Download or read book The Effects of a Proof Mapping Instructional Technique on High School Geometry Students and Their Ability to Write Geometric Proofs written by Leanne Linares and published by . This book was released on 2008 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Effects of Using Concept Maps as an Instructional Tool on High School Geometry Students Ability to Make Connections Between Geometric Concepts written by Judy Jieying Tan and published by . This book was released on 2008 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Teaching Strategies for Proof Based Geometry written by Kristina Chaves and published by LAP Lambert Academic Publishing. This book was released on 2014-09-25 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study aims is to discover the best methods for geometry students to master proof writing. Students who are taught how to write proofs in a traditional setting find proofs to be very difficult. Studies have been conducted regarding the use of dynamic geometry software in proof writing. To further study the effects of proof writing using dynamic geometry software, freshmen students enrolled in an honors geometry course at a high performing suburban high school in Louisiana were given several proofs to complete, along with self-reflection surveys. During phase one of this research, twenty-four students were allowed to use Geometer's Sketchpad while writing their proofs, while the other twenty-four students were using only paper and pencil to explore the figure involved in the proof. During phase two of testing, the control and experimental groups swapped places to uphold the equality standards of the course. Student self-reflection surveys show that some students enjoy writing proofs when using GSP, while others are indifferent. Along with the student surveys, the present study is an analysis of student work from those who had access to GSP to improve proof writing skills.
Download or read book The Effects of Proof on Achievement and Reasoning Ability of Students in Geometry written by Charles Garabedian and published by . This book was released on 1981 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Teaching and Learning Proof Across the Grades written by Despina A. Stylianou and published by Routledge. This book was released on 2010-09-23 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. By building and extending on existing research and by allowing a variety of voices from the field to be heard, Teaching and Learning Proof Across the Grades not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.
Download or read book Effects of Social Metacognition on Geometric Reasoning and Micro creativity written by Michael James Pawlikowski and published by . This book was released on 2014 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: As students have historically performed poorly on geometric proofs, curriculum and instruction reforms often target this topic. While previous research has focused on defining cognitive aspects of proof such as student proof schemes or types of geometric reasoning, they have neglected the ways in which face-to-face student interactions affect learning, reasoning, and knowledge construction in geometry. Indeed, little is known about how students influence one another while working together on geometric proofs. This study helps fill this research gap by synthesizing theoretical frameworks (proof schemes, geometric reasoning and social metacognition) to create a new framework to analyze students' creation of ideas (micro-creativity) and geometric proof processes. Then, this new framework is applied to two groups of students working on proofs. Two small groups of four high school geometry students each engaged in a series of tasks to investigate their proof ability and proving processes. A pre-test proof was given to each individual student to identify a baseline of their proof ability. Then students worked together on a group proof which was coded along the dimensions of social metacognition, geometric reasoning, and micro-creativity for statistical discourse analysis. Following the group-proof, a post-test proof was given to each individual student. The progression of tests helped identify students' conceptual, computation, and conclusion errors at each point in time. The regression analyses showed that both group's social metacognitive factors predicted different types of geometric reasoning and micro-creativity. When a student gave a command, it was often a new idea. When a student individually positioned themselves, it was often a recognition, a conjecture or a new idea.^When a student made a statement, it was often a systematization but seldom a recognition. When a student made a suggestion, it was often a recognition, inference, or a correct, new idea. After a groupmate disagreed, a student was more likely to express a conjecture or a correct idea. The post-test proof provided mixed results as student errors varied from the pre-test. One significant factor from the post-test revealed that between groups the weaker students showed overall improvement whereas the stronger students showed an overall decline. The findings of this study have implications for students, teachers, and researchers. When students work together on geometric proofs, they can correct one another's misconceptions, misuse of formulas, and false assumptions. For teachers, using instructional strategies like small group work can be beneficial for teaching geometric proof, but these groups need teacher facilitation to ensure all students acquire and retain good proof habits.^For researchers, it provides a new perspective on assessing students' geometric proof and proving processes, as well as evidence for the importance of examining socially constructed proofs.
Download or read book Proof in Geometry written by A. I. Fetisov and published by Courier Corporation. This book was released on 2012-06-11 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Download or read book Bulletin of the Atomic Scientists written by and published by . This book was released on 1961-05 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bulletin of the Atomic Scientists is the premier public resource on scientific and technological developments that impact global security. Founded by Manhattan Project Scientists, the Bulletin's iconic "Doomsday Clock" stimulates solutions for a safer world.
Download or read book Machine Proofs In Geometry Automated Production Of Readable Proofs For Geometry Theorems written by Jing-zhong Zhang and published by World Scientific. This book was released on 1994-04-06 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports recent major advances in automated reasoning in geometry. The authors have developed a method and implemented a computer program which, for the first time, produces short and readable proofs for hundreds of geometry theorems.The book begins with chapters introducing the method at an elementary level, which are accessible to high school students; latter chapters concentrate on the main theme: the algorithms and computer implementation of the method.This book brings researchers in artificial intelligence, computer science and mathematics to a new research frontier of automated geometry reasoning. In addition, it can be used as a supplementary geometry textbook for students, teachers and geometers. By presenting a systematic way of proving geometry theorems, it makes the learning and teaching of geometry easier and may change the way of geometry education.
Download or read book An Investigation of High School Geometry Students Proving and Logical Thinking Abilities and the Impact of Dynamic Geometry Software on Student Performance written by Lalitha Subramanian and published by . This book was released on 2005 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this study was to investigate (a) the role of a yearlong geometry course on high school geometry students’ logical thinking and proof construction abilities, (b) the linkage between students’ logical thinking and proof construction abilities, and (c) the impact of dynamic geometry software on students’ performance. In addition, this study also ventured to determine if the type of geometry course had any impact on students’ logical thinking and proof construction achievement. The sample for the study consisted of 1,325 high school geometry students enrolled in regular, honors, and mastery courses in four high schools from the school district affiliated with the Local Education Agency (LEA) during the academic year 2004-2005. Geometer’s Sketchpad[trade mark sign] (GSP) was assumed to represent the dynamic geometry software. Responses of students on two pre-tests and two post-tests, each with one on logical thinking and one on proof, were analyzed to address the research questions. Results of the analyses indicated no significant effect of the yearlong geometry course on the performance of students on proof tests but a fairly significant effect on the tests of logical thinking. Use of GSP was found to have some impact on honors and mastery students’ performance on proof post-tests. Honors students showed a higher logical thinking level than their regular and mastery counterparts in both GSP and non-GSP groups. There was a significant positive correlation between students’ performance on the tests of logical thinking and proof.
Download or read book Teaching Mathematics in Grades 6 12 written by Randall E. Groth and published by SAGE Publications. This book was released on 2012-08-10 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching Mathematics in Grades 6 - 12 by Randall E. Groth explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows preservice mathematics teachers the value of being a "researcher—constantly experimenting with methods for developing students' mathematical thinking—and connecting this research to practices that enhance students' understanding of the material. Ultimately, preservice teachers will gain a deeper understanding of the types of mathematical knowledge students bring to school, and how students' thinking may develop in response to different teaching strategies.
Download or read book Some Effects of an Activity Approach to Teaching Geometry in the High Schools in Afghanistan written by Mohammad Ibrahim Monier and published by . This book was released on 1977 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this study has been to investigate the effects of an activity approach to teaching geometry in certain high schools of Afghanistan. A brief review of the historical background of mathematics education especially in Afghanistan has been presented in this study. Students in the activity approach were involved in a Learning process using solution keys and practical activities to supplement lecture and textbook presentation. This approach was compared to traditional methods which consist of lecture, use of a textbook, and recitation based on memorization only. Participants in this study were students in two high schools in Afghanistan. Eight teachers were involved and a total of 602 students were randomly selected to participate in the study. Selected students were divided into experimental and control groups by means of an "even and odd" procedure. There were seven classes in each group, with each teacher teaching one or two classes in one of the groups. The activity approach consists of 48 activities (24 activities for each of the ninth and tenth grades) which were introduced as learning modules supplementing the presently used traditional approach. Six hypotheses were stated claiming no difference between the two approaches in common learning outcomes for students learning geometry, such as over-all achievement in understanding concepts, creative thinking, ability to recall concepts, ability to solve problems, ability to explain facts, and ability to set up step-by-step proofs for various theorems. The hypotheses were all tested statistically and were rejected in favor of their alternatives. Since there was no standardized test appropriate for testing the content of high school geometry programs in Afghanistan, three intermediate tests and a comprehensive final examination were constructed by a committee consisting of the experimental as well as the control group teachers. The tests and the final examination were administered to both groups at the same time. The tests together with the final examination were designed to measure the six specific learning outcomes in geometry mentioned earlier. The experimental design employed was a "post-test only control group design." The design was supplemented by three intermediate tests administered every other month during the 32 weeks (one academic year) duration of this study. The statistical analysis which consisted of computation of related mean scores for each one of the six specific learning outcomes in geometry and for each test including the final examination was computer processed. Finally a Student-t-test was used to draw conclusions related to each of the learning outcomes. Conclusions The following conclusions were drawn from the analysis of the data and from testing of the hypotheses. In comparison to the traditional approach, the use of activity approach: 1. Significantly improves a student performance in overall understanding of geometry. 2. Helps students achieve higher levels in creative thinking. 3. Helps students develop greater ability to explain geometric concepts. 4. Helps students improve their ability in solving geometric problems. 5. Helps students develop the ability to recall geometric concepts better. 6. Helps students to develop greater ability in setting up complete proofs for geometric theorems.
Download or read book An Introduction to Writing Mathematical Proofs written by Prof Thomas Bieske and published by Createspace Independent Publishing Platform. This book was released on 2017-05-29 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is designed to help students transition from calculus-type courses that focus on computation to upper-level mathematics courses that focus on proof-writing. Using the familiar topics of real numbers, high school geometry and calculus, students are introduced to the methods of proof-writing and pre-proof strategy planning. A supplemental workbook for instructors is available upon request from the author. The workbook includes chapter vocabulary lists, creative writing exercises, group projects, and classroom discussions.
Download or read book Helping Children Learn Mathematics written by National Research Council and published by National Academies Press. This book was released on 2002-07-31 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
Download or read book Second Handbook of Research on Mathematics Teaching and Learning written by Frank K. Lester and published by IAP. This book was released on 2007-02-01 with total page 1380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
Download or read book Proof Technology in Mathematics Research and Teaching written by Gila Hanna and published by Springer Nature. This book was released on 2019-10-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents chapters exploring the most recent developments in the role of technology in proving. The full range of topics related to this theme are explored, including computer proving, digital collaboration among mathematicians, mathematics teaching in schools and universities, and the use of the internet as a site of proof learning. Proving is sometimes thought to be the aspect of mathematical activity most resistant to the influence of technological change. While computational methods are well known to have a huge importance in applied mathematics, there is a perception that mathematicians seeking to derive new mathematical results are unaffected by the digital era. The reality is quite different. Digital technologies have transformed how mathematicians work together, how proof is taught in schools and universities, and even the nature of proof itself. Checking billions of cases in extremely large but finite sets, impossible a few decades ago, has now become a standard method of proof. Distributed proving, by teams of mathematicians working independently on sections of a problem, has become very much easier as digital communication facilitates the sharing and comparison of results. Proof assistants and dynamic proof environments have influenced the verification or refutation of conjectures, and ultimately how and why proof is taught in schools. And techniques from computer science for checking the validity of programs are being used to verify mathematical proofs. Chapters in this book include not only research reports and case studies, but also theoretical essays, reviews of the state of the art in selected areas, and historical studies. The authors are experts in the field.
Download or read book An Investigation of Tenth Grade Students Views of the Purpose of Geometric Proof written by Mary Katherine Gfeller and published by . This book was released on 2004 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this investigation was to describe tenth grade students' views of the purposes of geometric proof within the context of their learning. Classroom observations, the curriculum, assessment tools, journal questions, and a preconceptions questionnaire were used to provide context for the views expressed by students from a single classroom. Eleven classroom episodes selected from the classroom observations were used to describe the instructional context as well as discourse among the students during group work. The episodes provided details about how and when the classroom teacher addressed various purposes of proofs involving geometry concepts throughout two instructional units on coordinate geometry proofs and two-column proofs. The episodes also consisted of student discourse relating to the purposes of geometric proof as students worked on assigned proof problems. The students' views were examined through journal questions given at the beginning of selected days and through a post-instruction questionnaire and individual interviews. There were three main findings of the study. First, several students experienced difficulty in expressing their views of the purposes of geometric proof when asked directly. One-third of the students could only list properties or theorems they encountered during the unit on geometric proof. However, when these students were asked to describe the purpose for each column, all of the students listed both explanation and verification. Second, the students expressed limited views of the purposes of proof, referring mainly to verification. Only a few students mentioned explanation, systematization, and communication. However, students generally referred to at least two purposes of proof (explanation, verification, and communication) when describing the proving process involved in coordinate geometry. Third, the students' views of various purposes of geometric proof were diverse. Recommendations for future research include the examination of students' views of the purposes of geometric proofs for students who use paragraph form and studies to investigate the development of students' views of the purposes of proof as they gain more experience with formal proof writing and other methods of proof.
