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Social and Cultural Foundations of American Education/Choice/Against Vouchers

Vouchers are defined as “an entitlement extended to an individual by government permitting that individual to receive educational services up to the maximum dollar amount specified. The holder can normally redeem the voucher according to the preference at any institution or enterprise approved by the granting agency.”(Swanson and King, Good) School vouchers, also known as scholarships, redirect the flow of education funding, channeling it directly to individual families rather than to school districts. This allows families to select the public or private schools of their choice and have all or part of the tuition paid (Coulson).

Vouchers have been seen throughout history in various forms like the GI Bill, food stamps, and programs like Medicare and Medicaid.(Good) Milton Friedman is considered the “grandfather” of vouchers. He first proposed vouchers but was met with political opposition. At the time public views were pro government and over time that began to change as people became suspicious of government and the role of vouchers got backing by people. “Voucher plans were frequently discussed in the 1960’s, 1970’s, and 1980’s but they never became an actual point of policy.”(Good) In the 1980s consideration for school choice became policy when Ronald Reagan became President. Attempts failed, however, with a lack of congressional support, but because of the public attention, “it had become acceptable to talk about vouchers as public policy”(Good) and in some places became actual policy. Indeed the case of vouchers is a hot topic as some of the arguments against vouchers will be brought out.

Constitutionality
The legal heart of the matter is whether the program violates the U.S. Constitution's "Establishment Clause" which mandates the separation of church and state and prohibits government endorsement of religion.(Miner) “Historically, public funds have not been allowed to support the cost of private education. Recent legislation and landmark court decisions have started to erode this historic barrier.”(Good) The Wisconsin Supreme Court case in June 1998 in Wisconsin ruled that the use of public funds to support private parochial schools was not unconstitutional because the court took the position that “the voucher money went to parents, not schools and thus its purpose with regard to religion, was neutral.”(Good) The United States Supreme Court refused to hear the case, letting the ruling stand. Similar cases happened in Cleveland. Opponents of Vouchers argue that Government run voucher programs that give these funds to private schools that teach religion is a violation of the separation of church and state. “Americans must ask themselves if they feel it is right for citizens to be forced to subsidize religious education which may conflict with their beliefs” (Coulman).

Privatization
Vouchers are a way to provide opportunity for low-income students, in particular students of color. At the heart of the voucher movement, however, is a conservative agenda that seeks to privatize public education and funnel tax money into private schools, including religious schools. (Charney) The idea of privatization is to make schools part of the private sector and no longer government run. This was a part of Friedman’s plan. The argument is that government controlled schools are a monopoly and that if schools were to run themselves as consumer based, they would compete with each other for higher achievement. “It is argued that because schools are legislated as a basic monopoly, they have no external incentives to be competitive. Hence, choice advocates suggest that schools will improve only if market forces are applied.”(Good) However, Henry Levin notes that competition can result in what he calls “cream skimming, or the tendency of schools to choose students from more desirable backgrounds (less poor, higher prior achievement, etc.)” He goes on to say that there is concern that “they will fail to respond to the greater needs of disadvantaged and disabled students, and that they will lead to less expensive but not more effective education for poor children.”(Levin) Also most advocates of privatization, and competition in education “are not interested in public education per se, but are simply advocates of the private sector (i.e., they want to reduce the role of government in all aspects of society).”(Good) As Levin brings out, “it is not clear how much of this interest in finding answers to difficult questions and how much is simply directed at sustaining the debate.”(Levin) Milton Friedman himself, “dismissed the notion that vouchers could help low-income families, saying "it is essential that no conditions be attached to the acceptance of vouchers that interfere with the freedom of private enterprises to experiment." Vouchers were not designed to help low-income children.”(NEA) “Despite desperate efforts to make the voucher debate about "school choice" and improving opportunities for low-income students, vouchers remain an elitist strategy. From Milton Friedman's first proposals, through the tuition tax credit proposals of Ronald Reagan, through the voucher proposals on ballots in California, Colorado, and elsewhere, privatization strategies are about subsidizing tuition for students in private schools, not expanding opportunities for low-income children.”(NEA)

Results
Continuous research shows that studies fail to draw a comparison on the improvement in achievement when comparing voucher schools to public schools. “At present there is limited research evidence in America to support the value of vouchers improving students’ academic success in school.”(Good) The research that is there shows varied results. “those studies that showed a positive relationship between student achievement and school choice, the impact of school choice was minor, and other variables appeared to be more strongly associated with student achievement” (Good). Even in Milwaukee, “these advocates of choice indicated that there were sufficient numbers of missing cases that one cannot craw conclusions with complete certainty. There is no dependable research evidence available in the Milwaukee data to conclude that choice has had favorable impact on student achievement.”(Good) Current programs suggest that only a very small portion of eligible families apply for available tuition vouchers. Voucher opponents cite this as evidence that dissatisfaction with public schools is not widespread, and they are probably at least partially correct. In Milwaukee, fewer than 7% of eligible families apply for the voucher program, and in Cleveland the percentage is slightly smaller and has decreased in the three years of the program. Neither voucher program has produced the mass exodus from public schools that was forecast.(Metcalf and Tait)

Costs
"Vouchers would further limit already tight financing that causes districts to use outdated textbooks, computers and other equipment, to increase class sizes and to scrimp on teachers." Minnesota Education Association (An NEA affiliate). Andrew Coulson believes otherwise saying “the overwhelming majority of public schools are not underfunded, including those in depressed, inner-city areas. While there are some poorly funded districts scattered around the country, low funding is not the chief cause of decaying facilities and moribund materials.”(Coulson) He does not acknowledge that part of the money that is directed towards public school is set aside for vouchers, thereby limiting the financing for school districts. Mary Zapala, a principal from Milwaukee “claimed that the public schools in Milwaukee lost millions of dollars for students who were already in parochial schools.”(Good) She goes on to say “I like competition if it is fair. What seems to be wrong with this is that the playing field is not level. We have unionized teachers, licensing rules, required assessments they don’t. We have to take everyone. They can take a kid, get the money, and if there is any misbehavior, they can send him back to us mid-year.” The 'choice' remains with the private schools that will continue to pick and choose the students they wish to accept and reject. (Coulman) In Milwaukee, “special education spending accounted for 38 percent of net new K-12 spending from 1967 to 1991. The ability of voucher schools in Milwaukee to reject students with exceptional educational needs not only enables the private schools to focus on regular education; it also requires the Milwaukee Public Schools to spend a higher share of funds on special education.”(Molnar)

Conclusion
The focus of Vouchers is to sidestep the real issue of making public schools better for children. Given the research, Vouchers can have its benefits and detriments. The detriments outweigh the benefits and there are no current studies to show that vouchers are working. The methods for vouchers like lottery based vouchers, laissez-faire or first come – first admitted voucher plans are a ridiculous way of administering them. They are not evenhanded because they are not given to the most deserving student. A 1992 Carnegie Foundation report evaluated choice programs around the country and reached the following conclusions: (1) To the extent that choice programs benefit children at all, they benefit the children of better educated parents. (2) Choice programs require additional money to operate. (3) Choice programs have the potential to widen the gap between rich and poor school districts. (4) School choice does not necessarily improve student achievement.(Molnar) Voucher programs are intended to help the poor. However, they are being misused to further a debate about “school choice” and the underlying agenda of privatizing education.

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Social and Cultural Foundations of American Education/Choice/Charter Schools

As future teachers, we must be prepared for all of the changes that are constantly occurring in our schools. One major change over the last two decades is the introduction of Charter Schools. These schools of choice are becoming more common all over the United States and many teachers are needed to fill positions in them. But what are charter schools? Do they work? Will they change the face of the American school system?

Definition
Charter Schools are defined by the National Education Association as “publicly funded elementary or secondary schools that have been freed from some of the rules, regulations, and statutes that apply to other public schools, in exchange for some type of accountability for producing certain results, which are set forth in each charter school’s charter” (NEA.org). This charter is a contract which outlines the school’s overall mission, including everything from the goals of their programs to the way they will assess success. Charter schools allow students more flexibility and options than traditional public schools, a benefit that appeals to both parents and community leaders. According to the National Study of Charter Schools, the three most common reasons for establishing a charter school are to “realize an educational vision, gain autonomy, [and] serve a special population” (uscharterschools.org). These schools operate like traditional public schools in many ways, especially in that they cannot charge a tuition fee or levy taxes. Their funding primarily comes from the school district and state or federal grants, although they also receive money from private sectors, such as nonprofit organizations or philanthropists. They are also required to meet the accountability requirements of the federal Elementary and Secondary Education Act of 1965 (ESEA), as amended by the No Child Left Behind Act of 2001 (NCLB). If schools do not meet these requirements or the ones outlined in their charter they could risk being shut down by their authorizing bodies

History of Charter Schools
It is uncertain where exactly the idea of charter schools began. The term could have originated in New England in the 1970s when it was proposed that teachers be given contracts or “charters” to explore new educational approaches. The nation’s first true charter school, City Academy High School, opened in St. Paul, Minnesota in 1992 after the state passed the first charter school law. Four years later, eighteen more states had passes charter school laws and school choice was serving an extensive range of income and minority groups. Federal support for charter schools started in 1995 with the adoption of the Public Charter Schools Program (PCSP). According to the most recent reports, over one million students in forty states, Puerto Rico, and the District of Columbia attend one of over 3600 charter schools.

Establishment of Charter Schools
Charters are usually established “by individuals or groups based in both public and private sectors” (Vergari, 19). When it is decided to found a charter school, several steps must be taken. First is the exploration stage. During this period, state laws and policies should be examined and a core founding group should be assembled. A comprehensive school plan should also be designed. Next, a charter should be drafted asserting the mission statement, program objectives, the financial plan and any other major details necessary. At this point the proposal should be submitted. If they charter is approved, there are still many steps to take. The school must then finalize their formal operating plans and begin to recruit students and staff, including teachers and support. Once the school has opened its doors, the job is not done. Charter schools must continually “collect and interpret student performance data” to see how their teaching styles should be modified (uscharterschools.org). The work of those establishing a charter school is never done, as each charter school should successfully grow and evolve.

Benefits of Charter Schools
One of the major benefits of charter schools, in the opinion of many, is the way that they “counteract the effects of income level on educational opportunity by establishing expanded options for lower income families that are typically available only to wealthier families who are able to buy or rent homes in neighborhoods with more desirable schools” (Okala, 314). Charter schools are considered a voluntary alternative to court-ordered busing as a way to promote racial balance. Due to this, charter schools serve a higher percentage of low-income and minority students than traditional public schools (although special education students are less likely to attend). During the 2001-02 school year, approximately two-thirds of children in charter schools were minorities. According to a study conducted by the U.S. Department of Education, about 41 percent of charter school students were of African-American or Hispanic descent, while public schools only enrolled about 32 percent of students from these groups. In addition, charter schools enrolled 5 percent more students who received free or reduced lunches.

Next, charter schools give parents and students a much larger selection of options that they would not usually be privy to in the public school system. These options include more choices when it comes to the curriculum, budget, and the overall philosophy held by educators, as well as input involving the teaching staff. This can often result in more teacher and community involvement than in traditional public schools.

Charter schools are also considered ideal over traditional public schools by many of their proponents because of their system of accountability. Charter schools operate in an almost competition like atmosphere, where their performance can influence their ability to get and keep students, receive funding from public and private ventures and can even determine whether or not they will be allowed to remain open. Many proponents endorse the innovative nature of many charter schools. The best of charter schools “serve as laboratories for educational experimentation and innovation” (ECS.org). Without the regulations of traditional public schools to hold them back, educators and administrators can create and put into practice new teaching and learning tactics.

Weaknesses of Charter Schools
Because the concept of charter schools has been around for nearly two decades now, there has been ample time for people to realize their shortcomings. One argument is that the opportunity for choice in education could result in the “best” students and teachers being pulled from traditional public schools (Okala, 314). This argument is contradicted however, by an even larger negative – according to the National Education Association website, charter schools are fifty percent more likely to hire inexperienced and unqualified teachers. In fact, while 92 percent of teachers in traditional public schools held certification, only 79 percent of those in charter schools could boast this same qualification.

Charter schools as a whole are also not faring as well in terms of academic achievement as traditional public schools. A case study by the United States Department of Education revealed that out of five charter schools, all five were less likely to meet state performance standards. While over fifty percent of charter schools were meeting state standards in the 2001-02 school year, traditional public schools were slightly more successful. A study also revealed that students from charter schools “made considerably smaller achievement gains than they would have in traditional schools” (NEA.org).

Beyond Charter Schools
Although charter schools are the most prevalent of alternative schooling options, there are several other choices for those parents and students who want to learn in a different way. One example of this is the concept of magnet schools. A magnets school is a “public school that caters to students who are interested in certain academic subjects or who are interested in the arts” (Families.com). Unlike charter schools, many magnet schools require certain qualifications to enroll – this includes entrance exams, some of which are extremely difficult or minimum grade-point-average requirements. Oftentimes there are not enough spots for students in magnet schools, so those allowed in are chosen by a lottery. For example, The School of International Studies at Meadowbrook in Norfolk, Virginia, places their curriculum on the study of world cultures, languages, and military science. When a student enrolls, they choose one theme on which to focus, much like one would do in a college environment. Among the many requirements for enrollment at Meadowbrook, students must pass all of their fifth grade Standards of Learning exams and have at least a C+ average, plus must endure a sometimes lengthy lottery process.

Another choice for those wishing for alternative schooling options is homeschooling. Though homeschooling is quite controversial, it is a popular method. According to Homeschool.com, it is the “most flexible and diverse educational optional available today.”  The advantages of homeschooling are strengthened family bonds and the flexibility that students are allowed. Disadvantages include the loss of income, as one parent must stay home to educate the children and a lack of confidence in their ability to teach or how well their children are learning. While homeschooling has its advantages and disadvantages it is one of the most popular methods of alternative schooling.

Conclusion
Charter schools are still in the somewhat early stages of their development, so it is far too early to decide whether or not they are a great idea or just another fleeting moment in American education. The academic results of them are widely varied and the topic sparks debate nearly any time it is brought up. While it may be a long time before we know whether or not charter schools are here to stay, we as future teachers must be aware of what they are and how they can have an impact on us and the students we will one day teach.

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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


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Social and Cultural Foundations of American Education/Feedback/Effective Measurements

Ask any high school student what his or her goals regarding school are, and the answer will most likely have something to do with grades; these answers will vary from “I just want to pass” to “I want to make an A” to the most ambitious “I want to be valedictorian.” All of these replies point to this one simple truth in high school, that it is all about the grades, and this, in turn, means that it is all about the assessment. The problem is, school should be about learning, not having fantastic test-taking skills or a stellar ability to perform well on homework assignments, so the tricky part is left up to teachers: how to construct effective measurements of student abilities and learning.

Use a Variety of Measurements and Accommodate All Learners
I asked Dr. Chris Mason, the principal at the private boarding high school where I teach, what kinds of assessments he thinks teachers should use in their classrooms. He listed, “observations of students, verbal assessments, written assignments, (and) portfolios” (C. Mason, personal communication, September 21, 2007). It is crucial to use a variety of methods because students all have different learning styles, and it would be unfair to design just a certain type of measurement that would work well with only a certain type of learner.

Again, measurements should accommodate all learners, whether it is allowing for different learning styles, or considering students who may have learning disabilities or have other disabilities such as ADHD. Therefore, design all assignments and assessments with these students in mind. School guidance counselor, Joy Groves, advises to not create tests and assignment documents that appear disorganized or cluttered (having too-little white space) and if a test is very long, to divide it into sections (J. Groves, personal communication, September 22, 2007). Another thing to do is to make sure every student has plenty of time to complete in-class assignments and exams. Dr. Mason encourages making accommodations for students with different ability levels, as long as the accommodations are “reasonable and doable” (C. Mason, personal communication, September 21, 2007).

Make Homework Meaningful
The value of homework is currently a hot debate in education, and positions on whether or not it should be given vary greatly. If you, as a teacher, choose to give homework, you need to at least be sure that the homework is meaningful. It should not be just “busy work” (Rademacher, 2000).

Not only must a teacher make sure homework is meaningful, but the teacher must make sure students understand why they are doing the assignment. There must be a purpose, and it must be apparent. Acceptable purposes include: gathering background information in preparation for a new lesson or unit; practice; checking for understanding (Checkley, 2003) (with remediation to follow if the teacher finds understanding is lacking); or review (NEA, 2006).

Finally, make sure the homework is actually worth the students’ time. If you give a lengthy homework assignment, such as a week-long project, make sure it involves higher-level thinking (Checkley, 2003) and covers multiple topics or fully a major theme.

Create Effective Exams
Regarding effective exams, Mrs. Groves again uses that word, “variety.” If using the common type questions (multiple-choice, true/false, matching, and fill-in-the-blank type), she reasserts the idea of varying which types of questions appear. “Teachers could also, over time, develop enough different types of questions that they could create an extra section on their tests, and students could choose what sections they want to answer.” She explains how this allows students to be tested in the ways in which they are most comfortable, and the test itself therefore cannot “weaken what students have to tell you” (J. Groves, personal communication, September 22, 2007).

More effective than these common types of questions are those that require more critical thinking, typically short-answer responses. Dr. Mason prefers his staff to create tests that “require use of higher order thinking skills” and that call for identifying and solving problems (C. Mason, personal communication, September 21, 2007). Though they may be more cumbersome for teachers to grade, the short answer and even essay responses give the greatest opportunity for students to show what they really know, whereas in other question types, such as multiple-choice, they can simply guess. Mrs. Groves offered, “I do think it would be great to see writing prompts more prevalent on tests in all courses, including science and math, because that is shown as a national weakness, and you see colleges focusing on it.” She also mentions the new focus on writing by the re-designed SAT (J. Groves, personal communication, September 22, 2007).

Consider Alternative Assessments
A new trend in education is alternative assessments. Dr. Mason says, “I like them for students with learning differences” and Mrs. Groves says, “I definitely think alternative assessments are great ideas, whether it’s writing, group presentations, group projects” (C. Mason, personal communication, September 21, 2007, & J. Groves, personal communication, September 22, 2007). The North Central Regional Educational Laboratory defines alternative assessment as “any type of assessment in which students create a response to a question or task” in contrast to “traditional assessments,” where “students choose a response from a given list, such as multiple-choice, true/false, or matching” (NCREL, 2007).

The best kinds of alternative assessments are those that are closely related to real-world events (CCCOE, 2003). For example, in a business class, students may have to go through a mock process of purchasing a car, renting a house, and establishing a household budget. One specific assignment I’ve used in the past is a writing project designed to replace a more traditional test on the book, To Kill a Mockingbird. The assignment gives students four separate options, such as a critique option, a “what if?” creative writing option regarding a key character, and an option to compare and contrast a major plot point with how it’s presented in the book versus how it’s presented in the film. Each prompt requires critical understanding of the text, and students get to choose which options suits them best. Additionally, just the mere fact of being able choose sets the students at ease, because they often can feel overwhelmed with how much they are told to do and how little they feel they can choose to do.

Assess Frequently
You should assess students constantly in order to properly monitor their progress, and also to have the opportunity for interventions before students get too far behind (Many, 2006). A crucial step in the teaching process is tutoring after an exam (C. Mason, personal communication, September 21, 2007). Frequent assessment is also a way for you to know if you are teaching effectively. If assessments clearly show that students are not learning, you may need to alter your means of instruction

Keep it Simple
No matter how inventive your assessments may be, make sure to never make them too confusing. Write clear questions. Give clear instructions on assignments. Don’t give them “trick questions.”  Remember the goal is not to “win” in a game, but to give the student a chance (and a comfortable chance) to express what he or she has learned or can do.

For example, the following assignment is a challenge in itself just to understand what the teacher is looking for:

Write 6 sentences using the verb, “to be” in present tense. Write 6 sentences using 6 different action verbs in the present tense. Use 12 different subjects, intermixing nouns and pronouns.

The purpose of this assignment is to make sure students can correctly form verbs in the present tense, so a more effective way of presenting this would be to create a worksheet something like:

Complete the following sentences using the verb “to be” in present tense.

I _______________________________________________________.

My uncle _______________________________________________________.

The dogs _______________________________________________________.

They _______________________________________________________.

These books _______________________________________________________.

She _______________________________________________________.

Complete the following sentences using action verbs in present tense. Don’t use the same verb more than once.

He _______________________________________________________.

The basketball team _______________________________________________________.

Your teacher _______________________________________________________.

You _______________________________________________________.

We _______________________________________________________.

That dog _______________________________________________________.

Give your students every opportunity to be successful.

Give Students a Chance to Think
Life is just one big series of problems that need solutions, and the best way to get young people ready for the real world is to train them in solving problems. Whenever possible, give students assignments that make them think and figure, or, as Dr. Mason says, “require diagnosis and providing a plan to address a problem” (C. Mason, personal communication, September 21, 2007). Remember that education should not be all memorizing and regurgitation. Education is not merely about what students are to take in, but it is also about what students are able to put out.

Examples of this strategy in action:

 * History class: Rather than merely summarizing events and plotting them on a timeline, analyze a situation considering problem/solution. What was the problem?  How was it solved?  How might it have been solved instead?  Strategies of the Confederacy during the Civil War would be interesting to analyze like this.
 * Math class: Show a fully-worked algebra problem that is solved incorrectly, and ask the student to identify the place where the mistake was made and to then correctly solve the problem.
 * English class: Discuss a character in literature with a significant flaw, such as Torvald in Henrik Ibsen’s play, A Doll’s House. How did Torvald’s actions lead up to an unsatisfying ending for him (his wife leaves him), and how might he have changed to prevent his dismal outcome?

Conclusion
In the American school, assessment is the measure of all education, and this is critical to the point where it can seem like it is all education is. Assessment must be created carefully, and conscientious to needs of the student, both directly, and indirectly, in the case that it must provide adequate information to you, the teacher, so that you can, in turn, further help the student. Remember the importance of variety, incorporate higher-level thinking and writing as much as possible, and consider alternatives to common types of assessment while keeping in mind that your goal is not just to teach state standards, but also to prepare young adults for the rest of their lives.

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Statistical Analysis: an Introduction using R/R/Vectors

One of the most fundamental objects in R is the vector, used to store multiple measurements of the same type (e.g. data variables). There are several different sorts of data that can be stored in a vector. Most common is the numeric vector, in which each element of the vector is simply a number. Other commonly used types of vector are character vectors (where each element is a piece of text) and logical vectors (where each element is either or  ). In this topic we will use some example vectors provided by the "datasets" package, containing data on States of the USA (see ).

R is an inherently vector-based program; in fact the numbers we have been using in previous calculations are just treated as vectors with a single element. This means that most basic functions in R will behave sensibly when given a vector as a argument, as shown below. You may occasionally need to create your own vectors from scratch (although most vectors are obtained from processing data in already-existing files). The most commonly used function for constructing vectors is, so named because it c oncatenates objects together. However, if you wish to create vectors consisting of regular sequences of numbers (e.g. 2,4,6,8,10,12, or 1,1,2,2,1,1,2,2) there are several alternative functions you can use, including,  , and the   operator.


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Statistical Analysis: an Introduction using R/R/Random sampling

Random sampling
From the help page, we have seen that the sample function can take a number of different arguments. x must be a vector of items, size must be a number. Since 1:6 gives a vector of the numbers from 1 to 6, we can set x=1:6 and size=5. Here are 5 examples (note that the first 4 are equivalent, although the actual result will differ due to chance effects when sampling ).


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Statistical Analysis: an Introduction using R/R/Getting help

There are a number of ways to get help in R, and there is also a wide variety of online information. Most installations of R come with a reasonably detailed help file called "An Introduction to R", but this can be rather technical for first-time users of a statistics package. Almost all functions and other objects that are automatically provided in R have a help page which gives intricate details about how to use them. These help pages usually also contain examples, which can be particularly helpful for new users. However, if you don't know the name of what you are looking for, then finding help may not be so easy, although it is possible to search for keywords and concepts that are associated with objects. Some versions of R give easy access to help files without having to type in commands (for example, versions which provide menu bars usually have a "help" menu, and the Macintosh interface also has a help box in the top right hand corner). However, this functionality can always be accessed by typing in the appropriate commands. You might like to type some or all of the following into an R session (no output is listed here because the result will depend on your R system).


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Project+

This textbook is intended to teach fundamental project management skills for the Project+ certification offered by CompTIA, the Computing Technology Industry Association, a non-profit, vendor-neutral trade association. Project+ shows that one has the knowledge needed to manage projects. It provides validation of fundamental project management skills. The certification covers the life cycle of a project from initiation and planning through execution, acceptance, support and closure.

There are no prerequisites, and candidates are not required to submit an application or complete additional hours of continuing education.

Contents
Project+ divides project management into the following distinct phases:
 * /Initiating/
 * /Planning/
 * /Executing/
 * /Controlling and Monitoring/
 * /Closing/

title: Project+


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User:Whiteknight/Ext

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User:Whiteknight/Ext2

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Change Issues in Curriculum and Instruction/Other Issues Worth Investigating/24 May, 2007

1. Distraction:

2. Effective Consumption of Information:  Navigating the Ocean of Information

3. The Right Tool for the Job:  How can we find the appropriate tools (software, etc.) to achieve our various educational objectives?

4. Wiki and Rhetoric:  Re-evaluating Rhetorical Principles Based on Web 2.0 Innovations

5. Involving Parents in the Learning Process Through Web 2.0 Innovations

6. Addressing Resistance:  Converting the Web 2.0 Nay-Sayers

7. Making Connections Through Web 2.0:  Between Parents and Teachers, Teachers and Teachers, Teachers and Students, etc.

8. Diverse Curricular Support Materials:  YouTube and other Web 2.0 Innovators Providing Diverse Educational Resources

9. Tailoring Web 2.0:  How can we make these technologies engaging for diverse groups of people?

10. Helping Collaboration Exist in a Standards-Based Educational Environment


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User:Whiteknight/Templates

These are templates used in my user namespace, but won't likely be useful anywhere else. Some templates that create direct edit links to pages in my user space, or templates which contain my signature, have been protected against transclusion into other pages besides my user space. Other templates may be used in other places, if needed. I will revert any changes made to these templates: if changes need to be made to suit them for a particular application, please copy the code to a new location and edit it there.

Page Templates

 * Creates a link to a page that is not in my user namespace. Creates a direct link, an "edit" link and a "create" link. Floats the links on the right side of the page.

 * Creates a link to a page in my user namespace, an edit link, and a "create" link. Floats the links on the right side of the page.

 * Creates a link to any page, does not float the link.

External Link Templates

 * Creates a link to an external non-WMF site. floats the link on the right.

 * Creates a link to a WMF external link. Floats the link on the right.

 * Creates a link to a WMF external link. Does not float the link.

User Page Link Templates

 * Creates a link to another users' page. Creates links to the user page, the user talk page, an edit link and an optional "welcome" link for a user with no user talk page. Does not float the links.

 * Same as above, floats the links on the right.

Book Templates

 * Creates a link to a book, a link to an outline, a link to the goodbook template, a link to a notes page, and transcludes the contents of that notes page. Floats links on the right. May not be used outside my user namespace.

 * Creates a link to a book, a link to it's outline, and a link to it's notes page. Does not float links. May not be used outside my user namespace.

 * Creates an outline link for a book. Provides a link to an existing book, the notes pages, and the outline page. Floats links on the right. May not be used outside my user namespace.

Course Templates

Book Creator Gadget

 * My gadget to create new books using the <inputbox> extension. May not be used outside of my user namespace.

 * A generic starter stub for a new book, used primarily with by book creator gadget.

 * Instructions for creating a new book, used only with my book creator gadget.

Template Creator Gadget

 * My Template creator gadget, may only be transcluded into pages in my user namespace

 * Stub page used with my template creator gadget.

 * Instructions for using my page creator gadget.

 * custom insert symbol links for the edit window. Requires javascript.

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title: User:Whiteknight/Templates


text:
Statistical Analysis: an Introduction using R/Chapter 7

single variable. Introduce notation for GzLMs, including

y ~ stuff + error


text:
Ethnomedicine/Home Remedies/Saline Nasal Wash

What are the Benefits of Nasal Irrigation?

Simple Nose Washing
It is simple learning to wash your nose and nasal passages using only a bathroom sink. If the procedure is unpleasant, you're doing it wrong. First, learn to blow your nose into the sink instead of a tissue or handkerchief. Second, learn to push water into your nostrils/nasal passages by brushing wet hands along the sides of your nose. Use warm water. Afterwards, you may wait 10 seconds at first, blow your nose into the sink. Lastly, you can learn to get water further into your nasal passages by wetting your nose and tilting back your head.

Saline Nasal Wash
This remedy is used to treat any symptoms of mucus build-up in the nasal passages, caused by the common cold or chronic sinusitis. It consists of warm water (not too hot or it will burn your nose!) mixed with regular table salt. It can be applied through the nose using either a little spray bottle, or using a neti pot. A neti pot (often made of porcelain) resembles a tea pot that is used for nasal irrigation. It is used often in South Asian Culture and is known as Jala Neti, but is starting to be used more and more in Western Culture. To use this, one mixes the salt and water in the pot and sticks the spout through one nostril, head tilted slightly forward so the water may enter the nose, and the salt water is poured through one nostril and out the other nostril. Repeat on the other side, and make sure to gently blow your nose after using to get rid of excess water and mucus in the nasal passages. This method may be used as often as needed, up to about four times a day when you are sick. Some risks associated with using this remedy are not adequately draining all of the water out, which may lead to breathing problems later, or irritation of the lining of the nasal cavity.

See also: Wikipedia article on nasal irrigation.

Prepare isotonic saline solution
Please Note: The Mayo Clinic web site, in the directions for nasal irrigation, specifies using 1/4 tsp. salt to 2 cups (about 1/2 litre) of water - an isotonic solution. This is significantly less salt than is contained in the directions below. One of the mixtures is not an isotonic solution.

Prepare isotonic saline solution. This solution matches the concentration of salt found in the blood and natural tears. A warm saline solution is prepared to a 0.9% salinity (9g of salt (about 1 1/2 teaspoons) per litre of water). Non-iodized salt is better. The water should feel slightly warm to the touch. It is important to stir the mixture thoroughly in order to dissolve all the salt. The following are the stages of the ancient Jala Neti:

The salt is sometimes replaced with half salt and half sodium bicarbonate (baking soda). According to http://www.doctorhoffman.com/, sodium bicarbonate improves the mucus-solvent properties of the solution.

Stage one
Many people only practice stage one of Jala neti. This stage should always be performed whether it is the only stage you do or if you plan to do any of the more advanced stages. Each stage should eventually use about 1/4 litre (8 US fluid ounces) per nostril though a person may have to work up to this.

 * Lean over a sink and tilt your head to the side and slightly down toward the sink. Ideally, the chin and the forehead should be level with each other.
 * Place the spout of the neti pot in the upper nostril creating a complete seal and allow the saline solution to flow into that nostril, through the nasal passages, and out the other nostril.
 * Continue to breathe deeply through the mouth. This allows the water to flow from one nostril and out the other.
 * When the pot is empty, refill it and repeat on the other side. Beginners may prefer to use only half a pot on each side.
 * If the water seems to be blocking, switching back and forth several times may be needed.
 * If you will be doing only Stage One, follow the instructions under "After Stages are completed" to clear the nasal passages of remaining water.

If you are doing this for the first time, try to keep your soft palate closed. To find what this feels like, imitate how a congested person with a cold talks. They might say, "I cad't say adythig dorbally because by dose is codgested" instead of "I can't say anything normally because my nose is congested." Intentionally breathing only through your mouth, and not through your nose, also causes you to keep the soft palate closed. If you can keep the soft palate closed during stage one, this will prevent the irrigation solution from getting into your nose or throat.

Stage two
Since stage two washes the deepest parts of the nasal passage, it should only be performed after a round of stage one. If infections or large obstructions are present in the outer nasal cavity and not cleared by stage one, they could be driven deeper into the nasal cavity.

Beginners should use only stage one for the first few weeks to make sure they are comfortable with the process and to make sure that major blockages are clear.

Stage two involves lightly sniffing the water through each nostril and spitting it out the mouth. It is important not to swallow the water.

Though this stage is more difficult, it has a much deeper effect. People with chronic sinus infections may not see major improvement until this method is used.

Stage three
Before this stage, a round of both stage one and two is performed. It involves actually taking the water in the mouth and directing it out the nose.

After stages are completed
Once jala neti has been performed, it is important to eliminate any remaining water from the nose. The techniques may vary but it usually involves bending over from the waist to let the remaining saline solution drain out, breathing quick breaths out the nose in quick repetition, and gently blowing the nose. It is important not to close off one nostril or squeeze the nose in any way as this may cause water to be forced into areas that do not dry easily. A tissue may be used but is just held lightly surrounding the nose.

Pulsating nasal irrigation
Several medical reports indicate pulsatile nasal irrigation with a water pik type device is more effective than non-pulsating nasal wash products like bulb syringes, neti pots and squeeze bottles which rely simply on gravity and conventional flow at breaking down biofilm, general cleansing and removing bacteria.

.


text:
Wikijunior:Human Body/Medical - Laparoscopic Surgery

What is laparoscopic surgery ?
Laparoscopic surgery is unique and also interesting such in a way that a video cam (laparoscope) and some microscopic surgical instruments are used to perform an operation. There are many types of laparoscopic surgery, the most successful of which are laparoscopic surgery of the pancreas, liver, and bile duct. It is also known as minimally invasive surgery (MIS).

How is it done?
Let's take this as an example: laparoscopic surgery on the abdomen. To perform this intricate procedure, a surgeon will initially make a few tiny incisions on the part of the body. Tube-like instruments will then be inserted, and some type of gas - which, of course, is not hazardous - will fill the abdomen. This is to allow the surgeon to have a clear view of what is being carried out.

Why perform laparoscopic surgery?
This type of surgery is the next best thing to plastic surgery. Normal operations usually require large openings to gain access to the organs. These large opening can leave large scars. Since tiny surgical instruments are used in laparoscopic surgery, smaller openings are required; therefore, it results in smaller scars.

How does it help the body?
Laproscopic surgery can help the body like any other kind of surgery can, with the added benefit of using a small incision rather than something larger that would require more stitches. Smaller incisions heal faster and run a lower risk of developing infections.

The future of laparoscopic surgery
It will only be around for about 10 more years due to the rapidly developing nanotechnology field.


text:
User:Hoffmeier

→ de:user:Hoffmeier

title: User:Hoffmeier


text:
User talk:169.241.28.73

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 08:32, 25 May 2007 (UTC)

October 2010
We welcome and appreciate your contributions, but your recent edits to Wikijunior:Solar System/Jupiter had to be undone. Please see What is Wikibooks? to learn more about what contributions are beneficial to Wikibooks. It might not have been your intention, but your recent edit removed content from Wikibooks. When removing text, please specify a reason in the edit summary and discuss edits that are likely to be controversial on the page's talk page. If this was a mistake, don't worry; the text has been restored, as you can see from the page history. Take a look at the welcome page to learn more about contributing to this project, and if you would like to experiment, please use the sandbox. Thank you. – Adrignola talk 20:46, 18 October 2010 (UTC)

title: User talk:169.241.28.73


text:
User talk:169.241.28.75

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 08:32, 25 May 2007 (UTC)

 ~whatever~

title: User talk:169.241.28.75


text:
User talk:169.241.28.72

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 08:32, 25 May 2007 (UTC)

--Matiia (discuss • contribs) 19:14, 24 March 2015 (UTC)

Blocked
You cannot edit for 1 month due to disruptive editing. You are welcome to contribute constructively when editing privileges are restored. You may appeal this action with a reasonable argument by adding the text below. --Atcovi (talk ↔ contribs) 19:51, 23 April 2015 (UTC)

title: User talk:169.241.28.72


text:
Category:User hi

it:Categoria:Utenti hi ja:Category:User hi

title: Category:User hi


text:
Statistical Analysis: an Introduction using R/R/Objects

Objects
table is a more advanced version of tabulate: it doesn't produce a vector, but a "table" object.


text:
Statistical Analysis: an Introduction using R/R/Plotting

Plotting
One advantage of using objects is that R knows how to deal with them. For instance, plotting


text:
Statistical Analysis: an Introduction using R/R/Storing objects

R topic:   R is what is known as an "object-oriented" program. Everything (including the numbers you have just typed) is a type of object. Later we will see why this concept is so useful. For the time being, you need only note that you can give a name to an object, which has the effect of storing it for later use. Names can be assigned by using the arrow-like signs and   as demonstrated in the exercise below. Which sign you use depends on whether you prefer putting the name first or last (it may be helpful to think of  as "put into" and   as "set to").

Unlike many statistical packages, R does not usually display the results of analyses you perform. Instead, analyses usually end up by producing an object which can be stored. Results can then be obtained from the object at leisure. For this reason, when doing statistics in R, you will often find yourself naming and storing objects. The name you choose should consist of letters, numbers, and the "." character, and should not start with a number.


text:
Fermat's Last Theorem

 * /Cover/

 * /The Theorem/
 * /Pythagoras/
 * /Pierre de Fermat/
 * /Leonhard Euler/
 * /Sophie Germain/
 * /Gabriel Lamé and Augustin Louis Cauchy/
 * /Paul Wolfskehl/
 * /Andrew Wiles/
 * /Appendix/
 * /Bibliography/

L'ultimo teorema di Fermat

title: Fermat's Last Theorem


text:
Fermat's Last Theorem/Cover

This book will discuss one of the most famous theorems of mathematics. It will talk about that which is commonly called Fermat’s last theorem, the subject will be confronted from a principally historic point of view, the concepts and the theorems behind the proof being too complex even for the greater part of professional mathematicians. The book will follow a time based logic starting from the beginnings of mathematics up to arrival in our times, as a matter of fact having nevertheless been enunciated in 1637, the theorem has profound implications for many branches of mathematics and the premises that give birth to it begin right in the primordial days of mathematics.

Acknowledgment is given to the original version in Italian on Wikibooks of which this book is a translation.

title: Fermat's Last Theorem/Cover


text:
Circuit Idea/Op-amp Inverting Voltage-to-Current Converter

<<< contents - passive version - page stage >>>

How to Transform the Passive Voltage-to-Current Converter into an Active One

(Reinventing the Op-amp Inverting Voltage-to-Current Converter)

Circuit idea: The op-amp compensates the external losses caused by the load adding as much voltage to the input voltage source as it loses across the load.

Speculation: The active version is just an improved passive one
In this story, we begin revealing the secret of active voltage-to-current converters alias voltage-controlled current sources (VCCSs) or transconductance amplifiers. Let us start with the simplest and most intuitive op-amp inverting voltage-to-current converter.

Look first at the "bad" passive version (the top of Fig. 1) and then, at the "good" active version (the bottom of Fig. 1) of a voltage-to-current converter. It is not absolutely necessary to be clever:), in order to see that the active version contains the passive one + an op-amp connected in accordance with some powerful idea:

'Active V-to-I converter = passive V-to-I converter + op-amp + great idea ?''

It seems that there is a close interrelation between the two circuits: maybe, the active version comes from the passive one or maybe the active version is just an improved passive version? If it is, how has the passive circuit transmuted into an active one? What is the idea of this connection? What does the op-amp do in this circuit? Let's try to answer these questions by following the evolution of the passive circuit into an active one.

Problem: The real load affects the current

We already knew why the simple voltage to-current converter (as well as all the passive circuits) is an imperfect circuit - because its output current depends on the voltage drop VL across the load (Fig. 2). In this arrangement, the effective voltage difference VIN - VL determines the current IOUT instead of only the voltage VIN; .As a result, the current decreases. You can explore the circuit operation in a more attractive way, if you click Exploring button in the interactive flash movie or if you go to Stage 2 in the interactive flash builder.

We can look at the voltage VL from two contrary viewpoints. From the point of view of the input voltage source, the voltage drop VL is harmful; so, the input source "would like" this voltage not to exist. Contrarily, from the point of view of the load, VL is useful voltage drop as it usually serves as an output quantity; so, the load "would like" this voltage to exist and even it to be as much as possible high.

Obviously, there is a contradiction here - the voltage drop VL has to exist and, at the same time, not to exist. How do we solve this contradiction?

Basic non-electrical idea: Removing a disturbance by an "antidisturbance"
Remember what we do in real life when we solve some problem but a disturbance caused by others stands in our way. The classical remedy is to remove the cause of the disturbance. Only, it is not always possible to do that; then, we use another exotic solution - we remove the disturbance by an equivalent "antidisturbance". For this purpose, we use an additional power source (energy), which "helps" us (the main source) by compensating only the local losses caused by the undesired external quantity. This technique is associated with continuous wasting of additional energy but the result is zero (virtual ground ); so, we prefer to use it when we are rich and, at the same time, lazy enough:). Here are some funny examples.

If someone has broken our window in winter, we may turn on a heater (instead of just repairing the broken window); in summer, we turn on an air-conditioner. If the windows become dirty, we may switch on additional lamps inside the room to "help" the sun (instead of just cleaning the windows). When a car has come into collision with our car, the insurance company compensates the damages caused by the else's car (instead of just preventing the crash). If someone (e.g., our wife or a husband) is spending money from our account, we might begin depositing money into the account to restore the sum (instead of just scolding her/him:) When we go to a mountain, we stock with food, water, medicine, etc. to use them, if there is a future need (instead of just not going to the mountain:). In all these cases,

we have prepared (just in case) "standby" resources to use them, if there is a need to compensate eventual external losses.

Building the electric circuit

Now, let us put this powerful idea into practice. The voltage drop VL across the resistor R is harmful; so, following the recipe above, we have to remove it by an "antivoltage" -VL. In other words, we have to add so much voltage to the input (excitation) voltage source VIN, as much as it loses across the load L

Active V-to-I converter = passive V-to-I converter + "helping" voltage source

The best way to understand what real electronic components do is just to do their work. So, let us first build a "man-controlled" active circuit, in which a man (I might do this donkeywork:) produces the "anti-voltage" while you change the input voltage. For this purpose, I first place an additional supplementary battery BH in series to the load L (Fig. 3). Then, in order to compare the two voltages, I connect a zero indicator in point A, which shows the result of comparison VA = VH - VL. See how simple it is:

Add an adjustable battery in series with the load and make its voltage equal to the voltage drop across the load!

Exploring the electric circuit
In the beginning, imagine that there is not input excitation voltage VIN (see again Fig. 3 above). As a result, there are not any voltage drops and currents in the circuit; the needle of the zero indicator points to zero position. I am happy because there is nothing to do:)

If you increase the input voltage VIN, a current begins flowing through the load. As a result, a voltage drop VL appears across the load and the point A begins rising its potential VA (figuratively speaking, the input source "pulls" the point A up toward the positive voltage VIN). Only, I observe to my great displeasure:( that the needle deflects to the right and immediately react by decreasing the compensating voltage VH. Now, it "pulls" the point A down toward the negative voltage -VH until it manages to zero the potential VA (the virtual ground). Note that the two voltage sources are connected in series, in one and the same direction (- VIN +, - VH +) so that their voltages are added (let us assume that we traverse the loops clockwise). Regarding to the ground, they have opposite polarities.

In this way, the input voltage source is "helped"; its voltage increases so much (VL) as it loses across the load. As a result, the "harmful" voltage VL disappears; the point A has zero voltage; it behaves as a virtual ground. The passive voltage-to-current converter is "fooled": it has the illusion that there is not a load connected; it "thinks" that its output is shorted.

You can imagine what happens when you decrease the input voltage VIN under the ground. As above, I will adjust the battery voltage looking at the needle of the zero indicator, so that always VH = -VL. In electronics, in technics and in our world, this action is referred to as negative feedback (it is a great phenomenon).

Building the electronic circuit
Let us now try to make some electronic device do this donkeywork; an op-amp seems to be a good choice. For this purpose, we connect the op-amp's output in the place of the helping voltage source and the op-amp's input to point A so that the op-amp to "help" the input source (the op-amp's output voltage and the input voltage to be summed).

Op-amp V-to-I converter = passive V-to-I converter + "helping" op-amp

Exploring the electronic circuit
In the beginning, imagine as above that there is not an input excitation voltage VIN. As a result, there are not any voltage drops and currents in the circuit. There is almost not a voltage difference between the inverting and non-inverting input of the op-amp; now, it is "happy" because there is nothing to do:)

Positive input voltage
If the input voltage VIN increases, an output current IOUT begins flowing through the load L. As a result, a voltage drop VL appears across the load L and the point A begins rising its potential VA (the input source "pulls" the point A up toward the positive voltage VIN). Only, the op-amp "observes" that to his great displeasure:( and immediately reacts: it decreases its output voltage "sucking" the current IOUT until it manages to zero the potential VA. Figuratively speaking, the op-amp "pulls" the point A down toward the negative voltage -V to establish a virtual ground. It does this magic by connecting a part of the voltage produced by the negative power supply -V in series with the input voltage VIN. As above, the two voltage sources are connected in series, in one and the same direction (- VIN +, - VH +) so that their voltages are added. Only, regarding to the ground, they have opposite polarities.

Negative input voltage
If the input voltage VIN decreases under the ground, an input current IOUT begins flowing through the load L in opposite direction. As a result, a voltage drop VL appears across the load L and the point A begins dropping its potential VA (now, the input source "pulls" the point A down toward the negative voltage -VIN). Only, the op-amp "observes"' that and immediately reacts: it increases its output voltage "pushing out" the current IOUT until it manages to zero the potential VA (now, the op-amp "pulls" the point A up toward the positive voltage +V, in order to establish a virtual ground). It does this magic by connecting a part of the voltage produced by the positive power supply +V in series with the input voltage VIN. The two voltage sources are connected in series again, in one and the same direction (+ VIN -, + VH -) so that their voltages are added. Regarding to the ground, they have opposite polarities as above.

Conclusion. ''In the circuit of an op-amp voltage-to-current converter, the op-amp adds as much voltage to the voltage of the input source as it loses across the external load. The op-amp compensates the local losses caused by this external load (conversely, in the opposite op-amp inverting current-to-voltage converter, the op-amp compensates the losses caused by the internal resistor).''

Applications of the op-amp V-to-I converter
Once we created a perfect voltage-to-current converter, we may use it as a building block to build more complex compound circuits. For this purpose, we have only to connect consecutively the separate building blocks.

Staying after the circuit output
First, we may connect the op-amp voltage-to-current converter after circuits having voltage output; thus we make them produce current. For example, we have known how to build a simple current source

Simple current source = voltage source + passive V-to-I converter

Now, we can build a perfect op-amp constant current source (Fig. 6)

Op-amp current source = Voltage source + op-amp V-to-I converter

Its output current does not depend on the load resistance (more generally, on the voltage drop across the load).

Staying before the circuit input
Then, we may connect the op-amp voltage-to-current converter before circuits having current input; thus we make them perceive voltage. By applying this technique, we may assemble the famous active circuits of capacitive integrator (Fig. 7), inductive differentiator, diode logarithmic converter, etc.

Op-amp RC integrator = op-amp V-to-I converter + I-to-V C integrator

Op-amp RL differentiator = op-amp V-to-I converter + I-to-V L differentiator

Op-amp RD log converter = op-amp V-to-I converter + I-to-V D log converter

In all these circuits, the voltage drop across the respective I-to-V converters does not introduce an error (precisely speaking, it introduces an error but the op-amp removes it).

Acting as a transconductance amplifier

The op-amp V-to-I converter is an active circuit; so, we may expect it to amplify. Really, it acts as a linear circuit with transfer ratio k = IOUT/VIN [mA/V] or millisiemens having dimension of conductivity. That is why, they frequently name it transconductance amplifier (transconductance is a contraction of "transfer conductance"). Nevertheless, let us try to answer the question, "Is the op-amp V-to-I converter an amplifier?"

To answer this question, let's assemble the famous op-amp inverting amplifier by connecting consecutively an op-amp voltage-to-current converter (R1 and OA) and a bare resistor R2 acting as a simple current-to-voltage converter (Fig. 8)

Op-amp inverting amplifier = op-amp V-to-I converter + I-to-V converter

Note that the resistor R2 serves here as the load L from Fig. 5). This circuit will amplify power, if the output power is greater than the input one. So, the output voltage has to be higher than the input one because the current is the same.

Comparison between the passive and active version

Let us finally compare the two versions beginning by investigating the input and output resistances (for concreteness, let us assume a bare resistive load RL).

Input resistance. First, connect an ammeter in series with and a voltmeter in parallel to the converter's input; then vary the input voltage to investigate the input resistance. Maybe you remember that in the passive version, looking from the side of the input source we were seeing two resistors connected in series; so, the input resistance was RIN = R + RL. Now, we see only the resistor R because the op-amp has "neutralized" the load resistance RL.

It is wonderful, the load has disappeared! As a result, the input resistance is RIN = R and what is more interesting, it does not depend on the load resistance RL! In this case, the op-amp "helps" the input voltage in its striving to change the current.

Output resistance. Now, connect a voltmeter in parallel to and an ammeter in series with the converter's output; then, vary the load resistance (voltage) and observe the current to investigate the output resistance. Remember that in the passive version, looking from the side of the load, we were seeing only the resistor R; so, the output resistance was ROUT = R. Now, the situation is quite more interesting: when we vary the load voltage the current stays steady! But why?

In this case, the op-amp "opposes" the load in its striving to change the current. As a result, the voltage varies (even significantly) while the current stays unchanged; so, the output differential resistance tends to infinite.

Operating range. The op-amp does all these "magics" until it can change its output voltage (i.e., until it is within the active region). When it reaches the supply rail, the op-amp saturates, the magic ceases and the almost ideal active circuit becomes again an imperfect passive one:(. They name the maximum voltage drop across the load compliance voltage. Note that the passive version does not have such a problem; it is always imperfect.

Ground connection. In the passive version, the load is connected to the (real) ground while, in the active one, the load is "flying". More precisely speaking, it is connected to a ground but this is a virtual ground. In some cases it is sufficient but not in others.

Comparison with other techniques
The inverting configuration is not the only possible active voltage-to-current converter. There are other techniques, which excel, in some respect, the idea considered. Let's now consider briefly these techniques; then, we will dedicate special circuit stories to them.

Negative feedback. Exactly speaking, there is a negative feedback in the inverting configuration discussed here. Only, the negative feedback does not serve to keep up the output current; it serves only to keep up the compensating "antivoltage". In this arrangement, the op-amp is not actually interested in the current magnitude; it is interested only in the virtual ground magnitude. In the popular implementation - the non-inverting configuration, the op-amp (not the input voltage source) creates the output current, which passes through a constant resistor. Then, the op-amp keeps up the "copy" voltage drop VR across the resistor R equal to the "original" input voltage drop VIN. Simply speaking, the op-amp increases its output voltage by the value of the voltage across the load thus compensating it. As a result, the output current depends only on the VIN and R; it does not depend on all sorts disturbances. By adding an external transistor or by using the internal op-amp output transistors these circuits can drive grounded loads. Only, the negative feedback configurations have two big errors: the first is caused by the finite op-amp gain; the second - by the common-mode gain.

Bootstrapping. The famous Baron Munchhausen's idea can help us to achieve the same (and even better) result without using negative feedback. The according circuit implementation is referred to as improved Howland current source; no one knows why Motorola named it current source with feedback in 1973?!? The idea is as simple as above: the op-amp increases its output voltage by the value of the voltage drop across the load thus compensating it (compare with the inverting configuration where the op-amp produces an output voltage equal to the voltage drop across the load and adds it to the input voltage). Only, it does this magic "blindly" without using a negative feedback.

Negative resistance. The famous circuit of Howland current source exploits this idea;  Motorola named it a differential input op-amp current source in 1973. From one viewpoint, it consists of a negative resistor -R connected in parallel to the positive resistor R acting as a passive voltage-to-current converter. The result of this connection is that the negative resistor "neutralizes" (absorbs) the positive one and the effective differential resistance (the internal source's resistance) is infinite. The voltage-to-current converter behaves as a perfect current source, which drives a grounded load. Only, these circuits are not as stable as these exploiting a negative feedback.

Wikibooks
Circuit Idea (this book): Passive voltage-to-current converter reveals the basic idea behind the passive version. Passive current-to-voltage converter shows the basic idea behind the passive version of the "mirror" circuit. Op-amp inverting current-to-voltage converter reveals the basic idea behind the active version of the "mirror" circuit.

Wikipedia
Voltage-to-current converter introduces the passive and active versions of the circuit. Virtual ground scrutinizes the basic phenomenon behind the circuits with parallel negative feedback.


text: Template:The Cold War/Timeline

title: Template:The Cold War/Timeline


text:
Fermat's Last Theorem/Pythagoras

The origins of numbers is sometimes thought to be lost in the meanders of human history. As a matter of fact since ancient times man has studied numbers and their properties. In the beginning the study was dictated by practical necessity (measures geometrical, astronomical, economical, etc.) but subsequently some humans began to interest themselves in the properties of numbers and sought to understand not only how to solve problems but also why certain formulae or methods always gave the correct result. This desire of abstraction, desire of exploring the more intimate nature of numbers and of their properties saw one of its greatest exponents in Pythagoras.

Pythagoras
During his life Pythagoras passed the years of his youth navigating the length and breadth of the Mediterranean in search of knowledge. During his travels he learnt practically all the ideas in the field of mathematics possessed by the Egyptians and by the Babylonians but, while these peoples were interested principally in the practical applications, Pythagoras wanted to understand the why of mathematics and more generally of things. After some trials and tribulations he succeeded in founding a school of philosophy, this school differently to modern centres of instruction resembled more a sect where numbers were venerated like divine entities. He who entered the school had to divest himself of all his worldly goods which went into the common purse. An obligation of absolute secrecy with respect to the uninitiated was in force and many myths and legends arose around the school.

The theorem of Pythagoras
Pythagoras is universally famous for his theorem.

Given a and b two sides of a right-angled triangle and c its hypotenuse one has:

 * $$a^2 + b^2 = c^2 \,\!$$

In reality this equation was known by many other mathematicians of the era but Pythagoras became the father of it since he was the first to furnish a generic proof of the equation. He produced by means of a combination of logic and elementary geometry a proof for every right angled triangle. He then passed from an empirical proof for a finite number of cases to a proof as we currently understand it, that is a proof that it is always true for fixed preconditions. Proofs are those which differentiate mathematics from all other sciences. In sciences such as physics, chemistry, etc., the theories are based on theoretical considerations and on experimental trials but they are never considered definitive, they can always be overtaken by the evolution of knowledge. Instead in mathematics once a theorem has been proved, its veracity can no longer be open to discussion. The theorem of Pythagoras was true two thousand years ago and it will be true even in two thousand years from now. The link between Pythagoras’ theorem and Fermat’s last theorem is obvious, it is enough to substitute the power 2 with a generic power n in order to obtain Fermat’s theorem. In fact the theorem of Pythagoras is a particular case of Fermat’s theorem. Fermat was in fact studying the properties of the pythagorean triads (the solutions of the theorem of Pythagoras) when he enunciated his theorem.

title: Fermat's Last Theorem/Pythagoras


text:
Fermat's Last Theorem/Pierre de Fermat

Pierre de Fermat
Pierre de Fermat (1601–1665) - French Magistrate.

Although his work as a magistrate was very demanding, Fermat found the time to dedicate himself in a most profitable way to the study of Mathematics. Even though he was not a professional mathematician by training Fermat made important contributions in the study of functions and of the theory of numbers. Fermat conducted an intimate correspondence with various mathematicians of the era, but his natural reserve together with a notable reluctance in making known his discoveries resulted in his genius being discovered a long time after his death, when his son decided to collect his father’s papers and make them public. The famous enigma was idealised by Fermat while he was studying the Arithmetica of Diophantus of Alexandria, mathematician 212 A.D. to 298 A.D. Diophantus’ book collected together many elegant proofs of complete solutions to problems that mathematicians had faced over the course of centuries; reading the part concerning the Pythagorean triads, one supposes that Fermat may have had the idea of extending the power of 2 to a generic n. Fermat wrote in note in the book the enunciation of his famous theorem and then added:

"Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet."

 * [I have discovered a truly marvellous proof of this, which however the margin is not large enough to contain.]

The unresolved theorem
Fermat was accustomed to annotating his books: many theorems were found in their margins, generally without proof. The proof of these theorems was in some cases simple while in other cases it required hard work. The last theorem in fact takes its name from the fact of being the last of Fermat’s theorems to be proved, not from the fact of having been the last to be enunciated. To be precise, rather, its name was incorrect: until 1994 when it was proved, rather than a theorem it was strictly speaking a conjecture. The majority of mathematicians however used this name: in fact they held it true though not being able to prove it, given that the majority of the affirmations of Fermat had proved themselves true. It goes without saying that these facts are not sufficient to render a conjecture a theorem, but the majority of mathematicians in this particular case passed over this detail without too many problems.

title: Fermat's Last Theorem/Pierre de Fermat


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Fermat's Last Theorem/Leonhard Euler

Leonhard Euler
$$\mathbb{T}$$he publication of Fermat’s writings had generated opposing opinions among mathematicians. The majority of them recognised the usefulness but the fact that the greater part of the theorems were without proof or with incomplete proofs obviously reduced the immediate usefulness of them even if some mathematicians took the theorems as challenges to face and win. Many were faced and resolved but that which subsequently would be called the last theorem resisted all attempted assaults. Leonhard Euler obtained the first results a century after Fermat. Euler was a Swiss mathematician born in 1707 in Basel and died in 1783 in St. Petersburg. Initially Euler was to have become a theologian but Johann Bernoulli became aware of the extraordinary ability of the young man and convinced his father to let Leonhard become a mathematician. This was an enormous good fortune for mathematics given that Euler’s contributions range over so many areas of mathematics and are so profound as to render Euler one of the greatest mathematicians of the XVIII century if not rightly the greatest. Euler analysing the notes written by Fermat found an outline proof of the case n=4. Fermat had written this proof within another proof. In order to prove that case Fermat made use of a technique called infinite descent, Euler sought to utilise this technique for the other cases in such a way as to find a proof for all values of n. Initially he confronted the case n=3. He succeeded in resolving this case but had to make use of complex numbers, in reality other mathematicians had sought to adapt infinite descent to the case n=3 but it took a creative person such as Euler in order to understand that complex numbers were necessary in order to obtain a valid proof. Euler also sought to resolve n=5 but without results.

title: Fermat's Last Theorem/Leonhard Euler


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Fermat's Last Theorem/Sophie Germain

Sophie Germain
After Euler's progress, for around fifty years there were no improvements notwithstanding the fact that the last theorem had become the most famous problem in the theory of numbers. This situation changed radically thanks to Sophie Germain.

Sophie Germain was born in 1776 and died in 1831 and for all her life she had to fight against prejudice. In her society it was unthinkable that a lady of good standing dedicated herself to subjects such as mathematics, but Germain when small had read a book on the history of mathematics and remained fascinated by the death of Archimedes.

The legend recounts that when a roman soldier went to call Archimedes in order to conduct him in front of the centurion Archimedes refused to follow him being occupied with a geometric problem, for this reason the soldier ran him through. Germain was so struck by the fact that a man could have lost his life for mathematics that she decided to study it. Initially her decision was much opposed by her father, but with the passing of the years he had to resign himself to the wishes of his daughter deciding to support her. Germain found it very difficult to acquire modern mathematical techniques given that her tutors did not intend to teach them to her and she, being a woman, could not attend the university where courses in advanced mathematics were held. Germain then used the stratagem of passing herself off as a monsieur Le Blanc, a student who had withdrawn from the Ecole Polytecnique. Obviously she was not able to attend lessons but utilising this false identity she succeeded in getting herself the printed notes and the problems for the students attending that she solved and presented always under the same pseudonym. In the beginning the trick worked until the course professor, the great mathematician Joseph-Louis Lagrange, wanted to know the student who furnished those so ingenious solutions. Lagrange meeting Germain was surprised but pleased by the young woman and decided to help her in her study of the material.

Germain worked for years on the theory of numbers and also interested herself in Fermat's theorem. She obtained a result that she held to be very important but wanting confirmations on the validity of her discovery she decided to contact the then greatest authority, that is to say Carl Friedrich Gauss. Gauss had not interested himself in Fermat's theorem holding the enunciation in itself without interest, but when he received the letter from Germain he remained so impressed by her result as to dedicate himself to the problem and to confirm to Germain the validity of her method. Germain's idea was based on the use of a particular typology of prime numbers that were subsequently called Sophie Germain's prime numbers. For these prime numbers Germain succeeded in demonstrating that solutions of Fermat's theorem probably did not exist. Probably it meant that these eventual solutions would have had some properties so particular as to render the existence of these numbers difficult. Some of her colleagues analysing the problems defined by these prime numbers succeeded in proving that solutions did not exist for some of them, such as 5 or 7. Subsequently Gauss abandoned the theory of numbers in order to dedicate himself to applied mathematics and Germain without further support in the field of mathematics decided to concentrate on physics, where she made important contributions in the study of elastic vibrations.

title: Fermat's Last Theorem/Sophie Germain


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Fermat's Last Theorem/Andrew Wiles

Andrew Wiles
Andrew Wiles was born in the UK, the 11th of April 1953. From a young age he demonstrated a strong interest in mathematical enigmas and problems. When he was still a small child he loved to go into public libraries in search of books containing problems and enigmas. At the age of 10 years he found in a library the book The Last Problem by Eric Temple Bell. In this book the author described what came to be known as Fermat's Last Theorem from the Greeks up to the discoveries at the end of the 1800s. The young Wiles remained fascinated by the problem. An equation so simple to enunciate had eluded some of the most able mathematicians of the world and the boy then began to fantasise hoping to find the elementary proof that had eluded the others. Wiles hypothesised that Fermat did not have a knowledge in the mathematical field superior to his own and he therefore sought a proof with his limited knowledge. Obviously he was not able to find it, he would pursue Fermat’s Last Theorem for a good part of his life. Wiles became a professional mathematician and had to temporarily abandon his quest since finding a proof was thought to be too difficult for a young mathematician and that he didn’t hold that it could produce interesting mathematics in the immediate future. Wiles’ dissertation advisor was John Coates, and he directed Wiles in the study of elliptic curves. That was Wiles’ good fortune, since Wiles' was able to use his knowledge of elliptic curves to the proof of Fermat’s Last Theorem.

Elliptic curves and modular arithmetic
Specifically Wiles analysed some elliptic curves in modular arithmetic. While classic arithmetic deals with an infinite number of numbers, in modular arithmetic one utilises only a subset of values. Modular arithmetic was also called clock arithmetic, given that this utilised a modular arithmetic with modulo equal to 24. Everyone knows that if it is 18 hundred and one waits for 8 hours one does not find oneself at 26 hundred but at 2 hundred, given that when the clock arrives at 24 it starts to count again from 0. Modular arithmetic is a complete arithmetic like that classic, only that the numbers utilised are limited. Modular arithmetic furthermore has at its disposal some very interesting properties that render it particularly useful in some fields of mathematics. When a mathematician analyses an elliptic curve with modular arithmetic he extracts a series of solutions that are called L-series. Wiles worked much on elliptic curves and on their L-series accumulating experience that would become useful to him in the future.

The Taniyama-Shimura Conjecture
Towards the end of the 1950s the Japanese mathematicians Yutaka Taniyama and Goro Shimura formulated a conjecture known as the Taniyama-Shimura conjecture. This conjecture stated that every L-series of an elliptic curve could be associated with a specific M-series of a modular form. In substance this conjecture asserted that every modular form could be put in bi-unequivocal correspondence with an elliptic curve or, given in other terms, the modular forms and the elliptic curves were the same mathematical object seen from different points of view. This conjecture from the point of view of a mathematician is very important, in fact, if it were proved true, it would have meant that problems of elliptic curves centuries old would be able to be transferred into their modular forms and tackled with new mathematical tools. Obviously the converse would also be valid.

The convention of 1984
In 1984 a event happened that revolutionised the life of Wiles: during a convention in Germany Gerhard Frey demonstrated that whoever proved the Taniyama-Shimura conjecture would also automatically have proved Fermat's last theorem. Frey showed with a series of not too complex steps that in a hypothetical counterexample to Fermat's theorem (that is a valid solution of the equation an+bn=cn) one would be able to write it as an elliptic curve so particular and atypical as not to be able to be associated to any M-series of a modular form. Therefore proving the Taniyama-Shimura conjecture proved that this degenerate equation did not exist and that therefore Fermat's theorem was true. In reality almost everything tied to Fermat's theorem is not as simple as it seems, so much so that the development of a proof that tied Fermat's Last Theorem in an indissoluble manner to the Taniyama-Shimura conjecture caused the mathematicians of half the world to struggle for more than two years, and in fact Frey's initial proof was incomplete.

The secret work
In 1986 Wiles came to know that the link between the Taniyama-Shimura conjecture and Fermat's Last Theorem had been demonstrated. This seemed to Wiles a golden opportunity to use advanced mathematics (seeking to prove the Taniyama-Shimura conjecture) to attain the mathematical ambition of his life (proving Fermat's Last Theorem). Wiles decided to work in absolute secrecy, contrary to the prevailing ethos. While in many disciplines it is common when working on a project to maintain strict secrecy, in order to protect patent rights, in mathematics one follows the opposite approach. Mathematicians talked among themselves constantly, successive comparison is an optimum method for facing problems that seem insoluble and in theoretical mathematics the problem of the industrial secret practically does not exist. Wiles prepared himself carefully, he abandoned all his non-obligatory duties, took an impressive research that he was about to publish, divided it into a good number of articles in such a way as to be able to furnish a constant flux of works while he was working on the conjecture and sought to assimilate as much as possible on modular forms and elliptic curves. Wiles revealed the secret of his work only to his wife. In the first two years of work Wiles made progress utilising the group theory of Galois, although he was still a long way from the solution. The 8th of March 1988 Wiles was stunned to read in the Washington Post that the Japanese mathematician Yoichi Miyaoka had proved Fermat’s conjecture. In reality Miyaoka had not produced a complete proof but utilising differential geometry, a new branch of geometry he had put forward some optimum bases for the definitive solution. Unfortunately for Miyaoka his proof had a gap that although at the beginning did not appear grave, subsequently proved itself to be catastrophic and rendered it impossible to carry out a proof of Fermat’s Last Theorem using that technique. Finally Wiles, utilising a method called Kolyvagin-Flach, succeeded in associating a particular elliptic curve to its modular form. The problem for Wiles was that the method could not be extended to all elliptic curves. Wiles then classified all the elliptic curves into families and modified the method in such a way as to adapt it to single families.

Wiles, in order to utilise the Kolyvagin-Flach method, had to profoundly expand his knowledge of algebraic geometry and not being very expert decided in the end to confide himself to a trusted mathematical expert in the sector. Therefore Wiles contacted Nick Katz, a mathematician in his department. Given that the proof was very complex and voluminous an informal discussion in Katz’s study would not have been sufficient in order to sort out all the doubts, the two decided therefore to disguise their meetings as some post graduate lessons. Wiles would have given the lessons while Katz would have participated among the public. Wiles presented the lessons in a very technical and boring manner in such a way as to eventually discourage students. In fact after a few weeks only Katz remained of the class. Wiles thanks to the help of Katz went over his proof again which effectively seemed correct. Finally Wiles working speedily eliminated the remaining families and finally in May 1993 Wiles finished the proof laying low even the final recalcitrant family.

The Cambridge conference
At the end of June at Cambridge a conference was held on L-functions and their arithmetic. In this context, surrounded by some of the most brilliant mathematicians of the planet Wiles presented his proof in a series of three conferences. The 23rd of June the third and final conference took place and a lengthy applause concluded Wiles’ final conference. Fermat’s Last Theorem had been proved. All the world’s papers spoke of the event and in an afternoon Wiles became the most famous mathematician on the planet.

An error and its resolution
Wiles sent the proof to a journal in such a way that the editor of the journal could subject the proof to verification by a qualified commission. The editor of the journal, given the importance and complexity of the proof, subdivided the sheaf into six parts and entrusted them to as many commissioners. These analysed the manuscript piece by piece and contacted Wiles in order to obtain clarifications on unclear passages and presumed errors. One of the commissioners was Katz, the same mathematician that Wiles had contacted in order to verify the correct application of the Kolyvagin-Flach method. Unfortunately for Wiles, Katz identified an error.

Initially it seemed one of the many errors of little account that stud a complex proof. These errors are comparable to oversights and usually they are corrected in the space of a few hours but that error even if very subtle was also very insidious, in fact Wiles did not succeed in eliminating it. With the passage of time ever more persistent news of the gap spread within the mathematical community and also in the general papers such as the New York Times. Finally Wiles by means of e-mail communicated to the mathematical community that effectively there was a gap in the proof but that he expected to be able sort it out in a few weeks. After months of not being able to do so, and on the advice of a friend he decided to get help from an expert on the Kolyvagin-Flach method and he therefore contacted Richard Taylor. Taylor was one of the reviewers of the proof and was an ex-student of Wiles. They worked on the problem for many months, and towards the end of summer Wiles was demoralised to such a point as to propose to Taylor publicly declaring defeat, but Taylor convinced him to persevere at least until the end of September.

The 19th of September Wiles was analysing the Kolyvagin-Flach method seeking to understand why the method failed when he became aware that, although the method was insufficient in order to obtain a proof, it permitted a method called Iwasawa’s method to function. Iwasawa’s method had initially been utilised by Wiles for the proof but had been abandoned as insufficient. The same method, instead, utilised in conjunction with the Kolyvagin-Flach method, furnished a valid proof.

The proof
The 25th of October Wiles gave two manuscripts to the press, in the first there was the proof of Fermat’s Last Theorem and it carried his signature. The second manuscript specified some properties of some elliptic curves and was signed by Wiles and Taylor. The second manuscript served to prove a fundamental passage of the first manuscript. The publication of the manuscripts put an end to one of the most complex and difficult proofs that mathematics had ever developed.

Wiles and Taylor did not totally prove the Taniyama-Shimura conjecture, in fact the proof for all the cases arrived in 1999 by Christophe Breuil, Brian Conrad, Fred Diamond, and the same Taylor, that starting from the work of Wiles incrementally proved the remaining cases.

title: Fermat's Last Theorem/Andrew Wiles


text:
The Cold War/"A Forward Strategy to Freedom"

Ronald Reagan, a Republican, took over the American presidency in 1981, from the Democrat Jimmy Carter. He believed that the USA had a special, God-ordained position in the world - that of an ambassador for freedom. Because of this, he immediately went on the offensive against world Communism, saying, in 1984 in Berlin:

Mr. Gorbachev, tear this wall down.

Central America
One way by which he seeked to accomplish this was by combatting the advance of Communism in Central America. In 1983, when Cuban-backed forces staged a coup on the small island of Grenada, Reagan diverted a troop carrier of marines, on their way to Israel, to invade the island. The invasion was a straight-forward success. Reagan also covertly backed rebels against the Sandinista government in Nicaragua for most of his presidency, despite opposition from both Congress and the Senate.

SDI
Reagan also went on the offensive in the Arms Race, instigating the Strategic Defense Initiative (SDI) in 1983. This was an attempt to develop a space-based missile defense system, which would allow the USA to shoot down any incoming missiles using lasers. It never succeeded, but it did bring the USSR to the bargaining table, as they could not afford to keep up with the Arms Race. Together with the Soviet financial problems, SDI ended the Cold War.


text:
Talk:XForms/Insert

Questions: Is it possible to insert in an empty list?

My experience with the Chiba framework was:

After I deleted all items in a repeat list, it was impossible to insert a new entry?

Is this incapability a feature of the XForms specification?

Or is it only due to an improper xforms file or an improper implemented Xforms processor?

title: Talk:XForms/Insert


text: Fermat's Last Theorem/Bibliography

title: Fermat's Last Theorem/Bibliography