共查询到20条相似文献，搜索用时 890 毫秒
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应用三角形的基本不等式及Stewart定理,首先给出两个已知不等式的统一证明,其次建立两个新的几何不等式,最后提出两个相关的猜想。 相似文献
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将变换用于一个已知的几何不等式 ,得出了作者在文献 [1]中建立的一个三元二次型几何不等式的加强 ,讨论了加强结果的应用 ,提出并应用计算机验证了两个未解决的猜想 相似文献
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张琴娣 《中学数学研究(江西师大)》2011,(2):22-23
文[1]提出了5个代数不等式猜想,文[2]证明了猜想1和5是成立的,其余三个猜想均是错的．在本文中,笔者将给出猜想1的一个推广． 相似文献
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田富德 《中学数学研究(江西师大)》2014,(7):20-22
宋庆先生在文[1]给出了4个不等式猜想,杨志明先生在文[2]证明了文[1]的猜想1和猜想3,又提出了4个猜想．本文拟给出文[1]猜想3和文[2]的4个猜想的三角证明,并进行适当的统一推广． 相似文献
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刘健 《河北理科教学研究》2012,(3):10-12
涉及三角形内部一点的不等式是一类有趣的几何不等式,其中既有简单而美妙的结果,又有大量困难莫测的猜想．因而深受各个层次的读者的喜爱．本文中,我们给出这类不等式的两个新的结果． 相似文献
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关于Steiner-Lehmes定理外等长分角线的猜想的研究 总被引：1，自引：0，他引：1
王彦海 《乌鲁木齐成人教育学院学报》2004,12(3):82-85
给出了关于Steiner--Lehmes定理外等长分角线的三个猜想的证明，对结论进行了推广并给出新猜想。 相似文献
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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
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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
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The recent development of powerful new technologies such as dynamic geometry software (DGS) with drag capability has made possible the continuous variation of geometric configurations and allows one to quickly and easily investigate whether particular conjectures are true or not. Because of the inductive nature of the DGS, the experimental-theoretical gap that exists in the acquisition and justification of geometrical knowledge becomes an important pedagogical concern. In this article we discuss the implications of the development of this new software for the teaching of proof and making proof meaningful to students. We describe how three prospective primary school teachers explored problems in geometry and how their constructions and conjectures led them see proofs in DGS.
Constantinos Christou: Author for correspondence. 相似文献
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Nurit Hadas Rina Hershkowitz Baruch B. Schwarz 《Educational Studies in Mathematics》2000,44(1-2):127-150
In many geometrical problems, students can feel that the universalityof a conjectured attribute of a figure is validated by their action in adynamic geometry environment. In contrast, students generally do not feelthat deductive explanations strengthen their conviction that a geometricalfigure has a given attribute. In order to cope with students' convictionbased on empirical experience only and to create a need for deductiveexplanations, we developed a collection of innovative activities intended tocause surprise and uncertainty. In this paper we describe two activities, thatled students to contradictions between conjectures and findings. We analyzethe conjectures, working methods, and explanations given by the studentswhen faced with the contradictions that arose. 相似文献
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Nurit Hadas Rina Hershkowitz Baruch B. Schwarz 《Educational Studies in Mathematics》2000,44(1-3):127-150
In many geometrical problems, students can feel that the universalityof a conjectured attribute of a figure is validated by their action in adynamic geometry environment. In contrast, students generally do not feelthat deductive explanations strengthen their conviction that a geometricalfigure has a given attribute. In order to cope with students' convictionbased on empirical experience only and to create a need for deductiveexplanations, we developed a collection of innovative activities intended tocause surprise and uncertainty. In this paper we describe two activities, thatled students to contradictions between conjectures and findings. We analyzethe conjectures, working methods, and explanations given by the studentswhen faced with the contradictions that arose.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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This study explores interactions with diagrams that are involved in geometrical reasoning; more specifically, how students publicly make and justify conjectures through multimodal representations of diagrams. We describe how students interact with diagrams using both gestural and verbal modalities, and examine how such multimodal interactions with diagrams reveal their reasoning. We argue that when limited information is given in a diagram, students make use of gestural and verbal expressions to compensate for those limitations as they engage in making and proving conjectures. The constraints of a diagram, gestures and linguistic systems are semiotic resources that students may use to engage in geometrical reasoning. 相似文献
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证明涉及三角形平面上任意一点至三角形三顶点距离与三角形三边之间的3个不等式,确认这3个不等式的强弱关系,最后提出两个相关联的猜想. 相似文献