philipp Junker Jörg Härterich Klaus Hackl 《European Journal of Engineering Education》2016,41(2):172-191
Too difficult, too abstract, too theoretical – many first-year engineering students complain about their mathematics courses. The project MathePraxis aims to resolve this disaffection. It links mathematical methods as they are taught in the first semesters with practical problems from engineering applications – and thereby shall give first-year engineering students a vivid and convincing impression of where they will need mathematics in their later working life. But since real applications usually require more than basic mathematics and first-year engineering students typically are not experienced with construction, mensuration and the use of engineering software, such an approach is hard to realise. In this article, we show that it is possible. We report on the implementation of MathePraxis at Ruhr-Universität Bochum. We describe the set-up and the implementation of a course on designing a mass damper which combines basic mathematical techniques with an impressive experiment. In an accompanying evaluation, we have examined the students' motivation relating to mathematics. This opens up new perspectives how to address the need for a more practically oriented mathematical education in engineering sciences. 相似文献
11.
In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for acceptable reasoning across domains. We further argue that students’ acceptance of these values may be integral to their apprenticeship into proving practice; students who do not perceive or accept these values will likely have difficulty adhering to the norms that uphold them and hence will find proof confusing and problematic. We discuss the implications of mathematical values and norms with respect to proof for investigating mathematical practice, conducting research in mathematics education, and teaching proof in mathematics classrooms. 相似文献
12.
加拿大高中数学课程标准,关于数学学习过程,强调问题解决、推理和证明、反思回顾、选择工具和计算策略、联系、表述、数学交流;对学生的数学学习技能的掌握要求较低,但强调数学学习中用工具、强调数学理解与交流;在数学课程实施和保障中强调学生家长的积极作用;对教材编写提出明确要求;强调对数学知识方法的归纳和概括;对数学教学评价目标指向明确.因此,就目前中国高中数学课堂,应改进课堂教学环节;应树立全过程关注数学学习困难学生的意识;应讲道理、重过程,促进学生的理解;应利用教学评价促进学生的发展和优化教师的教学行为. 相似文献
13.
重建数学教学论课程体系是高师数学教育适应时代发展、应对改革挑战的客观需要,我们必须以高度的历史责任感从事建构工作。依据“成功之树”模式,数学教学论课程体系的建构围绕树根——数学教学信念、树干——数学教学理论、树枝——数学课堂教学、树叶——数学教学行为4个维度进行,以切实有效地帮助师范大学数学教育专业学生奠基从事数学教学工作的基本素养。 相似文献
14.
数学史有着重要的教育价值,将数学史融入数学课程是高中数学课程改革提出的新要求.对高中数学必修教科书中42则数学史内容的呈现方式,从引入方式、内容类型、呈现视角、呈现位置、信息载体和学习要求6个方面进行了探究和统计分析,发现其具有内容类型丰富、信息载体单一、学习要求程度较低等特点.因此,教科书中数学史内容的设计和编排,应注重数学史内容取舍中真实性和教育性的协调、呈现视角的丰富化、信息载体的多样化和学习要求的提高等方面. 相似文献
15.
Proof, Explanation and Exploration: An Overview 总被引：4，自引：0，他引：4
Gila Hanna 《Educational Studies in Mathematics》2000,44(1-3):5-23
This paper explores the role of proof in mathematics education and providesjustification for its importance in the curriculum. It also discusses threeapplications of dynamic geometry software – heuristics, exploration andvisualization – as valuable tools in the teaching of proof and as potentialchallenges to the importance of proof. Finally, it introduces the four papers in this issue that present empirical research on the use of dynamicgeometry software.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
16.
Bettina Pedemonte 《Educational Studies in Mathematics》2007,66(1):23-41
The paper presents a characterisation about argumentation and proof in mathematics. On the basis of contemporary linguistic
theories, the hypothesis that proof is a special case of argumentation is put forward and Toulmin’s model is proposed as a
methodological tool to compare them. This model can be used to detect and analyse the structure of an argumentation supporting
a conjecture (abduction, induction, etc.) and the structure of its proof. The aim of the paper is to highlight the importance
of structural analysis between argumentation and proof. This analysis shows that although there are clear cases of continuity
between argumentation supporting a conjecture and its proof, there is often a structural distance between the two (from an
abductive argumentation to a deductive proof, from an inductive argumentation to a mathematical inductive proof). 相似文献
17.
Science and mathematics education needs to serve several (possibly contradictory) motivating goals. One is found in the movement
for a universal literacy in the central principles and methods of the disciplines. The second is the need to provide the experiences
and background that makes possible the production of scientists and engineers. A complication in both efforts is that the
formal education takes place over many years, and the application of the layers of information, understanding, and sophistication
need also be aware of the age of the student and what has come before. These efforts require clear ideas as to the end goal
of the process and attention to assessment. Receiving less attention is the need to also feed and nurture the creative side
of those who would become professionals, as creative approaches will be a central and necessary aspect of their work and thought.
In this paper, I address the use of a course in mathematical modeling taught over a period of 25 years to undergraduate students
of mathematics, mathematics education, computer science, and engineering, as a method to open up creative pathways. Through
an historical discussion of the role and nature of creativity in the sciences and mathematics, a process to have students
find their creative voice is described in the context of this course. 相似文献
18.
M. Stewart Townend 《Teaching in Higher Education》2013,18(2):203-215
Case studies have long been used to support the mathematics education of undergraduate engineers. Changes in the mathematical ability of entrants to engineering programmes and, indeed, the changing nature of many of the programmes themselves indicate the need to make the students' mathematical experiences more 'user friendly'. We describe here an approach which uses case studies, not as illustrations of applications of mathematics after a mathematical topic has been discussed, but in a fully integrated central role as vehicles for whole group discussion from which the students 'discover' the necessary mathematics which is taught subsequently. Not only is the 'carrot' of the application then central to their learning, but the need for the mathematics being taught is also clearly demonstrated. This approach has been tried with a group of 50 first year engineers. The effects on student motivation, ability and knowledge retention are discussed together with an indication of the Integrated Case Studies which were used. 相似文献
19.
通过对学术形态、课程形态和教育形态数学文化的内涵、特征及提出的意义进行回顾反思,启发提出数学教育文化的概念、数学教育文化观的内容设想以及对中小学数学教学实践和当前的中小学数学课程改革具有的重要意义。 相似文献
20.
新一轮数学课程改革在课程目标、课程内容、教学方式、教材编排方式和评价方式等方面发生了深刻的变革,这些变革促进了中小学数学教育的发展.不过,课程改革也出现了一些问题,引发了一些论争,如关于数学生活化的论争、关于数学"双基"的论争、关于学习方式转变的论争、关于几何课程改革的论争和关于教材编排方式的论争等.检视这些论争并对其进行理性思考,有助于推动课程改革健康发展. 相似文献