共查询到20条相似文献，搜索用时 62 毫秒
1.
We present results from a classroom-based intervention designed to help a class of grade 10 students (14–15 years old) learn proof while studying trigonometry in a dynamic geometry software environment. We analysed some students’ solutions to conjecture-and-proof problems that let them gain experience in stating conjectures and developing proofs. Grounded on a conception of proof that includes both empirical and deductive mathematical argumentations, we show the trajectories of some students progressing from developing basic empirical proofs towards developing deductive proofs and understanding the role of conjectures and proofs in mathematics. Our analysis of students’ solutions is based on networking Boero et al.’s construct of cognitive unity of theorems, Pedemonte’s structural and referential analysis of conjectures and proofs, and Balacheff and Margolinas’ cK¢ model, while using Toulmin schemes to represent students’ productions. This combination has allowed us to identify several emerging types of cognitive unity/rupture, corresponding to different ways of solving conjecture-and-proof problems. We also show that some types of cognitive unity/rupture seem to induce students to produce deductive proofs, whereas other types seem to induce them to produce empirical proofs. 相似文献
2.
Michal Tabach Ruthi Barkai Pessia Tsamir Dina Tirosh Tommy Dreyfus Esther Levenson 《International Journal of Science and Mathematics Education》2010,8(6):1071-1090
According to reform documents, teachers are expected to teach proofs and proving in school mathematics. Research results indicate
that high school students prefer verbal proofs to other formats. We found it interesting and important to examine the position
of secondary school teachers with regard to verbal proofs. Fifty high school teachers were asked to prove various elementary
number theory statements, to write correct and incorrect proofs that students may use, and to evaluate given justifications
to statements from elementary number theory. While all the participants provided correct proofs to the statements, our findings
indicate that teachers are not aware of students’ preference for verbal justifications. Also, about half of the teachers rejected
correct verbal justifications. They claimed that these justifications lacked generality and are mere examples. 相似文献
3.
Liliane Beaulieu 《Interchange》1990,21(2):35-45
Conclusion The stories told above exemplify the ordinary as much as they document the extraordinary. In the practice of expository writing, definitions play as important a role as mathematical proofs. Also, specifying notation and vocabulary is usually at stake in the writing of textbooks. Although the making of concepts and conceptual settings puts an emphasis on definitions, proofs are in no way absent from this process: in the case of Bourbaki's treatment of Stokes' Theorem, proofs may have acted as a spark in the search for better settings. In the case of filters, the discovery of new concepts simplified some proofs and enabled the results to hold in a more general context. But the motivation for new concepts to be defined did not rise exclusively from a dissatisfaction with proofs that were deemed not rigorous enough. Moreover, the close interplay between the members' own research and the group's expository task tended to relegate proofs to a heuristic in the background of the group's preoccupations. 相似文献
4.
Mathematical proofs are not only the focus of every country’s mathematics curriculum reforms, but also the subject of research
on mathematics education. This paper is based on a survey of mathematics teachers, the goal of which was to investigate the
understanding of mathematical proofs of secondary school math teachers, their levels of mathematical proofs, and their ability
to comprehensively teach mathematical proofs. Preliminary results of the survey provide insight into several characteristic
aspects of Chinese secondary school teachers’ literacy of mathematical proofs. 相似文献
5.
This paper concerns proof presentation at the university level. We report on a study in which we observed ten mathematicians constructing or revising proofs for pedagogical purposes. We highlight the factors that they claimed to consider when completing these tasks. We found that intended audience and medium (lecture or textbook) influenced proof presentation. We also found that, although mathematicians generally valued pedagogical proofs featuring diagrams and emphasizing main ideas, these mathematicians did not always incorporate these aspects in the proofs they constructed or revised. 相似文献
6.
Esra Demiray Mine Işıksal Bostan 《International Journal of Science and Mathematics Education》2017,15(1):109-130
The purposes of this study are to investigate Turkish pre-service middle school mathematics teachers’ ability in conducting valid proofs for statements regarding numbers and algebra in terms of their year of enrollment in a teacher education program, to determine the proof methods used in their valid proofs, and to examine the reasons for their invalid arguments. A proof questionnaire containing three proof statements was administered to 115 pre-service middle school mathematics teachers in a large state university in Ankara, Turkey. The results showed that more than half of the pre-service teachers were able to conduct valid proofs for the given statements. In terms of year levels, it was seen that the seniors were the least successful group in conducting valid proofs for each statement. When pre-service teachers’ valid proofs were analyzed, it was concluded that mathematical induction and direct proof were the mostly used methods for the given statements. When pre-service teachers’ invalid arguments were analyzed, it was seen that “inserting numbers to verify the given statement” and “rewriting the givens in the statement” were the common reasons for stating invalid arguments. 相似文献
7.
从传递闭包的角度证明了判定一个关系是否具备传递性的充要条件,给出并证明了一条关于关系合成运算的定理。 相似文献
8.
9.
The starting point of our reflections is a classroom situation in grade 12 in which it was to be proved intuitively that non-trivial solutions of the differential equationf′=f have no zeros. We give a working definition of the concept of preformal proving, as well as three examples of preformal proofs. Then we furnish several such proofs of the aforesaid fact, and we analyse these proofs in detail. Finally, we draw some conclusions for mathematics in school and in teacher training. 相似文献
10.
欧阳耿 《喀什师范学院学报》2011,32(6):17-21
从逻辑、无穷观、极限论和证明的思路及具体的操作过程,分析了新发现的康托在实数集合不可数证明中所存在的四种错误,得到＂由于与现有经典无穷理论体系、经典极限论和经典数量体系密切相关的数学基础理论中所存在的缺陷,康托在这类证明中无法回避这四种很严重但却很隐蔽的错误＂的明确结论.特别是其中的逻辑错误使这样的证明无意中成了一种典型的数学魔术. 相似文献
11.
In a recent paper (Weber & Mejia-Ramos, Educational Studies in Mathematics, 76, 329–344, 2011), we reported findings from two small-scale interview studies on the reasons why and the ways in which mathematicians read proofs. Based on these findings, we designed an Internet-based survey that we distributed to practicing mathematicians working in top mathematics departments in the USA. Surveyed mathematicians (N?=?118) agreed to a great extent with the interviewed mathematicians in the exploratory studies. First, the mathematicians reported that they commonly read published proofs to gain different types of insight, not to check the correctness of the proofs. Second, they stated that when reading these proofs, they commonly: (a) appeal to the reputation of the author and the journal, (b) study how certain steps in the proof apply to specific examples, and (c) focus on the overarching ideas and methods in the proofs. In this paper, we also report findings from another section of the survey that focused on how participants reviewed proofs submitted for publication. The comparison of participant responses to questions in these two sections of the survey suggests that reading a published proof of a colleague and refereeing a proof for publication are substantially different activities for mathematicians. 相似文献
12.
高新华 《常熟理工学院学报》2002,16(3):41-43
设置严格的程序规则是各国行政诉讼中保障原告辩论权的通常做法。为了体现诉讼民主，实现行政诉讼的价值，必须强化原告的辩论权。行政诉讼可以分为辩论而收集证据的阶段，为确认证据而进行法庭调查和辩论的阶段以及法官根据辩论结果作出裁判的阶段。强化原告辩论权可从以下几方面着手；原告应有足够的手段取得必要的证据；双方当事人应有充分的机会在公开的法庭上提出主张和证据，并互相质证，辩论；辩论的效力必须得到确认；法院应保障当事人的平等辩论权。 相似文献
13.
应用Taylor展开式构造出Newton迭代法,论证了它的局部收敛性及收敛阶,然后指出了它的不足,并通过论证提供了三种改进方案。 相似文献
14.
Mohan Chinnappan Madduma B. Ekanayake Christine Brown 《International Journal of Science and Mathematics Education》2012,10(4):865-887
Within the domain of geometry, proof and proof development continues to be a problematic area for students. Battista (2007) suggested that the investigation of knowledge components that students bring to understanding and constructing geometry proofs could provide important insights into the above issue. This issue also features prominently in the deliberations of the 2009 International Commission on Mathematics Instruction Study on the learning and teaching of proofs in mathematics, in general, and geometry, in particular. In the study reported here, we consider knowledge use by a cohort of 166 Sri Lankan students during the construction of geometry proofs. Three knowledge components were hypothesised to influence the students’ attempts at proof development: geometry content knowledge, general problem-solving skills and geometry reasoning skills. Regression analyses supported our conjecture that all 3 knowledge components played important functions in developing proofs. We suggest that whilst students have to acquire a robust body of geometric content knowledge, the activation and the utilisation of this knowledge during the construction of proof need to be guided by general problem-solving and reasoning skills. 相似文献
15.
调和级数是级数理论中一种比较重要的发散级数,现行《数学分析》教材中,有关它的发散性证明学生在学习中不易掌握,本文从不同的角度介绍几种其他的证明方法,以加深学生对它的理解和认识。 相似文献
16.
罗素悖论的两个现代翻版——康托在集合论中的两个证明 总被引：5，自引：5，他引：0
欧阳耿 《喀什师范学院学报》2008,29(3):26-30
从经典无穷理论体系中的缺陷人手,分析了康托的实数集合不可数证明及康托定理=S＜==P（S）研证明与罗素悖论之间的本质性联系,发现它们与罗素悖论有完全相同的思路,但是康托犯了两个逻辑性错误而误用了这个悖论思路,使他这两个证明成了罗素悖论的两种畸形的翻版,并得到两个明确的结论——康托这两个证明中的思路与做法是错误的,这样的证明结果不具科学性;是现有经典无穷理论体系基础理论的致命缺陷导致这类错误的必然发生、存在与被认可。 相似文献
17.
Anders O. F. Hendrickson 《PRIMUS》2018,28(2):153-165
Teaching determinants poses significant challenges to the instructor of a proof-based undergraduate linear algebra course. The standard definition by cofactor expansion is ugly, lacks symmetry, and is hard for students to use in proofs. We introduce a visual definition of the determinant that interprets permutations as arrangements of non-attacking rooks on an n × n chessboard. We show that under this definition, many of the usual lemmas about determinants admit natural, insightful proofs that students themselves can readily discover. 相似文献
18.
19.
杨继光 《廊坊师范学院学报》2009,25(1)
汉译中古佛经中出现了许多新词、新义,可以纠正<汉语大词典>某些词条或义项书证过于滞后的缺点.仅就阿含部四部核心经典而言,其中新词、新义的语例比<语大词典>的书证时代提前1000年以上的就有16个之多. 相似文献
20.
从证据学的角度而言，经济犯罪与其他刑事犯罪相比较，在证据内容，证明关系，形式要件，证据的合法性等方面具有一定的共性，但学界对经济犯罪的证据特性研究与认知不够，经济犯罪的证据特性可归纳为可计量性，高技能性，多附带性，新复合性，从而，在司法控诉的过程中，时常遇到对经济犯罪的控诉举证不实，举证不当，举证不合法，举证不足，举证不力等方面的问题，并因此影响到定罪量刑的质量。 相似文献