Dedication Preface Foreword PART I: FRAME OF REFERENCE We begin with the idea of giving students the tools that increase their capacity for learning. The primary role of education is to increase student capacity for personal growth, social growth, and academic learning. Models of Teaching is an avenue to liberate student learning capacity and, by doing so, to help teachers take charge of their lives as teachers. CHAPTER 1: BEGINNING THE INQUIRY Creating Communities of Expert Learners On the whole, students are in schools and classes within those schools. Both need to be developed into learning communities and provided with the models of learning that enable them to become expert learners. We study how to build those learning communities. CHAPTER 2: WHERE MODELS OF TEACHING COME FROM Multiple Ways of Constructing Knowledge The history of teacher researchers comes to us in the form of models of teaching that enable us to construct vital environments for our students. Models have come from the ages and from teacher-researchers who have invented new ways of teaching. Some of these are submitted to research and development and how teachers can learn to use them. Those are the models that are included in this book. CHAPTER 3: STUDYING THE SLOWLY-GROWING KNOWLEDGE BASE IN EDUCATION A Basic Guide Through the Rhetorical Thickets We draw on descriptive studies, experimental studies, and experience to give us a fine beginning to what will eventually become a research-based profession. Here we examine what we have learned about how to design good instruction and effective curriculums. And, we learn how to avoid some destructive practices. CHAPTER 4: MODELS OF TEACHING AND TEACHING STYLES Three Sides of Teaching--Styles, Models, and Diversity We are people and our personalities greatly affect the environments that our students experience. And, as we use various models of teaching our selves -- our natural styles -- color how those models work in the thousands of classrooms in our society. Moreover, those models and our styles affect the achievement of the diverse students in our classes and schools. PART II: THE INFORMATION-PROCESSING FAMILYOF MODELS How can we and our students best acquire information, organize it, and explain it? For thousands of years philosophers, educators, psychologists, and artists have developed ways to gather and process information. Here are several live ones. CHAPTER 5: LEARNING TO THINK INDUCTIVELY Forming Concepts by Collecting and Organizing Information Human beings are born to build concepts. The vast intake of information is sifted and organized and the conceptual structures that guide our lives are developed. The inductive model builds on and enhances the inborn capacity of our students. CHAPTER 6: ATTAINING CONCEPTS Sharpening Basic Thinking Skills Students can develop concepts. They also can learn concepts developed by others. Concept attainment teaches students how to learn and use concepts and develop and test hypotheses. CHAPTER 7: THE PICTURE-WORD INDUCTIVE MODEL Developing Literacy across the Curriculum Built on the language experience approach, the picture-word inductive model enables beginning readers to develop sight vocabularies, learn to inquire into the structure of words and sentences, write sentences and paragraphs, and, thus, to be powerful language learners. In Chapter 19 the outstanding results from primary curriculums and curriculums for older struggling readers are displayed. CHAPTER 8: SCIENTIFIC INQUIRY AND INQUIRY TRAINING The Art of Making Inferences From the time of Aristotle, we have had educators who taught science-in-the-making rather than teaching a few facts and hoping for the best. We introduce you to a model of teaching that is science on the hoof, so to speak. This model has had effects, among other things, on improving the capacity of students to learn. We concentrate on the Biological Sciences Study Group, where for 40 years science teachers have shared information and generated new ideas. And, Inquiry training is a "best yet" model for teaching basic inquiry skills. CHAPTER 9: MEMORIZATION Getting the Facts Straight Memorization has had something of a bad name, mostly because of deadly drills. Contemporary research and innovative teachers have created methods that not only improve our efficiency in memorization, but also make the process delightful. CHAPTER 10: SYNECTICS The Arts of Enhancing Creative Thought Creative thought has often been thought of as the province of a special few, and something that the rest of us cannot aspire to. Not so. Synectics brings to all students the development of metaphoric thinking -- the foundation of creative thought. The model continues to improve. CHAPTER 11: LEARNING FROM PRESENTATIONS Advance Organizers Learning from presentations has almost as bad a name as learning by memorization. Ausubel developed a system for creating lectures and other presentations that will increase learner activity and, subsequently, learning. PART III: THE SOCIAL FAMILY OF MODELS Working together might just enhance all of us. The social family expands what we can do together and generates the creation of democracy in our society in venues large and small. In addition, the creation of learning communities can enhance the learning of all students dramatically. CHAPTER 12: PARTNERS IN LEARNING From Dyads to Group Investigation Can two students who are paired in learning increase their learning? Can students organized into a democratic learning community apply scientific methods to their learning? You bet they can. Group Investigation can be used to redesign schools, increase personal, social, and academic learning among all students, and -- is very satisfying to teach. CHAPTER 13: THE STUDY OF VALUES Role Playing and Public Policy Education Values provide the center of our behavior, helping us get direction and understand other directions. Policy issues involve the understanding of values and the costs and benefits of selecting some solutions rather than others. In these models, values are central. Think for a moment about the issues that face our society right now -- research on cells, international peace, including our roles in Iraq and the rest of the Middle East, the battle against AIDS, poverty, and who controls the decisions about pregnancy and abortion. Not to mention just getting along together. PART IV: THE PERSONAL FAMILY OF MODELS The learner always does the learning. His or her personality is what interacts with the learning environment. How do we give the learner centrality when we are trying to get that same person to grow and respond to tasks we believe will enhance growth? CHAPTER 14: NONDIRECTIVE TEACHING The Learner at the Center How do we think about ourselves as learners? As people? How can we organize schooling so that the personalities and emotions of students are taken into account? Let us inquire into the person who is the center of the education process. CHAPTER 15: DEVELOPING POSITIVE SELF-CONCEPTS The Inner Person of Boys and Girls, Men and Women If you feel great about yourself, you are likely to become a better learner. But you begin where you are. Enhancing self concept is a likely avenue. The wonderful work by the SIMs group in Kansas (see Chapter 3) has demonstrated how much can be accomplished. PART V: THE BEHAVIORAL SYSTEMS FAMILY OF MODELS We are what we do. So how do we learn to practice more productive behaviors? Let's explore some of the possibilities. CHAPTER 16: LEARNING TO LEARN FROM MASTERY LEARNING Bit by bit, block by block, we climb our way up a ladder to mastery. CHAPTER 17: DIRECT INSTRUCTION Why beat around the bush when you can just deal with things directly? Let's go for it! However, finesse is required, and that is what this chapter is all about. CHAPTER 18: LEARNING FROM SIMULATIONS Training and Self-Training How much can we learn from quasi-realities? The answer is, a good deal. Simulations enable us to learn from virtual realities where we can experience environments and problems beyond our present environment. Presently, they range all the way to space travel, thanks to NASA and affiliated developers. PART VI: INDIVIDUAL DIFFERENCES, DIVERSITY, AND CURRICULUM The rich countryside of humanity makes up the population of our schools. The evidence suggests that diversity enhances the energy of schools and classrooms. However, some forms of teaching make it difficult for individual differences to flourish. We emphasize the curriculums and models of teaching that enable individual differences to thrive. CHAPTER 19: LEARNING STYLES AND MODELS OF TEACHING Making Discomfort Productive By definition, learning requires knowing, thinking, or doing things we couldn't do before the learning took place. Curriculums and teaching need to be shaped to take us where we haven't been. The trick is to develop an optimal mismatch in which we are pushed but the distance is manageable. CHAPTER 20: EQUITY Gender, Ethnicity, and Socioeconomic Background The task here is to enable differences to become an advantage. The best curriculums and models of teaching do just that. In other words, if differences are disadvantages, it is because of how we teach. CHAPTER 21: CREATING AND TESTING CURRICULUMS The Conditions of Learning Robert Gagne's framework for building curriculums is discussed and illustrated. This content is not simple, but it is powerful. CHAPTER 22: TWO WORDS ON THE FUTURE The Promise of Distance Learning and Using Models of Teaching to Ensure that No Child is Left Behind. Afterword APPENDIX PEER COACHING GUIDES Related Literature and References Index

教学模式 = Models of Teaching

A new approximation heuristic for finding a rectilinear Steiner tree of a set of nodes is presented. It starts with a rectilinear minimum spanning tree of the nodes and repeatedly connects a node to the nearest point on the rectangular layout of an edge, removing the longest edge of the loop thus formed. A simple implementation of the heuristic using conventional data structures is compared with previously existing algorithms. The performance (i.e., quality of the route produced) of our algorithm is as good as the best reported algorithm, while the running time is an order of magnitude better than that of this best algorithm. It is also shown that the asymptotic time complexity for the algorithm can be improved to O(n log n), where n is the number of points in the set. >

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An edge-based heuristic for Steiner routing

The minimum rectilinear Steiner tree (MRST) problem arises in global routing and wiring estimation, as well as in many other areas. The MRST problem is known to be NP-hard, and the best performing MRST heuristic to date is the Iterated 1-Steiner (I1S) method recently proposed by Kahng and Robins (see ibid., vol. 11, p. 893-902, 1992). In this paper, we develop a straightforward, efficient implementation of I1S, achieving a speedup factor of three orders of magnitude over previous implementations. We also give a parallel implementation that achieves near-linear speedup on multiple processors. Several performance-improving enhancements enable us to obtain Steiner trees with average cost within 0.25% of optimal, and our methods produce optimal solutions in up to 90% of the cases for typical nets. We generalize I1S and its variants to three dimensions, as well as to the case where all the pins lie on k parallel planes, which arises in, e.g., multilayer routing. Motivated by the goal of reducing the running times of our algorithms, we prove that any pointset in the Manhattan plane has a minimum spanning tree (MST) with maximum degree 4, and that in three-dimensional Manhattan space every pointset has an MST with maximum degree of 14 (the best previous upper bounds on the maximum MST degree in two and three dimensions are 6 and 26, respectively); these results are of independent theoretical interest and also settle an open problem in complexity theory. >

Closing the gap: near-optimal Steiner trees in polynomial time

This dissertation examines the geometric Steiner tree problem: given a set of terminals in the plane, nd a minimum-length interconnection of those terminals according to some geometric distance metric. In the process, however, it addresses a much more general and widely applicable problem, that of nding a minimum-weight spanning tree in a hypergraph. The geometric Steiner tree problem is known to be NP-complete for the rectilinear metric, and NP-hard for the Euclidean metric. The fastest exact algorithms (in practice) for these problems use two phases: First a small but su cient set of full Steiner trees (FSTs) is generated and then a Steiner minimal tree is constructed from this set. These phases are called FST generation and FST concatenation, respectively, and an overview of each phase is presented. FST concatenation is almost always the most expensive phase, and has traditionally been accomplished via simple backtrack search or dynamic programming. The spanning tree in hypergraph problem is de ned, and is proven to be strongly NP-complete. The minimum-weight spanning tree (MST) in hypergraph problem is then motivated by showing that FST concatenation reduces to MST in hypergraph in a simple way. The MST in hypergraph problem is then formulated as an integer program using subtour elimination constraints. The spanning tree in hypergraph polytope, STHGP(n), is introduced and a number of its properties are proven. In particular, every constraint used in the integer program is shown to de ne a facet of STHGP(n). An alternate integer programming formulation based on cutset constraints is presented, but is shown to have an LP relaxation that is weaker xiv Abstract xv than that of the subtour formulation. A simple formula for the number of extreme points in STHGP(n) is shown, thereby generalizing the classical tree enumeration problem of Cayley to hypergraphs. A branch-and-cut algorithm for the MST in hypergraph problem is presented. This algorithm is applied to the FST concatenation problem. Experimental results are presented for a large set of problem instances of various sizes up to 1000 terminals. Optimal rectilinear and Euclidean Steiner trees are obtained for every instance. A single 2000 terminal Euclidean instance is also solved to optimality. These results show that the new algorithm is by far the fastest in existence, since the best previously published Steiner tree results are 70 terminals for rectilinear and 150 terminals for Euclidean, respectively. A number of directions for future work are outlined, and in conclusion it is noted that this two-phase approach works for any distance metric in any nite dimension | even the Steiner problem in graphs | provided a suitable FST generation algorithm is available.xv than that of the subtour formulation. A simple formula for the number of extreme points in STHGP(n) is shown, thereby generalizing the classical tree enumeration problem of Cayley to hypergraphs. A branch-and-cut algorithm for the MST in hypergraph problem is presented. This algorithm is applied to the FST concatenation problem. Experimental results are presented for a large set of problem instances of various sizes up to 1000 terminals. Optimal rectilinear and Euclidean Steiner trees are obtained for every instance. A single 2000 terminal Euclidean instance is also solved to optimality. These results show that the new algorithm is by far the fastest in existence, since the best previously published Steiner tree results are 70 terminals for rectilinear and 150 terminals for Euclidean, respectively. A number of directions for future work are outlined, and in conclusion it is noted that this two-phase approach works for any distance metric in any nite dimension | even the Steiner problem in graphs | provided a suitable FST generation algorithm is available.

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Spanning trees in hypergraphs with applications to steiner trees

Systems and methods are provided for integrating educational software. In one implementation, a first server receives an identifier of a second server that provides at least one source educational course. A second server receives metadata for the at least one source educational course and stores the metadata.

Systems and methods for integrating educational software systems

Several phases of the VLSI design process use rectilinear Steiner spanning trees in estimating wire length. Since the problem is NP-complete heuristics form the major portion of the collection of algorithms for this problem. Exact solutions are rare and very few have even been implemented. Thus they seem not to be practical. The authors first reduce the feasible solution space so that exact solutions are possible. Then they develop two branch and bound algorithms which achieve exact solutions. Distributing the computation between processors and parallel computation methods are currently being tested in an attempt to extend the size of the problems which can be actually solved. >

Optimum Steiner tree generation

An approach to the construction of rectilinear Steiner spanning trees that takes advantage of an elegant new representation to simply apply local improvement methods to the problem is presented. Use of a special type of Steiner tree allows the results to contain a minimum number of vias while achieving a significant reduction in wire length over previous methods. >

Local improvement in Steiner trees

Rectilinear Steiner spanning trees are used in several phases of the VLSI physical design process when collections of terminals must be connected to a common electrical point. The authors present a new linear time heuristic algorithm for generating these rectilinear Steiner trees. They begin with minimal spanning trees and transform those configurations which are never found in the shortest Steiner trees. This decreases the length of the spanning trees. In addition to its speed, the algorithm is straightforward and can be implemented efficiently. Empirical results demonstrate that reductions of over 13% in length are possible, while an average of over 8% reduction is achieved. This compares very favorably to much more complex algorithms. The algorithm is recommended for applications where many spanning trees are needed in a very short time. >

A linear-time heuristic for rectilinear Steiner trees

Instructional technology is rapidly expanding into all levels of society from a wide variety of government and educational institutions to corporate enterprises. We currently have unprecedented access to information and resources, yet with all the advances in technology and profusion of web sites, there is no standard on how to transform this deluge of content into instruction using technology. Specifically, there is a lack of direction on how to effectively sequence individual learning objects (reusable digital resources) that makes sound instructional sense. Before the potential for computer managed instruction can be completely realized, instructional design must be incorporated into instructional technology. The Mentor Project is designed to explore this issue by mediating between learning objects and instructional sequencing. In this paper, the authors present an XML meta-grammar to categorize learning objects in meaningful human terms, an XML meta-grammar for lesson sequencing, and a prototype of the sequence editor, a course authoring system.

The Mentor Project: from content to instruction

Two rectilinear Steiner spanning tree algorithms are presented, proven to be correct, and examined with regard to their complexity. It is shown that their worst case efficiencies are merely 1.5 times the optimum solution. These algorithms, when experimentally compared to existing algorithms, excel. They in fact produce the best solutions over 80% of the time and are never more than 1% from the best solution found.

N. Van Cleave

Papers

Optimum Steiner tree generation

Local improvement in Steiner trees

A linear-time heuristic for rectilinear Steiner trees

The Mentor Project: from content to instruction

Correct and Provably Efficient Methods for Rectilinear Steiner Spanning Tree Generation