The Illusion Of Linearity
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The Illusion Of Linearity
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Author : Dirk de Bock
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-30
The Illusion Of Linearity written by Dirk de Bock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-30 with Education categories.
This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.
The Illusion Of Linearity
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Author : Aleksandar S. Jovanović
language : en
Publisher: Springer
Release Date : 1989
The Illusion Of Linearity written by Aleksandar S. Jovanović and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Computers categories.
This book presents the reader with a comprehensive overview of the major findings of the recent research on the illusion of linearity. It discusses: how the illusion of linearity appears in diverse domains of mathematics and science; what are the crucial psychological, mathematical, and educational factors being responsible for the occurrence and persistence of the phenomenon; and how the illusion of linearity can be remedied.
Remedying Secondary School Students Illusion Of Linearity
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Author : Wim Van Dooren
language : en
Publisher:
Release Date : 2003
Remedying Secondary School Students Illusion Of Linearity written by Wim Van Dooren and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
Previous research has shown that many secondary school students improperly apply linear models when solving non-linear problems involving lengths, area and volume of similar plane figures and solids. This phenomenon is called the "illusion of linearity". This paper presents a teaching experiment in which we developed and tested a learning environment to help students overcome the illusion of linearity. The experiment was successful in improving students' performance on non-linear problems, but this improvement was disappointingly small. Moreover, there was a decline in students' performance on linear problems. So, the experiment was not successful in developing in students a profound conceptual understanding of proportional and non-proportional relations, which includes the disposition to distinguish between situations that can and cannot be modelled linearly. (Contains 2 endnotes, 2 figures and 3 tables.) [For complete proceedings, see ED500860.].
An Examination Of The Relationship Between An Illusion Of Linear Extent And An Illusion Of Direction
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Author : Suzanne G. Bousquet
language : en
Publisher:
Release Date : 1983
An Examination Of The Relationship Between An Illusion Of Linear Extent And An Illusion Of Direction written by Suzanne G. Bousquet and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Optical illusions categories.
Designing Effective Lessons On Probability
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Author : Jean-Marc Miszaniec
language : en
Publisher:
Release Date : 2016
Designing Effective Lessons On Probability written by Jean-Marc Miszaniec and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
This thesis is a summary of a pilot study adopting the design experiment methodology investigating alternative approaches to the teaching of probability – the classical approach (called ?Laplace approach? in our study) and the axiomatic approach (called ?Properties approach?) – and alternative pedagogical treatments of these approaches: with or without explicit refutations of common misconceptions by the teacher. Four short video-lessons were designed, focused on Bernoulli trials: ?Laplace-exposition?; ?Laplace-refutation?; ?Properties-exposition? and ?Properties-refutation ?. The primary misconception addressed in the study was the erroneous application of proportionality models: the misconception called ?illusion of linearity? in the context of probability. The design and layout of the videos’ visuals and audio were informed by the principles of cognitive load theory in multimedia to ensure optimal learning potential. Each lesson was tried with one volunteer participant, a post-college student. Each participant listened to the video-lesson assigned to him or her, solved six related probability questions, responded to a questionnaire and was interviewed one-on-one by the researcher. Data in the form of participants’ written responses, transcripts of the interviews and researcher’s notes were used for a thorough qualitative analysis and to inform future iterations of the study. Research suggests that the primary obstacles to probability education are misconceptions originating from cognitive biases and limitations. Often misconceptions in probability are attributed to intuitions. Intuitions are easily accessed and experience-based knowledge that can help or hinder individuals while problem solving. One question of this study was whether stating and refuting known misconceptions during a lecture-style lesson on Bernoulli trials (refutation treatment) promotes learning better than a lesson without the mention of misconceptions (exposition treatment). This study also intended to illuminate the nature of probability misconceptions, as research suggests that attributing them to ?intuitions? may be misleading. ?Intuition?, especially, ?robust intuition?, usually refers to a connected set of beliefs, but our observations suggest that students’ predictions about probability of events are based on something much less homogeneous and connected. Participants in the study did not have consistent and robust intuitions about Bernoulli trials but rather a weaker form of basic knowledge called phenomenological primitives. Their intuitions would have to be developed, perhaps through a frequentist approach to probability. Participants had a high distrust in their initial guesses – a symptom of the weakness or lack of ?robust intuition? – and this played an important role throughout the problem solving process. The Properties approach seemed to have more success than the Laplace approach because of its computational simplicity and because participants may have naturally implemented the Properties approach when thinking of chance events. The approaches did not seem to alter the use of misconceptions. The refutation treatment did not have the expected outcome on learning. Participants subjected to it performed better than those subjected to the exposition treatment but this could be because they ?knew? (were told) – not necessarily ?understood? – that changes to the number of trials and the number of desired events affect the probability of the desired event in a non-proportional manner. Future iterations of this study would explore further the above conjectures about the nature of the basis of students’ predictions about probability and the appropriateness of different approaches to probability to build on this basis. Also, other common probability misconceptions would be explored to determine their cognitive origins in order to inform the design of instructional content.
Drawing Amazing Optical Illusions
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Author : Tom McPherson
language : en
Publisher: Rocky Nook, Inc.
Release Date : 2024-07-15
Drawing Amazing Optical Illusions written by Tom McPherson and has been published by Rocky Nook, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-15 with Art categories.
Create mind-blowing artwork that pops off the page! Drawing complex three-dimensional art does not have to be intimidating. It may seem difficult or only for the advanced artist, but in this book author Tom McPherson breaks down in simple step-by-step instructions how anyone can create detailed, mesmerizing optical illusions even with little drawing experience.
In this groundbreaking book, McPherson details how to create cool artwork from scratch by learning basic drawing techniques and progressing to more complex skills and creations, including: Impossible Shapes: Optical 3D illusions of shapes that could not exist in reality Floating Shapes: Solid shapes that look like they hover above the paper 3D Line Art: Inventive 3D illusions on simple lined paper Anamorphic Buildings: Subjects drawn with extreme distortion that look realistic and 3D 5-Point Perspective: Drawing 3D fisheye views using perspective and curved lines And much more! This is the ultimate guide to mastering trick drawing and creating cool images that will impress your friends and family.
The Open Past Subjectivity And Remembering In The Talmud
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Author : Sergeĭ Borisovich Dolgopolʹskiĭ
language : en
Publisher: Fordham Univ Press
Release Date : 2013
The Open Past Subjectivity And Remembering In The Talmud written by Sergeĭ Borisovich Dolgopolʹskiĭ and has been published by Fordham Univ Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Philosophy categories.
If life in time is imminent and means an always open future, what role remains for the past? If time originates from that relationship to the future, then the past can only be a fictitious beginning, a necessary phantom of a starting point, a retroactively generated chronological period of "before." Advanced in philosophical thought of the last two centuries, this view of the past permeated the study on the Talmud as well, resulting in application of modern philosophical categories of the "thinking subject", subjectivity, and time to thinking about thinking displayed in the texts of the Talmud. This book challenges that application. Departing from the hitherto prevalent view of thinking in the Talmud in terms of anonymous thinking subjects, called "redactors" or "designer" of Talmudic discussions, the book reconsiders the modern reduction of the past to a chronological period in time, and reclaims the originary power (and authority) the past exerts in thinking and remembering displayed both in the conversations the characters in the Talmud have, and in the literary design of these conversations. Central for that task of reclaiming the radical role of the past are contrasting medieval notions of the virtual and their modern appropriations, thinking subject among them, which serve as both a bridging point and a demarcation between the practices of thinking of, and remembering, the past in the Talmud vis-a-vis other rhetorical and/or philosophical school and disciplines of thought. The Open Past suggests the possibility of understanding the conversations and the design of these conversations in the Talmud in terms of thinking in no time. This no time has several layers of meaning. In its weakest formulation, it means "in no single time" in the sense that the Talmudic conversations happen in no historically "real" time. More strongly put, it means, borrowing the language from film theory, that the Talmud requires a never consolidated difference between diegetical time, and the time of montage; which creates a no-one's time and place that in turn creates time and place for everyone else. Even more strongly, it means that performance of the conversations in the Talmud is constantly driven by, and towards, an always open past -- a power of that past is radically different from the power of either futuristic or chronological time.
Linear Algebra And Matrix Theory
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Author : Robert R. Stoll
language : en
Publisher: Courier Corporation
Release Date : 2013-05-20
Linear Algebra And Matrix Theory written by Robert R. Stoll and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-20 with Mathematics categories.
One of the best available works on matrix theory in the context of modern algebra, this text bridges the gap between ordinary undergraduate studies and completely abstract mathematics. 1952 edition.
Introduction To The Theory Of Linear Nonselfadjoint Operators
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Author : Israel Gohberg
language : en
Publisher: American Mathematical Soc.
Release Date : 1978
Introduction To The Theory Of Linear Nonselfadjoint Operators written by Israel Gohberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematics categories.
Powerful Environments For Promoting Deep Conceptual And Strategic Learning
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Author : Lieven Verschaffel
language : en
Publisher: Leuven University Press
Release Date : 2005
Powerful Environments For Promoting Deep Conceptual And Strategic Learning written by Lieven Verschaffel and has been published by Leuven University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Education categories.
Over the past years a substantial amount of research has been undertaken relating to the development of powerful learning environments for the acquisition in students of worthwhile educational objectives focussing on conceptual understanding, higher-order cognitive and metacognitive skills, and self-regulated learning. This research has been mainly undertaken from three distinct, but related perspectives in the study of learning and instruction, namely instructional psychology, instructional technology, and instructional design. Against this background a "research community" involving 14 European research teams has recently been initiated with the aim of interactively contributing to the advancement of theory and methodology relating to the design, implementation, and evaluation of powerful learning environments.This volume, based on the plenary lectures and working sessions during the community's third workshop, constitutes a collective output of this research community, focussing on the identification and analysis of major components and dimensions of powerful learning environments aimed at the promotion of deep conceptual and strategic learning in major domains of school curricula, like mathematics, physics, history, and social sciences.In Part I of the volume three chapters present general perspectives on the central theme of the third workshop. In Part II six studies are reported wherein novel learning environments for elementary and secondary mathematics education have been designed, implemented and evaluated. In Part III of the volume another set of five investigations is presented relating to the design, implementation and evaluation of powerful learning environments in other subject-matter domains (physics, history, social sciences) and in teacher training.