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User talk:Merchant85

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Good luck! --Derbeth talk 09:36, 16 May 2007 (UTC)

Image:Diagram of human retina.gif
Why do you copy images from other websites and give false license? There is a clear "(c) Encyclopaedia Britannica" so it is certainly not Creative Commons-licensed. --Derbeth talk 09:36, 16 May 2007 (UTC)

title: User talk:Merchant85


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Horticulture/Agastache

Agastache, or Giant Hyssop, is a genus of 9–12 species of perennial herbs in the family Lamiaceae, native to eastern Asia (one species) and North America (the rest).

Description
Most species are very upright, 0.5–3 m tall, with stiff, angular stems clothed in toothed-edged, lance shaped leaves ranging from 1–15 cm long and 0.5–11 cm broad depending on the species. Upright spikes of tubular, two-lipped flowers develop at the stem tips in summer. The flowers are usually white, pink, mauve, or purple, with the bracts that back the flowers being of the same or a slightly contrasting color.

Growing conditions
They are easily grown in moist, well-drained soil and prefer a sunny position. Winter hardiness varies; the hardiest is A. foeniculum, hardy to USDA hardiness zone 1 in the north of its range; A. nepetoides, A. rugosa, A. scrophulariifolia and A. urticifolia are hardy to zones 3–5 in the northern parts of their ranges.

Propagation
Propagate from seed or cuttings.

Pests and diseases
Agastache is relatively free of pests and diseases, with the exception of powdery mildew, rust, and other fungal pathogens that can affect the leaves during hot, humid weather if air circulation is poor.

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

title: Horticulture/Agastache


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Talk:Horticulture/Agastache

Species list from wikipedia

 * Species
 * Agastache aurantiaca. Mexico, southwestern USA (Arizona, New Mexico).
 * Agastache breviflora. Northern Mexico (Chihuahua, Sonora), southwestern USA (Arizona).
 * Agastache cana. Southwestern USA (New Mexico, western Texas).
 * Agastache foeniculum. Northern North America from arctic Canada south to Colorado and Wisconsin.
 * Agastache mexicana. Central Mexico.
 * Agastache nepetoides. Eastern North America from southern Ontario and southern Quebec south to Georgia.
 * Agastache pallida (syn. A. barberi). Northern Mexico (Chihuahua, Durango, Sonora), southwestern USA (Arizona).
 * Agastache pallidiflora. Southwestern USA (New Mexico, western Texas).
 * Agastache pringlei. Northern Mexico (Chihuahua), southwestern USA (New Mexico).
 * Agastache rugosa. Southeastern Russia (Primoriye), Japan, China, Korea, Taiwan, Vietnam.
 * Agastache rupestris. Arizona, New Mexico.
 * Agastache scrophulariifolia. Eastern North America from southern Ontario south to Georgia.
 * Agastache wrightii. Southwestern USA (Arizona, New Mexico).
 * Agastache urticifolia. Western North America from British Columbia south to California and Nevada.

title: Talk:Horticulture/Agastache


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Applied History of Psychology/Client Centred Therapies - principles, theory, and key figures

Client Centered Therapies - An Introduction
Client-centered therapies belong within humanistic psychology. Carl Rogers is known as the father of client-centered therapy. Partly in response to the psychoanalytic and behavioral schools that emphasized interpretations or manipulations, Rogers developed a non-directive therapy focused on creating a reflective space for individuals to actualize their potential. He later changed the name of this therapy to "person-centred therapy".

In a paper written by Carl Rogers (1979), he reviews briefly the central hypothesis of his person-centred therapy. He suggests that each of us has within us the resources to achieve self-understanding, as well as to alter our self-concept, our basic attitudes, and our self-directed behaviour. Rogers (1979) proposes that these resources can be tapped only within a very specific type of environment that are characterized by what he refers to as facilitative conditions.

According to Rogers (1979), there are three conditions that facilitate this growth: 1) Genuineness/Realness/Congruence; 2) Acceptance/Caring/Unconditional Positive Regard, and 3) Empathic Understanding.

Congruence refers to the therapist being transparent to the client, and not putting up a professional front. It would involve the therapist demonstrating congruence with what they are experiencing at the gut level, what is present in their awareness, and what they are expressing to the client. According to Rogers (1979), the more the therapist demonstrates congruence within the therapeutic environment, the more the client will be likely to change and grow in a positive manner.

Unconditional Positive Regard is the second facilitative condition and involves the therapist being with the client and accepting the client throughout therapy regardless of where they are at, and what feelings they are experiencing. Rogers (1979) believes that the more the client is prized in an unconditional manner, the more the client will be likely to grow and improve.

The final facilitative condition that Rogers (1979) proposed is empathy. The concept of empathy within therapy has been one of the heaviest researched facilitative conditions. Empathy refers to the idea that the therapist is able to capture sensitively and accurately the meaning and personal feelings that the client is experiencing. Additionally, empathy also implies that the therapist is able to successfully relay these feelings and the meaning they hold back to the client. At the very deepest level of empathic understanding, the therapist will not only be able to clarify the meaning of things in which the client is aware, but will also be able to clarify those things that are just below the client's awareness. Rogers (1979) believed that more empathic understanding was associated with greater improvements and growth within the therapy.

Four Waves of Rogers Therapy
The evolution of Roger's therapy/theory has undergone many changes throughout history. Of importance are four main periods in time that were marked by major changes. These changes are mentioned in Corey (2005) briefly, and more fully elaborated and discussed by Zimring and Raskin (1992) and Bozarth, Zimring and Tausch (2002).

During the 1940s, Rogers developed what was known as non-directive counselling. This creation was in response to the traditional directive psychoanalytic approaches of the time. Below is a list of the significance of what was put forth by Rogers in the first wave of his theory:

-emphasized that the therapist create a permissive and nondirective climate.

-challenged the concept that the "counsellor knows best".

-challenged traditional procedures used by many therapists like advice, suggestion, direction, persuasion, teaching, and interpretation.

-challenged the use of diagnostic procedures because he believed that they were often inaccurate, prejudicial, and misused.

-avoided sharing information about himself, and instead focused on reflecting and clarifying the client' verbal/nonverbal communications.

-aim was to gain insight into the feelings expressed by the client.

During the 1950s, Rogers renamed his approach to counselling client-centered therapy. At this time, a very important book was published by Rogers called "Client-centered Therapy" (Rogers, 1951), which began to reflect an emphasis on the client, rather than a therapists use of indirective methods. Of significance during this period was:

-a shift from clarification of feelings to examining instead more heavily the phenomenological world of the client.

-a strong focus on the clients internal frame of reference in order to gain an understanding of how people behave.

-a strong focus on the actualizing tendency, as the basic motivating force that leads to client changes.

Beginning somewhat in the late 1950s, but extending all the way into the 1970s, Rogers began to address what have become known as the necessary and sufficient conditions of therapy. During this time, among other books, Rogers published his nationally recognized book "On Becoming a Person" (1961). Of significance during this time period was:

-his hypothesis that the facilitative conditions were related to psychotherapy improvements. This prediction triggered decades of research in psychology and related fields.

-a strong focus on becoming one's experience was introduced, which involves an openness to experience, a trust in that experience, an internal locus of evaluation, and a willingness to be in process.

-the initial expansion of Rogers' ideas to education occurred and was called student-centered teaching.

The final phase, during the 1980s and 1990s, was marked by great expansion of Rogers' ideas to many facets of life. For this reason, Rogers changed the name of his approach to person-centered therapy. This time in history was of significance because it involved:

-an expansion to education, industry, conflict resolution, administrations.

-an influence on family, health care, and cross-cultural and racial activity.

-an involvement in politics, especially the search for world peace, which led to Rogers being nominated for the Nobel Peace Prize.

To this day, many researchers continue to be influenced by the seminal work conducted by Carl Rogers. To conclude, a list is provided below of current day researchers that have at the root of their work the ideas of Rogers (see Corey, 2005, pp. 183–184).

-Virginia Axline made use of Rogers ideas with children by using what is known as Play Therapy.

-Eugene Gendlin developed a technique known as focusing, in order to facilitate client experiencing within therapy.

-Laura Rice initiated that therapists make use of a technique known as systematic evocative unfolding as a way of recreating and potentially gaining a better understanding of a particular troubling experience.

-Leslie Greenberg from York University, and his colleagues, have encouraged therapists to facilitate emotional change within therapy, and have also applied his emotion focused therapy to couples and families.

-Jeanne Watson from OISE/UT has demonstrated the importance of empathy within therapy, and has encouraged making use of empathy to tap cognitive, affective, and interpersonal issues within therapy.

Carl Rogers

 * 1902 Born in Oak Park Ill.
 * 1924 BA, University of Wisconsin
 * 1928 M.A., Columbia University
 * 1931 Ph.D. Columbia University, Psychotherapy
 * 1940 Ohio State University, Columbus, professor of psychology
 * 1944 President of the American Association for Applied Psychology
 * 1945 University of Chicago, Chicago Ill. Professor psychology and executive secretary of the counselling center.
 * 1946 President of the American Psychological Association
 * 1955 Nicholas Murray Butler Silver Medal
 * 1956 First President of American Academy of Psychotherapist and special contribution award, American Psychological Association
 * 1957 professor in departments of psychology and psychiatry; University of Wisconsin
 * 1960 member of executive committee, University of Wisconsin
 * 1962 Fellow, Center for Advanced Study in the Behavioral Sciences
 * 1964 selected as humanist of the year, American Humanist Association
 * 1968 honorary doctorate, Gonzaga University
 * 1971 D.H.L., University of Santa Clara
 * 1972 Distinguished Professional Contribution Award from APA
 * 1974 D.Sc. university of Cincinnati
 * 1975 D.Ph. University of Hamburg and DS.Sc. University of Leiden
 * 1978 D.Sc. Northwestern University
 * 1984 Union for Experimenting Colleges and Universities, Cincinnati
 * 1987 Died of heart attack, associated with surgery for a broken hip, San Diego, California

from: http://www.muskingum.edu/~psych/psycweb/history/rogers.htm (some corrections made)

Carl Rogers' most famous and influential book was On Becoming a Person

Within this book, Carl Rogers highlights some significant learnings that he had accumulated over the thousands of hours he has spent with individuals in personal distress. These particular learnings are highlighted in a chapter entitled "This is Me". Rogers (1961) reports that these learnings has significance for him (at that point in his life/career), but admits that he is in no way attempting to present these learnings as a guide for anyone else. A brief description of each learning is helpful other to gain a deeper understanding of Carl Rogers, the researcher, the clinician, and the man. Each has been directly quoted from his book "On Becoming a Person" (Rogers, 1961).

1) In my relationships with persons I have found that it does not help, in the long run, to act as though I were something that I am not.

2) I find I am more effective when I can listen acceptantly to myself, and can be myself.

3) I have found it of enormous value when I can permit myself to understand another person.

4) I have found it enriching to open channels whereby others can communicate their feelings, their private perceptual worlds, to me.

5) I have found it highly rewarding when I can accept another person.

6) The more I am open to the realities in me and in the other person, the less do I find myself wishing to rush into "fix things".

7) I can trust my experience.

8) Evaluation for others is not a guide for me.

9) Experience is, for me, the highest authority.

10) I enjoy the discovering of order in experience.

11) The facts are friendly.

12) What is most personal is most general.

13) It has been my experience that persons have a basically positive direction.

14) Life, at its best, is a flowing, changing, process by which nothing is fixed.

Rogers describes these learnings as incomplete, scattered, and continuously changing. He also reports that he continues to learn and relearn them, and at times forgets to apply them. However, he mentions they are all of great importance to him and have become a large part of his inner values and ways of behaving.


text:
User talk:88.105.255.174

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 12:15, 16 May 2007 (UTC)

title: User talk:88.105.255.174


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User:Shreyasjoshis

Weedrat

title: User:Shreyasjoshis


text:
Horticulture/Rosmarinus officinalis

Rosemary (Rosmarinus officinalis) is a woody, perennial herb with fragrant evergreen needle-like leaves. It is native to the Mediterranean region and in Uruguay. It is a member of the mint family Lamiaceae, which also includes many other herbs. The name derives from the Latin name rosmarinus, meaning "dew of the sea".

Description
Forms range from upright to trailing; the upright forms can reach 1.5 m tall, rarely 2 m. The leaves are evergreen, 2-4 cm long and 2-5 mm broad, green above, and white below with dense short woolly hairs. The flowers are variable in color, being white, pink, purple, or blue.

Growing conditions
Well-drained soils in full sun. Grows well in containers.

Varieties

 * 'Albus': white flowers
 * 'Arp': leaves light green, lemon-scented
 * 'Aureus': leaves speckled yellow
 * 'Benenden Blue': leaves narrow, dark green
 * 'Blue Boy': dwarf, small leaves
 * 'Golden Rain': leaves green, with yellow streaks
 * 'Irene': lax, trailing
 * 'Lockwood de Forest': procumbent selection from 'Tuscan Blue'
 * 'Ken Taylor': shrubby
 * 'Majorica Pink': pink flowers
 * 'Miss Jessop's Upright': tall, erect
 * 'Pinkie': pink flowers
 * 'Prostratus'
 * 'Pyramidalis' (a.k.a 'Erectus'): pale blue flowers
 * 'Roseus': pink flowers
 * 'Severn Sea': spreading, with arching branches; flowers deep violet
 * 'Tuscan Blue': upright

Uses
The fresh and dried leaves are used frequently in traditional Mediterranean cuisine as an herb; they have a bitter, astringent taste, which complements oily foods, such as lamb and oily fish. A tisane can also be made from them. They are extensively used in cooking, and when burned gives off a distinct mustard smell, which can be used to flavor foods while barbecueing.

Since it is attractive and tolerates some degree of drought, it is also used in landscaping, especially in areas having a Mediterranean climate. It can in fact die in over-watered soil, but is otherwise quite easy to grow for beginner gardeners. It is very pest-resistant.

Rosemary is easily pruned into shapes and has been used for topiary. When grown in pots, it is best kept trimmed to stop it getting too straggly and unsightly, though when grown in a garden, rosemary can grow quite large and still be attractive. It can be propagated from an existing plant by clipping a shoot 10-15 cm long, stripping a few leaves from the bottom, and planting it directly into soil.

Rosemary is a useful food preservative, according to research published in 1987 by Rutgers University, New Jersey. Researchers at Rutgers patented a chemical derived from rosemary that compares favorably with BHA and BHT in its preservative properties.

Rosemary can be added as an unusual extra flavoring in lemonade.

Medicinal uses
Rosemary has been found to be a stimulant and mild analgesic, and has been used to treat headaches, poor circulation, and many ailments for which stimulants are prescribed.

It can be used as a disinfectant, as a mouth wash and to treat fever or rheumatism.

Externally it can be used in hair lotions; a few drops of Rosemary oil massaged into the scalp, then rinsed with an infusion of nettles can revitalize the hair. Used in this manner, it is supposed to prevent premature baldness. Rosemary is also reported to stop dandruff.

Hungary water was first invented for a Queen of Hungary to 'renovate vitality of paralysed limbs'. It was used externally and prepared by mixing 180g of fresh rosemary tops in full flower into a liter of fresh rosemary tops in full flower into a liter of spirits of wine. Leave to stand for four days then distill. It is also supposed to work as a remedy against gout if rubbed vigorously on hands and feet.

Rosemary has a very old reputation for improving memory, and has been used as a symbol for remembrance (during weddings, war commemorations and funerals) in Europe, probably as a result of this reputation. Students in ancient Greece are reported to have worn sprigs of rosemary in their hair while studying for exams to improve their memory, and mourners would throw it into graves as a symbol of remembrance for the dead. In Shakespeare's Hamlet, Ophelia says, "There's rosemary, that's for remembrance".

Rosemary and its constituents carnosol and ursolic acid have been shown to inhibit the growth of skin tumors and to provide a natural anti-oxidant protection against skin cancer and photodamage.

Health Precautions: In some cases, rosemary can cause autoimmune diseases. Rosemary in culinary or therapeutic doses is generally safe, however precaution is necessary for those displaying allergic reaction, or those prone to epileptic seizure. Rosemary essential oil is a powerful convulsant; if applied to the skin, it may cause seizures in otherwise healthy adults or children. Rosemary essential oil is potentially toxic if ingested. Large quantities of rosemary leaves can cause adverse reactions, such as coma, spasm, vomiting, and pulmonary edema (fluid in the lungs) that can be fatal. Avoid consuming large quantities of rosemary if pregnant or breastfeeding.

Maintenance
Cut flowers off to encourage more leaf production. In hardiness zones below 7, the plant should be brought indoors in winter.

Propagation
Most commonly propagated via stem cuttings.

Harvesting
Cut leafy stems (removing flowers, if present). Dry by hanging upside down in a dark area.

title: Horticulture/Rosmarinus officinalis


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Logic for Computer Scientists/Induction

Induction
Induction plays a crucial role at least in two aspect throughout this book. Firstly, it is one of main proof principles in mathematics and of course in logics. In particular it can be used to investigate properties of infinite sets. Very often it is used as natural induction, namely over the natural numbers. We will introduce it as a more general principle over well founded partial orders, which is called structural induction. The second aspect is, that it can be used as well to define infinite structures, as the set of well formed formulae in a particular logic or the set of binary trees.

We start with a very general structure over arbitrary sets, namely partial orders. A relation $$R$$ over $$A$$ is a partial order iff $$R$$ is reflexive, transitive and anti-symmetric (i.e. $$ ((x,y)\in R \land (y,x)\in R \Rightarrow x=y)$$). Partial ordered sets (p.o. sets) $$A$$ are usually written as $$ (A, \leq)$$.

Definition 1
The necessary structure for our induction principle is a partial order, such that there exist minimal elements. Given a p.o. set $$(A, \leq)$$, we define:
 * $$ x < y $$ iff $$x \leq y$$ and $$x\neq y$$.
 * $$(A, \leq)$$ is called well-founded iff there is no infinite sequence $$ (x_i)_{i\in N}$$ and $$ x_{i+1} < x_i, \forall i \geq 0$$.
 * $$X\subseteq A$$ is called a chain iff $$\forall x,y \in X : x\leq y$$ or $$y\leq x$$
 * $$(A, \leq)$$ is a total ordering iff $$A$$ is a chain.

Lemma 1
$$(A, \leq)$$ is well-founded, if every non-empty subset of $$A$$ has a minimal Element. Proof can be done by contradiction and will be given as an exercise.

We finally have the machinery to introduce the principle of complete induction:

Definition 2 (Complete (structural) induction)
Given a well-founded p.o. set $$(A, \leq)$$ and a predicate $$P$$, i.e. $$P : A \to \{true, false \}$$. The principle of induction is given by the following (second order) formula $$ \forall x \in A\; ( \forall y \in A\; ( y <x \Rightarrow P(y)) \Rightarrow P(x)) \Rightarrow \forall z \in A\; P(z) $$

Lemma 2
The induction principle holds for every well-founded set.

Proof: The proof is given by contradiction: Assume the principle is wrong; i.e. the implication is wrong, which means, that we have to assume the premise as true: $$\begin{matrix} \forall x \in A\; ( \forall y \in A\; ( y <x \Rightarrow P(y)) \Rightarrow P(x)) \equiv{true} (premise) \end{matrix}$$ and the conclusion as wrong: $$\begin{matrix} \forall z \in A\; (P(z)) \equiv =false= (conclusion) \end{matrix}$$ Hence we can assume that the set $$X = \{ x \in A \mid P(x) = false\} $$ is not empty. Since $$X$$ is a subset of a well-founded set, it has a minimal element, say $$b$$. From assumption (premise) we conclude $$\begin{matrix} (\forall y \in A\; ( y < b \Rightarrow P(y)) \Rightarrow P(b)) \equiv{true} (inst) \end{matrix}$$ Now we can distinguish two cases:
 * $$b$$ is minimal in $$A$$: Hence there is no $$y \in A$$, such that $$y < b$$.  Hence the premise  $$\forall y \in A\; ( y < b \Rightarrow P(y))$$ of the implication in  (inst) is true, which implies that the conclusion $$P(b)$$ is true. This is a contradiction to the assumption that $$b \in X$$!
 * $$b$$ is not minimal in $$A$$:  $$ \forall y \in A\; (y <b)$$ holds and it must be that $$P(y)$$ is true, because otherwise it would be that $$y\in X$$  and $$b$$ not minimal in $$X$$. Hence, again the premise  $$\forall y \in A\; ( y < b \Rightarrow P(y))$$ of the implication in  (inst) is true, which implies that the conclusion $$P(b)$$ is true. This is a contradiction to the assumption that $$b \in X$$!

An Example
In this subsection we will carry out a proof with induction in detail. For this we need the extension of p.O. sets:

Definition 3 (Lexicographic Ordering)
A p.O. set $$(A,\leq)$$ induces an ordering $$\ll$$ over $$A\times A$$: $$ \forall x,y,x\prime,y\prime \in A : (x, y) \ll (x\prime, y\prime)$$  iff
 * $$ x= x\prime$$ and $$y = y \prime$$ or
 * $$ x < x\prime$$ or
 * $$ x= x\prime $$ and $$y<y\prime $$

Lemma 3
If $$(A,\leq)$$ is a well-founded set, then $$(A\times A, \ll)$$ is well-founded as well.

Theorem 1
The Ackermann-function $$ACK$$ defined by the following recursion is a total function over $$N \times N$$

ACK(x,y) = if x=0 then y+1 else if y=0 then ACK(x-1,1) else ACK(x-1,ACK(x, y-1))

Proof: For the induction start we take the minimal element $$(0,0)$$ of the well-founded set, $$(N \times N, \ll)$$, where $$ \ll$$ is the lexicographic ordering induced by $$(N, \leq )$$. Hence, assume $$x=0, y=0$$. By definition of $$ACK$$, we conclude $$ACK(0,0)=1$$ and hence defined. Assume for an an arbitrary $$(m,n)$$, that $$ ACK(m', n')$$ is defined for all $$(m'. n') \ll (m,n)$$, if $$ (m,n) \neq (m',n') $$

We distinguish the following cases: Altogether we proved, that $$ACK(x,y)$$ is defined for all $$x,y \geq 0$$.
 * $$m=0$$: i.e. $$ACK(0,n) = n+1$$ and  hence defined.
 * $$m\neq0$$ and $$n=0$$: We know that $$(m-1,1) \ll (m,0)$$ and  $$(m-1,1) \neq (m,0)$$. From the induction hypothesis we know that $$ACK(m-1,1)$$ is defined, and hence $$ACK(m,0) = ACK(m-1,1)$$ as   well.
 * $$m\neq0$$ and $$n\neq 0$$: According to the definition of $$ACK$$ we have two cases to consider:
 * $$(m,n-1) \ll (m,n)$$ and $$(m,n-1) \neq (m,n)$$: From the      induction hypothesis we conclude immediately that $$ACK(m,n-1)$$ is defined.
 * $$(m-1,y) \ll (m,z)$$ and $$(m-1,y) \neq (m,z)$$: Independent      from the values of $$x$$ and $$y$$. If we assume $$y 'ACK(m,n-1)$$ and $$z=n$$, we again can conclude from the hypothesis, that $$ACK(m-1, ACK(m, n-1))$$ is defined and hence $$ACK(m,n)$$ as well

Problem 1 (Induction)
Prove the following lemma: If $$(A,\leq)$$ is well founded also $$(A \times A,\ll)$$.

Note: The lexicographical Order $$(A \times A,\ll)$$ is defined as follows: $$ (m,n) \ll (m',n') \iff \big( m<m' \lor (m=m' \land n \leq n') \big) $$

Problem 2 (Induction)
How many points of intersection could $$n$$ straight lines have at most? Find a recursive and explicit formula and show

Problem 3 (Induction)
Prove that a number $$x$$ is even if and only if $$x^2$$ is even.

Problem 4 (Induction)
Point by an indirect proof that there is not any greatest prime number!

Problem 5 (Induction)
Which prerequisite do you need that the following order

$$(\{A,\,B,\,C,\,0,\,1,\,2\},\leq)$$ is
 * 1) partial ordered
 * 2) total ordered
 * 3) well-founded?

Problem 6 (Induction)
An example of a well founded set is the power set $$P(M)$$ over a finite set $$M$$ which is comparable over the relation of the subset $$\subseteq$$. If $$M=\{1,\, 2,\, 3\}$$ then is e.g. $${1}\subseteq \{1,\, 2,\, 3\}$$ but $$\{1,\, 2\}$$ and $$\{2,\, 3\}$$ are not comparable. Give a definition of a relation $$B$$ in this way that $$( P(M),\, B )$$ is total ordered and well founded.

Problem 7 (Induction)
Examine which of the following partial order are total and which are well founded!
 * 1) $$(2^{\N},\subseteq)$$ with $$2^{\N}$$ is the power set for natural numbers.
 * 2) $$(\N,|)$$ with $$|$$ marks the relation "`is factor of"'.
 * 3) $$(\N\times\N,\ll)$$ with $$(m,n) \ll (m',n')$$ iff $$m<m'$$ or ($$m=m'$$ and $$n \leq n'$$).
 * 4) $$(\N^*,\preceq)$$ with $$\preceq$$ is the lexicographical.
 * 5) for $$\N^*$$, i.e. $$1 \prec 1.1 \prec 3 \prec 3.3.8$$

Problem 8 (Induction)
Give for the natural numbers $$\N$$ an order relation, that is
 * 1) both well-founded and total,
 * 2) total but not well-founded,
 * 3) well-founded but not total and
 * 4) neither well-founded nor total.

Problem 9 (Induction)
Prove, that a partial order $$(A,\leq)$$ is well-founded iff every non-empty partial set of $$A$$ (at least) contains a minimum element.

Problem 10 (Induction)
A root tree consists (a) of a single node or (b) of a node - that's the root of the tree - and at least one, but only at most finite many (part)trees, this one is bandaged over an edge with the root. Point formally by means of induction, that in every tree the number of the nodes $$n$$ around $$1$$ is taller than the number of the edges $$e$$, i.e. $$e = n-1$$.

Problem 11 (Induction)
Prove: If ε is a quality of the natural numbers $$\N$$ and it is valid then $$ \forall n \in \N$$ : ε(n) is valid.
 * 1) ε(0) and
 * 2) $$ \forall n \in \N$$ : [ε(n) $$\Rightarrow$$ ε(n+1)].

Note: The proof can be done by the fact that the principle of the complete induction in $$\N$$ (which should be proved) can be reduced to the principle of the transfinite induction for well founded orders.

title: Logic for Computer Scientists/Induction


text:
Statistical Analysis: an Introduction using R/Appendix

Online resources
See http://www.r-project.org/, in particular http://www.r-project.org/other-docs.html and http://wiki.r-project.org/.

Books
See http://www.r-project.org/doc/bib/R-books.html


text:
User talk:216.48.136.5

Thanks for experimenting with Wikibooks. Your test worked, and has now been removed. Please use Sandbox for any other tests you want to do, since testing material in modules will normally be removed quickly. Please see the welcome page if you would like to learn more about contributing to our project. Thanks. -- Herby talk thyme 13:38, 16 May 2007 (UTC)

title: User talk:216.48.136.5


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A-level Biology/Biology Foundation/biological molecules

Carbon, hydrogen, oxygen and nitrogen are the four most abundant elements in living organisms, and account for more than 99% of atoms found in living things. Carbon is present in all organic molecules and carbon atoms can join together to form chains or ring structures.

Polymers and Macromolecules

Macro refers to something that is large, and so macromolecules simply means large molecules, and there are only three types - polysaccharides, proteins (polypeptides) and nucleic acids (polynucleotides) (poly means 'many'). Macromolecules are such because they are made of many repeating subunits that are connected to each other.

=Carbohydrates=

All carbohydrates contain carbon, hydrogen and oxygen, and have hydrogen to oxygen present in the ratio 2:1 respectively.

Monosaccharides
Monosaccharides are sugars and are soluble - meaning that they dissolve in water, forming sweet solutions. Mono refers to one and saccharide means sugar - so monosaccharide means single sugar. Monosaccharides are classified according to the number of carbon atoms in each molecule - trioses (3 carbons), pentoses (5 carbons) and hexoses (6 carbons).

The structure of the most common monosaccharide, glucose, in both the alpha (on the left) and beta (on the right) isomer (two forms of the same chemical are known as isomers):.

An important note on the structure of both pentoses and hexoses is that the chain of carbon atoms is long enough to close up on itself and form a stable ring structure, as seen in the picture above.

 Roles of Monosaccharides

Simple sugars, such as glucose, are often used in biological organisms as a source of energy for respiration - the carbon hydrogen bonds within them are easily broken down to release a great deal of energy which in turn helps make ATP from ADP and phosphate. Secondly, monosaccharides can be used as building blocks for larger molecules (polysaccharides).

 Glycosidic bonds

If you look at the above image of glucose, you'll see a hydroxl (-OH) group on the top right of the image, highlighted in red. When two glucose molecules come together, the two hydroxyl groups line up alongside each other: one combines with a hydrogen atom from the other to form water, in turn forming an oxygen bridge across the two molecules, bonding them and creating a disaccharide- this bond is called a glycosidic bond. The reaction is known as condensation, and the reverse reaction - the addition of water is a hydrolysis reaction, which breaks down di/polysaccharides into their original monosaccharides.

Formation of a glycosidic bond:

Polysaccharides
As we saw before, monosaccharides joined by glycosidic bonds in condensation reaction become disaccharides, but if more than two monosaccharides are joined together it is known as a polysaccharide. It is important to note that polysaccharides are not sugars and examples of polysaccharides include starch, glycogen and cellulose, all polysaccharides made from glucose.

The reason glucose is converted into these polysaccharides is storage - left free in cells, glucose will dissolve and affect the osmotic potential of the cell, making it too concentrated. A condensation reaction to convert it to a polysaccharide (compact, inert and insoluble) - and when glucose is required again, the storage molecule (starch in plants, glycogen in animals) can be quickly hydrolysed in an enzyme controlled reaction.

 Animal Storage Molecules

Glycogen is the primary storage molecule in animals. Glycogen, as you can see in the above picture, is made of many 1,4 linked alpha-glucose molecules (1,4 linked means that they are linked by carbon atoms of 1 & 4 of successive glucose units). These chains branch out to the side, and the branches are formed by 1,6 linkages. The chains also coil up into helical structures, making their final structure more compact (useful for storage).

 Plant Storage Molecules

Starch is a mixture of two substances, amylose and amylopectin. Amylopectin is very similar to glycogen in that it is made of many 1,4 linked alpha-glucose molecules, and branches via 1,6 linkages - the main difference is that amylopectin branches less than glycogen. Amylose, on the other hand is a very long, unbranching chain of several thousand 1,4 linked glucose molecules, and as in glycogen and amylopectin, these chains curve to coil up into helical structures for compactness. Amylose chains are usually longer than amylopectin.

Cellulose is the other important polysaccharide - and is the most abundant organic molecule on earth. This is partially due to its structural role in cell walls and partially due to its slow rate of breakdown. The main difference between cellulose and the other two storage molecules you've seen is that cellulose is a polymer of beta-glucose, whereas the other two are from alpha-glucose. If you remember, the two isomers of glucose are different only in their location of the -OH and -HO group, on carbon atoms 1 and 4, respectively. See this picture for more details. This means that to form glycosidic bonds, subsequent glucose molecules must be at 180degrees to each other, or in other words, each must be upside down to the other to allow the -OH and -HO groups to bond. You can see the molecular structure of cellulose here:

These bonds result in a strong molecules because the hydrogen atoms form hydrogen bonds with oxygen atoms in the same glucose molecule and other neighboring glucose molecules. While these hydrogen bonds are individually weak, due to the large numbers of -OH groups, collectively they develop massive strength. Also, between 60-70 cellulose molecules become tightly cross linked to form bundles called microfibrils, which are in turn held together in bundles called fibres by further hydrogen bonding, making the entire structure even stronger.

 Cellulose in Cell Walls

Cellulose comprises around 20-40% of the average cell wall, with other molecules helping to crosslink the cellulose fibres. This is because cellulose fibres have a tensile strength almost equivalent to that of steel, meaning that it is very difficult to break cellulose, and this very strong cell wall is what allows plant cells to withstand large osmotic pressures - without it, the cell would burst when in a dilute solution. This allowance for high pressures help provide support for the plant by making the tissues rigid and are responsible for cell expansion during growth. Despite all the strength that cellulose has, it is also (very usefully), freely permeable.

=Lipids=

The most common type of lipids that you'll be expected to know about are triglycerides, usually known as fats and oils.

Triglycerides
All triglycerides are made from a glycerol 'head' and 3 fatty acid 'tails'. Glycerol is a type of alcohol. The fatty acids are organic molecules and all have a -COOH group attached to a hydrocarbon tail. Fatty acids are attached to glycerol by a condensation reaction.

One of their important properties is that they are insoluble in water - but soluble in certain organic solvents, including ether, ethanol and chloroform. This is because of the hydrocarbon tails of the fatty acids - which basically means that the tail is only carbon combined with hydrogen, creating no uneven distribution of electrical charge (unlike water molecules, which are polar). This means that they cannot mix freely with water molecules, and so are hydrophobic and non-polar.

Their roles are usually as fantastic energy reserves - as you'll see in the coming paragraphs they are incredibly rich in carbon-hydrogen bonds ready to be oxidised for energy. The same mass of lipid will have more energy than the same mass of carbohydrate. Fat also provides buoyancy in the form of blubber for sea mammals - whilst providing insulation, as it does for all mammals. They can also, in unusual circumstances be used as a metabolic source of water - oxidising them for energy converts them to carbon dioxide and then water. This is useful for animals living in the desert that do not have much or any water.

Saturated and Unsaturated
Unsaturated fatty acids are known as such as due to the kink (see picture) caused by the C-C=C-C bond (the C=C part is important), that it does not contain the maximum possible amount of hydrogen, and these form unsaturated lipids. The double bond (C=C) makes the fatty acid melt more easy, for example, most oils are unsaturated (and are usually liquid at room temperature) - it also makes them easier to digest. More than one kink is known as polyunsaturated, one kink is monounsaturated.

Saturated fatty acids on the other hand,, as you can see in the picture, contain the maximum amount of hydrocarbons and have no kinks.

Animal lipids are usually saturated and thus are fats, whereas plant lipids are usually unsaturated, for example olive oil and sunflower oil - usually oils.

Phospholipids
These are a special type of lipid, usually found in the plasma membrane of cells (see Chapter 1, among others). Each molecule has one end that is soluble in water, and the other which is not. This is because one of the fatty acids is replaced by a phosphate group which is polar and can dissolve in water - making it hydrophilic. The two remaining tails are still hydrophobic but the head is hydrophilic.

=Proteins=

Overview

Proteins have many important functions within organisms - and more than 50% of dry mass of most cells is protein. Their functions can include;

 * All enzymes are proteins
 * Antibodies are proteins
 * Essential component of cell membranes (glycoproteins, transport proteins etc.)
 * Structural support in the form of collagen

Amino Acids
Despite the range of functions listed above (which is by no means exhaustive), all proteins are made from only 20 different amino acids. All amino acids have the same basic structure - a central carbon atom which is bonded to an 'amine' group, -NH2 (on the left in the picture), and a carboxylic acid group, -COOH (on the right in the picture. The third bond to the carbon group is always a hydrogen atom (in purple). The remaining 'R' group, in yellow, is the fourth and variable group of atoms bonded to the central carbon. This is what makes amino acids differ from each other - and it is these R groups that change the shape of protein molecules and thus their functions. See picture:

The Peptide Bond
A peptide bond is one that is formed after two amino acids join each other in a condensation reaction - one loses a hydroxyl group from the carboxylic acid group (see above picture), which leaves free the carbon atom from the first amino acid to bond with the nitrogen atom of the second - the peptide bond. This molecule is now known as a dipeptide - but can be expanded upoun with additional condensation reactions to form a polypeptide.

Structure
Primary

The primary structure of a protein simply refers to the type of amino acids in the polypeptide chains and the sequence in which they are joined. As you can guess, with 20 different amino acids, and many many different combination, there are many different possible primary structures.

Secondary

The secondary structure of a protein is the effect that amino acids have on a polypeptide chain even if they are not directly next to each other, for example the α-helix we saw earlier, that is due to the attraction of the oxygen of the -CO group of one amino acid and the hydrogen of the -NH group of the amino acid anywhere else in the chain, forming a hydrogen bond. Another shape is the β-pleated sheet, which is a looser, but straighter shape. Sometimes there is no regular arrangement - it depends on the amino acids present.

Tertiary

The tertiary structure of a protein is the way in which a protein coils up to form a precise 3D shape. This can be because of the hydrogen bonds after the coiling or folding in the secondary structures, but other bonds such as a disulphide bonds can form between cysteine amino acids. Ionic bonds occur between positive and negatively charged 'R' groups. Hydrophobic parts of the polypeptide situate themselves in the centre of the polypeptide chain (away from water) and hydrophilic parts of the polypeptire situate themselves on the outside of the polypeptide chain (next to water). All affecting the tertiary structure of the polypeptide.

Quaternary

The quaternary structure is known as the association of different polypeptide chains within one protein. The same bonds as in the tertiary structure hold together the different polypeptide chains (hydrogen bonds, disulfide bridges and ionic bonds). Two examples of a proteins with a quaternary structure are haemoglobin and collagen.

Globular and Fibrous Proteins
A globular protein is simply one that appears to curl up into a ball - this is usually so that the proteins non-polar, hydrophobic R groups point into the centre of the molecule, making them water soluble, since water clusters around their outward facing hydrophilic groups, but water cannot get into the molecule. Enzymes are always globular proteins and thus globular proteins are involved in metabolic reactions. However, proteins that do not curl up into a ball, but form long strands are known as fibrous proteins, and are mostly insoluble. Keratin and collagen are examples of this.

Haemoglobin
An example of a globular protein that you must know about is haemoglobin. It is a pigment that carries oxygen and is found in red blood cells. It has four poly peptide chains, two α chains, two β chains, and is almost spherical. Each polypeptide chain contains a haem group, and is important and permanent part of a protein molecule that is not made of amino acids and is known as the prosthetic group. Each of these haem group contains an iron ion, Fe2+, and one oxygen molecule can bind with each iron ion. A complete haemoglobin molecule has four haem groups, and thus can carry four oxygen molecules at a time. The haem group is also responsible for the colour of haemoglobin - if haemoglobin is combined with oxygen (oxyhaemoglobin), it is bright red, else it is purple.

As with all globular proteins, the hydrophilic R groups pointing out maintain it's solubility in water - however this can be affect by a disease known as sickle cell anaemia. In this case, one amino acid of one of the β polypeptide chains, in a hydrophilic section is replaced which a different amino acid, the original being a polar amino acid, the replacement being non-polar. As you will see in the water section, this will cause problems. It makes haemoglobin much less soluble, and is unpleasant and dangerous in anyone whose haemoglobin is all of this faulty type.

Collagen
As previously mentioned, collagen is a fibrous protein that is found in skin, tendons, bones, teeth, cartilage and importantly in the walls of blood vessels and it is a generally important structural protein in many animals. The reason collagen is so strong is that it consists of three polypeptide chain, each in the shape of a helix, wound together to form a three stranded 'rope'. Nearly every amino acid in the chain is glycine, which is small, and allows the three strands to lie close together and form a tight coil, and hydrogen bonds bond the strands.

The cross-links between the collagen(the complete 3 stranded collagen molecule) form fibres, providing it with tremendous tensile strength (withstanding large pulling forces).

=Water=

Water is a major component of every cell, usually forming 70-95% of the mass of the cell, and the human body is around 60% water. If it were not for it being a dipole (see 'Dipoles and Hydrogen Bonds' below), water would be a gas at normal earth temperatures.

Solvency
Water is a good solvent for polar molecules and ions, because water collects around their hydrophilic edges and separates them. This is what happens in the process of dissolving - and so the chemical is free to move about and react with other chemicals within water. Non-polar molecules are insoluble in water and are pushed together by water if surrounded by it, for example, lipids.

It's solvency is also useful when water is used as a transport medium - in the blood, lymphatic, excretory and digestive systems of animals, and in the vascular tissues of plants.

Thermal Properties
The hydrogen bonds formed within water mean that it requires a relatively large amount of energy to change the temperature of water, meaning that large bodies of water are slow to change temperature and as a result are more stable habitats. This is useful in the animal body as there is a high proportion of water, and so a stable body temperature is easier to attain. Also useful in the body is that the process of evaporation transfers a large amount of energy and this is why sweating is effective in cooling the body.

A large amount of energy is required to convert water to ice and thus water is less likely to freeze. Also, ice less dense than water and thus when parts of a river, for example, freeze - the ice floats to the top and acts as an insulator for the rest of the water. This means that aquatic organisms can still survive since the whole river is unlikely to freeze.

Cohesion
Water molecules, partially because of their polarity, have a tendency to stick together, a property known as cohesion. This provides a high surface tension which allows very light animals to use the surface of the water as a habitat. It also means that water can move in long unbroken columns through vascular tissue in plants and is an important property in cells.

Dipoles and Hydrogen Bonds
Atoms in molecules are held together because they share electrons with each other. A shared pair of electrons forms a covalent bond - for example in a water molecule, two hydrogen atoms each share a pair of electrons with an oxygen atom. however, as this picture shows, there is an uneven distribution of charge, with oxygen getting more than its fair share and receiving a small negative charge, and both of the hydrogen atoms receiving less than their fair share, resulting in a positive charge.

This uneven distribution of charge is called a dipole. In water, the negative charges of the oxygen is attracted to the positive charges of the hydrogen atoms, and the attraction is called a hydrogen bond - weaker than a covalent bond but enough to have a significant effect. Molecules with dipole groups (-OH, -C=0 or >N-H), are known as polar as they are attracted to water molecules (since water is also a dipole molecule). These polar molecules are hydrophilic and tend to be soluble in water. Those molecules that are non-polar are not attracted to water and are hydrophobic.

= Additional =

Information that does not fit into the other sections, or is best grouped.

Food Tests
These are the important food tests - tests that tell you whether certain molecules are present in solutions.

An additional note regarding benedict's test - it requires excess benedicts reagent to react with all the present sugar. For the non-reducing sugar test, the reason the sugar solution is heated with dilute hydrochloric acid is to hydrolyse any glycosidic bonds present, to make the sugar a reducing one, so that it may reduce benedicts and cause the colour change. However, benedict's only works in a alkaline environment and thus sodium hydroxide must be added to neutralise it.

Inorganic Ions
Molecules are not the only type of substance that is important for the structure and metabolism of living organisms - they also need a wide variety of ions (see the below table). Ions are formed from individual atoms that have gained or lost one or more electrons and are therefore charged negatively or positively.


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User:Whiteknight/Nav

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Change Issues in Curriculum and Instruction/The Teacher as Learner and the Learner as Teacher

TEACHERS AS LEARNERS AND LEARNERS AS TEACHERS

Lauren Florin and Stephanie Sugioka—May 2007 Edited by Patti Horne

Introduction
As early as 1916 when John Dewey published his seminal work "Democracy and Education", it was acknowledged that learners should become active participants in the educational process. From this proposition it clearly follows that in learning from their own experience, students become, in a sense, their own teachers. The changed role of the learner has, in turn, implications for that of the teacher. Instead of the source of knowledge, teachers become facilitators of the learning process; that is, their role is to create the set of conditions under which students can best learn from their experiences. Moreover, teachers can fulfill this role only by becoming learners themselves, and a primary source of their learning must be their students. Simply put, teachers who learn become better teachers, and learners who teach become better learners. Although this idea seems straightforward enough, educators have been very slow to put it into practice. However, the rapid technological changes of the last few decades may well provide the catalyst that finally brings about these needed reforms in the field of education.

Teachers as Learners
As recently as the 1970s, college professors were expected to have mastered only one knowledge domain—that of their specialty. The walls of the ivory tower were, theoretically, impermeable, and students were to concern themselves only with their text and the knowledge conveyed to them by their professors. The professor was not expected to bring into the conversation his or her personal concerns, the interests or needs of the students, or even events in the outside world. However, in the last two decades, the academic cocoon has been blown wide open by the forces of globalism, multi-culturalism, and multimodalism (New London Group, 2000). No longer is it sufficient for educators to concern themselves with the narrow parameters of their chosen fields. They are expected to relate the content of their specialties to the lives of their students and to real-world concerns. To practice sound pedagogy, teachers must be learners in the broadest sense. Not only must they considerably extend the content of what they learn and teach, they must also subject the ways they acquire and convey their knowledge to rigorous scrutiny—to analysis, reflection, and evaluation (Wooldridge, 2001). Thus, for educators, the learning curve has grown steeper in almost every conceivable respect: They must learn not only what to teach but also how to teach; they must learn not only from written texts and from other experts in their fields but also from their colleagues, their students, and their observation of events in the world outside the academy. With knowledge doubling every year or so, 'expertise' now has a shelf life measured in days; everyone must be both learner and teacher; and the sheer challenge of learning can be managed only through a globe-gridling network that links all minds and all knowledge (Perlman, 1992).

Learning to Teach
How, then, in this new global, multicultural environment should teachers learn to teach? Unlike the previous static mode of instruction delivery, the current model calls for a dynamic process in which teachers should constantly learn from their practice in a "dialectical union of reflection and action" (Hoffman-Lipp, Artiles, & Lopez-Torres, 2003, p. 249). Moreover, even reflective praxis is insufficient for teachers to learn to teach effectively. Teachers must be open to the larger world of politics, culture, and society; they must be able to contextualize both what they learn and what they teach within a larger conceptual framework, "to conceive of their work in broader terms that incorporate sociopolitical contexts of teaching in addition to curricular and pedagogical concerns" (p. 250). No longer can educators afford to sequester themselves behind the walls of academe; rather they must subject both their own practices and the social forces around them to rigorous scrutiny if they are to learn to teach effectively. Teachers must become continual learners. In this world, where we have access to anything we need to know, the teacher's role has changed. Formal learning is becoming irrelevant. Informal learning, with student centered inquiry, is much more effective and develops life-long problem solving skills. Society needs citizens who can understand and reflect on ideas, work with others towards a common goal, analyze problems and follow through with solutions. To give students these types of skills we must "engage and empower them as we educate them for insight" (Marzano, 2001).

Learning from and about Students
Neither can teachers afford to distance themselves from the students they teach. In the new, learner-centered environment, they must be prepared to learn both about and from their students. The constructivist approach to education that emphasizes the student him or herself rather than the teacher as the source of knowledge is hardly new (Dewey, 1916). However, the belief that teacher and student should maintain a partnership based on mutual learning dominates thinking about pedagogical praxis to an ever-increasing extent—from the elementary grades to the college years. The term "dialogue education" has been used to characterize this more equitable relationship between teacher and student: "Two way, open dialogue needs to be a part of all learning activities" (Wikipedia, 2007). It has been demonstrated that class discussion in which students actively participate and are encouraged to raise questions and pose problems themselves may greatly increase critical thinking skills in students (Tsui, 2002). Thus teachers must learn how to create an environment in which students feel free to openly express and share their ideas. The perception that learning is a mutual experience in which they participate with the instructor has also been shown to contribute to higher cognitive skills in students (Tsui, 2002). Finally, if teachers are willing to abandon the outdated notion that they must be the sole source of knowledge and profess themselves willing and perhaps even grateful to learn from their students, they can model for their students the very learning process that they would most like their students to adopt: "Teachers should be examples of how learning works" (Kaplan, 1998). A perfect opportunity for teachers to learn from their students presents itself in the form of technological innovation within the classroom. Although computer literacy is becoming increasingly important for teacher effectiveness (Selber, 2004), many teachers continue to feel threatened by technologies that they have not mastered (and that some have not even tried). As educators sometimes struggle to engage today’s technology savvy students, allowing students to serve as technology trainers would be an excellent way to provide teachers with some high tech strategies that will captivate students and really get them involved in teaching and learning. Generation Youth and Educators Succeeding (Generation YES) is a national nonprofit organization based in Olympia, Washington, that does just that via GenYES, a program wherein students learn complex computer skills, lesson plan design, and instructional strategies so that they can serve as trainers for K-12 educators (http://www.soundout.org/teaching.html). Teachers could learn much from their young students, many of whom possess a great facility for the manipulation of technologies of all kinds. In being thus willing to learn from their students, teachers could not only model the learning process for their students but also validate the students' sense of self-efficacy, the affirmation of which has been shown to enhance student learning in itself (Hoyt & Ames, 1997).

Expanding Teacher Learning
The content of what a teacher must learn to be effective has thus increased exponentially. Not only must teachers learn how to use technology to enrich their teaching, they must also learn how to teach students to use it responsibly and mindfully. Moreover, the teacher must also learn about his or her students—their families, their cultures, their communities (Kaplan, 1998). They need to learn from and about their colleagues. In her book, A life in school: What the teacher learned, Jane Tompkins (1996) writes movingly of the ways in which academic life tends to isolate both faculty and students from themselves, from each other, and from the world around them. Yet disciplines and discourse communities overlap, and the educator should make an effort to participate in and foster the community of learners to which he or she belongs (Shulman & Shulman, 2004). Sadly, many forces militate against the need for teachers to learn broadly and deeply. The forces of competition, territoriality, and sheer lack of time tend to limit the sources that could enrich teachers' knowledge and improve their teaching. Minimal professional development and lack of adequate school funding further constrict their opportunities to learn about themselves, their students, and larger cultural and political issues. However, the forces of globalism, multiculturalism, and technological change mandate that teachers extend the boundaries of their learning beyond the strictures of their discipline and the walls of their classrooms and institutions to encompass the larger world that they must prepare their students to enter. In this world, where we have the ability to access endless amounts of information with the push of a button, is it not our job as teachers to learn how to filter through this information in order to find the best answers to our questions? Teachers and students can analyze the validity of data and the soundness of information together. This collaboration brings real learning to the process and reinforces the role of collaboration as it occurs in the real world.

The No Child Left Behind Act of 2001 requires that high quality professional development be provided for educators. This would be in hopes of sustaining and supporting high qualified educators. Borko (2004) identifies that professional development should be begin with these three major components: subject matter knowledge, student thinking, and instructional practices. She proposes a three phase plan to ensure research can be conducted to see that educators are provided with an appropriate program. Essentially professional development should begin with a single site. The program would be evaluated when facilitators then share the program with other schools. The final evaluation phase would then be to compare the program with other similar programs. This focused approach to professional development could work to identify and disperse a high quality program system-wide especially when there may be limited opportunities and funds.

Learners as Teachers
Just as teachers have had to alter their own methods and shift from being their students’ sole source of knowledge to one of the many sources, students also have had to shift from being passive receptacles of knowledge to active participants and even to being teachers themselves. Research in the areas of constructivist teaching practices, cooperative learning, and technology have opened new doors and have altered the roles and responsibilities of students today.

Learners and Constructivism
In the traditional classroom, teachers stand at the front of the classroom and present the information to the students. This process is seen as effective because teachers can present an immense amount of information in only a short period of time. The students are expected to absorb the information that the teacher presents and then recall it later on a test. Constructivist research has continued to show us how ineffective and inefficient this process is. Research results also found that in classes where teachers focus on imparting knowledge students indicate they are more likely to have a superficial interest in learning that subject. Conversely, when teaching focuses on students and challenging their perceptions, students report a deeper involvement with learning the subject (Trigwell, Prosser, & Waterhouse, 2004). Proponents of constructivism believe that if teachers shift their teaching practices, especially in mathematics and science, test scores will increase. The constructivist model promotes students as being active participants in the education process. Instead of sitting back and listening to the information, students must construct their own knowledge through meaningful experiences. In the constructivist classroom, the students drive the curriculum, focusing on specific topics that they want to study. One example of how students can accomplish this is through project-based learning. Students can, individually or in groups, generate questions about a real-world problem, investigate the topic through research, analyze and reflect on their findings, and devise solutions to the problem. They then can teach the rest of the students in the class, the teacher, and even the rest of the community about their specific topic. Essentially, they become experts on the topic. In this style of learning, the students take responsibility for their own learning because they truly are interested in it (Curtis, 2001; Lane, 2007; Marlowe & Page, 2005).

Class Discussion and Mutual Learning
Another way students become teachers in constructivist classrooms is through discussion. Class discussions are a central component of constructivism since the focus is on the process of learning instead of the product. It is not important whether the students get the right answer, what is important is how their thinking evolves. For example, the math strategy, math talk, is one in which students are given a word problem and asked to solve it. Then, through a class discussion, the students are encouraged to share and explain their solutions to the problem and justify their reasoning. The children are able to “gain greater understanding and ownership of mathematical concepts as they develop and express their own ideas” (Houghton Mifflin, n.d.). Since there are numerous ways to solve any given problem, the students become each other's teachers as they discuss not only their own logic but also the faults of their peers’ logic. This process is so effective because “hearing and analyzing others’ approaches can supply one with new perspectives; and frequent exposure to different approaches engenders flexible thinking” (Houghton Mifflin, n.d.). The age of the child does not matter; even kindergarteners can effectively be their peers' teachers during math talk (Kamii, 2000).

Cooperative Learning Groups
A similar method in the classroom where students become the teachers is the use of cooperative learning groups. Cooperative learning is characterized by small groups of students grouped together based on different skill levels. These heterogeneous groups work so efficiently because each student is held accountable for his or her own participation in the group, as well as the group's being held accountable for their overall performance. Cooperative learning can be used anytime a group needs to work together, whether it be on homework or on completing a class project. Since students are grouped with each other based on differing ability levels, students with certain strengths are able to coach the students with weaker abilities in a given area. This coaching, and subsequent teaching, often enables the students to learn a subject better because they are hearing it from a peer’s perspective. Teachers often approach a topic and attempt to explain it from a level that is much too complex; however, students are often better able to explain a topic because they know where to start. By working together as a team to help each other accomplish an ultimate goal, each individual uses his or her strength to help coach and teach the others so that everyone ends up learning up to his or her potential (Education Broadcasting Corporation, n.d; Surin, 2006).

The Teaching Learning Community
In a world where knowledge and information are abundant and so easily accessible, the roles of teachers and learners are transformed and blended. The walls of the classroom have been extended through new technologies and in this extended classroom roles must adapt. The teacher no longer is the imparter of knowledge and student the passive recipient. Both become part of a collaborative learning community. In this new way of teaching and learning students are empowered. They become self directed and take responsibility for their own learning. Teachers become mentors, guides, coaches and learners themselves. Through powerful web tools such as blogs and wikis, students and teachers have opportunities to create and contribute to knowledge and share ideas. They now can share ideas and communicate with learners world wide. In doing so, both teacher and learner will see the world differently and learn to appreciate the perspectives of others. These new technologies, with which our students are generally quite adept, threaten to widen the divide between teacher and student if teachers are unwilling to become learners and users of technology themselves. As digitally savvy students enter the classroom, teachers have the power to close that gap if they’re willing to extend their learning and teaching for the 21st century.

Learners and Web 2.0
More recently, technology has drastically changed how students learn in and out of the classroom. Teachers can no longer pretend to have all of the answers because students have an immense amount of knowledge at their fingertips with the internet; more specifically, Web 2.0 enables students to be not only learners but also teachers. Web 2.0 allows all users not only to post comments, articles, and reports on the internet but also to edit and respond to those articles and reports. Teachers can use wikis in their classrooms and have groups of students work together or individually to research and become experts on a topic and then post their reports on the internet for all to read and learn from. This new area of education is allowing all students to become the teachers to not only the students in their classes but to the world. Any student who is interested and wishes to explore and research a particular topic is able to do so and publish his or her work. This not only increases the motivation to do a good job, but since anyone can go in and edit the work, it helps students to be flexible and open to new ideas and procedures. This technology also enables any topic to be approached from multiple perspectives. Students in the past have grown up learning subjects such as history from only one biased perspective. Now, individuals will be able to help contribute to online textbooks and add sections about topics that have never before been taught in the public schools. This technology will revolutionize our education system as it becomes more widely used and accepted (Alexander, 2006; Standen, 2006).

Conclusion
Largely as a result of technological change, the forces of globalism, multiculturalism, and multimodalism have conspired to transform and ultimately enrich the roles of both teacher and learner. As teachers extend their learning, learners can claim full ownership of their knowledge in the process of teaching it to others. This results in more effective teachers as well as a greater depth of understanding in students. This model of mutual learning can reform the educational system from within and help it to realize maximum benefits for both teachers and learners.


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User:Whiteknight/New Book Guide/The Goal

Purposes for New Books
The process of creating a new wikibook serves several purposes:

 * 1) Enables you, the contributer, to teach a subject that you know.
 * 2) Enables other readers to learn the subject, without having to pay the exorbitant prices of textbooks.
 * 3) Inspires other wikibookians to contribute to your book, making it a better resource.

It has been said that the best way to learn a subject is to teach it, and so the first point above really is a double-edged sword. Not only can you as the author help other people to learn the subject, but you yourself could gain a better understanding and appreciation for it.

The second point above is another important one. Traditional printed textbooks are typically very expensive. On top of that is the fact that book publishers tend to create multiple editions of a book, one every couple of years. When a new edition of the book is released, the old versions become obsolete, even if they are more widely available, lower in price, and available used at a discount. Also, because wikibooks are available on the internet, books can be downloaded for free.

Qualities of a Good Book
To do this, a good book needs several qualities:

 * 1) A good plan
 * 2) Solid infrastructure
 * 3) Sharp Focus
 * 4) Broad Scope

Without all these things, books will likely become either eternal stubs, candidates for a costly merger, or complete orphans.

A Good Plan
A book needs a plan, a direction, a purpose. We don't need to write books that aren't helpful and informative. We don't need to reinvent any wheels. The best books are going to start out as outlines or plans. One chapter is going to lead into another. The material will be presented in a comprehensible order.

A Solid Infrastructure
The book should have a good, solid infrastructure. Readers should be able to navigate the book with ease, and new contributors should know exactly what information should go where. The naming convention should be consistent. A book should also create the necessary custom templates that it needs, and should also find and employ some other templates too.

A Sharp Focus
A book should have plenty of focus, and not be too broad or vague. A book titled "Physics" is probably not as good as a set of smaller, more defined books such as "Statics", "Dynamics", "Electromagnetic Waves", etc. When readers come to your book, in other words, they should know exactly what material it will contain. Another aspect of this is the fact that Wikibooks represents a complete library, in a sense: We already have books on the fundamentals of science, math, language, etc. Each new book does not need to cover the basics again and again. It is better to do one thing well than to do many things "well".

A Broad Scope
Every book needs to have a broad enough scope to cover the topic in full. A book such as "Introduction to subject X" can only cover, by definition, introductory material. By that same note, "Advanced Subject X" by definition only covers those topics that can be considered "advanced". A book about subject X should not artificially limit itself to only covering a certain aspect of subject X. A book on subject X should cover the whole thing. As an example of scope, consider the method by which university programs generally break the subject of economics into such classes as "Microeconomics", "Macroeconomics", et cetera. This division might be well and good for a semester-long classroom environment, but it doesn't make any sense to artificially divide the material up here on Wikibooks. Instead, we should have a single book titled "Economics" that will cover both the macro- and micro- sub-topics.

Practicality
On a note of practicality, these requirements are also prerequisites for a book to become a featured book. Gaining this distinction for your book will help it to expand and grow beyond what you can contribute yourself.


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User:Whiteknight/New Book Guide/The Need

The Need for a New Book
Hopefully your decision to create a new book will be mitigated by a specific need here at Wikibooks. Maybe it's a gaping hole in in our coverage of a specific subject ("I can't believe they don't have a calculus book!"), maybe there are many smaller books on the subject that could be effectively merged into a new monolithic book, or maybe there is a book that's so large and sprawling that it needs to be split into smaller books. Also, before you create a new book here, it is a good idea to ensure that the book is actually right for Wikibooks: If the answer to all these questions is "yes", Then you are well on your way to being able to start your project.
 * Is it allowed under policy?
 * Is Wikibooks the best wiki to host this material?
 * Will other people be able to contribute to it?
 * Will other readers be able to understand this subject?

It is important to make sure that your new book is actually a valuable resource. We may not currently have a book about "How to alphabetically arrange your wine bottle collection", but do we really need a book on that topic to begin with?

Finally, is this information that you are willing to write about—in large quantities—for a period of weeks, months, or even years? A Wikibook is a large project, and creating a good Wikibook requires strong drive, direction, and countless contributions from yourself and other users. A new Wikibook is a big deal, and you shouldn't start a new book if you aren't willing to invest the necessary time and energy into it.

Target Audience
Implicitly, if there is a need for your book, then there is somebody who needs it. This vague somebody is your target audience, and is who you are writing your book for. Because you are writing a textbook, your target audience will most likely be school students. However, even under the banner of "school students" there are a number of different classifications that are worth considering. Students can be separated by age: young children (the target audience of Wikijunior), Highschool students, University Students, and Professionals (The target audience of Wikiprofessional). Some subjects are not conducive to certain target audience, in the same way that certain styles of writing are not good for a target audience. For instance, we aren't going to attempt to teach young children about "SPARC Assembly Programming". We also aren't going to try and write a children's book using big words and complicated sentences.

Under the sub-heading of "University Students" also, there is a difference between different types of students. There is a distinct difference in the way a single subject can be taught between different groups of students: Statistics is taught differently between business majors (where it is taught predominantly using algebra), and mathematics students (where it is taught predominantly using calculus). Engineers generally like to learn the bottom line, while mathematicians might prefer to learn the derivations and proofs.

When considering this, there are multiple ways to go about creating a new book for your subject. Either you can make a book tailored specifically towards a single target audience ("Statistics for Mathematicians"), or you can make a single book ("Statistics") That will consider the topic from multiple angles. For instance, you can separate the book into 2 distinct sections (one for business readers, and one for mathematics readers), or you can separate each individual page into the different sections (one section for the algebraic formulas and results, and a bottom section for the calculus derivations). I generally prefer the last option, where we can write a single book, and separate out the individual pages into the "basic concepts" and "Advanced concepts" topics. This way, everybody can read (and contribute to) the same book, but people can pick and choose which sections to read for themselves.

In general, when we consider that the book at large can be created without considering the target audience, and that the sub-pages are created with consideration for the target audience, you the creator don't need to worry about audience until after the book is introduced. Knowing however that there is a disparity between the different types of information, it is a good idea to consider different methodologies for a particular subject when you are doing your research for the book.

Prerequisites
Do not hesitate to lay down a set of necessary prerequisites that your readers must have before they attempt to read your book. Requiring a standard background among all readers makes the job of the author easier: no need to review necessary material, and no need to define common terms. When possible, link to other Wikibooks that cover the necessary material. Also, if the prerequisites of your book change as the narrative progresses (progressively harder mathematics, for instance), don't hesitate to mention that students need to refresh a particular subject before continuing on.

On a related note, mention precisely what your book serves as a prerequisite for. That is, if your book sets a student up to read another more advanced book, you should mention that. If there are no other books available here on Wikibooks you can point the reader to external references for a continued study. As an author, you should also consider authoring the more advanced book, if one does not exist.


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User:Whiteknight/New Book Guide/The Problems

There are a number of problems that need to be considered, that many people don't always take account for.

Being Bold
Not everybody who comes to Wikibooks is comfortable being bold, and making all sorts of gigantic changes, additions, deletion, etc. If a book is poorly structured, it is foolish to think that anybody in the future is going to come in and make it better. It is unlikely that once a mistake is made, that it will ever be corrected. This is especially true of larger mistakes, because people will be less willing to undertake the effort to fix it. Wikibooks is home to over 3000 separate books. Even if we have 3000 active editors at any time, it is unlikely that any particular book will have even 1 regular contributor. Some books are very large, and they get that way by drawing a disproportionately large crowd of editors from the pool. If there are 1000 editors, there are probably going to be 9 editors each on the 100 biggest books, which leaves only 100 editors to manage the other 2900 books. To illustrate this fact, I am currently the primary contributor on nearly two dozen books (not the only contributor, certainly, but the most active) While other popular books can draw two dozen regular contributors to their pages.

Beyond sheer numbers, I must reiterate that not everybody is a project leader. If every editor who came to Wikibooks, even for a short period of time, were bold and made a significant change here, Wikibooks would be far better off. If a new editor found a book, renamed all the pages to have better names, fixed the TOC to be more helpful, and created a print version, more books would draw more editors. But, alas, this is not the case. The average editor simply isn't going to make big changes, isn't going to make big contributions, and isn't going to come back in the future to see if those changes get made at all. It is paramount, therefore, that new books be started off on the right foot, to inspire confidence among readers that the book is going somewhere, that somebody cares, and that this is a project worth getting involved in.

Having a Plan
When an author creates a new book, they typically have a plan in mind as to what the book will contain, and what direction the book will take. However, if this information isn't written down, and the author disappears, future authors will be confused and may ultimately avoid editing that book. If you have a plan for your book, make sure to write it down so that future editors know what your intentions are. If people have a plan to follow, they will be more likely to contribute to your book, and less likely to go off on a tangent that will reduce the quality of the book. Here are a few things that should be included in a good book-writing plan:

 * 1) The need behind the book (why you are making it in the first place)
 * 2) The definition of the book (scope, target audience, etc)
 * 3) Background and prerequisites
 * 4) Integrating your book with other books.

The Need
We've already discussed the need for a new book. However, when writing your plan it is a good idea to write down your rationale for why you want to write your book. This can be a good idea, so that as your planning progresses, you can double check that you are actually working towards your goals.

The Definition
Again, we have already discussed the definition of a book. We should always write down the book's definition explicitly, especially during the planning stages, so that you (and any helpers that you have) can ensure to keep all your work focused on that definition. If you add items to your outline that don't meet the book's definition, you should delete them, etc.

Background and Prerequisites
If you write down the necessary background and prerequisites for your book directly on the planning pages, you can ensure that everybody who reads your outline will be on the same page. Also, it can help you fight the urge to try and explain things again that your target audience should already know.

Integrating your Book
Your book is not always going to be a stand-alone resource, but instead will be interdependant on all the other books here at wikibooks. Other books may cite your book as a reference, and your book may cite other books as well. You can use existing books as a prerequisite for your new book, to help take care of our prerequsite problem easily. Also, your book may absorb and be merged with other pre-existing books, book stubs, and lone pages. It is a good idea to write down in your plan all existing pages and books that could have an effect on your new book. Make sure you differentiate between prerequisite books, reference books, and books that could possibly be merged into your new book. This way, when your new book is introduced to a bookshelf, you can have an organized plan as to what needs to be merged where, and what links need to be added to what books.

A New Plan
When creating a new planning page, this code stub can be used to ensure you fill in all the necessary information:

This is a planning page, not a book! == My Plan == (discuss here why you want to create the book, the need, the definition, the prerequisites, etc) == Intended Table of Contents == (draft your book's table of contents here. == Resources == (list books that will be useful as resources here, including prerequisites) == Existing Pages == (list pages here that might be merged into your new book here)

Presentation: Following NPOV and NOR
The principles of Neutral-Point of View (NPOV) and No Original Research (NOR) are as fundamental to Wikibooks as they are to other Wikimedia projects. However, unlike other projects, these issues are not as strictly codified on Wikibooks.

Here are a few points to make:
 * 1) Presenting known information in new, original, or novel ways does not constitute original research. Material, so long as that material is verifiable and unoriginal, may be presented in ways never seen before.
 * 2) The restriction of the scope of a book to a particular subset of information does not necessarily constitute a POV bias. The exclusion of certain lessons that are properly superseded by better lessons, or the exclusion of materials that are tangent to the prime narrative of the book, is acceptable. However, material may not be added to purposefully promote it, and material may not be excluded to purposefully obscure it. When multiple sets of possibly-conflicting information are available but not all included, it is always good to leave a note about why the book has chosen to include or exclude certain materials.
 * 3) The choice to use particular vocabulary or language in a book does not represent a bias.
 * 4) The use of new or original terms, descriptions, explanations, or demonstrations, does not represent original research unless it is the intent of the book to popularize those terms, descriptions, explanations, or demonstrations. The goals of a Wikibooks textbook are to provide information to students, and not to set a precedence among educators.

These are all just rough guidelines, of course. If you have any questions about these, and would like clarification, you can ask a message about it at the Reading Room.