共查询到20条相似文献，搜索用时 31 毫秒
1.
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
2.
The theoretical background and different methods ofconcept mapping for use in teaching and in research on learning processes are discussed. Two mathematical projects, one on fractions and one on geometry, are presented in more detail. In the first one special characteristics of concept maps were elaborated. In the second one concept mapping allowed students' individual understanding to be monitored over time and provided information about students' conceptual understanding that would not have been obtained using other methods. Regarding the students' individual concept maps in more detail there were some additional findings: (i) The characteristics of the maps change remarkably from fourth grade to sixth grade; (ii) There is some evidence that prior knowledge related to some mathematical topics plays a very important role in students' learning behaviour and in their achievement; (iii) Concept maps provide information about how individual students relate concepts to form organised conceptual frameworks; (iv) Long-term difficulties with specific concepts are able to be traced. These findings are discussed with regard to results of other studies as well as to their implications for the teaching of mathematics in the classroom. 相似文献
3.
As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
4.
李伟 《安徽教育学院学报》2009,27(6):11-15
在师范院校数学系基础课程中,高等代数作为数学系最重要的基础课之一,在建构学生知识体系中起着重要的基础作用。高等代数的学习是比较困难的。学生课听得懂,但习题无从下手。因为它的抽象性,学生还不习惯、也没有这方面的思维基本训练。分析问题的原因,主要是学生的学习习惯,尤其是数学思维方法存在着缺陷。具体说对数学思维个性品质的两重性认识不够。本文通过高等代数教学,对存在着的七种优秀思维品质所具有的两重性进行了剖析,旨在教学中应引起足够的重视。 相似文献
5.
金钰 《宁夏师范学院学报》2014,35(3):100-103
以宁夏师范学院数学与计算机科学学院学生为研究对象,分析造成数学专业学生数学理解困难的原因,通过营造合理的数学情境,使用变式教学,培养学生学习的合作能力,加强数学教师能力的培养、多途径地提供教学实践等方式改善学生的数学理解能力. 相似文献
6.
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
7.
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
8.
要教好线性代数课程,其核心问题就是要通过课堂教学,使学生理解相关的数学知识;训练和培养学生的思维能力以及数学交流能力;帮助学生寻找新旧知识之间的内在联系,使知识系统化;在巩固已有知识的基础上,让学生自己去发现新知识.要实现这一教学目标,训练学生掌握"数学证明"的概念和在实践中的应用至关重要.传统的做法往往是通过"定义一引理一证明一定理一证明一推论"这种复杂的、程序化方法来进行训练的.由于在初等代数课程中,学生很少接受严格数学证明的训练,所以这种俗套的做法成效甚微.相反,如果把线性代数的主题和概念用一种完全合理的探究式方法来引入,那么数学证明的概念和架构将牢固植根于学生的头脑,并且这种思维习惯将对他们后续课程的学习和掌握公理化推理方法都会有很大帮助. 相似文献
9.
What patterns can be observed among the mathematical arguments above-average students find convincing and the strategies these students use to learn new mathematical concepts? To investigate this question, we gave task-based interviews to eleven female students who had performed well in their college-level mathematics courses, but who differed in the number of proof-oriented courses each had taken. One interview was designed to elicit expressions of what students find convincing. These expressions were categorized according to the proof schemes defined by Harel and Sowder (1998). A second interview was designed to elicit expressions of what strategies students use to learn a mathematical concept from its definition, and these expressions were classified according to the learning strategies described by Dahlberg and Housman (1997). A qualitative analysis of the data uncovered the existence of a variety of phenomena, including the following: All of the students successfully generated examples when asked to do so, but they differed in whether they generated examples without prompting and whether they successfully generated examples when it was necessary to disprove conjectures. All but one of the students exhibited two or more proof schemes, with one student exhibiting four different proof schemes. The students who were most convinced by external factors were unsuccessful in generating examples, using examples, and reformulating concepts. The only student who found an examples-based argument convincing generated examples far more than the other students. The students who wrote and were convinced by deductive arguments were successful in reformulating concepts and using examples, and they were the same set of students who did not generate examples spontaneously but did successfully generate examples when asked to do so or when it was necessary to disprove a conjecture. 相似文献
10.
张玉成 《深圳信息职业技术学院学报》2011,9(2):35-39
符合学生专业学习需要的教学效果,是高职数学教育教学追求的目标。本文针对数学教学过程中有关有效教学时间、简单理解、有针对性处理教学内容,以及师生关系等与教学效果相关的教学思想与观念,阐述了数学教学效率意识的作用和意义,认为在高职数学教育教学中强调数学教学效率意识,对于高职数学教育教学的改革与发展有着重要的现实意义。 相似文献
11.
Woo-Hyung Whang 《Educational Studies in Mathematics》1996,30(3):289-312
The purpose of this study was to investigate language related difficulties and the language of cognitive processes of English-Korean bilingual students in solving mathematics word problems. Qualitative case study research methodology was used to collect, analyze, and present data. The principle of purposeful sampling was used to select six English-Korean bilingual students. Different types of bilinguals revealed distinct patterns of difficulties and languages in solving mathematics word problems written in English and Korean. Children in the transition stage that is unstable and changing revealed more difficulties in solving the mathematics word problems overall.This article is a summary of doctoral dissertation under the direction of James W. Wilson at the University of Georgia. 相似文献
12.
何凤波 《课程.教材.教法》2011,(8)
小学生数学学习情况调研显示:学生在数学计算、轴对称图形、观察物体、解决有确定答案问题等学习内容上有着明显优势,但对于理解计算过程、图形周长与面积概念的把握和解决开放问题有所不足;城乡小学生在数学各领域学习质量上的差别还依然明显。这启示我们,数学教材编写与课堂教学要发扬优势、弥补薄弱环节,有针对性地进行改革。 相似文献
13.
高效数学教学行为与低效教学行为相比较应该凸显科学性、智慧性与艺术性等特征.其中,科学性是指数学教师在教心、导学与发挥数学的教育性方面更具有合理性,即能够恰当确定教学目标以及教学重点与难点,在数学认知方面重视促进学生的深刻理解与帮助学生建立良好的数学认知结构,在非认知方面促进激发学生的数学求知欲与求识欲,在元认知方面给予学生必要的数学学习方法指导,恰到好处发挥数学的教育性,让学生适时沐浴数学精神、思想与方法,获得理性的数学思维的教育.智慧性是指在选择教学内容以及教学方法等方面具有智慧,在调控教学节奏方面也显现着教学的智慧.艺术性是指在教学、形体与板书语言方面以及管理方面显现着艺术特征. 相似文献
14.
SHI Ning-zhong GUO Min 《课程.教材.教法》2007,27(7):23-27
几何证明在本质上是一种方法论,学生学习欧氏几何、经过这种论证方法的训练是很有益处的。数学教学必须尊重学生身心发展的规律,有关逻辑推理的数学教学不能出现得太早。小学阶段主要是认同;初中阶段可以逐渐建立概念以及在此基础上的逻辑推理,但必须有物理背景;到了高中,才可以逐步渗透形式化的概念以及在此基础上的逻辑推理。过分强调演绎逻辑的数学教学,是不利于创新人才培养的。归纳推理有利于发现新的命题,是培养创新型人才所必需的。 相似文献
15.
Mathophobia, or excessive fear of mathematics, helps prevent many university students from succeeding in basic mathematics courses required for success in their disciplines. A program at San Francisco State University called Math Without Fear is designed to ameliorate mathophobia. The course seeks to move students from rigid reliance on rules without understanding (rule orientation) to an understanding of mathematical concepts and flexibility in problem solving (concept orientation). The instructional techniques of the Math Without Fear program do not enable all students to discard their rule orientation in one semester. An arithmetic and problem solving test appears to be a good advance predictor of which students will remain rule oriented, and separating these students into special sections of the Math Without Fear course is a promising means of increasing the program's success rate. 相似文献
16.
Tami S. Martin Sharon M. Soucy McCrone Michelle L. Wallace Bower Jaguthsing Dindyal 《Educational Studies in Mathematics》2005,60(1):95-124
Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage
in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results
from a classroom-based interpretive study of teaching and learning proof in geometry. The goal of this research was to identify
factors that may be related to the development of proof understanding. In this paper, we identify and interpret students'
actions, teacher's actions, and social aspects that are evident in a classroom in which students discuss mathematical conjectures,
justification processes and student-generated proofs. We conclude that pedagogical choices made by the teacher, as manifested
in the teacher's actions, are key to the type of classroom environment that is established and, hence, to students' opportunities
to hone their proof and reasoning skills. More specifically, the teacher's choice to pose open-ended tasks (tasks which are
not limited to one specific solution or solution strategy), engage in dialogue that places responsibility for reasoning on
the students, analyze student arguments, and coach students as they reason, creates an environment in which participating
students make conjectures, provide justifications, and build chains of reasoning. In this environment, students who actively
participate in the classroom discourse are supported as they engage in proof development activities. By examining connections
between teacher and student actions within a social context, we offer a first step in linking teachers' practice to students'
understanding of proof. 相似文献
17.
18.
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
19.
It has been claimed that writing to learn mathematics (WTLM) may benefit students' conceptual understanding as well as their
procedural ability. To investigate this claim, we collected data from students in two sections of an introductory calculus
course. In one of the sections, students used WTLM activities and discussed the activities after completing the writing; in
the other section, students used similar activities that did not involve writing but engaged them in thinking about the mathematical
ideas and in discussing the activities. The errors from the in-class and final exams of both groups of students were categorized
and analyzed for information about the students' conceptual and procedural understanding. We found no significant differences
between the WTLM group and the non-writing group, which suggests that the real benefit from writing activities may not be
in the actual activity of writing, but rather in the fact that such activities require students to struggle to understand
mathematical ideas well enough to communicate their understanding to others.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
Students’ judgments about “what counts” as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as mathematical, and how they make their judgments. Students completed a photo sorting activity; took, viewed, and captioned their own photos of mathematics; viewed and commented on classmates’ photos; and participated in a small group discussion. Across multiple sources of data, findings showed that students attended to two major features of photos and activities when making judgments: surface cues present in the photos, such as numbers and money, and the possibility for mathematical action. Some students looked for the possibility of mathematics, while others asked if mathematics was necessary. Students also gave higher ratings to activities with which they had personal experience. The article concludes with possible implications for practice. 相似文献