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Linear Algebra/Null Spaces

Among the three important vector spaces associated with a matrix of order m x n is the Null Space. Null spaces apply to linear transformations.

Range
Let T be a linear transformation from an m-dimension vector space X to an n-dimensional vector space Y, and let x1, x2, x3, ..., xm be a basis for X and let y1, y2, y3, ..., yn be a basis for Y, and consider its corresponding n × m matrix,

$$M= \begin{pmatrix} a_{11} & a_{12} & a_{13} & \ldots & a_{1m} \\ a_{21} & a_{22} & a_{23} & \ldots & a_{2m} \\ a_{31} & a_{32} & a_{33} & \ldots & a_{3m} \\ \vdots & \vdots & \vdots & \vdots & \vdots \\ a_{n1} & a_{n2} & a_{n3} & \ldots & a_{nm} \\ \end{pmatrix}$$.

The image of X, T(X), is called the range of T. T(A) is obviously a subspace of Y.

Since any element x within X can be expressed as

$$x=\sum_{i=1}^m c_i x_i$$,

$$T(x)=T(\sum_{i=1}^m c_i x_i)=\sum_{i=1}^n c_i T(x_i)$$

implying that the range of T is the vector space spanned by the vectors T(xi) which is indicated by the columns of the matrix. By a theorem proven earlier, the dimension of the vector space spanned by those vectors is equal to the maximum number of vectors that are linearly independent. Since the linear dependence of columns in the matrix is the same as the linear dependence of the vectors T(xi), the dimension is equal to the maximum number of columns that are linearly independent, which is equal to the rank. We have the following important conclusion:

The dimension of the range of a linear transformation is equal to the rank of its corresponding matrix.

Null Space
For example, consider the matrix:$$ A = \begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix} $$.

The null space of this matrix consists of the set:

 * $$\hbox{Null Space}(A) = \left\{\mathbf{\begin{pmatrix}

-2r \\ r \end{pmatrix} } : r \in \mathbb{R} \right\}$$

It may not be immediately obvious how we found this set but it can be readily checked that any element of this set indeed gives the zero vector on being multiplied by A. Clearly,

$$\begin{pmatrix} -2 \\ 1  \end{pmatrix} \in \hbox{Null Space}(A)$$ as

$$\begin{pmatrix} 1 & 2 \\ 2 & 4 \end{pmatrix}\begin{pmatrix} -2 \\ 1  \end{pmatrix} = \begin{pmatrix} 0 \\ 0  \end{pmatrix}$$.

Null Space as a vector space
It is easy to show that the null space is in fact a vector space. If we identify a n x 1 column matrix with an element of the n dimensional Euclidean space then the null space becomes its subspace with the usual operations. The null space may also be treated as a subspace of the vector space of all n x 1 column matrices with matrix addition and scalar multiplication of a matrix as the two operations.

To show that the null space is indeed a vector space it is sufficient to show that

$$ x_1,x_2 \in \hbox{Null Space}(A)\Rightarrow x_1 + x_2\in \hbox{Null Space}(A)$$

and

$$x \in \hbox{Null Space}(A) \Rightarrow \alpha x \in \hbox{Null Space}(A)$$

These are true due to the distributive law of matrices. The details of the proof are left to the reader as an exercise.

Null spaces of row equivalent matrices
If A and B are two row equivalent matrices then they share the same null space. This fact, which is in fact a little theorem, can be proved as follows:

Suppose x is an element of the null space of A. Then Ax = 0. Also since A is row equivalent to B so $$B = E_1E_2\cdots E_kA$$ where each $$E_i$$ is an elementary matrix. (Recall that an elementary matrix is the matrix obtained from performing any elementary row operation.) Now,

$$Bx = E_1E_2\cdots E_kAx = 0$$

and so x is in the null space of B as well. So the null space of A is contained in that of B. Similarly the null space of B is contained in that of A. It is now clear that A and B have the same null space.

Basis of Null Space
As the null space of a matrix is a vector space, it is natural to wonder what its basis will be. Of course, since the null space is a subspace of $$\mathbb{R}^n$$, its basis can have at most n elements in it. The number of elements in the basis of the null space is important and is called the nullity of A. To find out the basis of the null space of A we follow the following steps:
 * 1) First convert the given matrix into row echelon form say U.
 * 2) Next circle the first non zero entries in each row.
 * 3) Call the variable $$x_1$$ as a basic variable if the first column has a circled entry, and call it a free variable if the first column doesn't have a circled entry. Similarly call the variable $$x_2$$ basic if the second column has a non zero entry and free otherwise. In this way name n variables $$x_1,x_2...,x_n$$.
 * 4) If $$x_i$$ for any i, is a free variable, then let $$v_1$$ be the solution obtained by solving the system Ux = 0 where all the free variables are exactly 0, except for $$x_i$$ which is 1. If $$x_i$$ is not a free variable don't do anything.
 * 5) Repeat the above step for all the free variables getting vectors $$v_2,v_3$$ etc in the process.
 * 6) The set $$\{v_1,v_2...\}$$ is the required basis.

The key point in the above algorithm was that A and U have the same null space. For a complete proof of why the algorithm works we refer the reader to the excellent text book given in the references by Hoffman and Kunze.

Let us look at an example:

Suppose $$A = \begin{pmatrix} 1 & 1 & 0 & 1 & 5 \\ 1 & 0 & 0 & 2 & 2 \\  0 & 0 & 1 & 4 & -1 \\  0 & 0 & 0 & 0 & 0 \end{pmatrix}$$

The first step involves reducing A to its row echelon form U.

Now $$U = \begin{pmatrix} 1 & 0 & 0 & 2 & 2 \\ 0 & 1 & 0 & -1 & 3 \\  0 & 0 & 1 & 4 & -1 \\  0 & 0 & 0 & 0 & 0 \end{pmatrix}$$

We encircle the first non zero entries in each row by brackets:

$$U = \begin{pmatrix} (1) & 0 & 0 & 2 & 2 \\ 0 & (1) & 0 & -1 & 3 \\  0 & 0 & (1) & 4 & -1 \\  0 & 0 & 0 & 0 & 0 \end{pmatrix}$$

Clearly the free variables are $$x_4$$ and $$x_5$$ and the rest $$x_1,x_2$$ and $$x_3$$ are basic variables. Now we shall solve the system Ux = 0 with $$x_4 = 1, x_5 = 0$$ to get the vector $$v_1$$. Thus we need to solve,

$$\begin{pmatrix} 1 & 0 & 0 & 2 & 2 \\ 0 & 1 & 0 & -1 & 3 \\  0 & 0 & 1 & 4 & -1 \\  0 & 0 & 0 & 0 & 0 \end{pmatrix} \begin{pmatrix} x_1\\ x_2\\ x_3\\ 1\\ 0 \end{pmatrix} = \begin{pmatrix} 0\\ 0\\  0\\  0 \end{pmatrix} $$

This reduces to the following system on matrix multiplication:

$$\begin{pmatrix} x_1 + 2\\ x_2 - 1\\ x_3 + 4\\ 0 \end{pmatrix} = \begin{pmatrix} 0\\ 0\\  0\\  0 \end{pmatrix} $$

It is clear from here that $$x_1 = -2,\ x_2 = 1,\ x_3 = -4,\ x_4 = 1,\ x_5 = 0$$ is the solution.

Thus $$v_1=(-2,\ 1,\ -4,\ 1,\ 0)$$. Similarly $$v_2$$ is found to be $$(-2,\ -3,\ 1,\ 0,\ 1)$$.

The set $$\{v_1,v_2\}$$ is the basis of the null space and the nullity of the matrix A is 2. In fact this method gives us a way to describe the null space as well which would be: $$\{\alpha v_1 + \beta v_2 : \alpha,\beta \in \mathbb{R} \}$$ (Why? - Because the linear combination of solutions is also a solution)

Implications of nullity being zero
The example given above gives no hint as to what happens when there are no free variables in the row echelon form of A. All we said that in step 4 of our algorithm was that if $$x_i$$ is not a free variable then don't do anything. Following that logic, if no variable is free then we keep on doing nothing, leading to the conclusion that if no variable is free then the basis of the null space is an empty set i.e. $$\empty$$. In that case we say that the nullity of the null space is 0. Note that the null space itself is not empty and contains precisely one element which is the zero vector.

Now suppose that A is any matrix of order m x n with columns $$c_1, c_2,...c_n$$. Each $$c_i$$ is a vector in the m-dimensional space. If the nullity of A is zero, then it follows that Ax=0 has only the zero vector as the solution.

More precisely,

$$Ax = \begin{pmatrix} c_1 & c_2 & \ldots & c_n \end{pmatrix} \begin{pmatrix} x_1\\ x_2\\ \vdots\\ x_n \end{pmatrix} = x_1c_1 + x_2c_2 + \ldots + x_nc_n = 0 $$

has the trivial solution only. This implies that nullity being zero makes it necessary for the columns of A to be linearly independent. By retracing our steps we can show that the converse is true as well.

Let us examine the special case of a square matrix, i.e. when m = n. Now if the nullity is zero then there is no free variable in the row reduced echelon form of the matrix A, which is say U. Hence each row contains a pivot, or a leading non zero entry. In that case U must be of the form, $$ \begin{bmatrix} 1 & 0 & 0 & \cdots & 0\\ 0 & 1 & 0 & \cdots & 0\\ \vdots & \vdots & \vdots & \vdots & \vdots\\ 0 & 0 & 0 & \cdots & 1 \end{bmatrix} $$

or U must precisely be the identity matrix I. Conversely, if A is row equivalent to I then Ax = 0 and Ix = 0 have the same solutions, due to their being equivalent. Since Ix = 0 has only the trivial solution x = 0, so does Ax = 0. It follows that the null space of A is merely {0} and so the nullity of A is 0.

Thus nullity of A is 0 $$\iff$$ A is row equivalent to I.

Now if A is row equivalent to I then $$A = E_1E_2\cdots E_k$$ where each $$E_i$$ is an elementary matrix. Since a product of invertible matrices is invertible and each $$E_i$$ is invertible so A is invertible. Conversely if A was invertible, and U its row reduced echelon form then $$U=E_1\cdots E_kA$$ which is clearly invertible (by virtue of being a product of invertible matrices). Now a matrix containing a zero row can never be invertible (why?), so U has pivots in each row. It follows that there are n pivots all equal to 1, with zeros above and below them and so U = I. Thus A is row equivalent to I.

In summary, A is row equivalent to I $$\iff$$ A is invertible.

We can collect the entire argument in this section, to state the:

Theorem: For a square matrix of order n, the following are equivalent:
 * 1) A is invertible.
 * 2) Nullity of A is 0.
 * 3) A is row equivalent to the identity matrix.
 * 4) Columns of A are linearly independent.
 * 5) The system Ax = 0 has only the trivial solution.
 * 6) A is a product of elementary matrices.

It will be a good exercise for the reader at this stage to try to rewrite the proof of the theorem in detail.

Exercises
2 & 1 & -2 \\ 1 & -2 & 1 \\  -3 & 1 & 1 \\ \end{pmatrix}
 * 1) Evaluate null spaces and bases for:
 * 2) $$\begin{pmatrix}

$$ -2 & -1 & 4 & 2 \\  1 & -2 & 1 & 1 \\  -3 & 3 & -5 & -3 \end{pmatrix}
 * 1) $$\begin{pmatrix}

$$ 1 & 1 & 1 \\  1 & 0 & 1 \\  0 & 1 & 1 \end{pmatrix}
 * 1) $$\begin{pmatrix}

$$
 * 1) Show that null space of a matrix is a vector space.
 * 2) Prove the theorem regarding invertibility of a square matrix. Also by showing that A is invertible iff A$$^T$$ is, show that the condition that the rows are linearly independent can be added to the list.
 * 3) Is the solution set for Ax = b where b is a non zero vector (i.e. has at least one component non zero) a vector space? Give reasons.
 * 4) Let r be the number of basic variables associated with a n order matrix A (which is equal to those associated with its row echelon form). Show that A is invertible if and only if r = n.

title: Linear Algebra/Null Spaces


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Logic for Computer Scientists/Propositional Logic/Syntax

Syntax
For the definition of the syntax we have to assume a set of atomic formulae, which we take as the start of an inductive definition. With the help of three junctors and brackets as punctuation symbols we inductively define more complex formulae.

Definition 1 (Syntax of propositional Logic)
Assume a The set of propositional formulae is defined by the following induction: The different kinds of formulae are called conjunction, disjunction and negation. Note, that this is just a convention about wording, until now, we did not give any semantics to these junctors, which would justify these denotations.
 * countable set of atomic formulae $$P_i$$, where $$i=1,2,3,\cdots $$,
 * the junctors $$\land, \lor$$, and $$\lnot$$,
 * the punctuation symbols $$($$ and $$)$$.
 * Atomic formulae are formula.
 * If $$F$$ and $$G$$ are formulae, then $$(F\land G)$$ and $$(F\lor G)$$ are formulae.
 * If $$F$$ is a formula, then $$\lnot F$$ is a formula

This definition of the set of formulae also introduces a partial order in a very natural way, if we consider the concept of a subformula.

Definition 2 (Subformula)
A subformula of a formula is a substring, which is a formula.

Note that the relation "is subformula" is indeed a partial order.

The set of formulae together with the subformula-relation is a well-founded relation.

In order to facilitate notations We introduce the following abbreviations:

$$ A, B, C $$     instead of    $$P_1, P_2, P_3$$

$$ (F_1 \to F_2)$$  instead of           $$ (\lnot F_1 \lor F_2)$$

$$ (F_1 \leftrightarrow F_2)$$ instead of   $$((F_1 \land F_2) \lor (\lnot F_1   \land \lnot F_2))$$

$$ \bigvee^n_{i=1} ~F_i  $$ instead of    $$ (\cdots ((F_1 \lor F_2) \lor F_3)   \lor \cdots \lor F_n)$$

$$ \bigwedge^n_{i=1} ~F_i  $$ instead of  $$  (\cdots ((F_1 \land F_2) \land   F_3) \land \cdots \land F_n)$$

These notations (except the first one) are simple abbreviations; whenever those arrow-symbols or indexed junctors occur in a formulae, the corresponding subformula can be substituted according to this definition.

Coming back to our previous example you can see that $$ \lnot(ab(or1)) \to high(or1, o) \leftrightarrow (high(or1, i1) \lor high(or1, i2)) $$ can be written as a formula according to the above definition by introducing parenthesis: $$ (\lnot(ab(or1)) \to( high(or1, o) \leftrightarrow (high(or1, i1) \lor high(or1, i2)))) $$ The parenthesis are introduced in order to avoid any ambiguity. In order to increase readability, we will omit them whenever this is possible. If we additionally apply the above abbreviation rules we would result in the following formula: $$ (\lnot \lnot(ab(or1)) \lor $$

$$ ( high(or1, o) \land ( ( high(or1, i1) \lor high(or1, i2)) \lor $$ $$ (\lnot high(or1, o) \lor \lnot   ( high(or1, i1) \lor  high(or1, i2)) ) )))

$$

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


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User:Speregrination

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title: User:Speregrination


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User:Nowotoj

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My books and books I participate in
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title: User:Nowotoj


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Change Issues in Curriculum and Instruction/Reform Proposals

Reform Proposals

Written by: Lauren Florin and Tiffany Hall

.

Introduction
The world is changing and so must education. The Center for Gifted Education at the College of William and Mary suggests five generalizations about change. In no particular order, they are as follows: change is linked to time, change may be positive or negative, change may be perceived as orderly or random, change is everywhere, and change may happen naturally or be caused by people (Center for Gifted Education, 1998). Whatever the generalization, one thing is certain—change is inevitable. The first public schools were established in the United States in the 1600s. Since that time, the world has become a much different place than it was when the Puritans first landed on Plymouth Rock. If the United States is to retain its place as a world power, it is critical that education be responsive to the needs of an ever-changing world. To thoughtfully consider and eventually implement any type of education reform, one must consider three critical change areas: teachers, school leadership, and the needs of students academically and social-emotionally.

A Changing Demographic
Although the changing role of women in society has done wonders for girl power, it has had a detrimental affect on public education. Up until the 1970s, women aspiring to be something other than a housewife had few career choices other than those available in education, as clerical support, or in the lower echelons of the healthcare industry. Because choices were so limited, the small percentage of women earning bachelors degrees most frequently entered the teaching profession. Equal rights for women ushered in an era of intellectual, financial, and personal freedom that the typical American woman had never before experienced. The best and the brightest women were no longer enrolling in college to pursue fields of study traditionally dominated by women. No longer limited to teacher education programs, the best and the brightest women began to explore other fields of study. This led to a decline in female teacher quality as evidenced in a recent study by three University of Maryland economists. The results of their study conclude that “the likelihood that a highly talented female (one ranked among the top 10 percent of all high schoolers) will become a teacher fell from roughly 20 percent in 1964 to just over 11 percent in 2000” (Hoxby & Leigh, 2005).

The Trickle Up Affect
Since most school administrators were teachers at some point, administrators come from a pool of educators that are no longer considered the best and the brightest. This has had a negative impact on schoolhouse administration, particularly as the role of principal has changed. Traditionally, a principal has been seen as a manager of people rather than a manager of a community of learners. The role of the principal typically entailed resolving personnel issues, addressing discipline concerns, and staying abreast of school finances. Today’s principal must be radically different. Today’s principal must be a team leader rather than a manager. This requires the principal to relinquish control over many aspects of the school day “so that staff members can assume ownership of broad education issues” (Murphy & Schiller, 1992). The principal must establish the goal and vision; furthermore, he or she must move his or her team of highly competent and capable educators towards realization of that goal and vision. As the team leader, the principal must be well versed in all facets of curriculum and instruction and capable of fostering “positive learning climates characterized by high expectations for all” (Murphy & Schiller, 1992). This requires dynamic leadership. To prepare principals for this new role, training in “instructional leadership, planning for school improvement, administrative leadership, organizational ability, school environment and climate, communications, community and public relations, professional development and personal qualities” is necessary (Murphy & Schiller, 1992).

What Should Kids Learn and How and When Should They Learn It?
Countless aspects of society have experienced significant change since the first public schools were established in the New England states in the 1600s. At that time and for a significant period thereafter, the United States was largely an agricultural society. Although the nation is now largely industrial and technological, the school day and school year are still based on the needs of an agricultural society. As society has moved from one that is agricultural in nature, the public school system has not. Students are still expected to attend school for roughly seven hours each day for ten months out of the year. The school schedule is not typically crafted with the needs of the learner in mind. In fact, today’s school schedule is often at odds with the schedules of many families. The family of yesteryear most often consisted of a father who worked outside of the home and a mother who stayed home and managed the household. This is no longer true. Today’s students may hail from households that consist of two parents who work outside of the home, or that are headed by a single parent who works outside the home, while other students are being raised by elderly grandparents. For today’s families the daily school schedule can create childcare issues and may lead to frequent absenteeism. Families may benefit from year round school schedules or adjusted school hours. In addition, many teachers feel that, after the long summer break, too much time is spent reviewing material taught during the previous year. Given the consistent breaks during the year-round school system, less time would have to be spent on reviewing material. Students who have opportunities to learn throughout the day and the year learn best. These students are primarily kids from upper middle class homes whose parents have the resources to provide educational opportunities outside of school. As we work to close, or better yet, prevent, the achievement gap, lengthening the school day and/or the school year seems to make perfect sense. But year round schools are not a new idea and continue to face many obstacles, including cost and public acceptance and lack of supporting research. In addition, simply allocating more time is not enough. Effective use of time is critical and even within our current school calendar, precious little of the six and a half hour day is spent in engaged quality teaching and learning. If we really want to make a difference we must rethink how to use time more effectively to increase engaged learning time.

Coping with Student Diversity
Perhaps the greatest challenge faced by schools today is student diversity. “Students come to class with different levels of competence and academic preparation, different degrees of motivation to succeed in school work, different social skills and levels of maturity” (The Keys to Effective Schools, 2007). Along with these differences, there are differences in race and culture, socio-economic status, and belief systems. Despite all of these differences among students, for the most part, education continues to be geared toward white, middle class students. Some would argue for the need for a national curriculum; however, because of student differences, it is imperative that any common, national curriculum be differentiated to address the varying needs of all learners. In addition to academic needs, school reform must include programs that address the diverse social and emotional needs of a diverse student body. These programs may include guidance and counseling, character education, medical services on premises, a full-time social worker as a member of the school staff, social services available on premises, and multicultural education.

America’s Perfect Storm
A lack of highly qualified teachers, the limited presence of dynamic leadership, and the level of diversity among learners’ academic and social-emotional needs have all been created in part by societal changes. The Educational Testing Service (ETS) published a report entitled America’s Perfect Storm: Three Forces Changing Our Nation’s Future (2007). This report describes how the United States is currently in a “perfect storm” due to three forces: the differences in skill distributions, the changing economy, and the trends in demographics. The authors suggest that if America does not change its present course, then it is doomed for disaster. The first force is the gap in literacy and numeracy skills among both children and adults. According to research, the achievement gap in reading and math between students of different socioeconomic groups and racial groups has not decreased in the last twenty years. Internationally, the American students’ scores on standardized tests are average; however, the gap between the nation’s highest and lowest scoring students is among the highest in the world. Not only does testing indicate where problems may lie, but national surveys reveal that many working adults do not have the literacy skills to compete in the workplace. The second force is the country’s ever-changing economy. Due to the shift over the last fifty years in the types of jobs that are prevalent, adults who do not possess a high level of education are not able to earn as much money or take part in company sponsored training programs that further their skills. The third force stems from the demographic changes in the United States over the past twenty years. There has been an increasing number of immigrants from Hispanic countries. These immigrants traditionally do not have high levels of education; over half do not have a high school diploma, and eighty percent of those do not speak English very well. This "demographic shift" has quickly emerged as a major impetus for education reform, because, compared with the white majority, the two largest minority groups (Hispanics and African Americans) are achieving at much lower levels in schools (National Task Force on Early Childhood Education for Hispanics, 2004). This achievement gap will have profound effects on the future workforce and ability of this workforce to compete in the international world. Each of these forces is individually important; however, when analyzing the impact that they have together is something that will continue to grow. It is crucial that the necessary steps be taken through education reform so that America does not end up at the bottom. It must be ensured that certain segments of the population be given the chance to succeed in life (Braun, et al. 2007).

Reform in Education
Based on this report, most would argue that the public education system is in need of an overhaul. There are so many reform programs available that it makes it quite difficult to decide which is most effective and most beneficial to students. Within twenty years, the United States went from President Ronald Reagan calling for the abolishment of the U.S. Department of Education in 1982 to President George W. Bush enacting the No Child Left Behind Act (NCLB) in 2001, a sweeping education reform law. At present with NCLB in place schools that do not make adequate yearly progress for five consecutive years have one of five reform options: reopen the school as a public charter school, replace all or most of the school staff including the principal, enter into a contract with a private management company, turn the school over to state control, or engage in any other major restructuring of the school's governance arrangement (NCLB, 2002). In between Reagan and Bush, the nation has seen Outcomes Based Education (OBE) evolve from President George H.W. Bush’s First National Summit on Education held in 1989 and later the passing of President Bill Clinton’s Goals 2000: The Educate America Act. Each president and political party has had much to say about education, but has anyone really gotten it right? The problem is that every administration implements a program, but before it has been given enough time to see if it is effective a new administration comes in and implements a new plan.

Perhaps even more fundamentally, the many failed attempts at federal reform call into question whether education policy should in fact be initiated at the federal level. Up until the middle of the twentieth century, public schools were largely governed at the local level—by principals, mayors, and town boards of education (Kirst, 2004). However, beginning in the 1950s, when the federal government stepped in to implement racial integration in the schools, a tendency toward centralization of school governance has become increasingly prevalent. This trend accelerated in the early 1980s with the publication of such studies of A Nation at Risk, which claimed that the United States was falling behind in its ability to compete in a global economy as a result of its poor performance in educating its citizenry. Operating on the premise that local districts could not be trusted to initiate and implement effective policy, federal and state governments arrogated more and more power to themselves. Currently the state makes most of the important decisions concerning school governance, and the federal government indirectly wields considerable power as a result of tying the substantial educational funding it provides to specific conditions that must be met at the state and local levels (Kirst, 2004).

The most pressing problem created by this tendency toward increased centralization is the disenfranchisement of local education officials and educators. When most education policy is decreed from on high by a governor with perhaps little professional educational experience and the members of his appointed state board of education, who remain largely invisible to the local school community, then local officials, school administrators, and the teachers themselves are forced to carry out policies that they have had almost no role in creating. And yet if these policies prove ineffective, the public inevitably blames the local officials, administrators, and teachers, since this group is most visible and most likely to be "held accountable" (Epstein, 2004). The teachers, in particular, who have the most intimate knowledge of the student population and, in all likelihood, the best information for improving student performance, have virtually no power to create or administer education policy (Kirst, 2004). On the other hand, those who have only limited contact with the student population and very little professional expertise in education—presidents, governors, and other bureaucrats—have considerable power to make and implement major education policy reforms. It is thus not surprising that none of these reforms has succeeded in substantially improving the quality of education in America.

If these ineffective methods of reform are allowed to continue and if the local education authorities and educators continue to be denied the power to make and implement sounder policy, our education system is doomed to failure. This being said, the question arises as to how we are ever going to get the United States out of this “perfect storm”? Recently, two reform proposals have been written that do look at reforming the complete educational system.

American Schools: The 100 Billion Dollar Challenge
American Schools: The 100 Billion Dollar Challenge (2000), written by Drs. Dwight Allen and Bill H. Cosby, Jr., is an interesting proposal that suggests that the United States government treat education as a matter of national security and fund it accordingly. According to the Office of Management and Budget for the White House, in the year 2005 the Department of Education was allocated $56 billion dollars, while the Department of Defense was allocated $401.7 billion dollars. The future, and ultimate safety, of America depends on education. If the nation does not have well-educated citizens who can intellectually compete with the minds of others across the globe, then national security is in jeopardy. Allen and Cosby propose that the government spend $100 billion dollars a year on education, and in their book they provide a breakdown of exactly how that money will be spent. They also propose that schools provide year round schooling, looping, and suggest that schools remain open from 7:00 a.m. to 10:00 p.m. to allow students to follow a schedule that best fits them, as well as providing a place for students to go to do homework and study. Another problem is that American citizens do not have the necessary skills required in the workplace. The SCANS report was released in 1989 and outlines the basic skills that are needed for all students whether they plan to go on to college or a vocational school. Not only does the report outline the basic reading, writing, math, listening, and speaking skills, but it also outlines thinking skills and personal qualities that all students need (US Department of Labor). Allen and Cosby believe that the SCANS report is a good beginning to a curriculum, but more needs to be added to it.

Another major focus in education reform involves the teachers. In order for teachers to maintain a high enough standard to be effective, teacher education must be redefined to include a minimum of one to two years of a clinical practice, attract the best and the brightest students to the field of education and keep quality teachers in the field by paying teachers on the level of doctors, lawyers, and engineers, and change the way teachers interact and communicate with each other so that they are able to observe each other and provide and receive high amounts of feedback. Finally, Allen and Cosby propose that a national experimental school administration be established. There would be 100 NESA school districts established throughout the country. The schools in these districts would be state of the art and would participate in the new education research practices. These schools can be used as comparison schools and would be required to be in place for a minimum of twenty years (Allen & Cosby, 2000). .

Tough Choices or Tough Times
An alternative reform proposal, Tough Choices or Tough Times (2007) written by the New Commission on the Skills of the American Workforce, begins its report by refuting the basic premise of the American Schools reform proposal. It believes that spending more money on the overall system currently in place will not work, and even proposes that money can be saved by being more efficient with current resources. What must happen is that the whole system must change. The commission has devised a set of ten recommendations that it believes will change the system and allow the future generation to be successful in the workforce. Some of these recommendations include altering the programmatic schema of high school to include board examinations after tenth grade to prove that students have mastered a set of skills before they continue on to either community college, vocational school, or more advanced high school studies like Advanced Placement courses and International Baccalaureate programs. Upon completion, any student hoping to attend a university must take and pass another set of tests. Another recommendation is to recruit the next generation of teachers from the top percentile of high school graduates, as well as exponentially raise the salary for teachers based on their effectiveness, particular school they teach in, and their specific subject. Another component is to develop standards and assessments for the needs of tomorrow as well as implement universal preschool programs to even the playing field for young children before entering kindergarten. Finally, they propose to give the additional support to the students who need it the most as well as provide adults with the literacy skills that they need for the workforce. Finally, government funded job training programs are proposed to help unskilled individuals gain the skills that they will need to obtain a job (Tough Choices or Tough Times, 2007).

Conclusion
While both of these reform proposals contain both pros and cons, the question arises as to whether a reform proposal such as these could ever be implemented in the United States. Critics of the American Schools express that it is much too complex to ever “catch fire politically” (e-publishing reviews, 2000). The political issues are precisely the problem. Olson (2006) comments that the reform proposal is positive because it draws attention to the issues and creates a national conversation about them; however, unless an education reform proposal is snatched up by a major political contender such as the future president of the United States, there is no hope for either. Education is in the political ball field getting tossed back and forth from party to party. Is there hope for education when a new reform is implemented every four to eight years?

Response #1
I would implement universal preschools to all three and four year olds in the United States. These programs would be run by the school districts and be taught by certified teachers who were trained in early childhood education. They would also include a parental education component to try and teach parents the importance of not only education but of staying involved in their children’s education. I would choose preschool as my one reform initiative because research has shown the importance of preschool not only for the academic development of young children but also for the social and emotional component. A huge problem in the United States is the achievement gap in students of different socioeconomic groups. Sadly, this achievement gap can be seen from the first day of kindergarten and it continues throughout high school. This is due to numerous reasons. Research shows that parents in low socioeconomic groups are not as involved in their children’s academics, and they do not understand what their children should already know by the time they enter kindergarten. Sadly, a child who enters kindergarten significantly behind his or her peers has little chance of ever catching up. This is why it is so important that all children, regardless of income, be given the opportunity to attend preschool. Studies such as the High/Scope Perry Preschool project, the Chicago Child-Parent Center program, and the Abecedarian project all show the importance of preschool throughout the lifetime. They report that for every one dollar invested in the program, the public saved more than seven dollars (considering the cost of special education, retention in grade, and incarceration). These two studies followed the children that attended the preschools through adulthood and found that those that attended preschool had higher graduation rates, reduced crime rates, fewer special education placements, and were retained less in school (Bracey, 2003). While preschool is not the complete answer to an educational reform, it is a start and it is well worth the investment.

Response #2
I would implement a redesigned education delivery system based on the suggestions in Tough Choices or Tough Times (2007) because it is an excellent way to tap into student interests and to prepare students for fields of study and careers that are best suited for them. The revamped delivery system includes a series of “gateway tests” that must be passed before enrolling in secondary or postsecondary programs that are of interest to the students (Tough Choices or Tough Times, 2007). Also included are a variety of programs that can meet the academic needs of students regardless of their postsecondary aspirations. In most public school systems, there is great emphasis on preparing students to enroll in traditional four-year colleges. Some students have no interest in completing a four-year degree and would much rather enter the workforce upon graduation. The delivery system discussed in Tough Choices or Tough Times would prepare students for the traditional four-year college, as well as for trade school or a technical college. By gearing K-12 education toward student interests, the curriculum can become more focused allowing students to pursue studies that interest them and that they feel will best prepare them for their careers of choice. It is suggested that by implementing such a delivery system, the dropout rate will decrease and enrollment in postsecondary programs will increase (Tough Choices or Tough Times, 2007).

Response #1
The absence of teacher involvement in the development of reform proposals is one of the greatest obstacles to national school reform. As part of my preparation to contribute to this chapter of our class textbook, I read several books, reports, and articles about reform proposals and the crisis of public education in America. In none of my reading did I come across any reference to teacher input in the design of reform proposals. Although many school reform proposals included giving teachers increased responsibility in the decision making process at the school level, I could find no evidence that any of the suggested reforms came at the urgings of teachers. I think of all the information I reviewed, the one thing that bothered me more than any other is the fact that when President George H.W. Bush held the First National Summit on Education in 1989, none of the participants were teachers. All present were governors. In his address to the governors assembled, President Bush said, “I hope that you will join me to define national goals in education for the first time. From this day forward let us be an America of tougher standards, of higher goals, and a land of bigger dreams. And our goals--(applause)--our goals must be national, not federal. And that's why I welcome the initiatives of the National Governors Association.” After reading that statement, I wondered why teachers weren’t included since that was the first time national goals for education were being established. To “welcome the initiatives of the National Governors Association” without regard to the input of teachers or any group representative of teachers, such as the National Education Association, was a slap in the face to educators everywhere. The president, governors, school administrators, or anyone with an opinion can say whatever they want about what needs to happen in education, but without teachers having a voice in the discussion, I am afraid that whatever evolves from the discussion, good or bad, will not stand a chance for effective implementation within the classroom. Without teacher input into these sweeping reform programs, teacher buy in would be a challenge making implementation very difficult. Teachers are repeatedly treated as anything but professionals and lack of teacher involvement in the development of a national school reform program is just another example of that. As a teacher, how can you expect me to readily embrace a reform program that might drastically change how I perform my duties without my input? Especially if the reform program is the brainchild of a roomful of politicians. I doubt that the president of the United States would ever hold a summit on the national crisis of obesity without a single doctor present. Teachers are long overdue the opportunity for a serious discussion on a national level about what is wrong with the American school system and what can be done to fix it.

Response #2
I believe that a lack of sufficient monetary funds in education is a huge obstacle to national school reform. To thoroughly reform the education system in the United States, I believe that we do need to invest more money into education. Our education system is not working; this can be seen in our flat test scores and our huge achievement gaps. In order to fix our education system, we need to completely change the way our schools operate. This requires money, and lots of it. I completely agree with American Schools: The 100 Billion Dollar Challenge (2000). We do need to treat education as a matter of national security and fund it accordingly. Teachers need to be compensated like other professionals, they need to have further training in the field before they are left in their own classroom, and they need to have more time to plan. All students need to have the opportunity to attend preschool, they all need access to computers and the internet, and they need to be able to stay at school later in the day to accommodate their needs and the needs of their families. Finally, we need to start implementing research based practices into our classrooms on a daily basis. To do this, teachers need to be trained in the new practices and given the resources to effectively implement them. All of this requires money: money that the current school system does not have. We cannot implement a national school reform, or a local school reform for that matter, without the appropriate funds. The way the system works now, not all schools receive the same amount of money. It is often the case that the schools that need to most funds receive the least. How can we expect our lowest students to close the achievement gap if they do not even have appropriate school supplies, let alone access to technology or high quality teachers. Unless the government takes a long look at the realities of our education system and realizes that money is a huge issue, there is no way that a national school reform could be implemented.


text:
Cookbook:Potato Gratin

Potato gratin is a wonderful dish that is easy to make. It is a good accompaniment for roast lamb or roast chicken, but is as delicious served on its own with a green salad.

Ingredients

 * 5 medium sized waxy potatoes, peeled or unpeeled
 * 4 cloves of garlic, chopped (smoked garlic is good for this dish if you can get it)
 * ½ pint reduced fat crème fraîche, single cream, or a mixture of semi-skimmed milk and crème fraîche
 * 3 oz good quality Gruyère, Challerhocker, or Emmentaler cheese, freshly grated.
 * 1 lemon
 * Salt (such as sea salt) and pepper
 * Fried pancetta, bacon cubes, or other cooked pork (optional)

Procedure

 * 1) Preheat the oven to
 * 2) Slice the potatoes very thinly (about ⅛" thick), if possible using a mandoline to achieve evenness, and place them in some fresh water.
 * 3) Swish around the potatoes in the water to get rid of the starch, because that excess starch can make the dish a little unpleasant.
 * 4) Pour away the water and place the potatoes on a wooden surface. Then pat dry with a paper towel or kitchen towel, which is important because otherwise the remaining water will mix with the cream, causing curdling problems.
 * 5) Return the sliced potatoes to a bowl and add the cream and chopped garlic. Add a generous pinch of salt and some pepper.
 * 6) You can also add a few fresh herbs (thyme is particularly good) but this is up to you.
 * 7) Peel the zest of the lemon and add it to the mixture.
 * 8) Mix well, so the cream gives a good coating to all the potatoes.
 * 9) Pile the potatoes into a buttered, oven-proof dish. The size is if course difficult to gauge but the potatoes should not be layered more than about 4 thick.
 * 10) Grate a generous amount of cheese, and spread over the mixture.
 * 11) Pop it all into the oven and leave until the top layer of cheese and potatoes are brown and the cream is bubbling and running down the side of the dish. This will take about 40 minutes.
 * 12) For a final flourish before serving, grate a goodly amount of fresh nutmeg over the cheese.

Notes, tips, and variations

 * Some people tend to layer the potatoes in the heat proof bowl first and then pour the cream over. Some find this unreliable as the cream does not diffuse through all the layers, and the potatoes in a higgledy-piggledy pile in the bowl may be more attractive to some.
 * Swiss Appenzeller cheese is also a good choice.

title: Cookbook:Potato Gratin


text:
Java Programming/Tutorials

Tutorials include:
 * 1) Creating a Notepad application

title: Java Programming/Tutorials


text:
User:Alexsmail/What to read

This page will not be maintained. It will have historical information. New updates are available in my blog http://alexsmail.blogspot.com/ on Russian only.

See [Что почитать]

= Recently read books: =
 * 1) Frederick Forsyth "The Day of the Jackal" 100% - political detective.
 * 2) Winston Churchill "Muscles of the World" 100%
 * 3) Fridreich August fon Hayek "The way to slavery" 100% - political, social-philosophical essay.
 * 4) Karel Capek "First rescue team" 100 % - philosophical essay.
 * 5) Karel Capek "War with salamanders" 100 % - philosophy-political essay.
 * 6) Bernard Gerber "Ants" 100% - mix of elements of science fiction, the adventure novel and philosophical essay.
 * 7) Umberto Eco "L'isola del giorno prima" ("Island on the eve") 0% - I haven't mastered
 * 8) Umberto Eco ""Il pendolo di Foucault" " ("Foucault's pendulum") 100% - I don't like it
 * 9) Umberto Eco "In noma dela Rosa" ("In the name of the Rose") 100%

See [Прочтённые недавно книги]

= Recommended books: =
 * 1) Oscar Wild "Dorian Grey's Portrait"
 * 2) George Orwell "1984"
 * 3) Strugatskich "Waves Extinguish a Wind"
 * 4) Strugatskich "Picnic on a Roadside"
 * 5) Jule Vern "Mysterious Island"
 * 6) Umberto Eco "In noma dela Rosa" ("In the name of the Rose") - for the philosphy books fan

See [Рекомендую прочитать] = Planning to read (friend's recommendations): =
 * 1) Ken Kizi "Flight above a jack of a cuckoo".
 * 2) Paul Koelyo "Veronicas Decides To Die".
 * 3) Paul Koelyo "11 minutes".
 * 4) Paul Koelyo "Alchemist".
 * 5) Ernest Hemingway "After whom calls a bell?"
 * 6) "Adventures of Gallant Soldier Shvejk".
 * 7) Nabokov "Feat".
 * 8) Victor Hugo "The Person Whom are Dared ".
 * 9) George Orwell "Farmyard".
 * 10) T.Erenbugr. "Trest D.E."
 * 11) Summa Technologiae, S. Lem.

See [Планирую прочитать]

= Another user's "what to read page" =
 * Panic's books read

title: User:Alexsmail/What to read


text:
User talk:203.132.67.81

Welcome to Wikibooks. We invite everyone to contribute constructively to our collection. Take a look at the welcome page if you would like to learn more about contributing. However, unconstructive edits are considered vandalism, and if you continue in this manner you may be blocked from editing without further warning. Please stop, and consider improving rather than damaging the hard work of others. Thanks. Webaware talk 15:28, 19 May 2007 (UTC)

title: User talk:203.132.67.81


text:
User talk:Max Naylor~enwikibooks

Welcome message
Hello, and welcome to Wikibooks!

Here are some tips to help you get started:
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 * You can get to this page by clicking the tab at the top of the page labeled with your registered username.
 * If you are a Wikipedian, see Wikibooks for Wikipedians for a primer on how things work here (it's a little different).
 * If you want to base your work here on materials from Wikipedia, please use WB:RFI (requests for importation) to bring the material over in compliance with the GFDL.
 * If you're an instructor and plan on using Wikibooks for a class project, see Guidelines for class projects
 * Please say hello at the Staff Lounge with any questions or ideas.
 * Eventually, you might want to read the Manual of Style and Policies and Guidelines.
 * Please take a look at Naming policy before starting a new book.
 * Remember to maintain a Neutral point of view.
 * Explore, be bold in editing pages, and have fun!

You will find more resources in Community Portal. If you want to ask a question, visit the Study help desk, the Staff lounge, IRC channel or ask me personally on my talk page. For site news, see the Bulletin board. It might be a good idea to add this page to your "watchlist" so that you can see when any new information is posted there. You can do that by clicking the tab labeled "watch" at the top of the page.

Good luck!

You might also be interested to read our Cookbook policy page, and talk to other Cookbook editors. Webaware talk 15:45, 19 May 2007 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Max Naylor. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Max Naylor~enwikibooks that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:26, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 05:14, 19 April 2015 (UTC)

title: User talk:Max Naylor~enwikibooks


text:
Annotations of The Complete Peanuts/References

This is a hack to get references to appear only once in the printed version, rather than per-chapter. Simply adding <references /> directly in the print version doesn't work, it has to be included. =References=


text:
Change Issues in Curriculum and Instruction/Isolation

Isolation in Education By Patti Horne and Rose Hotchkiss May 2007

This page is currently under construction

Introduction: Education and the Culture of Isolation
For well over a century, a culture of isolation has prevailed within the American education system. Teachers have jealously guarded the turf of their specialties, subjects have been insulated from one another by compartmentalization, and students have been encouraged to compete as individuals in the high-stakes game called school. The same forces that have created isolation within the system have created a monolithic barrier between it and the nonacademic, or "real," world and have even resulted in a disjunction within the psyches of both teachers and students—an alienation from self. As early as 1983, noted educator and speaker Parker Palmer wrote, of the deep pain he detected in many teachers, "I call the pain that permeates education 'the pain of disconnection.' Everywhere I go, I meet faculty who feel disconnected from their colleagues, from their students, and from their own hearts" (p. x). This situation has prevailed both within the public school and the higher education system. Thus Jane Tompkins, professor of English at Duke University, wrote in 1996, "Higher education, in order to produce the knowledge and skills students need to enter certain lucrative professions, cuts students off from both their inner selves and the world around them" (p. 223).

Of course, this culture has reflected the values of the larger society—those of monetary profit, individualism, and competition. However, the larger world is changing, and if it is to thrive, the education system must change as well. "In today's increasingly individualized and specialized world it is unlikely that any one person possesses enough knowledge and ability for every circumstance" (Dettmer, Thurston, & Dyck, 2002). The forces of globalism, multiculturalism, and multimodalism demand a spirit of cooperation and collaboration that must inevitably demolish the traditional barriers of this culture of isolation—both within and without. Even in the early twentieth century, some thinkers recognized that effective education depends on the freedom of learners to interact with each other and with the world around them (Dewey, 1916). As Palmer says, real learning does not occur until "teacher and learners and subjects" are brought into "vital community with one another" (p. xix).

How Isolation Impacts Learners
The American Dream is founded on the belief that if someone works hard enough he or she can become anything, essentially a self-made success. Each generation believed that their children would be better off than them. As Friedman shares, “We are growing concerned that we are not going to retire as well-off as our parents did, and our kids probably are not going to be as well-off as we were” (Friedman, 301). He theorizes that the world is flattening. With the advances of technology, the world has become a global economy. Americans are not isolated from the rest of the world. If we are to remain competitive, we have to educate our children to be participants in this shrinking world. They must know how collaborate and look at situations from multiple perspectives. These skills can only be developed through cooperative learning and collaborative experiences with other students and teachers. To expect a student to sit at a desk all day and not talk is actually doing them a disservice. We need to help students learn and refine the social skills required to be a contributing member of the global economy. Constructivists contend that it is through social discourse that true learning occurs (Jonassen, 12). No longer should we teach students to “do it by themselves”. In fact, we should encourage them to work with others. Collaboration is emerging as a preferred method to competition in many educational settings. As Jonassen purports, “groups collaboratively build more meaningful knowledge than individuals alone” (Jonassen, 34) It is essential that education no longer isolate learners from other students, teachers, the community or the world.

Another issue of isolation that affects learners is that of teaching content in isolation. Father Guido Sarducci’s Five Minute University video on YouTube demonstrates quite well how little is retained when the information is “given to students” so that they can “give it back” on a test. As this video demonstrates, learning that occurs in isolation results in short term memory gains. Father Guido Sarducci’s belief is that five years after college graduation graduates remember very little of the material they “learned”. It is very easy to laugh at this video because we can all identify with its truths. Research on authentic learning confirms that when students learn in context, such as real-world problem-based learning, long term memory gains are made. Despite the research to support this type of instruction, evidence of its use is not always evident.

High stakes testing adds to the isolation problems encountered by learners today. Subjects are taught according to pacing guides that specify what content is to be covered when. This isolation of discrete units in time robs students of opportunities to thread content and connect big ideas. In a moment of discovery the student might question a topic covered previously (or not yet covered) and the teacher may find he or she is unable to seize the teachable moments because of the isolating effects of the scope and sequence he or she is mandated to follow. High stakes testing also has teachers and students focused on isolating the correct answer. It could be argued that the idea that there is only one right answer to any given problem is an educational step backwards. Duffy and Cunnigham’s text refers to Rorty’s pragmatism (1991) which states “knowledge is not a matter of getting it right but rather of acquiring habits of action for coping with reality” (Duffy & Cunningham, 1). If students are to be educated with a global view of the world then they need to have the flexibility of thinking to look for multiple solutions to a problem.

Isolation of teachers vs collaboration
Teaching is very much a social profession, yet teacher isolation remains a common characteristic in school districts across the nation and is a major cause of teacher attrition (Heider 2005). Twenty-five percent of teachers leave the profession by the end of their first year (Norton, 1999), and as many as forty-six percent of new teachers nationwide leave within the first five years of service (Ingersoll, 2002). New teachers enter a work environment where staff members have been working together for long periods of time and friendships and social groups are already formed. In addition they are often given the most difficult students, the fewest and worst resources and supplies, and left, for the most part, on their own. In response to this problem, many state education associations have developed formal mentoring programs. The most traditional mentoring programs involve the pairing of new teachers with veteran teachers. These mentoring programs, however, tend to have many flaws. New teachers and mentor teachers alike are often so overburdened with demands on their time and their individual work loads that they have little time to meet. In addition, many of the mentors lack training on how to mentor new teachers. Oftentimes the mentors are chosen simply because they have been in the building for the longest period of time. In many cases the general school organization exacerbates the problem. Mentor teachers are sometimes working on a different hall, or wing of the building, in a different grade level, or different subject. The new teacher and his/her mentor may not be given any common planning time. Compounding the problem, new teachers are often uncomfortable or embarrassed to ask for help. They end up feeling frustrated and unsupported. The insolated environment of the classroom prevails.

A focus on using technology solely as an information downloading resource reflects the "isolated teacher" phenomenon. In contrast, focusing on technology's use for collaboration and communication opens the door to creating a new model in which teachers are able to work in a community of educators. Traditionally, Internet technology provided e-mail and list serves, where participants can voice concerns, complaints, and questions and possibly get responses. With Web 2.0 technology, teachers have a world of support at their fingertips. Teachers can network with others around the globe extending the traditional boundaries of teacher collaboration. Web 2.0 technology provides more immediate feedback and greater feelings of support as teachers actively share knowledge and experiences. Web 2.0 technology tends to reduce teacher isolation and increases teacher communication, collaboration, and interdependency (Johnson, et al. 1999). New on-line communities, in the form of Blogs and Wikis exist solely for the voices of teachers. “What is true of Web 2.0 will be true of Teacher 2.0 – dynamic, outward facing, community building, radically democratic, initiatory, active and interventionist; how the Web is changing is how teaching will change (Doyle, 2007)."

Subject Isolation: The Fragmented Curriculum
Though the topic of departmentalization vs. self contained classrooms has been debated since the start of the twentieth century little research exists on the issue. How content should be structured remains a hot topic. Education reform spanning 60 years, however has shown that “students achieve more and are better able to apply their knowledge when they experience collaboratively planned and taught interdisciplinary curricula (Hensen 2006).” Yet, over the years, departmentalization has increased and has filtered down even to the lower grades of elementary schools.

In self contained classrooms the teacher is responsible for all subject areas of the curriculum throughout the school day. In a departmentalized setting, however, teachers specialize in one, or possibly two, subject areas and students move from one teacher to another throughout the school day. Proponents of self contained classrooms state that departmentalization isolates subject areas, guaranteeing less integration, and denies students the opportunity to make connections. Unfortunately, even in self contained classrooms, boundaries often exist around the subject areas. Traditional schooling treats the subjects as separate entities taught in isolation from each other. “Consider, for example, the inability of the present curriculum to deal with even very ordinary cause-effect sequences: automobiles generate exhaust emissions, which contribute to the greenhouse effect, which alters climates, which determine rainfall and growing seasons, affecting water tables and sea levels, and thus the economy and political stability, which essentially determines who lives and who dies. To study that sequence in formal schooling, it is necessary to combine, at the very least, math, geology, chemistry, physics, meteorology, agriculture, economics, and political science (Brady 1996).” State academic standards generally lack cross disciplinary design coherence. Academic standards, however, are not a curriculum, but rather should serve as a framework around which the curriculum is designed. Additionally, teachers tend to teach the standards with a focus on objectives, checking them off one by one as they are taught. Students learn a little bit of everything, but rarely have opportunities to see how it all connects or to understand the interrelatedness of things as they exist in the real world (Brady 1996). Problem-solving strategies with real-world connections would help to bring meaning to subject matter and greatly enhance student learning. Many schools are adopting the UBD design of curriculum writing which involves making connections between broad concepts that overlap all disciplines. UBD uses instructional strategies based on current brain research, the teacher focuses on the learner's understanding of content and the ability to use the information rather than on the memorization of isolated bits of information (Understanding by Design, 2007).

In order to reduce isolation of subject matter and truly integrate curriculum, teachers must make a mental shift from a topical, fact-based curriculum to a concept based curriculum. Topics and facts are related to specific things, people, places, and/or situations. Concepts transfer. For example; ‘the life cycle stages of the butterfly’ and ‘key historical figures in the development of a state’ are topical, factual knowledge. The conceptual, transferable understandings are ‘life cycles ensure the continuation of a species’ and ‘leaders and events can shape the social, economic, and political directions of a nation.’ What are often referred to as the “Big Ideas of Science” are concepts that cut across disciplines, such as change, order, and systems. We as educators are often unaware of the discipline based concepts and therefore cannot structure learning around conceptual relationships that are truly interdisciplinary. To bring coherence to our fragmented curriculum teachers must understand the difference between a topic and a concept, a fact and a generalization. Teachers must then work collaboratively to create relevant curricula that connect students to their world. We must treat our students as “thinkers, seekers of understanding, and creators of knowledge (Erickson, 2007).”This can easily be accomplished with problem-based learning. Problem-based learning is a total approach to education; a learner-centered educational method. It is based on real-world problems. Students use real-life situations to bring meaning to the curriculum and no longer feel that the course work is "isolated" to the classroom. Students come up with problems that interest them and through research become the experts about the topic. By studying the curriculum through project based learning, students become aware of not only the importance of all of the subjects that they study, but they are able to see the relationships between all of the subjects in a meaningful way. Examples of project based learning can be seen all over the United States everywhere from kindergarten through college. Research has shown that project based learning increases student engagement, decreases absenteeism, improves test scores, and increases cooperative learning.

Isolation of information vs Web 2.0 (information sharing)
Before the emergence of the internet, students researching a topic relied mainly on encyclopedias and other texts to locate information. The encyclopedia entries presented a general overview of the topic. If no information was found in the encyclopedia, the learner had to search through card catalogs in hopes of finding a book with information on the topic. After finding a match in the card catalog, it was possible to learn that the book was not available at that time. This process was very time consuming and not always productive. The technologies of today allow individuals to access information from around the world in a matter of seconds. The collaborative nature of Web 2.0 enables learners to easily connect not only to the needed information but to other students, teachers and experts in a given field. This “mediated immersion allows students to actively construct knowledge” and is being used to enrich the educational opportunities provided to students in even the most rural regions (Dede, 7). Students in remote areas are able to engage in Socratic discussions with others through the use of tools such as Wikipedia. With internet access a learner has almost limitless educational possibilities. Traditional education (by the book learning) often centered on instruction that presented one point of view, generally that of the authors or historians. Students rarely had the opportunity to experience different vantage points on a topic such as the Civil War. Technology now enables a topic to be approached from multiple perspectives. Students can search the Library of Congress and examine primary documents from different members of society during the time of the Civil War. They can also listen to speeches and musicians from that period. The use of these tools and the ensuing discussions greatly enhance the development of critical thinking skills in students. The LEAP (Liberal Education and America’s Promise) program’s report names seven principles necessary for education reform. These principals were derived from a national poll of business leaders. Five of the principles relevant to this topic are:

1. Immerse all students in analysis, discovery, problem solving and communication. 2. Engage the big issues. 3. Connect knowledge with choices and action to prepare students for citizenship. 4. Emphasize personal and social responsibility in every field of study. 5. Establish a culture of shared purpose and continuous improvement.

As Friedman states in The World Is Flat, “In the future, how we educate our children may prove to be more important than how much we educate them” (Friedman, 302). Many educators and parents suggest that it is not important to teach today’s youth discreet pieces of information (facts) that could easily be retrieved on the internet. They further caution that information given to students today may be obsolete in the not too distant future. Instead, it is argued that our schools need to teach students to use technology as “Mindtools” to analyze, synthesize, and evaluate the tremendous amount of information available and to construct new knowledge and make informed decisions (Jonassen, 10). The author of A Whole New Mind: Moving from the Information Age to the Conceptual Age summarizes this fundamental shift and what it means to future workers by stating: “If you want to be sure that you are what I call an untouchable (i.e., someone who remains marketable) you need to constantly focus on developing your right-brain skills---such as forging relationships rather than executing trans- actions, tackling novel challenges instead of solving routine problems, and synthesizing the big picture rather than analyzing a single component.” (Pink, 2005) Web 2.0 has great potential to support educators as they work to address the LEAP program's findings and prepare students for an interdependent, global economy.

 * Essay Question(s): What steps can teachers take to counter issues of isolation in their schools and classrooms? What are the benefits of minimizing isolating factors in education today?


text:
User talk:Panic2k4/Books Read

I've just created new page m:b:en:Wikibooks/User:Alexsmail/What to read? So you can see books that I'm going to read their. alexsmail 16:38, 19 May 2007 (UTC)

title: User talk:Panic2k4/Books Read


text:
Logic for Computer Scientists/Propositional Logic/Semantics

Definition 3 (Semantics of propositional logic)
For the semantics of our formal language of propositions we do not refer to a specific intended interpretation. Moreover we only are interested in truth values. We assume an initial assignment of truth values to atomic formulae and based on this, we define the truth value of more complex formulae. The set of truth values is the set $$\{true, false\}$$. An assignment for a set $$D$$ of atomic formulae is a function

$$\mathcal{A} | D $$$$ \to \{true, false\}$$. Let $$E$$ be the set of formulae containing $$D$$, i.e $$E \supseteq D$$ and exactly those formulae which can be  constructed from $$D$$ according to the definition of the syntax. Then the extension of $$\mathcal{A}$$ on $$E$$, $$\mathcal{A}_E | E \to \{true, false\}$$, is given as:

 * $$A \in D$$ : $$ \mathcal{A}_E(A) = \mathcal{A}(A)$$

\begin{cases} \;\;\,true & \text {if } \mathcal{A}_E(F) = true \text { and }  \mathcal{A}_E(G) = true \\ \;\;\,false & otherwise \end{cases} $$ \begin{cases} \;\;\,true & \text {if } \mathcal{A}_E(F) = true \text{ or } \mathcal{A}_E(G) = true \\ \;\;\,false & otherwise \end{cases} $$
 * $$ \mathcal{A}_E((F\land G)) =
 * $$ \mathcal{A}_E((F\lor G)) =

\begin{cases} \;\;\,true & \text {if } \mathcal{A}_E(F) = false \\ \;\;\,false & otherwise \end{cases} $$
 * $$\mathcal{A}_E(\lnot F) =

In the following we will omit the index $$E$$ to indicate the extension of an assignment $$\mathcal{A}$$. Note that this is the right place to name formulae of type $$(F \land G)$$ as conjunctions, formulae of type $$(F \lor G)$$ as disjunctions and formulae of type $$\lnot F$$ as negations.

The following is an example evaluation by means of the definition of $$\mathcal{A}$$: Assume as given $$\mathcal{A}(A) = true,\text { }  \mathcal{A}(B) = true$$  and $$\mathcal{A}(C) = false$$, then

$$\mathcal{A}( \lnot((A\land B) \lor C))$$
 * $$\text{ } =

\begin{cases} \;\;\,true & \text { if }   \mathcal{A}((((A \land B)) \lor C)) = false \\ \;\;\,false & \; otherwise \end{cases}$$
 * $$\text{ }=

\begin{cases} \;\;\,false & \text { if }   \mathcal{A}((((A \land B)) \lor C)) = true \\ \;\;\,true & \; otherwise \end{cases}$$

\text{ }= \begin{cases} \;\;\,false & \text { if }   \mathcal{A}((((A \land B))))= true \text{ or } A(C) = true \\ \;\;\,true & \; otherwise \end{cases}$$

\text{ }= \begin{cases} \;\;\,false & \text{ if }   \mathcal{A}((((A \land B)))) = true \\ \;\;\,true & \; otherwise \end{cases} $$

\text{ }= \begin{cases} \;\;\,false & \text{ if }   \mathcal{A}(A) = true  \text { and }  \mathcal{A}(B)= true\\ \;\;\,true & \; otherwise \end{cases}$$

 * $$\text{ }= false$$

Definition 4
Let $$\mathcal{A}$$ be an assignment and $$F$$ a formula. $$\mathcal{A}$$ is called assignment for $$F$$, if $$\mathcal{A}$$ is defined for every subformula of $$F$$. If $$\mathcal{A}$$ is an assignment for $$F$$ and $$\mathcal{A}(F) = true$$ we call $$\mathcal{A}$$ a model for $$F$$ and we write $$ \mathcal{A} \models F$$ If $$\mathcal{A}$$ is an assignment for $$F$$ and $$\mathcal{A}(F) = false$$, we write $$\mathcal{A} \nvDash F$$.

A formula $$F$$ is called satisfiable, iff there is a model for $$F$$, otherwise $$F$$ is called unsatisfiable. $$ F$$ is called valid (or a tautology) iff every assignment for $$F$$ is a model. We write $$\models F$$ rsp. $$\nvDash F$$.

Theorem 1
A formula $$F$$ is valid, iff $$\lnot F$$ is unsatisfiable.

Proof: $$F$$ is a tautology

iff every assignment for $$F$$ is a model for $$F$$

iff every assignment for $$F$$ (which is of course, also an assignment for $$\lnot F$$) is not a model for $$\lnot F$$

iff $$\lnot F$$ has no model

iff $$\lnot F$$ is unsatisfiable.

Definition 5 (Consequence)
A formula $$G$$ is called a consequence of the formulae $$F_1,\cdots, F_k$$, if for every assignment $$\mathcal{A}$$ for $$G$$ and $$F_1,\cdots, F_k$$ holds: if $$\mathcal{A}$$ is a model for $$F_1, \cdots, F_k$$, then $$\mathcal{A}$$ is a model for $$G$$. We write $$\{F_1, \cdots, F_k\} \models G$$.

The following theorem is a simple consequence from definitions:

Theorem 2
$$G$$ is called a consequence of the formulae $$F_1,\cdots, F_k$$,

iff $$ ((\bigwedge^k_{i=1} ~F_i) \to G)$$ is a tautologie

iff $$ ((\bigwedge^k_{i=1} ~F_i) \land ~\lnot G)$$ is unsatisfiable.

Obviously the validity of a formula depends only of the assignments for its atomic subformulae: If $$\mathcal{A}$$ and $$\mathcal{A}'$$  are assignments for $$F$$ and if they yield the same value for every occurring atomic subformulae, then $$\mathcal{A}(F) = \mathcal{A}'(F)$$ holds. As a consequence we can state, that it suffices for a test of the validity of a formula $$F$$ to check the infinitely many assignments of its atomic subformulae. Such a check can be depicted easily in a tableau of the following form, where $$F$$ is an arbritrary formula, containing $$n$$ distinct atomic formulae $$\mathcal{A}_i$$.

When applying this procedure it might me helpful to introduce intermediate results for subformulae, as done in the following example.

Note that we just have depicted an algorithm to check the validity of a formula. Assume the Formula contains $$n$$ atomic subformulae, then our just constructed tableaux contain $$2^n$$ lines. To estimate the costs for such an exponential algorithm, assume that the computation of one line takes 1 micro-second. Is $$F$$ contains only 100 atomic subformulae the computation of the tableau would take $$2^{100}$$ micro-seconds.

Truth Tables
The problem whether a propositional formula is satisfiable is called SAT and the corresponding tautology problem is called TAUT.

SAT is an NP-complete problem, and hence it is not known whether SAT is tractable or not. Whether TAUT is in NP is still an open problem. For TAUT we know, that it is in NP iff NP is closed under complementation. SAT and TAUT, both, play a prominent role in the study of complexity theory, in particular with respect to the question whether $$P = NP$$.

Problem 1 (Propositional)
Compute truth tables for the following formulae. Decide for each formula whether it is valid (a tautology), satisfiable or unsatisfiable.
 * 1) $$(A \land B) \land (B \to C)$$
 * 2) $$(A \land B) \leftrightarrow (\lnot A \lor \lnot B)$$
 * 3) $$(\lnot A \lor \lnot(\lnot B \lor A)) \lor A$$
 * 4) $$(A \to (B \land C)) \leftrightarrow ((A \to B) \land (A\to C))$$
 * 5) $$(A \lor (B \land A)) \land ((C \lor \lnot C) \to \lnot A)$$
 * 6) $$((C \lor B) \land (C \lor \lnot B))\land\lnot C $$
 * 7) $$\lnot(\lnot A \lor \lnot(\lnot B \lor \lnot A)) $$
 * 8) $$(A \to (B \to A))$$
 * 9) $$(A \lor (B \land A)) \land ((C \lor \lnot C) \to \lnot A)$$
 * 10) $$((A \lor \lnot B) \lor ((\lnot A \land \lnot C) \land B))\leftrightarrow ((A \lor \lnot C) \lor \lnot B)$$
 * 11) $$\lnot(A \land \lnot(B \land \lnot C))$$

Problem 2 (Propositional)
"What is the secret of your long life?" a 100-year old man was asked. He answered: "I apply the following diet rules very strictly: If I drink no wine at dinner then I have always fish. Whenever I take fish and wine for dinner, it is without garlic. If I have garlic or wine I avoid fish"
 * 1) Formalize these rules with the help of propositional logic.
 * 2) Try to simplify the advice of the 100-year old man.

Problem 3 (Propositional)
Define the following functions recursively by induction over the construction of propositional formulae: Note: For
 * 1) $$\alpha(F)$$: Set of atomic formula in $$F$$
 * 2) $$\beta(F)$$: Number of the binary junctors $$\land$$ and $$\lor$$ in $$F$$

$$ F$$ = $$(\lnot(A \lor B) \lor C)$$ $$ \land $$ $$((\lnot A \lor B) \land C) $$ $$\alpha(F) = \{A,B,C\}$$ and $$\beta(F) = 5$$ holds.

Problem 4 (Propositional)
Given the formulae $$F_n $$= $$A_1$$ $$\stackrel{\cdot} \vee \cdots \stackrel{\cdot} \vee A_n$$, in which $$A_1,\dots,A_n$$ are atomic formulae ($$n \geq 1$$) where $$\stackrel{\cdot} \vee$$ denotes exclusive or. Prove for all $$n \in \N$$: A suitable assignment $$\mathcal{A}$$ for  $$F_n$$ is a model for $$F_n$$ (i.e. $$\mathcal{A} \models F_n$$) iff $$ \mathcal{A}(A_i)=1$$ halds for an odd number of $$\mathcal{A}_i$$ ($$1 \leq i \leq n$$).

Problem 5 (Propositional)
In the following we investigate formulae, in which only atoms $$A_1,\dots,A_n$$ occur.
 * 1) How many of such formulae with different truth tables exist at most?
 * 2) Is there for every truth table a formula? If yes, please indicate a construction!

Problem 6 (Propositional)
If the colonel was not in the room during the murder then he cannot know the weapon of the murderer. The butler lies or he knows the murderer. If Lady Barntree is the murderer then the colonel was in the room during the murder or the butler lies. The butler knows the murderer or the colonel was not in the room during the murder. The policeman concludes that Lady Barntree is the murderer. Give propositional variables for every statement of the argumentation. Write the argumentation as a set $$M$$ of propositional formulae of the prerequisites and the conclusion as a propositional formula $$F$$.

Problem 7 (Propositional)
Formalize the following expressions and then simplify the corresponding formulae and the verbal propositions.
 * 1) It is not true that his mother is English and his father French.
 * 2) It is not true that he is studying physics but not mathematics.
 * 3) It is not true that the wages are going down and the prices are going up.
 * 4) It is not true that it is not cold or rainy.

Problem 8 (Propositional)
The professor proposes to make a new conception for the lunch in the University restaurant: Help the management to fulfill the wishes of the professor. For this
 * 1) There must be bread with every lunch if there is no dessert.
 * 2) If bread and dessert are served then is be no soup.
 * 3) If soup is served then there is no bread.
 * 1) formalize the three propositions (as implications, disjunctions/conjunctions) and combine them into one logical formula.
 * 2) Give a truth table for this logical formula. Is there a model for the formula?
 * 3) Give a colloquial verbalization for the assignment.


text:
User:Alexsmail/Scratch

In computer science, object composition (not to be confused with function composition) is a way and practice to combine simple objects or data types into more complex ones. Compositions are a critical building block of many basic data structures, including the tagged union, the linked list, and the binary tree, as well as the object used in object-oriented programming.

Composition is contrasted with subtyping, which is the process of adding detail to a general data type to create a more specific data type. In composition, the composite type "has an" object of a simpler type, while in subtyping, the subtype "is an" instance of its parent type. Composition does not form a subtype but a new type.

A real-world example of composition may be seen in an automobile: the objects wheel, steering wheel, seat, gearbox and engine may have no functionality by themselves, but if you compose them, they may form an automobile object, which has a higher function, greater than the sum of its parts in a trite sense.

Composited (composed) objects are called fields, items, members or attributes, and the resulting composition a structure, storage record, tuple, user-defined type (UDT), or composite type. The terms usually vary across languages. Fields are given a unique name so that each one can be distinguished from the others. Sometimes an issue of ownership arises: when a composition is destroyed, should objects belonging to it be destroyed as well? If not, the case is sometimes called aggregation. For more, see the aggregation section below.

Special:Export

title: User:Alexsmail/Scratch


text:
User:Gert4gt

just here to help improve the site when i can. all the best...

title: User:Gert4gt


text:
Turkish/Computing in Turkish

Typing in Turkish isn't as hard as you think. However, be aware that there are some major differences.

Keyboard layout
Turkish has two different keyboard layouts: Turkish-F and Turkish-Q, both of which are quite commonly used.

Turkish-F
This keyboard layout was designed in 1955 by İhsan Yener. During its design, the Turkish Language Academy (TDK) investigated letter frequencies in Turkish and used this statistical basis to design the Turkish-F keyboard. It provides a balanced distribution of typing effort between the hands - 49% for the left hand and 51% for the right.

Using these keyboard layouts on your computer
You don't have to buy a new keyboard to be able to use these layouts. Below you can find instructions on how to implement these layouts on Windows or MacOSX. Unfortunately information on how to do this on various Linux distros is currently unavailable.

On Windows

 * 1) Click on Start
 * 2) When the Start menu opens up, click on Control Panel
 * 3) * If you are on Category View, click on Date, Time, Language and Regional Options, then Regional and Language Options.
 * 4) * If you are on Classic View, click on Regional and Language Options.
 * 5) Click on the Languages tab.
 * 6) Under Text services and input languages, click on the Details button.
 * 7) Click on the Add button.
 * 8) Here you will find a large list of languages. Choose Turkish, then tick the Keyboard layout/IME tick box. This will enable you to choose from a wide range of different keyboard layouts. Choose either Turkish-F or Turkish-Q (preferably the latter). Then click OK.
 * 9) The Turkish language (and your chosen keyboard layout) has just been added to your list of Installed services. To easily switch between English and Turkish, click on the Language bar... button under Preferences.
 * 10) When that window pops up, tick the following tick boxes:
 * 11) * Show the Language bar on the desktop.
 * 12) * Show text labels on the Language bar.
 * 13) Then click OK.
 * 14) Now that you've done that, click on the OK or Apply buttons to have your changes saved.

On macOS

 * 1) Open “System Preferences” (gears icon)
 * 2) Click on “Language & Region” and add Turkish to your list.
 * 3) Go back to the main menu, and choose “Keyboard”.
 * 4) In the fourth tab, “Input Methods” click the + button and search for Turkish. You’ll see 2 variants of the F-keyboard and 2 variants of the Q keyboard.
 * 5) Select one or multiple, and click “Add”.
 * 6) Close the Window.
 * 7) That's all.  Once you've done this, a little flag ([[Image:Flag_of_the_United States.svg|20px]] for English, [[Image:Flag_of_Turkey.svg|20px]] for Turkish) will appear in the top bar of your screen.  You can use this to change languages, and as a shortcut to your Keyboard settings. Alternatively, use ctrl-space to switch between input methods.

title: Turkish/Computing in Turkish


text:
Talk:The Scientific Method/Components of the Method

I've added a large block about axioms. It should be revised to fit format of the book (I am speaking about math and physics instead of whole science). This block was compiled from History_of_geometry and my own knowledge. alexsmail 19:32, 19 May 2007 (UTC)

The part about axioms is absolute rubbish and needs to be revised.

Calling something which is in itself logical absolutes "based on faith" pretty much speaks for itself. That whoever did the edit is evidently unable to grasp basic logic and hence refers to it as "faith" shows that this person is either 1. trolling, 2. uneducated on the matter, or 3. deliberately trying to dilute the repute of scientific method.

Simpy as that.

Unless someone beats me to it, these portions will be edited.

Thought I was going to correct a couple typos. ..
But it's really more of a mess than I wanted to deal with. Needs a rewrite.


text:
Genetic Information/Probability

History of probability and information

One of the ancient expressions of information dealing with entropy also deals with information and the number of possible outcomes in an event.

The sound eye, udjat, shows it clearly.

Here, for example, is where we find the history of African ways of combining a system of two to a system of three compartments applied by the artists in the graphic form.

Mathematical language shows these expressions, the destroyed parts of Horus' eye, to result into six compartments that exhibit exponential equations of the form: $$y = ac^{bx}$$ often expressed in the West with the Greek symbol : $$\phi(x) = ac^{bx}$$. Where c is the base and in this case equals two. This same c in other useful mathematical expressions can be 10 or more often e as an approximated value of natural logarithm. Why logarithm?

The ancient forms of udjat parts are $$2^{-1}$$, $$2^{-2}$$, $$2^{-3}$$, ... Because the base number 2 is raised to powers, -1, -2, -3... that we call exponents, the exponents are the logarithms and they are here with their bases resulting into fractions of unitary numerators equal to respective probabilities for equally likely outcomes of events exemplified by udjat parts.

The hieroglyph P for this particular event was initially represented in the arts by 64 squares in a grid reference where each small square had a unit area. Of all the 64 squares, the debate was centered on one. The information therefore varied inversely with probability as it does in the modern communications theory. Words such as magic and beauty were employed to mean infinity and outcome. The area study was called seked S from which the integral symbol S in calculus would be derived.

Weighted information of each class since the ancient time has always involved multiplying log (1/P) by probability Pi of the class.

<>

Table of Contents

title: Genetic Information/Probability


text:
Celestia/Snapshots and Movies

Introduction
Under some operating systems, Celestia can create a snapshot, recording its current on-screen display to a file. It also may be able to create a video recording of a sequence of frames while it is running. Other operating systems may require an external screengrab or video recording program.

Linux
Currently video recording from within celestia does not work. A file is created, however it is empty.

Image screenshots work as expected.

MacOS X
Screenshots and movie recording have not yet been implemented in the osX version of Celestia. For the moment you can use system commands to take some screenshots.

Some people have reported that CaptureMe does a reasonable job of recording movies.

Windows
When running the Windows version of Celestia, both snapshots and movies can be created:

 * Select the menu option "File/Capture Image..." or type the  key to record a snapshot of the current view.

 * Select the menu option "File/Capture Movie..." or type  to start recording a movie of what Celestia is showing.

 * Type  to actually start (or pause) the recording.

 * Type  to finish recording.

title: Celestia/Snapshots and Movies


text:
English for B2 Students/Answers

Unit 1 Answers

 * of, of
 * 1) TBC
 * 2) TBC
 * 3) TBC

Unit 2 Answers

 * 1) is smoking
 * 2) am studying
 * 3) have - use present simple to describe possession
 * 4) am meeting - use present continuous to describe future arrangements
 * 5) am having - have here describes an action so we use present continuous

Unit 3 Answers

 * 1) Have you ever eaten - we use present perfect because we mean at any time in your life
 * 2) went - we use past simple because we know when it happened: last year
 * 3) have never seen
 * 4) hasn't eaten - don't forget the third person s with he and she
 * 5) went - we use past simple because the question tells us when: last summer

Unit 4 Answers

 * 1) If I were very rich, I would stay in 5 star hotels.
 * 2) If I go out on Saturday, I will drink red wine.
 * 3) If I hadn't woken up this morning, I wouldn't have learned about conditionals.
 * 4) If I could choose any wife, I would choose Shakira.
 * 5) I will buy a new DVD if I get paid this week.

Unit 5 Answers

 * 1) I'm going - we use going to because it is a plan
 * 2) arrives - we can use present simple when talking about timetabled events
 * 3) will win - we usually use will to talk about predictions
 * 4) will you - for questions about unplanned events use will
 * 5) am going to visit

Unit 6 Answers

 * 1) used to
 * 2) usually
 * 3) used to or no longer
 * 4) usually
 * 5) no longer

Unit 8 Answers

 * 1) The burglars had escaped  when the police arrived.
 * 2) When she  arrived the party had finished.
 * 3) When they got to the hospital she had given birth.
 * 4) Before we came to London we had lived in 10 different cities.
 * 5) He had been on a plane so he was tired.

Unit 9 Answers

 * 1) to live
 * 2) to buy
 * 3) tell
 * 4) going
 * 5) to close

Unit 10 Answers

 * 1) I'm very sorry but you mustn't smoke here.
 * 2) Sir, you have to leave your passport at the reception.
 * 3) My doctor says that I shouldn't smoke.
 * 4) The bus was cancelled so we had to take the taxi.
 * 5) I don't have to go to work on Saturday because the office is closed.

Unit 11 Answers

 * 1) beautiful new striped
 * 2) long curly black

Grammar

 * 1) have travelled
 * 2) am resting
 * 3) [am] eating
 * 4) leaves
 * 5) will have
 * 6) went

Vocabulary

 * of
 * 1) done
 * 2) uncle
 * to
 * 1) ferry
 * 2) would
 * on
 * 1) play truant

title: English for B2 Students/Answers


text:
English for B2 Students/Unit 4

= If I had €1,000,000, I would live in Spain =

Aim of this lesson: Recognize and use the different conditionals in English and revise means of transport.

Speaking Questions
''Talk about these questions with a partner. Try to expand your answers and give reasons rather than short answers.''

 * Where did you go on your last holiday? How did you travel?  Whom did you go with?
 * What is your perfect holiday destination?
 * Do you prefer beach holidays, city breaks, resorts or adventure holidays?
 * Do you pack a lot of things or just the basics like clothes and money?
 * What are the 5 most important tourist places in your country?

Grammar Focus - 1st, 2nd and 3rd conditionals
Conditional sentences are used to talk about possible situations and the result of those situations.

Vocabulary - Travel & Transport
Look at the table below. Do you know the correct definitions for these types of transport? Click on the text for the correct answers.

Speaking with conditional sentences
''Work with a partner, if you can, and ask/answer these questions. If you're on your own you should think about these questions and write your answers instead.''

 * How long would it have taken you to get here if you had walked?
 * How will you get to work if it rains tomorrow?
 * If you were going to take a vacation, where would you go?
 * If you could drive any car you wanted, what would it be?
 * If you had gone to London on holiday last year, what would you have done?

Exercises
Try these questions to see if you can use 1st, 2nd and 3rd conditionals correctly. The answers can be found here.

Complete the following sentences using the correct conditional form:

 * 1) If I were very rich, I _______________ in 5 star hotels (stay).
 * 2) If I _______________ (go out) on Saturday, I will drink red wine.
 * 3) If I hadn't woken up this morning, I _______________ about conditionals (not learn).
 * 4) If I could choose any wife, I _______________ Shakira (choose).
 * 5) I _______________ (buy) a new DVD if I get paid this week.

Grammar Reference
For further information about conditional sentences see ../Tenses and Forms/.

title: English for B2 Students/Unit 4


text:
User talk:72.211.230.149

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.

Xania talk 21:29, 19 May 2007 (UTC)

title: User talk:72.211.230.149


text:
User talk:24.14.126.233

Xania talk 21:45, 19 May 2007 (UTC)

title: User talk:24.14.126.233


text:
User talk:76.195.234.36

Xania talk 22:39, 19 May 2007 (UTC)

title: User talk:76.195.234.36


text:
User:Kfasimpaur

I'm Karen Fasimpaur.

I work in the field of educational technology, working with schools to use mobile technology to improve learning. I have also worked in textbook publishing and software development and have taught school.

I have been looking for a creative (non-work related) project and have also been thinking about contributing more free open content to the world. Now seems like a good time.

Some links:

Kids Open Dictionary

My Open Ed blog

My work-related blog

Wikinomics (a great book)

My sandbox

8/4/08 - The video remix of Wikibooks Animal Alphabet book now has over 10,000 views on TeacherTube!

8/3/08 - We have launched the first Kids Open Dictionary. It is licensed as a public domain resource, and we see it as fundamental building block for many OER projects and hope that it will be used by teachers, students, publishers, hardware manufacturers, VARs, and others.

We just added support for MediaWiki wikitext, and I am eager to create glossaries for a few Wikibooks to see how it works. Stay tuned!

10/20/07 - I love Wikijunior and am constantly amazed by how few people in the educational community know about. I am being bold by taking on some advocacy for this project. To do this, I am sharing information about Wikijunior and Wikibooks as a part of presentations I am making at educational conferences about Open Ed. I would appreciate anyone's feedback on this.

I am also working on creating metadata on some of Wikibooks more mature books for OER Commons. This will then also feed into ccLearn and other repositories. I am hoping that this will help bring more people to Wikijunior to use the resources here and to contribute.

10/19/07 - I'm working on a prototype for a Simple kids dictionary. I'm having a lot of ambivalence about whether to try to put it in Wikijunior or just host it myself. Stay tuned for more on this.

7/6/07 - I've also made some other formats of the Animal Alphabet book (various formats of video and an ebook).

7/12/07 - The following photos are in Wikimedia Commons for possible use in the World of Work book:

6/11/07 - I made this video version of the Wikijunior Alphabet book - Download -

6/10/07 - Recently, I'm doing some work on the Wikijunior Human Body book. I'd like to start a Wikijunior book on Africa at some point.

title: User:Kfasimpaur


text:
Principles of Finance/What is Finance?

What is Finance?
Finance is an imprecise generalization that may encompass several branches of economics, law and general know-how on managing valuable assets. From simple currency and property to bonds and other more complex financial instruments. More specifically, one can state that through financial analysis and decisions, planned actions can be taken regarding the collection and use of those assets as to optimize financial resources toward the objectives of an organization (states, companies and businesses) or individual.

Types of finance:
 * 1) Overdraft
 * 2) Bank term loans
 * 3) Asset-based finance
 * 4) Receivables Finance
 * 5) Invoice discounting
 * 6) Angel funding
 * 7) Venture capital
 * 8) Personal resources

title: Principles of Finance/What is Finance?