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[转载]Science Blog 2012年07月06日 20:19 (星期五)
xupeiyang 2012-7-6 21:41
http://scienceblog.com/ China has higher childhood diabetes rate than U.S. Life’s molecules could lie within reach of Mars Curiosity rover Astronomers discover Houdini-like vanishing act in space The key (proteins) to self-renewing skin Smaller volcanoes could cool climate When to rein in the stock market? Rarely. Certain parenting beliefs are detrimental to moms’ mental health Robot eyes get more human Employees’ Interests Predict How They Will Perform on the Job Project 1640 Sifts Through Starlight to Reveal New Worlds Endowment effect in chimps can be turned on and off Device swaps sight for sound to help impaired reach out Strawberries help cardio health via protein Nrf2 Surgeons perform better in OR if they receive structured training in simulator
个人分类: 科学博客|1967 次阅读|0 个评论
高阶丢番图方程
ws987 2010-10-13 07:44
high degree diophantine equation 高阶丢番图方程,如费马大定理,其实研究的人很少,所谓高处不胜寒。费玛大定理,历史上研究的很多,但无一正确。 怀尔斯好像证明了,得到了学界的承认。但它所使用的复变函数和黎曼及langlands的基本构造其实不很正确--必须使用的hecke conversion theorem的证明中,把两条平行线当做完整围道。这样看来,除了初等数论,我们没干什么。其实实数方法在整数方程中毫无用处,是不同性质的问题。 我从高中知道FLT 起想了无数方法研究FLT,最终发现只能在整数中研究才有效。从新审视整数的结构给了我灵感,结合很早就有的模下对数的设想,我决定用代数的方法分析模里的函数,传统的抽象代数在我看来,其实很不代数,我需要计算直觉上的代数,模里的代数就很好,甚至比实数里更好。 作模下对数,得到一个复合的模,我称为第一,第二部分代数,在实验完他们的用处的最后,我证明了 c^q=a^p+b^p ,a,b0,pq40 无解 ModuDigAna.pdf |HeckeConversionTheorem
个人分类: 生活点滴|1841 次阅读|0 个评论
[转载]Change:March/April 2010: In This Issue
geneculture 2010-5-4 02:43
Frame of Reference: Open Access Starts with You by Lori A. Goetsch Federal legislation now requires the deposit of some taxpayer-funded research in open-access repositoriesthat is, sites where scholarship and research are made freely available over the Internet. The National Institutes of Health's open-access policy requires submission of NIH-funded research to PubMed Central, and there is proposed legislationthe Federal Research Public Access Act of 2009that extends this requirement to research funded by 11 other federal agencies. Academic Researchers Speak by Inger Bergom, Jean Waltman, Louise August and Carol Hollenshead Non-tenure-track (NTT) research faculty are perhaps the most under-recognized group of academic professionals on our campuses today, despite their increasingly important role within the expanding academic research enterprise. The American Association for the Advancement of Science reports that the amount of federal spending on RD has more than doubled since 1976. The government now spends about $140 billion yearly on RD, and approximately $30 billion of this amount goes to universities each year in the form of grants and contracts. Taking Teaching to (Performance) Task: Linking Pedagogical and Assessment Practices by Marc Chun Imagine a typical student taking an average set of courses. She has to complete a laboratory write-up for chemistry, write a research paper for linguistics, finish a problem set for mathematics, cram for a pop quiz in religious studies, and write an essay for her composition class. Her professors almost exclusively lecture (which, it's been said, is a way for information to travel from an instructor's lecture notes to the student's notebook without engaging the brains of either). And somehow she is supposed to not only learn the course content but also develop the critical thinking skills her college touts as central to its mission. Why Magic Bullets Don't Work by David F. Feldon We always tell our students that there are no shortcuts, that important ideas are nuanced, and that recognizing subtle distinctions is an essential critical-thinking skill. Mastery of a discipline, we know, requires careful study and necessarily slow, evolutionary changes in perspective. Then we look around for the latest promising trend in teaching and jump in with both feet, expecting it to transform our students, our courses, and our outcomes. Alternatively, we sniff disdainfully at the current educational fad and proudly stand by the instructional traditions of our disciplines or institutions, secure in our knowledge that the tried and true has a wisdom of its own. This reductive stance is a natural one. As university faculty who work within disciplines, we have each chosen a slice of human knowledge about which we are passionate, and we often settle on the most expedient (but sound) answer to the question of how to teach so that we can move on to the interesting issues and problems that led us to pursue academic careers in the first place. Further, the professional demands on us and the rewards for our work generally do not align with high levels of sustained effort invested in teaching. However, what we tell students about mastering our respective disciplines are the same truths that apply to finding effective instructional strategies: The devil is always in the details, and nuance is critical. Yet in our desire to do right by our students and still invest the bulk of our efforts in teaching content, we put our faith in over-simplified generalizations that never seem to realize the full benefits that they promise. There have been many sweeping statements made regarding the best ways to teach students in the 21st century. Two of the most au courant are traditional lectures are ineffective and internet-based technologies help students learn. There is empirical evidence to support the truth in each of these statements, truebut only if they meet specific parameters, which rarely carry over from their origins in educational research to guide their implementation in practice. Are lectures bad for learning? When we look beyond the rhetoric surrounding instructional practices to examine data, it turns out that bad lectures do limit students' learning and motivation. However, good lectures can be inspiring and have a positiveeven transformativeimpact on student outcomes. Given this unenlightening information, the real question becomes, What differentiates a good lecture from a bad one? Good lectures share a number of key properties with any type of effective instruction. They begin by establishing the relevance of the material for students through explicit connections with their goals or interests. They activate prior knowledge by connecting new content with what students already know and understand or problems with which they are currently grappling. They present information in a clear and straightforward manner that does not require disproportionate effort to translate into terms and concepts meaningful to students. They limit the information presented to a small number of core ideas that are thoroughly but not redundantly explained. Studies that systematically control the relevant features of lectures find significant learning benefits for students when these principles are implemented. However, the large-scale correlative studies of instructional format and student achievement that report negative outcomes for lectures do not control for or even ask about the presence or absence of these features. Thus it may be that the negative findings are a more accurate reflection of generally lackluster or ill-informed implementation of this teaching technique than a condemnation of the technique itself. Of course, simply knowing or even applying these general principles for effective lecturing does not guarantee positive results. Students enter courses with differing backgrounds, levels of prior knowledge, goals, and interests. Given that each of the guidelines above explicitly frames practice in terms of characteristics that vary by learner, the underlying challenge is to find ways to connect with the broadest cross-section of students and find supplemental or alternate means of connecting with those who do not fit that mold. Many instructors succeed at this through the use of assignments that require students to grapple with problems prior to the lecture. Others use clickers to stimulate engagement and structure situations in which the information presented is salient. However, the effective use of such practices involves understanding the students at whom the course is targeted. Is technology good for learning? Both the definitions and the uses of instructional technology are highly varied, so conversations about its benefits and limitations also tend to rely on overly broad generalizations. The two major foci of these discussions currently are game/simulation-based learning and so-called Web 2.0 technologies that allow users to interact with each other via the internet and to contribute content of various types directly to websites. Advocates claim that these applications are important for improving student learning outcomes; they enhance relevance for students by engaging them through the generationally preferred medium of digital media and provide them with opportunities to actively engage with a course's content. While there are indeed instances where such benefits are realized, they are not reflected in comprehensive literature reviews or meta-analyses of the research. There is a simple explanation for this: not all uses of a technology are created equal. The key features that drive engagement and learning pertain to the designs that underlie the technology rather than to the technology itself. When games and other digital learning environments are developed in accordance with principles of effective instruction, they achieve positive results. But they do not yield better results than less sophisticated instructional delivery systems that use the same instructional designs. Why? Because the active ingredients that affect students' learning are the same in both cases. One of the most durable descriptions of this phenomenon is Richard E. Clark's grocery truck metaphor: Media are mere vehicles that deliver instruction but do not influence student achievement any more than the truck that delivers our groceries causes changes in our nutrition (Clark, 1983, p. 445). What the new media do offer are tools for interacting with instructors, peers, and content in ways that are not affordable or possible otherwise. When these interactions offer opportunities to observe or manipulate information and phenomena in meaningful ways, they can facilitate learning. Generally, the features that are most helpful for students include enabling the representation of concepts at multiple levels of abstraction (e.g., via concrete representation, abstract functional models or mathematical models), providing opportunities for more extensive practice than would otherwise be possible and offering immediate feedback to direct further learning efforts. While they are potentially valuable learning tools, such technologies need to be designed in such a way that they are not confusing or overwhelming for the students who will use them. With any software, there is a learning curve for mastering the interface used to interact with it. To the extent that the interface functions in a standard way, students will be able to draw on previous technology experiences in using it. However, if it is significantly different from familiar interfaces, they will need to invest substantial effort in mastering its use before getting to content-related learning. The greater the departure from familiar software environments, the steeper the learning curve. Thus the technology itself can act as a learning impediment for students with limited technology backgrounds. It may be the case that the potential learning benefits offered outweigh the cognitive costs, but it should not be assumed without evidence that this will be the case. The role of cognition There are two threads linking effective lectures and effective technology use. The first is consideration of what students bring to the table in terms of goals, interests, and prior knowledge. The second is the deliberate management of the opportunities for students to engage with content in order to focus their investment of mental effort on key ideas. In educational research, a powerful framework for considering these factors jointly is cognitive load theory (CLT). When games and other digital learning environments are developed in accordance with principles of effective instruction, they achieve positive results. But they do not yield better results than less sophisticated instructional delivery systems that use the same instructional designs. CLT operates under the central premise that learners are only capable of attending to a finite amount of information at a given time due to the limited capacity of the working (short-term) memory system. So it is necessary to carefully manage the flow of information with which learners must grapple. It is likely that anyone who has taken an introductory course in educational or cognitive psychology will have heard of George Miller's (1956) magical number that people can only process seven information elements at a time, plus or minus two. However, what many people do not know is that this number is probably a substantial overestimate. Miller obtained his finding by asking people to listen to strings of random numbers and recite them back as accurately as possible. These numbers were not linked to any context, and he assumed that they were ubiquitous placeholders for any type of information that people might need to process. What did not occur to Miller is that people use strings of numbers for many everyday tasks and have developed memory strategies to retain them. Think, for example, of how you remember a telephone number or your social security number; most people group the digits into two or three chunks (e.g., XXX-XXXX or XXX-XX-XXXX). It is these chunks that occupy space in working memory and help to organize the information so that it does not get lost. Subsequent research holds that the upper limit of our short-term memory is actually closer to four information pieces or chunks. Given these tight bandwidth constraints, how do human beings handle any complex taskespecially one that has more than four discrete elements? To simplify, we handle the task-relevant information much as we would a phone number: we divide it into meaningful units based on our knowledge of the content and task structure. The more knowledge we have about a task, situation, or content area, the more efficiently and adaptively we are able to map discrete pieces of information onto schemas. These schemas are the abstract representations of our knowledge that serve as integrated templates for rapidly organizing the relevant facets of a situation. With deeper, more meaningful, and more interconnected knowledge, our schemas become more refined, nuanced, and capable of encoding increasing amounts of incoming information as a single chunk. Information that would occupy only one chunk for an advanced learner might be viewed by a novice as several discrete pieces of information. Cognitive load is conceptualized as the number of separate chunks (schemas) processed concurrently in working memory while learning or performing a task, plus the resources necessary to process the interactions between them. Therefore a given learning task may impose different levels of cognitive load for different individuals based on their levels of relevant prior knowledge. Cognitive load is experienced as mental effort; novices need to invest a great deal of effort to accomplish a task that an expert might be able to handle with virtually none, because they lack sufficiently complex schemas. When cognitive load (the information to be processed) exceeds working memory's capacity to process it, students have substantial difficulties. The most straightforward effect is that they are unable to learn or solve problems. However, other problematic outcomes can also occur. First, students may revert to using older or less effortful approaches to the problem that impose a less heavy load on working memory. This means that previously held misconceptions or erroneous approaches may be brought to bear, reinforcing knowledge that is counter to the material they are trying to learn. Second, students may default to pursuing less effortful goals. In other words, they may procrastinate. In such situations, thinking about the whole of a complex task may be so overwhelming that students turn to more manageable activities: checking their email, cleaning their desks, or taking on whatever other chores do not exceed their processing ability. (Rumor has it that faculty have similar experiences.) For this reason, one of the strategies for overcoming procrastination is to reduce the magnitude of a goal by breaking a large task into its component parts and dealing with only one piece at a time. This limits the complexity of the task faced, which reduces the cognitive load it imposes to manageable levels. Managing cognitive load in teaching In order to optimize the benefits of instruction, CLT prioritizes available information according to the type of cognitive load it imposes. Intrinsic load represents the inherent complexity of the material to be learned. The higher the number of components and the more those components interact, the greater the intrinsic load of the content. Extraneous load represents information in the instructional environment that occupies working memory space without contributing to comprehension or the successful solving of the problem presented. Germane load is the effort invested in the necessary instructional scaffolding and in learning concepts that facilitate further content learning. Cognitive load is conceptualized as the number of separate chunks (schemas) processed concurrently in working memory while learning or performing a task, plus the resources necessary to process the interactions between them. In this context, scaffolding refers to the cognitive support of learning that is provided during instruction. Just as a physical scaffold provides temporary support to a building that is under construction, with the intent that it will be removed when the structure is able to support itself, an instructional scaffold provides necessary cognitive assistance for learners until they are able to practice the full task without help. Extensive instruction typically provides multiple levels of support that are removed gradually to facilitate the ongoing development of proficiency. Processing the information provided as scaffolding imposes cognitive load. However, to the extent that it prevents the cognitive overload that would otherwise result for a learner struggling with new material, it is cost beneficial. Thus, the three driving principles of CLT are: 1) present content to students with appropriate prior knowledge so that the intrinsic load of the material to be learned does not occupy all the available working memory, 2) eliminate extraneous load, and 3) judiciously impose germane load to support learning. For any instructional situation, the goal is to ensure that intrinsic, extraneous, and germane load combined do not exceed working memory capacity. But how can we manage this? Although we do not control the innate complexity of the material we teach, we can assess the prior knowledge of our students to ensure they understand prerequisite concepts. If they have schemas in place to facilitate the processing of the new concept, their intrinsic load is lower than if they need to grapple with every nuance of the material without the benefit of appropriate chunking strategies. This is an opportunity to effectively use technology. The use of clickers during lectures or short online assessments to be completed prior to attending class can provide a quick picture of which necessary elements students have in place before a new concept is introduced. If they lack the prerequisite knowledge, then the instructor should teach or provide that material first in order to prevent the advanced material from exceeding students' ability to process it. The good news about extraneous load is that it should be eliminated whenever possible rather than managed. In fact, there are a number of simple and straightforward principles for doing so in instructional materials as well as in the classroom. Some have to do with the information presented. For example, ancillary information that is not directly on point should be eliminated. This includes things like biographies of historic figures in science texts when the instructional objective is to teach a theory or procedure. While it may be an interesting human-interest story to consider whether or not an apple really fell on Newton's head, processing that information detracts from the working memory available to understand gravitational theory or how to solve problems using the law of gravity. Other practices target the presentation of information. For example, it is better to integrate explanatory text into a diagram than to keep it separate, because the cognitive load of mentally integrating the information can be avoided when they are collocated. On the other hand, reading aloud the text that students are looking at forces redundant processing of the same information and impedes their ability to retain the material. Because sensory information enters working memory through modality-specific pathways, which themselves have limited bandwidth, it is helpful for information to be distributed across modalities wherever possible. It is also helpful for all necessary information to enter working memory at approximately the same time. Thus, the first example uses linguistic and visual information together, which distributes the information across modalities and avoids the unnecessary load of holding the information from the diagram in working memory while searching for the appropriate text or vice versa. In contrast, the second example overloads the pathway that handles verbal information because it simultaneously delivers read and spoken information. It also requires that information from the text be held in working memory while the speech is processed, because people typically read to themselves much more quickly than words are read aloud. Germane load is a highly complicated issue. Building scaffolds for learning imposes cognitive load. Novices being introduced to material for the first time need a great deal of explicit instruction, using very small chunks of information, to deeply process new information or problem-solving strategies. As they acquire more knowledge and skill, though, the external scaffolding which initially helped them becomes unnecessary and redundant. If such learning supports are not eliminated for those students, they cease to facilitate learning as germane load and begin to hinder it as extraneous load. This expertise reversal effect is the biggest challenge for developing effective instruction, because students do not all attain the same level of comprehension at the same time. What is germane and helpful load for one student may be extraneous and harmful for another. Effective Practices The keys to applying cognitive load theory effectively in a course are advance planning and the ongoing monitoring of students' progress. Because the central premise of CLT is to optimize the allocation of students' working memory resources for mastering particular information, it is vital to identify very specifically what the instructional objectives are for the course as a whole and for each class meeting or module. If we cannot be precise about what we want students to know and be able to do, we will not be able to structure their experiences to help them accomplish this. Next, we need to sequence the objectives so as to present material in the order in which it is needed. If some topics build on others in the course, the prerequisite pieces should be taught before they are needed. For example, we should teach processes and procedures in the same sequence that students will perform them, so that work products from preceding steps can be used in subsequent steps. If the concepts, knowledge, or skills being taught do not have an inherent sequence, then it is generally most effective to order them from simplest to most complex. Once we have figured out what content needs to be taught and the appropriate progression of topics, it is most helpful to students when we let them in on the secret. Trying to impose order on disconnected information is highly effortful. If we simply turn students loose on the material without presenting clearly what they should be trying to get from it and how it fits into the larger picture of the course's content, much of their cognitive resources will be allocated to figuring out what information is important (extraneous load) rather than focusing on constructing the knowledge necessary to meet our learning objectives. Although the logic of the course content and sequence may be obvious to us as knowledgeable instructors and content experts, our students arrive without the benefit of the schemas we have developed. Regardless of their previous experiences (or perhaps because of them), they sincerely appreciate knowing up front what they will be learning, what is expected of them, how they will be assessed, and how all of these elements fit together. When these components of the course are unclear, students invest substantial effort in figuring them out. Further, they may reach incorrect conclusions, which leads to more extraneous effort as they work at cross purposes to the course. Having mapped out the information in the course, we also need to determine how well students comprehend any knowledge on which later course content depends. This does not mean that we must burden our students (and ourselves) with exams or large assignments every week. Instead, we can use lightweight, rapid assessments that are not formally graded but are attuned to the key concepts upon which the new material draws. These can include short online surveys on the content that must be submitted a few days before class, quick check-in conversations as class begins, or multiple-choice questions on key issues that students must respond to using personal response systems (clickers). These tools are most effective when students are accountable for submitting a response but not for the accuracy of their answers. The purpose is to inform the instruction we provide rather than to increase students' anxiety (i.e., emotionally invoked extraneous load) about not knowing a correct answer. If students generally have a strong grasp of the prerequisite material, the likelihood of cognitive overload will be small, less scaffolding will be needed, and they can move directly into problem-solving. But if their understanding is weak, it will be important to review the prior material in detail, structure the new content as much as possible, and move slowly through it. When introducing problem-solving procedures to novices, providing worked examples is a very helpful practice. This involves demonstrating and explaining the reasoning processes that are involved in solving a class of problems, using a representative example. This helps to manage cognitive load effectively in several ways. When a problem is taken on, there are two sources of potential load for a learner. The first is the need to structure the information provided to effectively frame and analyze the problem. The second is the application of appropriate problem-solving strategies. The worked example both demonstrates problem-framing and provides a concrete model of an appropriate problem-solving strategy. sincerely appreciate knowing up front what they will be learning, what is expected of them, how they will be assessed, and how all of these elements fit together. This reduces the degree of uncertainty under which the students are working on three fronts. First, it allows them to map concrete instances onto relevant schemas, facilitating effective chunking. Second, it reduces their reliance on highly effortful trial-and-error attempts to identify productive solutions, which substantially increase cognitive load and time spent without providing any learning advantage. Last, it breaks the procedure down into distinguishable steps that can be considered in smaller, more manageable chunks. After walking through a full example, an excellent way to help students practice without getting overloaded is to provide a partially worked example and ask them to pick up where the completed part of the example leaves off. Having them practice the last steps first ensures that all aspects of the strategy to be learned are practiced. In complex, open-ended problems, students can get off track midway through an exercise and never have the opportunity to practice its later elements. As students become proficient in the later steps, they can be given problems with fewer steps completed for them. In this way, instructors can effectively control the overall level of cognitive load imposed by the problem and ramp up to full problems after students have developed effective schemas and chunking strategies. Practice makes perfect As students encounter repeated instances of problem types during their learning, their strategies become more nuanced (to accommodate small differences between the problems) and less effortful to execute. As they practice, their skills require less and less conscious monitoring, which reduces the level of cognitive load that problem-solving imposes. This lets them efficiently address problems of increasing complexity. Experts are able to solve problems beyond the scope of what laymen can handle precisely because their core problem-solving procedures impose virtually no load on working memory. Therefore, they can assimilate very subtle nuances and much more complex problem features with their extra cognitive capacity. The benefits of practice are just as powerful for teachers as they are for students. Teaching effectively and using cognitive load theory to guide practice is challenging. It requires the focused consideration of many details regarding our students, their knowledge, and our instructional goals. But with sustained effort, careful observations of what seems to yield more efficient and effective learning, and a willingness to make changes as necessary, these practices become less effortful. This frees up our own working memory resources to use for addressing both further complexities in addressing the learning needs of our students and the subtleties of our own disciplinary passions. Resources 1. Bernard, R. M., Abrami, P.C., Lou, Y., Borokhovski, E., Wade, A., Wozney, L., Wallet, P. A., Fiset, M. and Huang, B. (2004) How does distance education compare with classroom instruction? A meta-analysis of the empirical literature. Review of Educational Research 74 :3, pp. 379-439. 2. Bernard, R. M., Abrami, P. C., Borokhovski, E., Wade, C. A., Tamim, R. M., Surkes, M. A. and Bethel, E. C. (2009) A meta-analysis of three types of interaction treatments in distance education. Review of Educational Research 79 :3, pp. 1243-1289. 3. Clark, R. C., Nguyen, F. and Sweller, J. (2005) Efficiency in learning: Evidence-based guidelines to manage cognitive load , John Wiley Sons, San Francisco. 4. Clark, R. E. (2001) Learning from media: Arguments, analysis, and evidence , Information Age Publishing, Charlotte, NC. 5. Cowan, N. (2000) The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences 24 , pp. 87-185. 6. Feldon, D. F. (2007) Cognitive load in the classroom: The double-edged sword of automaticity. Educational Psychologist 42 :3, pp. 123-137. 7. Kalyuga, S., Ayres, P., Chandler, P. and Sweller, J. (2003) The expertise reversal effect. Educational Psychologist 38 :1, pp. 23-31. 8. Mayer, R. E. (2009) Multimedia learning , 2 Cambridge University Press, New York. 9. Miller, G. A. (1956) The magical number seven, plus or minus two: Some limits on our capacity for processing information. The Psychological Review 63 , pp. 81-97. 10. Schwartz, D. L. and Bransford, J. D. (1998) A time for telling. Cognition Instruction 16 :4, pp. 475-522. 11. van Merrinboer, J. J. G. and Sweller, J. (2005) Cognitive load theory and complex learning: Recent developments and future directions. Educational Psychology Review 17 :2, pp. 147-177. David Feldon is an assistant professor of STEM education and educational psychology at the University of Virginia. His research examines the development of expertise in science, technology, engineering, and mathematics through a cognitive lens. He also studies the effects of expertise on instructors' abilities to teach effectively within their disciplines. http://www.changemag.org/index.html Editorial: Motivating Learning by Margaret A. Miller Knowing how students learn and solve problems informs us how we should organise their learning environment and without such knowledge, the effectiveness of instructional designs is likely to be random . John Sweller (Instructional Science 32: 931, 2004.) I've written in the past about the things we want students to learn, how we help them learn, and about resistance (mine and virtually everyone else's) to change. In this issue, those concerns converge. Determining what we want students to learn is the amazingly difficult first step in developing assessments of that learning, as the article by Dary Erwin and Joe DeFillippo demonstrates. And Marc Chun talks about linking teaching, learning, assessment, and the ultimate use of higher-order thinking skills by both teaching and assessing those skills through tasks that mimic how they will be used in real life. But what particularly intrigues me is the connection between cognition and change. Educational psychologists have developed a number of constructs to explain how the mind works. In this issue, David Feldon suggests that a familiarity with cognitive load theory can be a big help in developing effective pedagogies, for example, a framework we see invoked in Carl Wieman's attempts to improve science instruction. But there is other knowledge about human cognitive architecture that can also be useful as we think about teaching and learning. For instance, the human cognitive default is to solve problems with as small a mental investment as possible; we typically retreat to earlier mental models and quicker and less effortful automated problem-solving strategies when new information threatens to overwhelm us. So as Feldon suggests, teachers need to find some way to keep the investment low enough and the cognitive load light enough that those mechanisms don't come into play. We can also exploit the fact that we're more likely to try to solve problems in areas that are important to us by showing students the relevance of what we're teaching to their lives and concerns. But given the fundamentally conservative nature of human cognition, perhaps the question should be, why doesn't the whole learning system grind to a halt? In a way, it's remarkable that we ever learn anything at all. I remember that when my son was about a year old, he developed the locomotive strategy of scooting around on his knees (it beat crawling, since he could carry things). Once he had built up calluses thick enough to protect those knees, it was a remarkably efficient way to get from point A to point B, and it halved the height from which he would fall if something went wrong. I remember thinking at the time, what will ever motivate him to get up on his hind legs and wobble around when a misstep would cause him to fall from twice the height? What will prompt him, in short, to face the perils of change when things work so well and comfortably for him as they are? Come to think of it, our bipedal walk is a great metaphor for our alternation between imbalance and stability. The act of walking, researchers have discovered, is a continual falling forward, regaining our balance, then falling forward again. Something impels us to lift that foot and risk the fall, then we consolidate our new position momentarily, then we lift that foot and fall again, and so on. At the species level, there are clearly advantages in the impulse to generate, test out, and practice both old and new survival strategies (e.g., bipedalism) that can give one an evolutionary edge. But what lies on top of that drive for individual students? How do we motivate them to lift one foot and put it down a little ahead, let us help them organize and consolidate their momentary new equilibrium, and then lift the other? I think the answer can be found by looking not at learning in school but at spontaneous learning, particularly during play. When they play, children seem to be motivated by several things. Curiosity, for one. Another stimulus is wanting to master the environment (a bone-deep tendency, crucial to the human race's survival, that is as dangerous as fire when out of control but as just as life-giving when contained), which is why children need plenty of free play where they make up the rules (as opposed to playing board games or participating in sports). A third stimulus may be the desire to imitate and take one's place among trusted and admired others, either peers or adults. Those tendencies don't need to be lost as one ages, as the success of Elderhostel attests to, although Grandgrindian schooling can certainly grind them down. So our job as teachers may be to stand in what Vygotsky called the zone of proximal development, the stage in their cognitive growth that students haven't quite gotten to yet, and beckon them forward into what for them is uncharted but possibly alluring territory (the ending of Huckleberry Finn floats into my mind, where Huck tells Jim that it's time to light out for the territories, or the song by Jacques Brel in which he mentions his childhood longing for le Far West). We motivate students to make that leap by stimulating their curiosity about the subject; by showing our own passion for it; by lessening the dangers of the move as we, knowing what their current maps look like, show them the path from there to here and how to organize their understanding of the new landscape; and by giving them as much control as possible over the learning environment. But more: I point you to Matt Procino's account (in the Listening to Students in the previous issue) of taking over a class in child development. He modeled for students the very behavior he wanted them to exhibit in life as a result of what they learned in his class by soliciting sometimes uncomfortable feedback as he learned how to teach. Similarly, he had earlier let his Outward Bound students see that he too was afraid of the challenges he was asking them to take on but that they could summon the courage to do so becausesee?he was doing it. From the point of view of the students, an admired other gave them two things to imitate: not only how you scale a cliff but how you deal with the fear of scaling a cliff. People generally can't be dragged or whipped into forward movement; they'll run back to their earlier spot of equilibrium the minute the threat (of bad grades, for instance) stops. I know that I plant my feet stubbornly whenever I feel bullied (leading one professorwho tried to argue me into liking Wordsworth's Michael, a poem I detest to this dayto say to me in exasperation, Miss Miller, why are you sometimes so dense ?) But I'm apt to leap joyfully ahead when beckoned by someone I trust and admire into knowledge that he or she is passionate about. And I want to be among the people who inhabit that new zone. That's why, at the end of a successful dissertation defense, I always say to the newly minted PhD, Welcome to the community of scholars.
个人分类: 高等教育学|149 次阅读|0 个评论
3rd International Pedagogical Research in Higher Education Conferences
geneculture 2010-5-3 21:53
We are pleased to announce the third PRHE conference which will be held in Liverpool from the 25th -26th October 2010. The timing has been arranged to follow on directly from the ISSOTL conference which will be held for the first time in Liverpool (19-22 October 2010) http://www.issotl.org/conferences.html The PRHE conference is a biennial event which brings together, in an intimate and welcoming environment, researchers and practitioners to share research findings, promote rigorous pedagogical research and build collaborative research networks. The theme of the PRHE conference is: 'Research-teaching linkages to enhance student learning. The 2010 PRHE conference will, as usual, be organised by Liverpool Hope University but this year the location of the conference will be in Liverpool city centre at the University of Liverpools Foresight Centre, an award winning facility for conferences and events. Keynote speakers: KEITH TRIGWELL - The University of Sydney Professor of Higher Education - Institute for Teaching and Learning Title: Studies relating research, teaching and learning in higher education Abstract : There is very little empirical evidence to support the claim by large numbers of academic staff that there is a positive correlation between teaching and research. A meta-analysis of work reported up to 1995 indicates that the correlation is near zero (Hattie and Marsh, 1996) despite others arguing that better researchers are better teachers. Studies with more of a qualitative focus have more recently provided information from different perspectives, but there is still much contention surrounding this field of study. This presentation will briefly review this research and then focus on a recent study (Prosser, et al., 2008) that has shown that among research-active teaching academic staff, variation in the nature of the description of their research focus is found to be related to variation in the quality of their approach to teaching. Where the research focus is on wholes or themes, the teaching is more likely to be described as student-focused with the intention of changing or developing students conceptions of the subject matter. Where the research focus was more on parts or components of disciplinary fields, the teaching was more likely to be described in teacher-focused ways with the intention to transfer information to students. In other words, the way academic staff experience their research is related to the way they experience their teaching. This relationship is both logical and empirical, and is supported by qualitative data (Trigwell and Prosser, 2009). All this suggests that it is not the quantity of research that is associated with quality of teaching, but how scholarship in the discipline or profession is maintained and developed that is important. This may apply to non-research active as well as to research active academic staff (Prosser, et al., 2008, p13). Given that there is an association between student-focused conceptual change teaching and the quality of student learning (Trigwell, et al., 1999), the issue becomes more of one based on the teachers understanding of subject matter than has hitherto been considered. read more Mick Healey - University of Gloucestershire Professor of Geography and Director of the Centre for Active Learning, Title: Engaging Students in Research and Inquiry Abstract We need to encourage universities and colleges to explore new models of curriculum . Government and funding bodies should incentivise and support the radical realignment of undergraduate curricula: we require curricula that are transdisciplinary, that extend students to their limits, that develop skills of inquiry and research , and that are imbued with international perspectives. There are several models that we might explore. They should all: Incorporate research-based study for undergraduates (to cultivate awareness of research careers, to train students in research skills for employment, and to sustain the advantages of a research-teaching connection in a mass or universal system ) Paul Ramsden, Chief Executive of the Higher Education Academy, in his invited contribution to the Department of Innovation, Universities and Skills Debate on the Future of Higher Education (2008, 10-11, emphasis added) The argument of this session can be simply stated: all undergraduate students in all higher education institutions should experience learning through and about research. My interest in developing students as researchers originated through explorations over the last few years into ways to enhance the linkage between teaching and discipline-based research. The conclusion to arise from that work is that one of the most effective ways to do this is to engage our students in research and inquiry; in other words, to see them as producers not just consumers of knowledge. Many undergraduate research programmes are for selected students and may well be outside the formal curriculum, e.g. in summer enrichment programmes. However, here it is suggested that the key to mainstreaming undergraduate research and inquiry is to integrate it into the curriculum. The session will explore the variety of ways in which undergraduate research and inquiry based learning are undertaken using numerous mini-case studies from different disciplines, departments and institutions in UK, mainland Europe, Australasia and North America. read more Jan Meyer - The University of Durham Professor of Education and the Director of the Centre for Learning, Teaching, and Research in Higher Education, Title: Threshold concepts and opportunities for research on student learning Abstract The threshold concepts framework presents a number of opportunities for research into student learning. At the heart of the notion of a threshold concept there is, in the process of associated learning, a transformation characterised (in varying degrees) by cognitive, ontological, discursive, and epistemic, shifts in the learner. There is a transformed view of subject landscape the world looks different, a repositioning of self in relation to the subject and its disciplinary discourse as in for example beginning to think like an historian, a new way of knowing accompanied by characteristic disciplinary forms of reasoning and explanation. This observation opens up new terrain for research on student learning and, in doing so, it presents a new set of research questions and methodological challenges; in particular how, and at what response level, and in what mode of liminality these shifts can be quantitatively or quantitatively modelled. The discourse of threshold concepts is often conducted at a metaphoric level; the visual-spatial-temporal metaphor of a transformative portal that leads from a liminal space (limen is Latin for threshold) to a new space, a new landscape, a repositioning or transfiguration of self. In the encounter of threshold concepts the liminal condition essentially captures the temporal dynamics of learning journeys that are enacted (towards and through) the portal, as well as the statics of stuck places. Thus provoked by, for example, the troublesome (counter-intuitive, alien) nature of many threshold concepts, the state of liminality invites research attention, and particularly so in terms of modelling that can inform pedagogic responses. The dynamics of the liminal space present conceptually fertile opportunities to re-address some of the classic student learning research questions of the past three or more decades. .
个人分类: 高等教育学|111 次阅读|0 个评论
MODERN is a European platform
geneculture 2010-4-26 23:50
MODERN is a European platform MODERN is a European platform which promotes the modernisation of higher education management. Under the leadership of ESMU, MODERN is a consortium of 10 core and 28 associate partners who have joined forces to provide a structured answer to the fragmentation in the supply of management support to HEIs, their leaders and managers. MODERN is a three-year EU-funded Structural Network (2009-2011) under the Lifelong Learning (ERASMUS) programme. MODERN responds to the Modernisation Agenda of the European Union and to the need to invest in people, to support future leaders and encourage the professionalisation of higher education management at all levels. The overall objective is to ensure HEIs' competitiveness to meet challenges in their external environment and respond to the needs of society. http://www.highereducationmanagement.eu/
个人分类: 高等教育学|264 次阅读|0 个评论
Abraham Flexner
geneculture 2010-4-26 19:50
Abraham Flexner Abraham Flexner (1866-1959) devoted his life to the improvement of teaching and research in America, initiating the modern American medical school and serving as first director of the Institute for Advanced Study at Princeton. Abraham Flexner was born on Nov. 13, 1866, in Louisville , Ky. He attended the Louisville High School and returned to it as a teacher after his graduation from Johns Hopkins University in 1886. Four years later he opened a college preparatory school in Louisville and put to a successful test his belief that inspired teaching plus the enthusiasm and competitive spirit of youth made the usual administrative rules, records, reports, and classroom examinations unnecessary. Flexner married in 1898. In 1905 he began graduate studies in education at Harvard University . His concern turned to the institutions and practices of graduate and professional training. He traveled in England , Germany , France , Canada , and the United States . In 1910 his report to the Rockefeller Foundation on medical education set into motion comprehensive reforms which led to the subsequent rise of American medical education to world leadership. Flexner followed this with an investigation of prostitution in Europe and with further research and writing on problems of teaching. As a consultant with the Carnegie Foundation for the Advancement of Teaching and, from 1913 to 1917, as assistant secretary of the General Education Board of the Rockefeller Foundation, Flexner prepared a statement published as A Modern School (1916). In these pages Flexner emerges as one of America's chief spokespersons for what became known as educational progressivism. He believed in universal education for literacy and a rigorous and demanding academic curriculum for the gifted and interested. During most of the 1920s Flexner continued working for the improvement of medical education as the director of studies and medical education of the General Education Board. Flexner next began examining higher education, visiting universities in England and Germany. In 1930 his Universities: American, English, German appeared. He saw universities not as popular institutions reflecting the desires and whims of society but as intellectual leaders. Universities must at times give society, not what society wants, but what it needs, he wrote. In 1930 he was asked to establish the Institute for Advanced Study in Princeton, N.J., and to serve as its first director; now he could put his ideas concerning the place of research in society and the world of learning into practice. His answer to a new fellow who asked what his duties were was typical: You have no duties, only opportunities. He served as the institute's director until 1939 and as director emeritus thereafter. He died on Sept. 21, 1959, in Falls Church, Va. Further Reading Flexner's views on universities are discussed in Alexander D. C. Peterson, A Hundred Years of Education (1952). Further background on education is in Stuart G. Noble, A History of American Education (1938; 2d ed. 1954). □
个人分类: 高等教育学|299 次阅读|3 个评论
Best Graduate Schools(英文原版)
geneculture 2010-4-24 21:42
Best Graduate Schools Home Education Best Graduate Schools U.S. News analyzed more than 12,000 graduate programs to bring you this year's rankings. Select a discipline for access to our top program rankings. America's Best Graduate Schools Business Best Business Schools A-Z Business School Listings America's Best Graduate Schools Education Best Education Schools A-Z Education School Listings America's Best Graduate Schools Engineering Best Engineering Schools A-Z Engineering School Listings America's Best Graduate Schools Law Best Law Schools A-Z Law School Listings America's Best Graduate Schools Medical Best Medical Schools A-Z Medical School Listings Grad Tools Paying for Grad School Video: New in 2011 More School Rankings The Sciences Library and Information Studies Social Sciences and Humanities Health Public Affairs Fine Arts Online Graduate Degrees Online Business Degrees Online Education Degrees Online Engineering Degrees Online Nursing Degrees http://www.usnews.com/sections/education/index.html http://www.usnews.com/articles/education/worlds-best-universities/2010/02/25/worlds-best-universities-top-400 http://www.usnews.com/articles/education/best-graduate-schools/2010/04/23/americas-best-graduate-schools-article-index.html
个人分类: 高等教育学|289 次阅读|1 个评论
Higher Order Elliptic Equations and Positivity
ChinaAbel 2010-1-13 20:31
Higher Order Elliptic Equations and Positivity
个人分类: Higher Order Partial Differential Equati|152 次阅读|0 个评论
英国大学最新排名2008
genius331 2008-12-24 07:16
The official RAE data are at: www.rae.ac.uk PDF附件: 英国大学最新排名2008
个人分类: 大学排名|4251 次阅读|0 个评论
“近亲繁殖”是中国高校进步的致命障碍
npan 2008-9-24 11:34
中国高校中的近亲繁殖,是指一直以来专业教师主要从本校培养学生中选留。此制不知何处学来(前苏联?)且弊端多多. 但几十年沿用至今,确令人诧异不解。此近亲繁殖有百害而无一利, 现择其要如下: 1. 近亲繁殖在其机理上自然尊崇本家。 从其本质上是反突破, 反创新的。其结果大致为全面退化。 2. 当学术水准与团体亲合度有矛盾时,是否合群 便成为最重要的留校考量。 结果大多是不具挑战性格之人留做人师。 3. 一旦留校, 论资排辈自成应遵之矩。 任何出格超越均不被鼓励。 待到棱角磨圆, 媳妇方能成婆。 4. 学校内山头林立是另一必然。 一切多以山头利益为优先考虑。 动辄相互制肘, 内耗频然。 零星外来人才要麽择山头为靠,要麽成边缘人物自生自灭。 ......。 此弊不除,则进步无望, 惶论世界一流?
个人分类: Higher education|2952 次阅读|3 个评论

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