text:
Kagan's Articles - FREE Kagan Articles
Dr. Spencer Kagan
Structures for Standards
To cite this article: Kagan, S. Structures for Standards. San Clemente, CA: Kagan Publishing. Kagan Online Magazine, Summer 2000. www.KaganOnline.com
Imagine this: After hearing a lecture and reading events leading up to the civil war, students pair up. In each pair, one is assigned the role of a southern plantation owner, the other is a northern abolitionist. They play Paraphrase Passport in role for about five minutes. In the process they become more engaged with and later will retain more of the content. Further, they have become better able to articulate oral arguments, and they have strengthened their listening and communication skills. All of this occurred with no special lesson planning on the part of the teacher because the teacher is versed in Kagan structures. Paraphrase Passport just seemed like the appropriate structure to use in that teachable moment.
Later in the lesson, the students create a Team Mind Map of the events of the war. They retain more content (many students are visual learners) and obtain valuable information processing skills, learning to organize and chunk information and distinguish core concepts, main ideas, and supporting elements. Through the Kagan structures students surpass the standards: They go beyond the content and skills of the discipline because embedded in each structure are additional learning opportunities — a hidden curriculum. As the students use Team Mind Mapping they learn skills of taking turns, reaching consensus, and respecting ideas different from their own — all of which will serve them well in the job world of the twenty-first century which places at a premium teamwork and communication skills. By using Kagan structures teachers enhance dramatically their students' learning of the discipline content, skills of the discipline, and life skills.
Structures are powerful tools enabling teachers to reach the standards and reach beyond the standards.
Structures provide a remarkable, unique approach to reaching high standards. Intelligently applied, they allow educators to deliver the content and skills called for in the various standards documents without rewriting the curriculum. Further, the structures provide an added benefit — they foster life skills which are at the heart of curriculum reform.
Road Map
II. Perplexing Problems: The Standards Movement
III. Simple Solutions: Structures for Standards
IV. Advantages of the Structural Approach
A Road Map
To fully understand the power of structures for the standards and beyond, it is helpful to understand the curriculum reform movement — the place from which the standards spring — and the problems associated with the standards movement. Thus this essay is divided into four parts: Visions of the Curriculum Reform Movement, Problems with the Standards Movement, the Solution Provided by the Structural Approach, and Advantages of the Structural Approach. We will see that the present curriculum reform movement has the potential to guide us toward the very best of curriculum and instruction, but that the standards movement is often implemented in ways which create the very worst of curriculum and instruction. Given the multiple abuses and problems associated with standardized testing and the standards movement, it is tempting to tar with the same mop everything associated with standards. This would be tragic because the curriculum reform movement springs from an inspired place and offers hope and direction for education. We must distinguish the visionary curriculum reform movement from the narrow minded and constricting use of standardized testing. With that background in place, we will examine how structures provide a unique solution to reaching standards — a solution which is easy to implement and which ensures the acquisition of discipline content, discipline skills, and life skills.
I. Powerful Visions: Curriculum Reform
The curriculum reform movement is nothing less than a foresighted response of educators in various disciplines to the need to align curriculum and instruction with the needs of students and society for the twenty-first century. The vision for education which is outlined by the curriculum reform movement is diametrically opposed to the abuses which standardized testing have wrought.
The curriculum reform movement has occurred because expert educators in all disciplines have for some time been reevaluating curriculum, asking how it must be restructured to meet the needs of students as they enter life in the twenty-first century. To prepare students for their work and lives in the twenty-first century, we must refocus our goals as educators, away from memorization and toward thinking; away from accumulating skills to be blindly applied to predetermined problems, toward the ability to re-conceptualize problems and create novel problem solving tactics.
There is a common understanding among forward-looking educators that in the face of the information and technology explosions and associated increases in complexity and interdependence in the workplace and in life, students must be prepared with thinking, teamwork and communication skills. Memorization of one more fact is of relatively little value when a host of new facts are being generated every moment. Ability to analyze, synthesize, and communicate information becomes increasingly important. We cannot predict what information our students will work with; but we can predict with confidence that they will need to have highly honed thinking and communication skills. The way students think, communicate, and work together becomes the primary curriculum. The content students think about becomes secondary. At the core of a curriculum for the twenty-first century are thinking skills and teamwork skills, including communication skills. These skills are at the heart of the curriculum reform movement.
Following this logic, eight major themes emerge from those attempting to align curriculum to twenty-first century life. Those themes are echoed in standards and curriculum guides published by National Council of Teachers of Mathematics (nctm.org), National Science Teachers Association (nsta.org), National Council for the Social Studies (ncss.org/home2.html) and the National Council of Teachers of English (ncte.org).
In Box 1 are the eight common themes of the curriculum reform movement, themes which cross-cut the disciplines, expressed in different ways within each discipline. They represent an inspired vision for twenty-first century education and the standards by which we should measure educational practice.
|Box 1: Eight Common Themes of the Standards Movement
|1. Teach for Understanding; Thinking, not Rote Memorization
|Movement is away from memorization of spelling words, toward the analysis of author's intent
|Away from rote algorithms, toward problem solving using multiple approaches; Exploring thinking
|Away from products of science, toward the process of science
|Away from isolated factlets, toward inquiry; Balance breadth with depth
2. Cultivate Positive Attitudes, Engagement, Joy with the Curriculum
|Positive language experiences
|Math explorations
|Positive attitudes; Cultivate wonder; Emphasize process over content
|Cultivate conditions for learning; Appropriate attitudes; Participatory classroom democracy
|3. Foster a Process Orientation through Ongoing Learning Cycles
|Eight stage writing process; Into, through, and beyond literature
|Teach algorithms as a three step process (concrete, connecting, symbolic); Open-ended explorations
|Process science; Inquiry; Emphasis on ability to make new discoveries rather than ability to memorize details of past discoveries
|Investigation of social phenomena using a range of inquiry methods
4. Develop Communication Skills
|Listening, speaking, reading, and writing as communicative competencies
|Write math; Talk through problems; Discuss thinking; Communicate problem-solving approaches and math understandings via teacher, whole-class, team, and pair discussions; Written communication should be nurtured
|Write Science; Emphasize alternative ways to display data
|Persuasive essays; Oral Reports; Debate
|5. Broaden the Curriculum through Multiple Sources and Multiple Approaches
|Communicate via electronic media; Understanding and communication via a wide range of genre
|Variety of ways to compute; Mental math; Computer Math; Books, newspapers, World Wide Web as sources of data
|Internet sources; Investigations beyond the class and lab
|Gather data from variety of sources; Oral histories; Historical documents; Multiple ways to demonstrate knowledge
|6. Integrate Instruction through Interdisciplinary Connections
|Reading and writing across the curriculum
|Math across the curriculum; Applied mathematics
|Scientific method applied within all disciplines
|Global connections; Integration from variety of fields within and across disciplines; Thematic connections across topics
|7. Emphasize Environmental/Social/Civic Issues and Responsibilities
|Critical analysis and evaluation; Debate, critiques, written arguments
|The mathematics of social issues (population explosion; pollution and extinction rates; Emphasis on change rates, projections and predictions
|Design to satisfy human and environmental needs; Social implications of discoveries and technologies (cloning, gene therapy, nuclear energy); Valuing as integral to science; Animal and human subject rights
|Preparation for the office
of citizen; Inclusion of valuing, decision making; Analysis of persistent issues
and current dilemmas; Balance rights and responsibilities of individuals and society
|8. Emphasize Technological Literacy
|Word processing; Computer Assisted Outline and Thought Organizers
|Data Base Manipulation; Spread Sheet Programing; Computer Assisted Graphing and Data Display
|Virtual Experiments; Virtual Labs; Web Explorations of space, earth, sea, plants, animals and the human body.
|Impact of technology on all aspects of society; Use of technology for gathering, analyzing, storing and reporting social science data
Eight Common Themes of the Standards Movement
1. Teach for Understanding; Thinking, not Rote Memorization
Knowing a fact is almost useless if we cannot understand, analyze, apply, evaluate, and synthesize it with other information. Thinking and imagining become more important than knowing. We cannot predict the types of problems our students will be called upon to solve in their lifetimes, but we can predict that problem-solving skills will serve them well.
2. Cultivate Positive Attitudes, Engagement, Joy with the Curriculum
Because the information and technology explosions are ongoing, we must prepare students to be life-long learners. If we cultivate joy in learning, today's students will become lifelong learners.
3. Foster a Process Orientation through Ongoing Learning Cycles
The process orientation reinforces thinking and positive attitudes, and better prepares students for dealing with new information, information we can today only very dimly imagine.
4. Develop Communication Skills
As we move into an increasingly high technology and interdependent workplace, teams become the norm. As such, communication skills become survival skills. There is a recognition that development of communication skills is preparation for the job world of the future, but also communication within content areas is one of the the most powerful tools we have to promote learning. Consider this quote from a standards document: "Students should become better at listening, paraphrasing, questioning, and interpreting other's ideas." It is found not in a language arts standards document; it is pulled from the latest standards document from the National Council of Teachers of Mathematics (NCTM, 2000, p. 61). It is recognized that advances in math and science will be made to the extent that today's youth acquire teamwork and communication skills.
5. Broaden the Curriculum through Multiple Sources and Multiple Approaches
The text as a source of knowledge will be replaced by multiple media sources. The internet is just a harbinger of the multiple ways in which information will be generated, stored, displayed and retrieved. Students who are taught to rely on single sources of information are not prepared for twenty-first century life.
6. Integrate Instruction through Interdisciplinary Connections
It is increasingly understood that instruction which is not interdisciplinary does not promote transferable skills. As stated by the National Council of Teachers of Mathematics, "Opportunities to use strategies must be embedded naturally in the curriculum across the content areas.' (NCTM, 2000, p. 54). Major advances in all fields will occur with increasing frequency at the interface of the disciplines. Students need integrated instruction if they are to be prepared to work productively in a world in which state-of-the-art medical practice demands an understanding of molecular electronics and international finance depends on the study of culture. As educators for the future we simply cannot afford to treat the disciplines as isolated.
7. Emphasize Environmental/Social/Civic Issues and Responsibilities
In an interdependent world a company's decision to use a new chemical reduction process may impact on the global water supply of future generations; the decision to clear land for homes may lead to extinction of valuable species as well as irreversible changes in the planets ecology and possibly even the future habitability of earth.
8. Emphasize Technological Literacy
The technology explosion is pervasive and accelerating. A few years ago at workshops when I would ask teachers how many were up on E-mail, only a few hands would go up. Today almost all hands go up. Daily communication with others around the globe is common. Only a few years ago no one questioned the idea of mail as a medium of communication. Today it becomes increasingly archaic to think about actually licking a stamp, placing it on an envelope, carrying the envelope to a mail box, and then waiting days for a response. In the face of the accelerating technological explosion which is transforming all areas of work, communicating, recreation, and travel, a primary mission of schooling for the twenty-first curriculum is technological literary.
The eight components of the curriculum reform movement are visionary. If implemented they will ensure survival and prosperity as we enter a far more complex and interdependent world. It is no wonder that springing from curriculum reform comes a movement to measure how well schools are doing in aligning their outcomes with the best of curriculum. The standards movement springs from the rich and fertile ground prepared by the curriculum reform movement. Unfortunately, the form the standards movement has taken has brought problems. Ironically, in an attempt to implement the visionary goals of the curriculum reform movement, the standards movement has pressed education in directions diametrically opposed to the visionary goals. Instead of creating a twenty-first century curriculum, the standards movement is pushing us backward toward curriculum and instruction which at best was suited for a nineteenth-century world.
II. Perplexing Problems: The Standards Movement
1. Standardized Tests
Most of the problems associated with the standards movement spring from standardized testing. Well intended as it is, the attempt to test how well schools are producing outcomes aligned with the best of curriculum has for the most part been self-defeating. Instead of encouraging schools and districts to deliver a better curriculum, standardized tests put pressure on teachers to dilute the curriculum and ignore the very best of teaching. To fully outline the problems with standardized tests is beyond the scope of this article, but several points should be recognized by every concerned educator, including the failure of the tests to measure high standards and the failure of the tests to measure progress toward standards.
Failure to Measure Standards. Norm-based standardized tests are designed to discriminate students, to rank them from high to low. They are not designed to measure high educational standards. Imagine for a moment you have the opportunity to observe test designers in action as they select items for a norm-based standardized test. There are two possible test items the test designers are considering. One test question is very important and is an excellent measure of the extent to which students are learning a core concept. Lets call this question The Core Question. The other question is a trivial, non-essential bit of information we will call the Trivial Question. Now imagine further than most students either know the core concept and get the Core Question right, or do not know the Core Question and get the Core Question wrong. During test construction the Core Question will be tossed out because it does not discriminate among students. Because most students scored the same on the question it does not discriminate among students. Imagine further that about half the students get the Trivial Question right and about half get it wrong. The Trivial Question will be retained and included in the final version of the standardized test because it discriminates. From the point of view of norm-based standardized test construction, the trivial question is a "good" question even though it tests relatively meaningless information. Norm based standardized tests are not designed to measure high standards, only to discriminate among students. The tragedy: The resulting standardized tests, admittedly not designed to measure the most important curriculum, determine to a large extent what curriculum is taught.
We can conclude that every norm-based standardized test should be packaged with a product warning: Because of the way standardized tests are constructed, obtaining high scores on standardized tests does not necessarily mean obtaining high standards.
Failure to Measure Annual Development. When standardized tests are not administered at the beginning and end of the school year in each grade they do not measure development. Imagine for a moment there are two schools, one in a poor area and one in a wealthy area. At the end of the school year a standardized test is administered and the students in the wealthy school score on an average 85% and the students in the poor school score an average of 55%. The wealthy school is lauded as an excellent school and the poor school is seen as a failure. Had developmental data been available, we would realize the poor school is actually the far better school. The poor began the school year at 15% for a gain of 40%; the wealthy school began the school year at 85% and the students did not gain at all!
Thus we can conclude that every standardized test should be packaged with a second warning: Because of the way standardized tests are administered, a school which scores higher than another school is not necessarily producing more learning.
Failure to Measure Long-Term Development. Cohort administered standardized tests lead to another set of false interpretations. Students in a district score 45% in science in fourth grade and 75% in eighth grade. The district is applauded for its excellence in science instruction because it is posting great gains. Had developmental data rather than cohort data been available though, we would discover that that the eight graders scored 75% when they were in fourth grade, and have made no gains! It is invalid to assume that the eighth graders of today scored like the fourth graders of today four years ago when they were in fourth grade. They may simply be a strong (or weak) cohort. To make these comparisons even less valid note that different tests are administered to fourth and eighth graders and tests are changed over time so differences between groups might be due not to excellence or weakness of curriculum or instruction, but rather to differences in test difficulty.
Thus we can conclude that every standardized test should be packaged with yet a third warning: Because of the way standardized tests are administered, differences among cohorts should not be interpreted as developmental progress or lack of developmental progress.
Standardized tests lead many to confuse high scores with high standards. In fact, a deeper examination of the standards reveals that standardized tests do not measure what the curriculum reform movement holds to be best in education. In many cases they actually measure the opposite, focusing on breadth rather than depth, memorization rather than thinking, content over skills, and a very limited notion of what is important for students to learn. Standardized tests are too often an exercise in trivial pursuit; the curriculum reform movement would have us instead focus on acquisition of deep understanding and meaning.
2. Pressure on Teachers and Administrators
In the last few months there has been considerable national press regarding the standards. The articles have centered on the disclosures of cheating on the tests — cheating by school administrators and teachers!
• Headline, editorial, USA Today, June 15, 2000: "Teachers fail ethical test"
• Cover, Newsweek, June 19, 2000: "Why Schools Cheat"
• Headline, lead article Newsweek, June 19, 2000: "When Teachers Are Cheaters"
Ironically, these headlines come at the very time when there is general support for character education in our public schools. An indispensable element in any approach to character development is the modeling of character virtues by adults in authority. How can we develop honesty among the youth of the nation if teachers and administrators are modeling and encouraging dishonesty? What possible meaning can "integrity" have when during the test the teacher posts the answer sheet above the pencil sharpener?
If the cheating on standardized tests by teachers and administrators was occurring in one or two isolated cases, it could be dismissed. But it is more widespread. See Box 2.
|Box 2: Teachers and Administrators Cheating
|Potomac, Maryland
|Teachers tap pencils on
the desks of students during the exam to point out errors. The principal displays
a map of the geographic area on which the students are being tested during a social
studies exam. A teacher calls students to the front of the room to, as one student
euphemistically put it, "fix or finish stuff." Students are given extra
time on exams. After the exam the principal calls students into her office after
exams to "review" items; she asks them to "look at this one again,"
to improve test scores.
|Columbus, Ohio
|Students at an elementary school claim adult tutors told them correct answers during the test. (This is the same school that received praise from President Clinton because of raised test scores).
|Austin, Texas
|The Austin Independent School District is indicted by the Texas grand jury on charges of criminal tampering. The charge: to raise scores, low scoring students were excluded from the test.
|Fairfax County, Virginia
|A teacher is placed on leave while being investigated for giving students exam answers.
|New York, New York
|About 50 teachers and administrators from 30 different schools are accused of urging their students to cheat on standardized tests. One teacher left the math exam answers posted by the pencil sharpener. A second teacher changed her tone of voice while reading a test passage to focus students on the critical parts. A third teacher, after discovering the test essay topic, gave students a "special lecture" on the topic.
1. Abuses Predictable. Stories about teachers cheating on tests grab attention — they produce "Man Bites Dog" type headlines. Upon reflection, however, we should not be too surprised by revelations of teachers and administrators fudging on tests. The teachers and administrators have been placed in a classic conflict of interest situation: They are asked to administer and proctor exams the outcomes of which will determine financial rewards and recognition for their schools, real estate values for their neighborhoods, and, for themselves: personal status, wages, and, in the case of principals, future employability. Would we feel comfortable having a judge sit judgement on a case involving a family member? Would we allow a mother to score the driver licensing exam of her child? Why then do we place teachers and administrators in the position of administering and proctoring standardized tests the outcomes of which will be interpreted as a measure of their own competency?
2. Cheating Not the Problem. Contrary to the impressions conveyed by the headlines, almost all teachers and administrators are honest and would not dream of fudging on the tests. But the pressure on them to have their students score well creates subtle abuses, often undermining good instruction. There is pressure on teachers to teach to the standardized test, even if the test does not cover the most important information. This can trivialize the curriculum. How many teachers are willing to say, "I know this information will not be on the test, but it is very important, so I will spend a great deal of class time on it to make sure my students understand this core concept?" How many are willing to say, "I know this information will be on the test, but it is trivial. I will cover instead core concepts not on the test, but more important for my students to learn?"
3. View and Treatment of Students
If the measure of success in an educational system is how many correct answers a student can produce on a standardized test, then there is pressure to view schooling as a long-term assembly line, with the students passing along the line each year, receiving information and skills. The student is viewed as an empty vessel to be filled. What we know, however, is that to the extent we treat students as clever, intelligent problem solvers, they become clever, intelligent problem solvers. The view of students we adopt influences the curriculum and instruction we adopt and becomes a meta-communication to students which impacts profoundly on their self-concept, self-esteem, and willingness to fully engage in the learning process. Do we want to communicate to students that their worth is measured by the sometimes trivial items on a standardized test, rather than by their learning, improvement, and engagement with the curriculum?
4. Ignoring Individual Differences
Because standardized tests view all skills through the filter of the verbal-linguistic and mathematical intelligences, if every student is to be assessed on the same content in the same way, we create a strong bias in favor of students strong in the academic intelligences and against students strong in other intelligences. But not all students learn or express themselves in the same way; they have different patterns of intelligences (Kagan & Kagan, 1999). Students who are weak in the verbal-linguistic and/or mathematical intelligences blossom when given alternative ways to acquire and demonstrate their knowledge and skills.
Bruce Campbell tells the case study of a student who was not mastering her multiplication facts. She had practiced extensively, but the facts eluded her. The student was very strong in artistic talents. Bruce asked her to simply draw pictures on flash cards which had on them her most often missed multiplication facts. After drawing the pictures the girl simply knew the facts, and retained them years later.
Unfortunately, when teachers are under pressure to cover the curriculum likely to be on a standardized test, they feel less freedom to take the time to respond to individual differences in learning styles or intelligences.
5. Pressure on Students
Students are anxious before the standardized exams. They internalize the notion that the exam score is a measure of their worth as a student and, in some sub-cultures, even their worth as a person. The anxiety and pressure on students is transferred to the learning situation, constricting learning and the desire to continue education.
6. Trivialization of Curriculum
Because tests, by virtue of their construction, usually weigh assessment of knowledge more heavily than thinking skills, there is pressure on teachers to "cover the curriculum." Knowing that test scores will reflect knowledge of facts, information, and rote skills more than depth of understanding, teachers feel pressure to sacrifice depth in favor of breadth. The result: a curriculum which is, as often lamented, an inch deep and a mile wide.
The pressure to cover the curriculum narrows the vision and creativity of teachers; they do not feel free to respond to the unique needs of their class or of individual students — they have the curriculum to cover. Teachers do not feel the luxury to go in depth in areas of their own personal interest, the very stuff of which good teaching is made. With teachers feeling less free to follow their own passions, they lose the ability to become inspired role models for students. Rather than creators of dynamic learning experiences, teachers are increasingly relegated to feeling like (and becoming) one more station in a continuous predetermined assembly line.
In the press to make sure they cover the curriculum teachers lose the ability to respond creatively to the teachable moment. They are pressured away from allowing students to discover and construct meaning. They are pressured toward becoming a dispenser of facts and information. Understanding an algorithm becomes secondary to being able to carry out its steps. But a skill without understanding is a dead end. Students can not advance in math, or any other subject, without understanding.
Even more frightening is the extent to which the standardized tests are driving classroom practices. In many Texas high schools, course work is put on hold for the whole month of January. January is devoted to test preparation. Group projects are cut in favor of more direct instruction. Art and music classes are cut in favor of "academic rigor." (Scherer, 2000). In preparation for a test which will contain the question "Circle 1/3 of three umbrellas," teachers have students practice circling 1/3 of three ice cream cones. Precious class time which could help students understand the concept of fractions and the meaning of 1/3 is instead spent in rote practice of responses — responses not understood, and, following the test, soon to be forgotten. In the words of a student commenting on the impact of standardized tests, "ÉI worry that teachers are being less creative because of the SOL tests and that their teaching has become less exciting... I wish they would be concerned about students understanding — not just memorizing — facts." (Ernst, 2000, p. 77)
III. Simple Solutions: Structures for Standards
We have on the one hand powerful visions for curriculum reform springing from the curriculum reform movement. We have on the other hand perplexing problems springing from the standards movement. Can we realize the visions while side-stepping the problems? Structures provide a simple solution.
Structures are uniquely suited to realize the foresighted visions of the curriculum reform movement without falling into the traps associated with the standards movement. To fully understand the power of structures for standards we need to first do a component analysis of the standards and to distinguish curricular and instructional approaches to the standards.
A. Component Analysis of the Standards
To foster the highest aspirations of the standards movement we need to be analytic. That is, we need to analyze the standards. It turns out that standards call for students to learn the content of the discipline and the skills of the discipline. Often one standard calls for both. For example, a mathematics standard calls for students to use numbers in a variety of equivalent forms. The content component of the standard includes knowing the parts of a fraction and what they signify (declarative knowledge). The skill component of the standard includes knowing how to manipulate fractions and convert them to decimal form (procedural knowledge).
Whether we focus on the content or the skill component of the standard determines to an important extent our approach to curriculum, instruction, and assessment. It also determines the extent to which we will realize our mission as educators for the twenty-first century. If we focus relatively exclusively on teaching and testing the content component to the detriment of the skills component, we will fail to deliver a curriculum which will best prepare our students for the twenty-first century.
|Box 3: Content and Skill Components of Sample Standards
|Discipline Content
|Discipline and Life Skills
|Compare and synthesize information about an author from two sources.
|Author's Background
|Compare/Contrast; Synthesis; Weighing Information Depending on the Source
|Use numbers in a variety of equivalent forms including fraction, decimal, and percent.
|Equivalent numerical expressions
Compare/Contrast; Analysis; Evaluation
|Explain daily, monthly, and seasonal weather changes on earth.
|Weather patterns
|Gathering data; Recognizing patterns; Applying prior knowledge; Positing explanations; Testing alternative hypotheses; Evaluating alternative explanations; Presenting data and conclusions
|Explore the meaning of American culture by identifying the key ideas, beliefs, patterns of behavior, and traditions that help define it.
|American Culture
|Identify key ideas; Find Patterns; Relate items to a central concept
Examine sample standards broken into their content and skill components (Box 3). In each case the content component may or may not be of use to a student in their twenty-first century jobs, but in every case the skill components will be. As we teach a history lesson, what is more important, that the students memorize the dates and locations of the battles of the war, or that they acquire skills in analyzing, comparing and contrasting, synthesizing, and communicating information? If we see our primary goal in the history lesson as to have students master facts and information, to better master the declarative content, we are teaching with an outdated approach. What is more likely to serve our students over the course of their lifetime — the facts of history or the skills and procedural knowledge (including information processing skills) which are obtained in the context of a good history lesson? The skills of reasoning, understanding points of view different from one's own, processing and communicating information in many ways are certain to serve our students well throughout their lives. Thus if we are teaching for the twenty-first century we see the history content as an opportunity for students to acquire essential skills. In this view the study of history is to a great extent the means, the end of education is a more thoughtful, intelligent citizen.
The same argument holds in every discipline. If we see our job as getting students to master types and patterns of weather, we will have them memorize facts — facts which are of relatively little present interest and questionable future utility. If we see our job as fostering ability to approach data in a scientific way, we are providing our students skills for a lifetime. Clearly both the content and the skills are important, but content without skill is an empty curriculum.
Analyzing the standards into their content and skill components casts the problems of standardized tests into clearer perspective. The tests emphasize the content, driving teachers to "cover the curriculum." We cannot neglect the content, but we must emphasize the skills — they are the heart of the curriculum for the future. The content should be acquired in the context of engagement, in the context of skill acquisition. If we realign teaching to emphasize the skills component of the standards we provide students tools for a lifetime. If we realign our testing programs tests to emphasize skills over facts, we will accomplish three things: we create a meaningful context in which content can be learned and retained, we drive curriculum in an intelligent direction, and we end much of the testing abuse because teachers will orient toward teaching for understanding and teaching for essential skills, not memorization of information, information to be memorized for a test and soon forgotten.
B. Curricular vs. Instructional Approaches to the Standards
In preparing to reach any standard an educator must answer questions regarding curriculum, instruction, and assessment. For example, in preparing to teach the unit on explaining daily, monthly, and seasonal weather changes, the teacher must ask what is essential for students to know, how that content is best taught, and how learning will be assessed.
Curriculum Questions: Is it essential for students to know types of clouds, water cycle, impact of melting of polar ice caps, states of water, weather patterns over centuries, El Nino, difference and lack of difference between hurricanes, cyclones, and tornadoes; fog and clouds, etc? Is it more important for students to be acquainted with many facts or some basic principles in depth?
Instruction Questions: What percent of time should be spent on lecture, reading, individual worksheets, group projects, individual projects, cooperative structures? Should students report to, teach, and tutor each other? What sources of information should students have inside and outside of class? How much should there be student choice vs. teacher determination of topics for study, sources of information?
Assessment Questions: Should students be allowed to choose a mode of demonstrating knowledge? Should we design tests to measure what percent of predetermined information is acquired, or provide opportunities for each student to demonstrate his/her unique acquired understanding?
Content vs. Skills — Our Focus Drives Curriculum, Instruction and Assessment. Focusing on the content aspects of the standard drives educators toward very different answers to these three sets of questions than does focus on the skill components. If as a teacher I am primarily concerned with content, I might be more likely to choose breadth over depth in curriculum, direct instruction over team projects, and standardized tests. If on the other hand I am more concerned with skills, I might conclude that quantity of coverage is not as important as developing inquiry skills; that instruction which allows hands-on investigation might better lead me to my goals than would lecture, readings and worksheets. Also I might lean toward performance evaluation and/or portfolios rather than standardized tests to allow each student to demonstrate in a unique way his/her own skill acquisition.
To the extent we are aligned with the best of the curriculum reform movement, we move away from an exclusive or even primary focus on content and instead emphasize skill acquisition. We move away from broad coverage of curriculum with little depth, exclusive use of teacher selected and disseminated information, and exclusive use of uniform assessment techniques which assume all students can best express their learnings in the same way. The curriculum reform movement encourages us to move toward depth of understanding, accommodation of individual differences in learning preferences and styles, and a range of instructional strategies and assessment approaches.
C. The Structural Approach to Standards
The structures are a unique approach to realizing the best of the curriculum reform movement: They empower us to align learning with the goals of curricular reform without falling into the traps associated with the standards movement. Structures emphasize the skills of the discipline while delivering the content of the discipline.
As students do a Team Statement on the meaning of democracy, they are reviewing the content of the discipline in a meaningful context, but they are doing so much more. Because of the curriculum embedded in the Team Statement structure the students are practicing democratic decision making and developing teamwork skills. As students do a Pairs Compare on the advantages and disadvantages of two ways of structuring a paragraph, they are learning about the importance of topic sentences, supporting details, and concluding sentences. But at the same time they are developing their communication skills, evaluative skills, and skill at compare/contrast thinking. As students do a Same-Different comparing a frog and a toad they are acquiring discipline content but at the same time acquiring analytic thinking, one of the core skills of science. They are obtaining life skills as well, including understanding points of view different from their own, communication skills, and developing the visual/spatial intelligence.
While delivering both the content and skills of the discipline, the structures provide an added bonus — they develop a range of life skills. For example, as we have students work on equivalent fractions in the structural approach we often have them working in cooperative teams. In the process they learn to communicate their thinking, understand points of view different from their own, praise one another, and develop teamwork skills, communication skills, and relationship skills.
The structural approach recognizes skills are best acquired not as a separate, add-on curriculum, but rather via the instructional strategies used daily in the classroom — it takes an instructional rather than curricular approach to the standards which allows acquisition of curricular skills and life skills without creating separate lessons on those skills. By intelligent choice of structures the teacher delivers all three components of the standards without creating separate lessons for each.
Once a teacher knows a range of structures and their domain of usefulness, the teacher can easily include structures so that students obtain the skills of each standard without treating those skills as separate content or curriculum. The skills are a hidden curriculum, embedded in the structures. For example, when students do a Pairs Compare on any content, they acquire compare/contrast skills. When they do Paraphrase Passport, regardless of the content, they acquire core communicative competencies. When they do a Team Statement they acquire diversity skills and synthesis skills. When they do Team Mind Mapping or Categorizing they acquire information processing skills, including ability to chunk and categorize information in a variety of ways.
In the structural approach reaching the skills component of the standards becomes easy. All a teacher needs to do is deliver the content with an appropriate range of structures, structures selected to foster the desired skills.
Let's re-examine the standards using the structural approach.
Language Arts
• Standard: Compare and synthesize information about an author from two sources.
• Content: Author's Background
• Skills: Compare/Contrast; Synthesis; Evaluate Sources
The teacher knows that Pairs Compare is an excellent structure to foster compare/contrast skills and Team Statements foster synthesis. So in structuring for the skills of this standard the teacher includes Pairs Compare and Team Statements, first having the students do a Pairs Compare on two sources, and later do a Team Statement to synthesize their knowledge. In the process students weigh information according to its source, a life skill.
• Standard: Use numbers in a variety of equivalent forms including fraction, decimal, and percent.
• Content: Equivalent numerical expressions.
• Skills: Compare/Contrast; Analysis; Evaluation
The teacher knows that Mix-N-Match is designed to help students find things which match, so might use a three-way Mix-N-Match activity in which students find fraction, decimal and percent equivalents. To cement learnings about equivalency, the teacher might have students work on converting fractions to decimals and percents using RallyCoach or Pairs Check. To foster compare/contrast, analysis, and evaluation the teacher might use RoundTable with each student in turn making entries to a three-way Venn Diagram to compare/contrast, analyze, and evaluate the three forms of expressing ratios. Life skills are obtained as well because embedded in the Pairs Check structure is an opportunity to learn to praise, tutor, and receive help. Embedded in the RoundTable structure are opportunities for students to learn to take turns and respect the contributions of others. RallyCoaching reinforces turn taking but also fosters listening, helping, and praising skills.
• Standard: Explain daily, monthly, and seasonal changes on earth.
• Content: Weather patterns
• Skills: Gathering data, Recognizing patterns, Applying prior knowledge, Posting explanations, Testing alternative hypotheses, Evaluating alternative explanations.
This standard lends itself to a cooperative project in which students gather data, plot it, analyze it, interpret it, and test alternative hypotheses. Co-op Co-op weather projects would allow acquisition of all of these skills. Students learn the facts about weather in a meaningful context. In the process of the lesson the teacher might use Find My Rule to hone inductive reasoning and Find the Fiction to foster evaluative thinking. Co-op Co-op has a powerful embedded curriculum: Students learn the power of interdependence, and synergy — that the whole is much more than the sum of its parts.
Social Studies
• Standard: Explore the meaning of American culture by identifying the key ideas, beliefs, patterns of behavior, and traditions that help define it.
• Content: American Culture
• Skills: Identify key ideas; Find patterns; Relate items to a central concept
As part of this lesson the teacher might first use 4S Brainstorming to have students generate beliefs, behaviors, and traditions. Once the items had been generated, the teacher might have the student use Categorizing to group them. Team Mind Mapping would be a natural follow-up because it is excellent to foster the skills of identifying key ideas and grasping how ideas relate to a central concept. In the process of using these structures students learn information generation and processing skills — essential skills for a future marked by an information explosion.
Notice, by teaching with a range of structures the teacher fosters both the content and the skill components of each standard: The skills are acquired as a function of the instructional strategies selected and the content is acquired within a meaningful context. In addition, there is a powerful embedded curriculum associated with the structures — a life skills curriculum.
The structural approach breaks the traditional distinction between curriculum and instruction. It recognizes there is a curriculum embedded in instruction. How we teach determines to a tremendous extent what is learned. As the students do Categorizing and Team Mind Maps they learn cognitive skills for a lifetime, skills which will serve them well in the information age. Over the course of their lives, the skills students have learned as a function of the structures will serve them more than the content they acquire. Their content will shift many times; the skills they bring to that content is the new constant.
IV. Advantages of the Structural Approach
The structural approach is but one approach to realizing the visions which emanate from the curriculum reform movement. But it represents a powerful alternative to exclusive focus on content on one hand, or inspired but impractical skills programs on the other. Teachers who would ignore skills and try to "cover the curriculum," leave their students ill prepared for the world they will encounter. Teachers who develop or use complex skills programs find themselves without enough time to implement those programs while dealing with the demanding scope and sequence of curriculum. Further, special skills programs have a half-life. Almost all teachers and administrators can resonate to the following scenario: "Last year we worked on conflict resolution, the year before that it was higher-level thinking skills — one complex program replacing another."
Because the structural approach delivers the skills as part of the instructional system rather than as a separate curriculum, it does not run the risk of being replaced by next year's new curriculum — it is embedded in the structure of daily life in a classroom.
There is much which can be said in favor of the structural approach to standards. Among the most important points are the following:
|10 Advantages of the Structural Approach
|1. Proven Achievement
2. Skills Aligned with Standards
3. Resolving the Learning Paradox
4. Side-Stepping the Transference Gap
5. Redundancy
6. Preparation Time
7. Teacher Reactions
8. Student Reactions
9. Not Test Driven
10. Breaking the Replacement Cycle
1. Proven Achievement
The Kagan structures are designed to embody the very most demanding of the principles of cooperative learning and so produce the gains of cooperative learning. Cooperative learning has been extensively researched and found to produce academic achievement gains across the range of subject matter, grades, and student populations (Johnson, 1981 Sharan, 1994; Sharan,1984; Slavin, 1983a; Slavin, 1983b; Slavin, 1985).
2. Skills Aligned with Standards
As students engage in the structures, they acquire a range of skills: thinking skills, communication skills, teamwork skills, and diversity skills. The structures broaden the curriculum making group process and peer input sources of thought and information. Further, the structures foster engagement and a positive attitude toward learning and the curriculum. Thus the structures directly address most of the eight common themes of the curriculum movement.
3. Resolving the Learning Paradox
There is a paradox I call the learning paradox: Attempting to memorize information usually leads to less memory than involvement with the content with no attempt to memorize. When we ask students to memorize the dates and events of an historical period, they retain that information, at best, for the test, but soon forget it. If, instead, they spend time doing a project on that time period, without special effort they retain a great deal of information, including dates and events. The learning paradox: Trying to commit something directly to memory leads to less memory than producing engagement with the content. The paradox is easy to resolve. When we produce engagement, we generate multiple connections to the content making storage and retrieval more likely. When we work directly on memory, the facts remain isolated, decreasing the probability of long-term memory and retrieval. When interactive structures are used, the brain is far more engaged in far more ways, dramatically increasing memory compared to methods directly attempting to increase memory.
4. Side-Stepping the Transference Gap
When we teach thinking skills as a separate program, students may learn the skills but fail to apply them in new contexts because they were acquired only within the context of the thinking skills program. Lawyers all take a course in ethics, but it is a separate course, not integrated with the other courses. The meta-communication: Ethics is interesting but not really part of what we need to think about on a daily basis as a lawyer. Separate curricula lead to encapsulated thinking which fails to be applied in new contexts. When we teach conflict resolution skills as separate content, students pass the test on the topic, but fail to apply the conflict resolution methods to resolve conflicts when they leave the classroom and encounter a conflict on the playground. Whenever the situation of acquisition is too discrepant from the situation of performance, a transference gap is created. The students learn about the skill, but they do not acquire the skill. It does not become part of them. They do not transfer it to new contexts. The structures represent an opportunity to acquire the skills called for in the standards and to practice them in a broad range of content areas and contexts, so the transference gap is reduced greatly.
5. Redundancy
The structures represent an embedded curriculum — a curriculum embedded in instruction. Because of this there is a great deal of redundancy and practice which ensures acquisition of skills. Students, for example, might do Mind Mapping in Language Arts, Social Studies, and Science. Through Mind Mapping important thinking skills are acquired, but they are practiced on a daily basis. Because those skills are not taught just one time in just one content area, they are not memorized for a test, soon to be forgotten. The skills acquired through repeated use of the structures become part of the student, skills for a lifetime.
6. Preparation Time
Because the structures do not involve special materials or even special lesson planning, they dramatically cut down preparation time. A teacher experienced with the structural approach uses the structures as part of any lesson — the structures become part of what it is to be a teacher. This means the structures are implemented on a regular basis, not just when the teacher has time to prepare a special lesson.
7. Teacher Reactions
Teachers do not resist the structural approach to standards. Rather than one more program to be layered on, the structures are viewed as tools which make the teacher's job easier. Because the structures are simple and presented in a step-by-step format, they are easy to learn and easy to use, so the typical teacher resistance to new and complex programs is strikingly absent in the structural approach.
8. Student Reactions
Students love the structures. They enjoy the interaction, movement, and variety. Most observers looking for the first time at a classroom in which a range of structures are used are struck by the intense level of engagement among all students. The structures are designed to hold every student accountable, accounting for engagement and learning for all.
9. Not Test Driven
To a large extent, what is tested is what is taught. Imagine for a moment a teacher who knows a relatively unimportant fact will be on a standardized test but an important concept will not. What will be emphasized in class? The wonderful thing about structures is that they deliver the skills component of the standards no matter what content is taught. Structures insure that important skills will not be dropped, even if not tested.
10. Breaking the Replacement Cycle
The structures are an integrated approach to instruction. That is, they are used as part of any lesson. In the structural approach, we tell teachers, "Don't teach a cooperative learning lesson. Make cooperative learning part of every lesson by using cooperative learning structures." "Don't teach a multiple intelligence lesson. Make multiple intelligences part of every lesson through structures." "Don't teach separate lessons on character development and thinking skills. Make character development and thinking skills part of every lesson by choice of structures." Through this integrated approach, we break the education replacement cycle. When complex special programs are designed to implement new approaches to education, we devote two years on a new thinking skills program and then replace that program with two years on character development, only to in turn replace the character development program with the next year's new thing. Because the structures are used to deliver the thinking skills program, the character development program, and any new program which comes down the education pike, they break the replacement cycle, ensuring that students will acquire a twenty-first century curriculum regardless of the present program thrust of a school or district.
In Sum
Education suffers when we engage in either-or thinking. The question should not be content vs. skills, curriculum approaches vs. instructional approaches, or standards vs. no standards. The structural approach provides a way to break the either-or thinking that leads to destructive pendulum swings. The structural approach focuses on content and skills, delivering a curriculum via instruction. The structural approach offers one way to reach the highest visions of the curriculum reform movement without falling into the traps of the standards movement. Most importantly, students and teachers find the structural approach easy to implement because it is based on simple structures which are easy to learn, fun to use, and powerful in their ability to reach, nay, surpass the standards.
Ernst, K. SOL Tests Create Unfair Pressure. Educational Leadership, 2000, 57 (5), 77.
Johnson, D.W., Maruyama, G., Johnson, R., Nelson, D. & Skon, L. Effects of cooperative, competitive and individualist goal structures on achievement: A meta-analysis. Psychological Bulletin, 1981, 89, 47-62.
Kagan, S. & Kagan, M. Multiple Intelligences. San Clemente, CA: Kagan Publishing, 1999.
National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2000.
Scherer, M. Not by tests alone. Educational Leadership, 2000, 57 (5), 5.
Sharan, S. (Ed.) Handbook of cooperative learning methods. Westport, CT: Greenwood Press, 1994.
Sharan, S., Kussell, P., Hertz-Lazarowitz, R., Bejarano, Y., Raviv, S., Sharan, Y. Cooperative learning in the classroom: Research in desegregated schools. Hillsdale, NJ: Lawrence Erlbaum Associates, 1984.
Slavin, R. E. Cooperative Learning. New York: Longman, 1983a.
Slavin, R.E. When does cooperative learning increase student achievement? Psychological Bulletin, 1983b, 94, 429-445.
R. Slavin, S. Sharan, S. Kagan, R., Hertz-Lazarowitz, C. Webb, & R. Schmuck (Eds.) Learning to cooperate, cooperating to learn. New York: Plenum, 1985.
Web Links
National Council of Teachers of Mathematics (http://www.nctm.org)
National Science Teachers Association (http://www.nsta.org)
National Council for the Social Studies (http://www.ncss.org/)
National Council of Teachers of English (http://www.ncte.org)


text:
Limavady Grammar School Year 9 pupil, Caitlin McMahon, has enjoyed a successful spell recently in her favourite sport of Judo.
Last Saturday, Caitlin participated in the All-Ireland Judo Championships, picking up a bronze medal in the under 40 kgs. section.
The week previously Caitlin participated in the North West Open Judo Championship in Derry, and was delighted when she placed 1st in the same category. The school congratulates Caitlin.

subset: commoncrawl


text:
Full Moon in Pisces ~ Embrace Your Magic!
Just past midnight, September 6th, a magical, spellbinding Full Moon in Pisces (at 14 degrees) illuminates our world. Luna joins dream-weaver Neptune, bringing a most romantic and enchanting vibe. This Full Moon reminds me of Cinderella (surely a Pisces!), and the moment she meets her Fairy Godmother, and Bippity Boppity Boo, her cinder rags fall away, transforming into a shimmering gown, and she is ready for the ball.
Like silver moonlight reflected on water, this Full Moon can hypnotize you, and put you in her thrall, or even throw you off course with her magical tricks. Is it true or illusion? Only time will tell. For now, give yourself permission to daydream. To play in the fields of your imagination—the place where all dreams are possible. Become your own Cinderella at the ball!
Draw of the energy of the Sun in opposite sign Virgo to ground you and keep it real. Alas, all magical coaches turn back into pumpkins, but you may find that the magic of this Full Moon, lives full and alive in your psyche for some time to come.
My natal moon is in Pisces, 14 degrees, and I have transiting Neptune there as well. So, I'm really feeling this Full Moon! On one hand, it's deeply expansive and creative…on the other, it is like diving into a watery emotional world. So, for now, I'm embracing being both a mermaid and Cinderella, and planning my amazing, shimmering ball gown!!
Happy Illuminations!


text: Please ensure that thread titles are concise and accurate to the topic of your discussion. There are now also thread prefixes, please use those as applicable. Intended uses are below. Bug - Issues with the site or chapters Suggestion - Recommendations to the site or forums Novel Suggestion - Recommendations of new novels you would like GT to look into. Question - Questions on certain features/novels/etc General - General topics that don't belong to one of the above.


text:
Kean Stage Presents Royal Drummers and Dancers of Burundi at Wilkins Theatre, 10/20
Kean Stage presents the Royal Drummers and Dancers of Burundi at Wilkins Theatre on Saturday, October 20, 2012 at 7:30 p.m.
The ultimate African drum experience! One of the greatest percussion ensembles in the world, the Royal Drummers and Dancers of Burundi have passed down their traditions and techniques to each generation for centuries. The thunderous sound of the drums combines with breathtakingly graceful athletic dances as the Drummers channel the pulsating rhythmic energy and creative spirit of a nation. Their "Burundi beat" has influenced musicians from Joni Mitchell in the 70s to Adam Ant in the 80s.
Tickets are $30 for the general public; $20 for seniors and children.
Kean University is located at 1000 Morris Avenue in Union, N.J. Tickets are available at the Wilkins Theatre Box Office, 1000 Morris Avenue, Union, N.J., 908-737-SHOW (7469), and online at www.keanstage.com.


text:
Previous PageAssign : verb :(a) to give legally
• To assign a right to someone• To assign shares to someone
• He was assigned the job of checking the sales figures.
• Assignation of shares to someone• Assignation of a patent
• Assignment of a patent or of a copyright• To sign a deed of assignment
• He was appointed managing director with the assignment to improve the company's profits.• The oil team is on an assignment in the North Sea.
©2019 english-for-students.com


text:
One Screen Sunscreen roller blinds
Our One Screen Sunscreen blinds are made from a specially designed fabric which lets in plenty of light, while protecting your home from the sun's harmful uv's.
Our One Screen Sunscreen blinds block out up to 95% of the sun's harmful rays, which is a great for energy efficiency.
One Screen is mould and mildew resistant, of high quality strength and durability.
Fully fade resistant, perfect for our harsh Australian conditions.
Easy to clean with a damp cloth and soapy water.
Our One Screen Sunscreen blinds provide a great level of day time privacy and protection, whilst still mainting your outside view, but beware, you have no night time privacy with any Sunscreen blinds when the inside is lighter than the outside, so you may need to look at a complimenting blockout blind creating the ever popular day/night blind or you may like to add a blockout curtain.
This range of Sunscreen blind fabric is 30% polyester with 70% pvc coating. It is compliant with the building code of Australia's requirements for class 2 to 9 and is Eco friendly, fire retardant and comes with a 5 year fabric warranty.
Comes in 8 fantastic colours - white, wallaby, sand, ice, grey, dune, charcoal and black. 4 more to come soon.
You may purchase directly online but we do recommend requesting a fabric swatch first as the colours will differ from the computer screen to the real thing and please be aware that dye lots will also differ.
The sizes here are a standard guide only and you are welcome to order direct, but we do prefer, to please email a request for an order form, as all our blinds are custom made to your requirements.
All our blinds are standard as over roll, meaning you see the fabric, not the roll. Our blinds also come standard with oval anodised bottom rail and white heavy duty pvc chain with a stainless steel chain joiner. Your package will also include installation instructions and of course child safety chain lock down.
Should you require a different bottom rail or different coloured chain, please email your request or request a custom made roller blind order form after you place your order, alternatively you may order direct by email or call our office number between weekdays of 7am till 3 pm.
View the specs of our One Screen Sunscreen blind fabric here and look for the One Screen logo.
|Shipping Weight
|Unit Of Measure
Be The First To Review This Product!
Help other Curtain Trend Pty Ltd users shop smarter by writing reviews for products you have purchased.


text:
In the words of Don Bosco, "Only God knows the good that can come about by reading a good Catholic book."
The Australian Province has recently opened an on-line Book Shop as a way of getting more Salesian books into the hands of readers. We have many wonderful authors in the Salesian family who have published numerous books. This new online shop with give Australians a one stop shop to find them all in the one place. The new Book Shop on the Province website sells a wide range of Salesian and Catholic book, and more are being added every week.
Coinciding with the launch of the Book Shop is the launch of a new Salesian prayer book. Salesian Youth at Prayer has been compiled by Br Tristan O'Brien and published by the Salesians of Don Bosco Australia-Pacific. The book is a collection of prayers and reflections for designed for young people. This is first of many such publications that will be written, published and marketed by the Social Media team.
The Salesian Book Shop has also been given the rights to sell the YOUCAT series of publications. YOUCAT, short for Youth Catechism of the Catholic Church, aims to be an aid for youth to better understand the Catechism of the Catholic Church. The book, drafted in the form of a conversation, is intended for use by young Catholic around the world and is available in 25 languages, including Arabic and Chinese. The catechism has 304 pages and consists of four chapters with 527 questions and answers.
The DOCAT focuses on the social teaching of the Catholic Church, and shows young people how to work towards building a "civilisation of love". Written in the popular style associated with the series, DOCAT tackles tough questions on issues like politics and economics, human rights, the family and the environment. This book comes with its own phone App.
Books can be purchased at: www.salesians.org.au/bookshop
Ashley Trethowan


text:
Drain Repairs & Drain Renewal
Drain repair and drain renovation can now be done with the minimum of cost and disruption.
Drains and sewers may crack due to ground movement, subsidence, corrosion or tree root ingress. This can lead to blockages and leaks. Whatever the problem, we guarantee we can solve it and return it to full function as soon as possible.
Drain Repairs & Excavations
If you suspect a problem with your drainage system but can't quite locate a specific area of concern, then we have the specialist drain investigation equipment to find out the cause of any problems. A CCTV drain survey will uncover any issue, particularly if drain access is difficult, and help us come to an expert drain repairs solution.
When drain repairs aren't possible, then a drain excavation may be necessary to rectify any broken drain pipes. We have the specialist equipment to carry out extensive drain excavations by digging up the system and replacing the broken drain pipes with quality piping. As we've had over 40 years of industry experience, you can be certain that the results our Drainage engineers achieve will be precise and guaranteed to last.
From a simple gully replacement to a complete drain excavation, here at Drainscan Ltd we know how to get your drainage system working to its full potential again.


text:
Day after day they just keep on happening. Yet another random attack on a lone female. This time in Reading during the evening rush hour, the female victim simply sat in a bus shelter waiting for a bus to come. No where is safe!!!
Woman assaulted in Reading town centre
Oct 30, 2014 16:28 By Natasha Adkins Get Reading
At around 5.10pm yesterday a woman was waiting at a bus stop in Cheapside when a man assaulted her
A woman in her 20s was assaulted while waiting for a bus in the town centre.
At around 5.10pm yesterday the woman was standing at a bus stop in Cheapside when a car stopped nearby.
A man got out of the car, spoke with the woman, then grabbed her wrist.
The woman managed to get away and was not hurt in the incident.
The man was described as Asian, in his 20s or early 30s, around 5ft 7in, of slim build with dark wavy hair and a thin beard around his jaw line. He was wearing dark jeans, a dark grey top and trainers.
He was driving a small dark blue four-door hatchback.
Anyone who witnessed the incident or with information that may assist the investigation, should contact police on 101 quoting reference number 43140229516.
- Teen Girl Sexually Assaulted On Bus In Salford By 'Asian' With Warts On His Face
- E-fit Of 'Asian' Wanted For Sexual Assault On Bus In Gravesend
- Video: Muslim Thugs Firebomb Paris Bus Shouting Allah Akbar
- Muslim Pervert Who Performed Sex Act On Bus Fails To Show Up At Court
- Police Appeal After Schoolgirl Sexually Assaulted On Bus By 'Asian' Pervert
- Heres Another Bus Sex Attack Commited By A Brazen Muslim Pervert
- Convicted Sex Offender Javed Montakhab Denies Sex Attack On North East Bus
- Police Appeal For Pervert Who Sexually Assaulted Girl, 13, On Bromley Bus


text: Description Features Recommended Accessories Have you ever been to an insanely fancy restaurant which has a beautiful outdoor patio that somehow stays warm even in the fall? That's because they've probably invested in a couple of patio heaters. They do this so you can be nice and toasty while you eat mysteriously small portions of food at exceedingly high prices. You can save money and do this in your very own backyard with a Brander Patio Heater! This heater is outfitted with a 45,000 BTUs stainless steel burner which can keep you and your guests warm from up to 8 feet away. Additionally, any standard 20lb propane tank can be stored in the stainless steel tank shroud so that it is hidden and out of sight while using the heater. Believe us when we say that it is the best and most cost efficient way of extending your backyard season. Keep your backyard guests warm with 45,000 BTUs from a stainless steel burner Capable of heating up a radius of up to 8 feet 32" diameter reflector which measures up to 7' high (so unless you are taller than that, you won't be bonking your head on this sucker) Can store a standard 20lb propane tank right in the tank shroud – hidden and out of sight! Brander believes in safety first as it will automatically shut off if tipped over Reliable battery ignition system gets it started quick and easy Patio heater clearances to combustibles: 18" from top and 24" from side or reflector. Propane hose and regulator is included Buy BRANDER PATIO HEATER COVERS


text:
FAC Gift Shop & Holiday Gift Gallery Artist Application
Artists who have not exhibited with the FAC before must fill out the following form to be considered for addition to the Firehouse's Gift Shop artist roster. Artwork submitted must demonstrate the quality and skill of the intended medium and must be original, handmade, and created by the artist in the last 3 years.
Mediums accepted include ceramics, photography, paintings, original prints, drawings, wood, metal, jewelry, blown glass, slumped glass, stained glass, mixed media and some accessories. The following items will not be accepted: clothing (except for hand-woven pieces and accessories), university themed items, food, and toiletry items.
Applications are reviewed on a revolving basis. Accepted artists will be contacted by FAC staff to arrange drop-off of their work.
The Firehouse's annual holiday boutique, Holiday Gift Gallery, highlights regional artists by showcasing their work for sale to the public in a festive extension of the year-round gift shop. Over one thousand Norman shoppers visited the FAC during last year's Holiday Gift Gallery, browsing the selection of original and unique artwork in a variety of mediums and learning more about the community of artists represented at the FAC.
The FAC is seeking seasonal items of varying price points to captivate customers who are looking for both gifts and décor. Especially popular are affordable, holiday-themed ornaments. Artwork submitted must be original, handmade, and created by the artist in the last 3 years. The 2018 Holiday Gift Gallery is open to regional artists working in a wide range of mediums; work accepted includes ceramics, photography, paintings, original prints, drawings, wood, metal, jewelry, blown glass, slumped glassed, stained glass, mixed media pieces, seasonal décor, and some accessories. Items not accepted include clothing (except for hand-woven items), university themed items, food, and toiletry items.
New artists must submit this completed digital application by Monday, October 15 at midnight. This short application requires the inclusion of sample images of artwork. The FAC Gallery Committee will review all applications and sample images submitted to determine the acceptance of the artist to Holiday Gift Gallery. Artists will be informed of their acceptance status before drop-off begins on October 22. Incomplete applications or applications submitted without images will not be considered. No new artists will be considered without a completed digital application. Accepted artists will be assigned an artist number and then may proceed through the following artwork drop-off process.
Only artists accepted to the FAC's Gift Shop roster are invited to submit their works in person during the Holiday Gift Gallery artwork drop off (October 22 - 26, 2018). For more information, please email email@example.com.
FOR FULL INFORMATION INCLUDING COMMISSIONS, DATES, AND PUBLICITY, VISIT http://normanfirehouse.com/events/index.cfm?page=holidaygiftgallery.


text: We are making a few changes to the forums including a new technical section. There is a lot of work to do still as we have thousands of posts to go through with useful information but it is making navigation and finding information for members a lot easier. If you go to the forums, we have a new section called GTiR Wiki In the GTiR technical section part of the wiki, we have broken down into sub categories so members can easily find the information they require. We currently have the following - Buyers Guide / Part No's / Specifications Brakes ECU / Boost Controllers / Mapping Engine Exterior / Bodywork Gearbox / Clutch / Transmission / LSD Ignition Interior Servicing / General Items Track Day Preparation Wheels and Tyres Air Filter Dump Valve Electrical / Lighting / Gauges Exhaust Fuelling / Ignition ICE and Security Intercooler / Radiator Oils Suspension / Handling / Steering Tubro / Manifold Aero to come. We will also be dedicating a special section to the technical side of things with new ideas and products that have been developed. If you notice anything or would like to make some suggesions then please do.


text:
⚡ In Opeyemi Agenda Africa: the Akinyemi Green Security Energy and Growth
Sociology Paper: Race and Ethnicity Essay Sample Best Essay Writing Service https://essaypro.com?tap_s=5051-a24331 Get access to this section to get all help you need with your essay and educational issues. One problem that seems to be increasing over time is the unmarried birth rates in America. Increasing from 18.4% of all births in 1980 to over 40% in 2010(FP-12-06), the current rate is showing that over the last 3 decades teens are becoming more apt to engage in pre-marital sex. The changing in norms and values over the past three decades has lead to a huge increase in unmarried birth rates increasing. It's not really against cultural norms to engage in the hook-up or have sex with more than one partner in your life like it Series Ceiling Sensors DT-300 Dual Technology to be. Over half of all minority births were to unmarried women, with an alarming 74% of births among black women, 54% to Hispanics(FP-12-06). 74% of blacks while nearly 50% of them were single, also common amongst Hispanics almost 20%(FP-12-06). On Vanillin Substitution Electrophilic Aromatic of other hand Whites are at a low 30% total of all births being premarital (FP-12-06). Among teens experiencing a nonmarital birth, 45% of the babies were born to single mothers versus 44% to cohabiting mothers(FP-12-06). According to statistics, the increase of age is related to increased rate of cohabiting unmarried births, with a decrease in single mothers. Based on statistics mothers who are less educated are more likely to have premarital birth than those who are highly manifolds. Minorities leading the way with the most premarital babies, over half being single mothers, this plays a big role in a majority being drop and having to work to support the baby. Causing a developing an endless cycle amongst blacks and other minorities. With the mother having little education, education thus becomes second to the child, and only having one parent present can develop some withdrawal from love. Thus at a young age the child then goes searching for this love and can come at the cost of a premarital baby. One out of every five children was born into poverty in 2010(FP-12-17), with higher levels amongst minorities. Amongst the minorities, blacks have the highest numbers with 38% native born and 34% foreign-born children born into poverty(FP-12-17). Hispanics are a very close second with 31% native born and 40% foreign-born children being born into poverty(FP-12-17). Whites and Asians are amongst the bottom with Geometry Problem Set 2 of lowest rates of child poverty birth rates(FP-12-17). A child being born into poverty can be due Prateeksha Curriculum Gehlot Vitae a number of causes such as education level of the parents, age, or family trend. A child born into poverty is more likely to keep the endless cycle going and stay in poverty and have children at a young age thus bringing another child into poverty thus creating an endless cycle that's very hard to break. Thus being the reason being that Blacks and Hispanics, they tend to have children at a younger age and with no set partner makes education come second to supporting the child. With little education, finding a good job is very hard with the economic struggles multiple jobs are needed to stay a float for some. Of these single parent households 48% are mother only and 22% being father only, a minimal 11% of children born into poverty are from married couples(FP-12-17). Almost 50% of all children • Address Adding type the bar My Computer a In • Open printer into poverty the educational attainment of the parent are less than high school diploma(FP-12-17). The pattern seems inevitable, with Blacks and Hispanics starting younger than any other race and achieving lower levels of education leads to a higher percentage of birth rates into poverty. Waiting for marriage before engaging in sexual reproduction seems to be a decreasing norm or value amongst our culture but for those who do wait the rewards are astounding hose who do wait to have a kid the average married couple waits 3 years before having in Opeyemi Agenda Africa: the Akinyemi Green Security Energy and Growth first-born child(FP-12-11). This can lead to both parents obtaining the desired level of education, and gives both parents time to land a steady job to support the family. Which SCDE here - poverty level chances for the child and proves that the longer one waits the higher ones chances of education attainment may be which also lowers the poverty levels. Hispanic women come in with the least amount of waiting time with only 2.5 years to have their first born child, while blacks waiting 10-11 months longer than Hispanics, while whites wait on average 3.3 years(FP-12-11). The time between wedding day and the first-born child is a positive correlation with educational attainment. - Obesity century Australian in the 21st within File children median time for first birth of those III II-Unit less than high school diploma is less than 22 months after marriage versus those with college education is almost twice as long with 44 months(FP-12-11). Conflict perspective is based off of class struggle that focuses on the negative conflicts within ones society. Blacks and Hispanics first came to our society as slaves, factory workers, and had to earn citizenship, forced towards the bottom of the class hierarchy. Being in the bottom of the class can mean numerous things, having to works as Instructions for Model and Isolated Execution Innovative Software and indentured servants educational attainment was never Geometry Problem Set 2 of option, so therefore it was not a moral instilled into minority races. They than began having children born into this vicious cycle and they too had to follow in their parents footsteps, thus providing class struggle amongst these races which with class struggle amongst them must meant some other race being the whites 071-CompInvestI Europeans are benefiting from their struggles. To this day minorities are fighting for many of the rights and equal attainment, being brought here in the bottom and working their way to the top has been a struggle. With the bottom of the social class and lower levels of education, lower income, jobs Registrations Now for 2016 Accepting more physical and demanding, those 8 UNFCCC CDM Members Executive Martin-Luther-King-Strasse and the Head Board of lower levels are more like to marry in same class level. Thus being the main reason Hispanics and blacks are so likely to have children at younger age and obtain lower education levels and be stuck in poverty. Knowing only one way to live as children its been an instilled value from day one that has been hard to break from many minorities thus they started with their backs against the walls. Best Custom Essay Writing Service https://essayservice.com?tap_s=5051-a24331


text:
Donny and Denese moved to Summerland in 2009 from Edmonton, Alberta. Both were born and raised in Manitoba. They purchased the orchard in 2009 and began their new life in Summerland. When the orchards was purchased, it was primarily an apple orchard with only 68 peach trees. Due to the poor condition of the apple trees, the over 300 trees were removed and mulched. As of 2014, Donny and Denese have grown their orchard to about 140 peach trees, 295 nectarine trees, 160 apricot trees and 120 plum trees. The plantings are not yet complete and the farm will continue to grow.
We offer U-Pick so everyone can better experience the orchard, and the feel and smell of fresh fruit hanging on the tree. If you don't want to pick, we are happy to pick for you. We also have a selection of frozen and canned fruit and jams made from our fruit available year round. During our harvest, we also have amazingly tasty homemade fruit pies.
We strongly believe in organic farming practices and value the high quality of our fruit and the eco-harmony of our orchard. We want our children to experience the pleasure of eating a fresh peach directly from the tree without fear of harm from pesticides or other chemicals. We are certain you will appreciate and enjoy this experience as well. See you soon.


text:
Delete Duplicate Files from Your Mac with Easy Duplicate Finder
Everybody has duplicate files, but most people prefer to pretend they don't exist. Why? Because it takes hours to go through your stuff and find duplicates. Luckily, there are lots of apps that will help you find, delete and manage duplicate files on your Mac. Let's have a look at an app that makes deleting duplicates a breeze, Easy Duplicate Finder.
1. Add folders you want to scan (simply drag and drop them into the "Include to scan" area)
2. Start the scan and watch its progress
- Include and exclude certain file types
- Compare files by content (byte-by-byte comparison)
- Scan your iTunes and iPhoto media libraries for duplicates
- Scan your Mac Mail for duplicate emails and contacts
Like most Mac apps, Easy Duplicate Finder is not free. There is a free trial version that let you manage up to 10 duplicates. When you reach the limit, you can still scan for duplicate files as much as you want, but you won't be able to delete them through the program. The full version costs $39.95.Posted by Liz D. from ReviewHarbor.net


text:
Blue Microphones Bottle
- Remove this product from my favorite's list.
- Add this product to my list of favorites.
Blue Microphones Bottle
The Bottle is Blue's flagship recording tool and its highest achievement in quality and innovation. It combines low noise and superb transient response integrated with the Bottle Caps interchangeable capsules.


text:
- Home
- WASPA top clubs
- WASPA in the world
- Philosophy and tournaments
- WASPA tournaments winners
- Euro 2016 project
- The best pictures of the WASPA blog
- Frequently Asked Questions (FAQ)
- Project "Brazil 2014"
- The popular tournament systems
- Interviews
- Wofür steht die WASPA?
- Ce qu'il faut savoir sur la WASPA
- "Tutto su WASPA" in Italiano
- WASPA Test Matches
- Youth in action project
- Russia 2018 project
- Best WASPA club jerseys
- Season 2015-2016
- Forthcoming events
Wednesday, 16 November 2016
Subbuteo gathering in Jakarta
Steve won his two games while Arudyo defeated Aldo. Local players explained the FISTF official it's hard to develop the game in Indonesia as there are no Subbuteo sets on sale.
It was great to see action again in Indonesia and there will hopefully be some bigger tournaments in the near future.
Publié par Vincentcop à l'adresse 21:17
|Leave a reaction!
Subscribe to: Post Comments (Atom)


text:
Chair, Department of Chemistry and Biochemistry
- Employer
- University of Texas at El Paso (UTEP)
- Location
- El Paso, Texas
- Salary
- Salary and benefits
- Posted
- Oct 12, 2018
- Closes
- Nov 11, 2018
- Field of specialization
- Analytical, Biochemical, Catalysts, Computers / Computational / Informatics, Education, Energy, Energy / Fuels, Environmental, Food, Forensic, General / Technical, Green Chemistry, Inorganic, Materials, Medicinal / Clinical, Microbiological, Nuclear / Radiochemical, Organic, Organometallic, Petrochemicals, Physical, Polymers, Theoretical
- Work Function
- Administration, Management-General, Research-Basic, Teaching-Graduate, Teaching-Undergraduate
- Job Type
- Full time
Position Description
The University of Texas at El Paso (UTEP) is seeking an innovative leader to serve as Chair in the Department of Chemistry and Biochemistry. Research activities in the Department reflect all major areas of chemistry, and faculty receive extramural funding from federal and state programs, private foundations and industry. The successful candidate is expected to be an active leader and researcher who has a strong vision for developing and strengthening educational and research initiatives. Applicants must have a distinguished record of scientific achievement, demonstrated leadership skills, and a commitment to the education and mentorship of both students and faculty. Candidates should have relevant administrative experience and an understanding of key issues affecting faculty recruitment, promotion and retention. The Department is especially interested in candidates who will contribute to the diversity and excellence of the academic community.
Required Qualifications
- PhD in Chemistry (or Biochemistry with Chemistry emphasis)
- Demonstrated leadership skills
- Excellent management skills
- Distinguished record of research and teaching
- Current academic rank of tenured associate or full professor (or equivalent non-US rank)
Application Instructions and Contact Information
Applicants should submit a curriculum vitae, contact information for 5 references, and a letter of interest addressing research, educational, administrative and leadership goals.
Review of applications will begin November 1, 2018 and will continue until the position is filled.
Questions about this position should be directed to Search Committee Chair, Dr. Michael Kenney at firstname.lastname@example.com.
To apply, please go to: https://utep.interviewexchange.com
More searches like this
- Analytical Teaching-Undergraduate Full time jobs in El Paso
- Biochemical Teaching-Undergraduate Full time jobs in El Paso
- Catalysts Teaching-Undergraduate Full time jobs in El Paso
- Computers / Computational / Informatics Teaching-Undergraduate Full time jobs in El Paso
- Education Teaching-Undergraduate Full time jobs in El Paso


text:
Get professional homework help from # - they can do any assignment online.
Get professional homework help online with expert assignment solvers from Assignment Geek - 24/7 online support.
Looking for paper writing services? Ewritingservice.com is your best choice.
Writemypaper123.com provides excellent help writing paper.
There comes a time when, with all the best will in the world you may need some professional help with your school homework. This does not mean that you are taking the easy option or that you are failing, it means that you have identified that you need some additional support.
You have probably already explored some of your other options such as getting help from a friend or relative; looked at the possibility of an after school homework support group; checked out some of the options available.
Ideally you need to be looking for professional support that is readily available; is qualified in the subject area that you are studying; is a trained teacher; has a good track record for enabling students and their help is realistically priced.
Start by making a list of what you need support with. Be specific. If you write done the difficulties that you have now, it will be easier to relay that information to the tutor that you may choose to support you.advice-on-getting-qualified-school-assignment-assistance
There is a lot to consider, but there are some really good support services out there that are sure to meet your requirements.


text:
Learn about this topic in these articles:
Green Bay Packers
- In Green Bay Packers
…Taylor, halfback Paul Hornung, tackle Forrest Gregg, linebacker Ray Nitschke, end Willie Davis, tackle Henry Jordan, cornerback Herb Adderley, and safety Willie Wood. They won championships in 1961 and 1962 and followed with three straight championships starting in the 1965–66 season. On January 15, 1967, in the inaugural Super BowlRead More


text:
Employee Volunteering Program
Awarded to an Employee Volunteering Program that delivers a significant, sustained and successful benefit to beneficiaries.
The contribution may include general or skilled volunteering. Any organisation, corporate, government or other not for profit that provides employee volunteering programs is eligible.
Organisational size and resources will be considered to ensure small organisations have equal opportunities to achieve this award.
Excellence Volunteering Award
Awarded to a Volunteer Involving Organisation for demonstrating a commitment to going beyond best practice volunteer management.
This should include reference to the application of the eight standards in the National Standards for Volunteer Involvement: Leadership and Management, Commitment to Volunteer Involvement, Volunteer Roles, Recruitment and Selection, Support and Development, Workplace Safety and Wellbeing, Volunteer Recognition, Quality Management and Continuous Improvement.
This judging will take into consideration that national standards can be adapted for different size organisations.
Please use at least one example of a program which fulfils this criteria and how it does so.
Inclusion Award
Awarded to a Volunteering Involving Organisation that achieves the inclusion of individuals or groups who are often excluded from mainstream or traditional volunteering. Inclusion can be with respect to any groups within society that experience disadvantage, isolation or discrimination, including but not restricted to CALD communities, Aboriginal and Torres Strait Islanders, people with disability, the aged, gender or sexual identity groups, recent migrants and refugees.
Innovation Award
Awarded to a Volunteer Involving Organisation for an innovative, unique volunteering program or model that engages volunteers, and makes a significant contribution to the work of the volunteer involving organisation, improving its ability to achieve its purpose and objectives, and to deliver positive outcomes.
Research Collaboration
Awarded to a partnership/collaboration between a researcher and an organisation which makes a significant contribution to the advancement of an evidence base in the volunteering sector regarding one or more of the following or an alternative subject related to volunteering:
- Benefits of volunteering;
- Impact on programs by volunteers;
- Volunteer management processes, leadership or delivery;
- Volunteer retention and development;
Organisational size and resources will be considered to ensure small organisations have equal opportunities to achieve this award.


text:
:: Morning Moment
Today we had a proper sunrise - you know, one of those sunrises where the sun actually appears over the horizon. There was a little bit of cloud down low but it was close enough to count I reckon. It's been a while too; heaps of mornings lately where we've had clouds making for dark dawns however this morning was a bright one. Great to get some morning light back into the lens! There's not much relief for the surfers though - it's small and weak once again and the early high tide isn't helping. If you want waves you'll need to head to the airport - fly to Victoria, Southern WA or maybe somewhere in the Northern Hemisphere. Yesterday they ran the Mavericks Invitational Big Wave competition at Half Moon Bay just South of San Francisco - sounds like it wasn't as big as they'd hoped but in the end Santa Cruz charger Peter Mel put himself in the most critical waves taking out the event. Check out the review at Surfer Mag
Got yourself a 2013 Sprout Daily Calendar yet? Be quick - they're almost gone! Order Online - Pick Up locally or we can mail it out to you. Even send it to you overseas if you want!


text:
The Brokerage division is capable of handling your needs for real estate transacations at all levels. Contact us directly to discuss your needs.
Anjos Realty Services (ARS) is a multi-facet company that also provide Real Estate Brokerage Services. John Anjos, the president of the company has had extensive real estate experience as a broker for over 30 years.
ARS also is involved in Florida and can assist you in locating property in that state.
Additionally, one-on-one counseling is available to assist you in your investment interests in Real Estate.


text:
By Pannenberg M.
Read Online or Download A characterization of a class of locally compact Abelian groups via Korovkin theory PDF
Best symmetry and group books
The 20 th Fighter staff joined the eighth Air strength Command in Dec of '43, flying the P-38 in lengthy diversity bomber escort function. the gang later switched over to the P-51 in July of '44. the gang destroyed a complete of 449 enemy plane in the course of its wrestle travel. Over one hundred fifty photographs, eight pages of colour, eighty pages.
Multiplizieren von Quantengruppen
Inhaltsangabe:Einleitung: Quantengruppen als quantisierte Universelle Einhüllende von Lie-Algebren sind Gegenstand der vorliegenden Arbeit. Sie bietet eine Einführung in die Thematik, setzt lediglich Grundkenntnisse der Darstellungstheorie Halbeinfacher Lie-Algebren voraus, wie sie etwa bei Humpfreys, Jacobsen, Serre oder Bourbaki vermittelt werden, und ordnet die Darstellungstheorie der Quantengruppen in die Physik konformer Feldtheorien ein.
- The subgroup structure of the finite classical groups
- Abstract Harmonic Analysis: Structure and Analysis, Vol.2
- Introduction to the renormalisation group and to critical phenomena
- Einstein Static Fields Admitting a Group G2 of Continuous Transformations into Themselves
- Representation of Lie groups and special functions. Recent advances
Additional info for A characterization of a class of locally compact Abelian groups via Korovkin theory
Example text
It follows easily from this lemma that that n is at least spanned by all x w, ∈ n+ w ∈ Sn . 2 The x w ∈ n + w ∈ Sn form a basis for n. Proof We give two proofs of this important result. First proof. 7). 3). 2] we see that ˜ n has a basis given by all x˜ w words w ˜ in the s˜j which do not involve subword of the form s˜j2 . Hence, the subalgebra ˜ n of ˜ n generated by the x˜ i is isomorphic to n . Also let ˜n denote the subalgebra of ˜ n generated by the s˜j , so that ˜n is isomorphic to the algebra on generators s˜1 s˜n−1 subject to relations s˜j2 = 1 for each j.
Next, forget about A, and take care of n − 1 . Continuing this way we will get a chain of admissible transpositions which transform T to T . Finally, note that this chain yields a reduced word. 9 If and ≈ . ∈ W n and ∼ for some ∈ W n , then ∈W n Proof Let = T . 7, = S . As ∼ , the tableaux S and T have the same shape. 3(iii), it suffices to show that we can go from S to T by a chain of admissible transpositions. 8. The following is the main result of this chapter. 10 We have W n = W n Moreover, T ≈ S ⇔ the tableaux T and S have the same shape ⇔ T ∼ S .
1 Define a linear map w = n →d by d−1 w if w ∈ dS , 0 otherwise, Degenerate affine Hecke algebra 32 for each w ∈ Sn . Then: (i) is a homomorphism of -bimodules; (ii) ker contains no non-zero left ideals of n ; (iii) the map f n → Hom is an isomorphism of h→h d n -bimodules. n Proof (i) Follows easily using S d = dS . (ii) It is enough to show that n t = 0 for any t ∈ n . By multiplying t with an appropriate group element on the left, we may assume that t = y∈D yhy with each hy ∈ and hd = 0. Now t = hd = 0, as required.