Science and Mathematics Education Commons^™

Intonation And Compensation Of Fretted String Instruments, Gabriele U. Varieschi, Christina M. Gower

Gabriele Varieschi

We discuss theoretical and physical models that are useful for analyzing the intonation of musical instruments such as guitars and mandolins and can be used to improve the tuning on these instruments. The placement of frets on the fingerboard is designed according to mathematical rules and the assumption of an ideal string. The analysis becomes more complicated when we include the effects of deformation of the string and inharmonicity due to other string characteristics. As a consequence, perfect intonation of all the notes on the instrument cannot be achieved, but complex compensation procedures can be introduced to minimize the problem. …

Hypothesis Generation And Testing: A Template For Biomedical Research, Michael Hoffmann

Michael H.G. Hoffmann

This argument map provides a template for the testing of hypotheses in biomedical research. It can be used in science education to direct students' attention to all components that need to be clarified to justify a scientific hypothesis in a specific experimental setting, including the justification of appropriate sample sizes in experiments, determination of background theories, description of experimental design, data collection methods, significance level, etc. To use this template, go to http://agora.gatech.edu/, search for argument map 3363, and copy the map.

Philosophical & Institutional Innovations Of Kenyon Leech Butterfield And The Rhode Island Contributions To The Development Of Land Grant And Sea Grant Extension, Michael Rice, Sarina Rodrigues, Kate Venturini

Michael A Rice

Carl F. Craver And Lindley Darden: In Search Of Mechanisms: Discoveries Across The Life Sciences, Stuart Glennan

Stuart Glennan

Carl Craver and Lindley Darden are two of the foremost proponents of a recent approach to the philosophy of biology that is often called the New Mechanism. In this book they seek to make available to a broader readership insights gained from more than two decades of work on the nature of mechanisms and how they are described and discovered. The book is not primarily aimed at specialists working on the New Mechanism, but rather targets scientists, students and teachers who are looking for a broad, philosophically and historically informed image of discovery in the life sciences.

Scientists And Animal Research: Dr. Jekyll Or Mr. Hyde?, Andrew N. Rowan

Andrew N. Rowan, DPhil

Why is the public so sensitive about the use of a few tens of millions of animals in research when they do not object to killing hundreds of millions of pigs and cows and billions of chickens for our meat diet? Why is animal research considered so bad despite the public's high opinion of science (and scientists)? Perhaps it is the image of the scientist as an objective and cold individual who deliberately inflicts harm (pain, distress, or death) on his (the public image is usually male) innocent animal victims that arouses so much horror and concern. This paper does …

The Nature Of Science: A Perspective From The Philosophy Of Science, Juli T. Eflin, Stuart Glennan, George Reisch

Stuart Glennan

In a recent article in this journal, Brian Alters (1997) argued that, given the many ways in which the nature of science (NOS) is described and poor student responses to NOS instruments such as Nature of Scientific Knowledge Scale (NSKS), Nature of Science Scale (NOSS), Test on Understanding Science (TOUS), and others, it is time for science educators to reconsider the standard lists of tenets for the NOS. Alters suggested that philosophers of science are authorities on the NOS and that consequently, it would be wise to investigate their views of current NOS tenets. To that end, he conducted a …

Cognitive Effects Of Argument Visualization Tools, Michael H.G. Hoffmann

Michael H.G. Hoffmann

External representations play a crucial role in learning. At the same time, cognitive load theory suggests that the possibility of learning depends on limited resources of the working memory and on cognitive load imposed by instructional design and representation tools. Both these observations motivate a critical look at Computer-Supported Argument Visualization (CSAV) tools that are supposed to facilitate learning. This paper uses cognitive load theory to compare the cognitive efficacy of RationaleTM 2 and AGORA.

“Theoric Transformations” And A New Classification Of Abductive Inferences, Michael H.G. Hoffmann

Michael H.G. Hoffmann

Based on a definition of “abductive insight” and a critical discussion of G. Schurz’s (2008) distinction of eleven “patterns of abduction” that he organizes in four groups, I suggest an even more comprehensive classification that distinguishes 15 forms in an alternative structure. These forms are organized, on the one hand, with regard to what is abductively inferred—singular facts; types; laws; theoretical models; or representation systems—and, on the other, with regard to the question whether the abductive procedure is selective or creative (including a distinction between “psychologically creative,” as in school learning, or “historically creative”). Moreover, I argue that theoretical-model abduction—which …

Lam Map Of Nagel's Core Argument In "The Problem Of Global Justice" (2005), Michael H.G. Hoffmann

Michael H.G. Hoffmann

This map is also available online: http://tinyurl.com/23vweqm

Lam Map Of Thomas Nagel (2005), The Problem Of Global Justice, Michael H.G. Hoffmann

Michael H.G. Hoffmann

This map is also available online: http://tinyurl.com/22o9q9q

The Debate About The Stern-Review And The Economics Of Climate Change, Michael H.G. Hoffmann

Michael H.G. Hoffmann

This map is -- in a different form, with linked sub-maps -- also available online: http://tinyurl.com/y9jlsxv

Argument Visualization In The Political Arena: The Debate On Global Climate Engineering, Michael H.G. Hoffmann

Michael H.G. Hoffmann

A map that shows a certain point in a fictitious deliberation which is supposed to be ongoing and open-ended, driven by the motive of participants to support or to criticize any of the assumptions mapped out so far by further arguments. This map is mainly based on recent publications on geo-engineering

Learning From People, Things, And Signs, Michael H.G. Hoffmann

Michael H.G. Hoffmann

Starting from the observation that small children can count more objects than numbers—a phenomenon that I am calling the “lifeworld dependency of cognition”—and an analysis of finger calculation, the paper shows how learning can be explained as the development of cognitive systems. Parts of those systems are not only an individual's different forms of knowledge and cognitive abilities, but also other people, things, and signs. The paper argues that cognitive systems are first of all semiotic systems since they are dependent on signs and representations as mediators. The two main questions discussed here are how the external world constrains and …

The Complementarity Of A Representational And An Epistemological Function Of Signs In Scientific Activity, Michael H.G. Hoffmann, Wolff-Michael Roth

Michael H.G. Hoffmann

Signs do not only “represent” something for somebody, as Peirce’s definition goes, but also “mediate” relations between us and our world, including ourselves, as has been elaborated by Vygotsky. We call the first the representational function of a sign and the second the epistemological function since in using signs we make distinctions, specify objects and relations, structure our observations, and organize societal and cognitive activity. The goal of this paper is, on the one hand, to develop a model in which both these functions appear as complementary and, on the other, to show that this complementarity is essential for the …

A Classroom Teacher's Reflection On Learning Sustainability, Sandra Wooltorton

Sandra Wooltorton

Ethics For Industrial Technology Majors: Need And Plan Of Action, Kurt A. Rosentrater, R. Balamuralikrishma

Kurt A. Rosentrater

The recent introduction of sessions dedicated to “Industrial Technology” in the annual ASEE conference is testimony that this discipline has gained its rightful place in the company of engineering and engineering technology. This new level of partnership and collaboration between engineering and technology programs promises to be a step in the right direction for society at large. Engineering and technology majors both supplement and complement each other’s knowledge and skills and it is crucial for educators to build bridges of active interaction. This paper takes aim at one specific as well as basic need in teamwork and interdisciplinary projects – …

Limits Of Truth: Exploring Epistemological Approaches To Argumentation, Michael H.G. Hoffmann

Michael H.G. Hoffmann

Some proponents of epistemological approaches to argumentation (Biro, Siegel, Lumer, Goldman) assume that it should be possible to develop non-relative criteria of argument evaluation. By contrast, this paper argues that any evaluation of an argument depends (a) on the cognitive situation of the evaluator, (b) on background knowledge that is available for this evaluator in a certain situation, and (c)—in some cases—on the belief-value-system this person shares.

Logical Argument Mapping: A Method For Overcoming Cognitive Problems Of Conflict Management, Michael H.G. Hoffmann

Michael H.G. Hoffmann

A crucial problem of conflict management is that whatever happens in negotiations will be interpreted and framed by stakeholders based on their different belief-value systems and world views. This problem will be discussed in the first part of this article as the main cognitive problem of conflict management. The second part develops a general semiotic solution of this problem, based on Charles Peirce's concept of "diagrammatic reasoning." The basic idea is that by representing one 's thought in diagrams, the conditions that determine interpretations can become visible, we can "experiment" with them, and we can change them eventually. The third …

Who Believes What? Clearing Up Confusion Over Intelligent Design And Young-Earth Creationism, Marcus R. Ross

Marcus R. Ross

The question of what differentiates young-Earth creationism (YEC) from Intelligent Design (ID) has resulted in inaccurate and confusing terminology, and hinders both understanding and dialogue. Though both YEC and ID groups have drawn distinctions between themselves, previous attempts to classify design-based positions on origins have been unable to adequately resolve their relationships. The Nested Hierarchy of Design, a multiple-character classification system, categorizes teleological positions according to the strength of claims regarding the reality, detectability, source, method, and timing of design, and results in an accurate and robust classification of numerous positions. This method avoids the philosophical and theological pitfalls of …

Ethics For Industrial Technology, Kurt A. Rosentrater, Radha Balamuralikrishma

Kurt A. Rosentrater

This paper takes aim at one specific, as well as basic, need in teamwork and interdisciplinary projects – ethics and its implications for professional practice. A preliminary study suggests that students majoring in industrial technology degree programs may not have adequate opportunity to formally study and engage in ethical aspects of technology vis-à-vis the practices of the profession. It is reasonable to assume that the ethical dilemmas faced by an industrial technologist would parallel those of engineers and managers. To address this issue, this paper identifies a domain of knowledge that would constitute a necessary background in ethics for industrial …

What You Should Know To Survive In Knowledge Societies. On A Semiotic Understanding Of 'Knowledge', Michael H.G. Hoffmann

Michael H.G. Hoffmann

Different situations - like school and workplace - demand different forms of knowledge. Even more important, in particular for lifelong learning, are forms of knowledge we need for managing movements between those situations. To develop a better understanding of how to 'navigate' knowledge boundaries, this paper analyzes, firstly, interviews with scientists interpreting familiar and unfamiliar graphs. Our goal is to identify those forms of knowledge that should receive special attention in education. Secondly, the article elaborates - based on Peirce's semiotic - an epistemologically reflected semiotic model to describe the role and conditions of knowledge.

How To Get It. Diagrammatic Reasoning As A Tool Of Knowledge Development And Its Pragmatic Dimension, Michael H.G. Hoffmann

Michael H.G. Hoffmann

Discussions concerning belief revision, theory development, and "creativity" in philosophy and AI, reveal a growing interest in Peirce's concept of abduction. Peirce introduced abduction in an attempt to provide theoretical dignity and clarification to the difficult problem of knowledge generation. He wrote that "An Abduction is Originary in respect to being the only kind of argument which starts a new idea." These discussions, however, have led to considerable debates about the precise way in which Peirce's abduction can be used to explain knowledge generation. The crucial question is that of understanding how we can get the new elements capable of …

Learning By Developing Knowledge Networks. A Semiotic Approach Within A Dialectical Framework, Michael H.G. Hoffmann, Wolf-Michael Roth

Michael H.G. Hoffmann

A central challenge for research on how we should prepare students to manage crossing boundaries between different knowledge settings in life long learning processes is to identify those forms of knowledge that are particularly relevant here. In this paper, we develop by philosophical means the concept of a dialectical system as a general framework to describe the development of knowledge networks that mark the starting point for learning processes, and we use semiotics to discuss (a) the epistemological thesis that any cognitive access to our world of objects is mediated by signs and (b) diagrammatic reasoning and abduction as those …

Peirce's "Diagrammatic Reasoning" As A Solution Of The Learning Paradox, Michael H.G. Hoffmann

Michael H.G. Hoffmann

How can we reach “new” levels of knowledge if “new” means that there is something “evolved” that cannot be generated simply by deduction or by induction from what has been given before. The paper’s first goal is to show that two paradigmatic attempts at solving this so-called “learning paradox,” Plato’s apriorism and Aristotle’s inductivism, form two horns of a dilemma: While the inductivist cannot justify any representation of data without assuming a priori given hypotheses, the apriorist cannot justify why a certain application of given ideas is correct without being caught in an infinite regress. The second goal is to …

Lernende Lernen Abduktiv: Eine Methodologie Kreativen Denkens, Michael H.G. Hoffmann

Michael H.G. Hoffmann

No abstract provided.

Peirces Zeichenbegriff: Seine Funktionen, Seine Phänomenologische Grundlegung Und Seine Differenzierung, Michael H.G. Hoffmann

Michael H.G. Hoffmann

No abstract provided.

Die Paradoxie Des Lernens Und Ein Semiotischer Ansatz Zu Ihrer Auflösung, Michael H.G. Hoffmann

Michael H.G. Hoffmann

No abstract provided.

Mathematik Als Prozess Der Verallgemeinerung Von Zeichen: Eine Exemplarische Unterrichtseinheit Zur Entdeckung Der Inkommensurabilität, Michael H.G. Hoffmann, Manfred Plöger

Michael H.G. Hoffmann

No abstract provided.

Problems With Peirce's Concept Of Abduction, Michael H.G. Hoffmann

Michael H.G. Hoffmann

Abductive reasoning takes place in forming "hypotheses" in order to explain "facts." Thus, the concept of abduction promises an understanding of creativity in science and learning. It raises, however, also a lot of problems. Some of them will be discussed in this paper: After analyzing the difference between induction and abduction (1), I shall discuss Peirce's claim that there is a "logic" of abduction (2). The thesis is that this claim can be understood, if we make a clear distinction between inferential elements and perceptive elements of abductive reasoning. For Peirce, the creative act of forming explanatory hypotheses and the …

Erkenntnistheoretische Grundlagen Des Lernens: Lernen Als Verallgemeinerung, Michael H.G. Hoffmann

Michael H.G. Hoffmann

Ziel dieses Beitrages ist es, ein Projekt der am Institut für Didaktik der Mathematik (IDM) in Bielefeld beheimateten Arbeitsgruppe Erkenntnistheoretische und semiotische Grundlagen des Mathematik-Lernens vorzustellen und in eine bestimmte Richtung mathematikdidaktischer Forschung einzuordnen, wie sie von Michael Otte vertreten wird, dem Leiter der genannten Arbeitsgruppe. Dabei geht es insbesondere um mögliche Beziehungen zwischen Philosophie und Mathematik-Didaktik.