Islam word has been derived from arabic languge word salam, it meaning is peace ofcourse islam is religion of peace and humanity , which is not only religion of muslim but also religion of the entire universe.Since the early 1980s, commentators have argued that Islam is suffering a crisis of identity, as the crumbling of Islamic civilization in the modern age has left Muslims with a profound sense of alienation and injury. Challenges confronting Muslim nations -- failures of development projects, entrenched authoritarian regimes and the inability to respond effectively to Israeli belligerence -- have induced deep-seated frustration and anger that, in turn, contributed to the rise of fundamentalist movements, or as most commentators have preferred to say, political Islam. But most commentators have been caught off guard by the ferocity of the acts of mass murder recently committed in New York and Washington. The basic cruelty and moral depravity of these attacks came as a shock not only to non-Muslims, but to Muslims as well. The extreme political violence we call terrorism is not a simple aberration unrelated to the political dynamics of a society. Generally, terrorism is the quintessential crime of those who feel powerless seeking to undermine the perceived power of a targeted group. Like many crimes of power, terrorism is also a hate crime, for it relies on a polarized rhetoric of belligerence toward a particular group that is demonized to the point of being denied any moral worth. To recruit and communicate effectively, this rhetoric of belligerence needs to tap into and exploit an already radicalized discourse with the expectation of resonating with the social and political frustrations of a people. If acts of terrorism find little resonance within a society, such acts and their ideological defenders are marginalized. But if these acts do find a degree of resonance, terrorism becomes incrementally more acute and severe, and its ideological justifications become progressively more radical.
To what extent are the September 11 attacks in the US symptomatic of more pervasive ideological undercurrents in the Muslim world today? Obviously, not all social or political frustrations lead to the use of violence. While national liberation movements often resort to violence, the recent attacks are set apart from such movements. The perpetrators did not seem to be acting on behalf of an ethnic group or nation. They presented no specific territorial claims or political agenda, and were not keen to claim responsibility for their acts. One can speculate that the perpetrators' list of grievances included persistent Israeli abuses of Palestinians, near-daily bombings of Iraq and the presence of American troops in the Gulf, but the fact remains that the attacks were not followed by a list of demands or even a set of articulated goals. The attacks exhibit a profound sense of frustration and extreme despair, rather than a struggle to achieve clear-cut objectives. Some commentators have viewed the underpinnings of the recent attacks as part of a "clash of civilizations" between Western values and Islamic culture. According to these commentators, the issue is not religious fundamentalism or political Islam, but an essential conflict between competing visions of morality and ethics. From this perspective, it is hardly surprising that the terrorists do not present concrete demands, do not have specific territorial objectives and do not rush to take responsibility. The September 11 attacks aimed to strike at the symbols of Western civilization, and to challenge its perceived hegemony, in the hope of empowering and reinvigorating Islamic civilization. The "clash of civilizations" approach assumes, in deeply prejudiced fashion, that Puritanism and terrorism are somehow authentic expressions of the predominant values of the Islamic tradition, and hence is a dangerous interpretation of the present moment. But the common responses to this interpretation, focusing on either the crisis of identity or acute social frustration in the Muslim world, do not adequately explain the theological positions adopted by radical Islamist groups, or how extreme violence can be legitimated in the modern age. Further, none of these perspectives engage the classical tradition in Islamic thought regarding the employment of political violence, and how contemporary Muslims reconstruct the classical tradition. How might the classical or contemporary doctrines of Islamic theology contribute to the use of terrorism by modern Islamic movements?
By the eleventh century, Muslim jurists had developed a sophisticated discourse on the proper limits on the conduct of warfare, political violence and terrorism. The Qur'an exhorted Muslims in general terms to perform jihad by waging war against their enemies. The Qur'anic prescriptions simply call upon Muslims to fight in the way of God, establish justice and refrain from exceeding the limits of justice in fighting their enemies. Muslim jurists, reflecting their historical circumstances and context, tended to divide the world into three conceptual categories: the abode of Islam, the abode of war and the abode of peace or non-belligerence. These were not clear or precise categories, but generally they connoted territories belonging to Muslims, territories belonging to enemies and territories considered neutral or non-hostile for one reason or another. But Muslim jurists could not agree on exactly how to define the abode of Muslims versus the abode of others, especially when sectarian divisions within Islam were involved, and when dealing with conquered Muslim territories or territories where sizable Muslim minorities resided. Furthermore, Muslim jurists disagreed on the legal cause for fighting non-Muslims. Some contended that non-Muslims are to be fought because they are infidels, while the majority argued that non-Muslims should be fought only if they pose a danger to Muslims. The majority of early jurists argued that a treaty of non-aggression between Muslims and non-Muslims ought to be limited to a ten-year term. Nonetheless, after the tenth century an increasing number of jurists argued that such treaties could be renewed indefinitely, or be of permanent or indefinite duration. Importantly, Muslim jurists did not focus on the idea of just cause for war. Other than emphasizing that if Muslim territory is attacked, Muslims must fight back, the jurists seemed to relegate the decision to make war or peace to political authorities. There is a considerable body of legal writing prohibiting Muslim rulers from violating treaties, indulging in treachery or attacking an enemy without first giving notice, but the literature on the conditions that warrant a jihad is sparse. It is not that the classical jurists believed that war is always justified or appropriate; rather, they seemed to assume that the decision to wage war is fundamentally political. However, the methods of war were the subject of a substantial jurisprudential discourse. Building upon the proscriptions of the Prophet Muhammad (SWS), Muslim jurists insisted that there are legal restrictions upon the conduct of war. In general, Muslim armies may not kill women, children, seniors, hermits, pacifists, peasants or slaves unless they are combatants. Vegetation and property may not be destroyed, water holes may not be poisoned, and flame-throwers may not be used unless out of necessity, and even then only to a limited extent. Torture, mutilation and murder of hostages were forbidden under all circumstances. Importantly, the classical jurists reached these determinations not simply as a matter of textual interpretation, but as moral or ethical assertions. The classical jurists spoke from the vantage point of a moral civilization, in other words, from a perspective that betrayed a strong sense of confidence in the normative message of Islam. In contrast to their pragmatism regarding whether a war should be waged, the classical jurists accepted the necessity of moral constraints upon the way war is conducted.
Muslim jurists exhibited a remarkable tolerance toward the idea of political rebellion. Because of historical circumstances in the first three centuries of Islam, Muslim jurists, in principle, prohibited rebellions even against unjust rulers. At the same time, they refused to give the government unfettered discretion against rebels. The classical jurists argued that the law of God prohibited the execution of rebels or needless destruction or confiscation of their property. Rebels should not be tortured or even imprisoned if they take an oath promising to abandon their rebellion. Most importantly, according to the majority point of view, rebellion, for a plausible cause, is not a sin or moral infraction, but merely a political wrong because of the chaos and civil strife that result. This approach effectively made political rebellion a civil, and not a religious, infraction. The classical juristic approach to terrorism was quite different. Since the very first century of Islam, Muslims suffered from extremist theologies that not only rejected the political institutions of the Islamic empire, but also refused to concede legitimacy to the juristic class. Although not organized in a church or a single institutional structure, the juristic class in Islam had clear and distinctive insignia of investiture. They attended particular colleges, received training in a particular methodology of juristic inquiry, and developed a specialized technical language, the mastery of which became the gateway to inclusion. Significantly, the juristic class engaged as a rule in discussion and debate. On each point of law, there are ten different opinions and a considerable amount of debate among the various legal schools of thought. Various puritan theological movements in Islamic history resolutely rejected this juristic tradition, which reveled in indeterminacy. The hallmark of these puritan movements was an intolerant theology displaying extreme hostility not only to non-Muslims but also to Muslims who belonged to different schools of thought or even remained neutral. These movements considered opponents and indifferent Muslims to have exited the fold of Islam, and therefore legitimate targets of violence. These groups' preferred methods of violence were stealth attacks and the dissemination of terror in the general population. Muslim jurists reacted sharply to these groups, considering them enemies of humankind. They were designated as muharibs (literally, those who fight society). A muharib was defined as someone who attacks defenseless victims by stealth, and spreads terror in society. They were not to be given quarter or refuge by anyone or at any place. In fact, Muslim jurists argued that any Muslim or non-Muslim territory sheltering such a group is hostile territory that may be attacked by the mainstream Islamic forces. Although the classical jurists agreed on the definition of a muharib, they disagreed about which types of criminal acts should be considered crimes of terror. Many jurists classified rape, armed robbery, assassinations, arson and murder by poisoning as crimes of terror and argued that such crimes must be punished vigorously regardless of the motivations of the criminal. Most importantly, these doctrines were asserted as religious imperatives. Regardless of the desired goals or ideological justifications, the terrorizing of the defenseless was recognized as a moral wrong and an offense against society and God.
It is often stated that terrorism is the weapon of the weak. Notably, classical juristic discourse was developed when Islamic civilization was supreme, and this supremacy was reflected in the benevolent attitude of the juristic class. Pre-modern Muslim juristic discourses navigated a course between principled thinking and real-life pragmatic concerns and demands. Ultimately, these jurists spoke with a sense of urgency, but not desperation. Power and political supremacy were not their sole pursuits. Much has changed in the modern age. Islamic civilization has crumbled, and the traditional institutions that once sustained the juristic discourse have all but vanished. The moral foundations that once mapped out Islamic law and theology have disintegrated, leaving an unsettling vacuum. More to the point, the juristic discourses on tolerance towards rebellion and hostility to the use of terror are no longer part of the normative categories of contemporary Muslims. Contemporary Muslim discourses either give lip service to the classical doctrines without a sense of commitment or ignore and neglect them all together. There are many factors that contributed to this modern reality. Among the pertinent factors is the undeniably traumatic experience of colonialism, which dismantled the traditional institutions of civil society. The emergence of highly centralized, despotic and often corrupt governments, and the nationalization of the institutions of religious learning undermined the mediating role of jurists in Muslim societies. Nearly all charitable religious endowments became state-controlled entities, and Muslim jurists in most Muslim nations became salaried state employees, effectively transforming them into what may be called "court priests." The establishment of the state of Israel, the expulsion of the Palestinians and the persistent military conflicts in which Arab states suffered heavy losses all contributed to a widespread siege mentality and a highly polarized and belligerent political discourse. Perhaps most importantly, Western cultural symbols, modes of production and social values aggressively penetrated the Muslim world, seriously challenging inherited values and practices, and adding to a profound sense of alienation. Two developments became particularly relevant to the withering away of Islamic jurisprudence. Most Muslim nations experienced the wholesale borrowing of civil law concepts. Instead of the dialectical and indeterminate methodology of traditional Islamic jurisprudence, Muslim nations opted for more centralized and often code-based systems of law. Even Muslim modernists who attempted to reform Islamic jurisprudence were heavily influenced by the civil law system, and sought to resist the fluidity of Islamic law and increase its unitary and centralized character. Not only were the concepts of law heavily influenced by the European legal tradition, the ideologies of resistance employed by Muslims were laden with Third World notions of national liberation and self-determination. For instance, modern nationalistic thought exercised a greater influence on the resistance ideologies of Muslim and Arab national liberation movements than anything in the Islamic tradition. The Islamic tradition was reconstructed to fit Third World nationalistic ideologies of anti-colonialism and anti-imperialism rather than the other way around. While national liberation movements -- such as the Palestinian, Kashmiri or Algerian resistance -- resorted to guerrilla or non-conventional warfare, modern day terrorism of the variety promoted by Osama bin Laden is rooted in a different ideological paradigm. There is little doubt that organizations such as the Jihad, al-Qaeda, Hizb al-Tahrir and Jama'at al-Muslimin were influenced by national liberation and anti-colonialist ideologies, but they have anchored themselves in a theology that can be described as puritan, supremacist and thoroughly opportunistic. This theology is the byproduct of the emergence and eventual dominance of Wahhabism, Salafism and apologetic discourses in modern Islam.
The foundations of Wahhabi theology were put in place by the eighteenth-century evangelist Muhammad ibn 'Abd al-Wahhab in the Arabian Peninsula. With a puritanical zeal, 'Abd al-Wahhab sought to rid Islam of corruptions that he believed had crept into the religion. Wahhabism resisted the indeterminacy of the modern age by escaping to a strict literalism in which the text became the sole source of legitimacy. In this context, Wahhabism exhibited extreme hostility to intellectualism, mysticism and any sectarian divisions within Islam. The Wahhabi creed also considered any form of moral thought that was not entirely dependent on the text as a form of self-idolatry, and treated humanistic fields of knowledge, especially philosophy, as "the sciences of the devil." According to the Wahhabi creed, it was imperative to return to a presumed pristine, simple and straightforward Islam, which could be entirely reclaimed by literal implementation of the commands of the Prophet(PBUH), and by strict adherence to correct ritual practice. Importantly, Wahhabism rejected any attempt to interpret the divine law from a historical, contextual perspective, and treated the vast majority of Islamic history as a corruption of the true and authentic Islam. The classical jurisprudential tradition was considered at best to be mere sophistry. Wahhabism became very intolerant of the long-established Islamic practice of considering a variety of schools of thought to be equally orthodox. Orthodoxy was narrowly defined, and 'Abd al-Wahhab himself was fond of creating long lists of beliefs and acts which he considered hypocritical, the adoption or commission of which immediately rendered a Muslim an unbeliever. In the late eighteenth century, the Al Sa'ud family united with the Wahhabi movement and rebelled against Ottoman rule in Arabia. Egyptian forces quashed this rebellion in 1818. Nevertheless, Wahhabi ideology was resuscitated in the early twentieth century under the leadership of 'Abd al-'Aziz ibn Sa'ud who allied himself with the tribes of Najd, in the beginnings of what would become Saudi Arabia. The Wahhabi rebellions of the nineteenth and twentieth centuries were very bloody because the Wahhabis indiscriminately slaughtered and terrorized Muslims and non-Muslims alike. Mainstream jurists writing at the time, such as the Hanafi Ibn 'Abidin and the Maliki al-Sawi, described the Wahhabis as a fanatic fringe group.
Nevertheless, Wahhabism survived and, in fact, thrived in contemporary Islam for several reasons. By treating Muslim Ottoman rule as a foreign occupying power, Wahhabism set a powerful precedent for notions of Arab self-determination and autonomy. In advocating a return to the pristine and pure origins of Islam, Wahhabism rejected the cumulative weight of historical baggage. This idea was intuitively liberating for Muslim reformers since it meant the rebirth of ijtihad, or the return to de novo examination and determination of legal issues unencumbered by the accretions of precedents and inherited doctrines. Most importantly, the discovery and exploitation of oil provided Saudi Arabia with high liquidity. Especially after 1975, with the sharp rise in oil prices, Saudi Arabia aggressively promoted Wahhabi thought around the Muslim world. Even a cursory examination of predominant ideas and practices reveals the widespread influence of Wahhabi thought on the Muslim world today. But Wahhabism did not spread in the modern Muslim world under its own banner. Even the term "Wahhabism" is considered derogatory by its adherents, since Wahhabis prefer to see themselves as the representatives of Islamic orthodoxy. To them, Wahhabism is not a school of thought within Islam, but is Islam. The fact that Wahhabism rejected a label gave it a diffuse quality, making many of its doctrines and methodologies eminently transferable. Wahhabi thought exercised its greatest influence not under its own label, but under the rubric of Salafism. In their literature, Wahhabi clerics have consistently described themselves as Salafis, and not Wahhabis.
Salafism is a creed founded in the late nineteenth century by Muslim reformers such as Muhammad 'Abduh, al-Afghani and Rashid Rida. Salafism appealed to a very basic concept in Islam: Muslims ought to follow the precedent of the Prophet and his companions (al-salaf al-salih). Methodologically, Salafism was nearly identical to Wahhabism except that Wahhabism is far less tolerant of diversity and differences of opinion. The founders of Salafism maintained that on all issues Muslims ought to return to the Qur'an and the sunna (precedent) of the Prophet. In doing so, Muslims ought to reinterpret the original sources in light of modern needs and demands, without being slavishly bound to the interpretations of earlier Muslim generations. As originally conceived, Salafism was not necessarily anti-intellectual, but like Wahhabism, it did tend to be uninterested in history. By emphasizing a presumed golden age in Islam, the adherents of Salafism idealized the time of the Prophet and his companions, and ignored or demonized the balance of Islamic history. By rejecting juristic precedents and undervaluing tradition, Salafism adopted a form of egalitarianism that deconstructed any notions of established authority within Islam. Effectively, anyone was considered qualified to return to the original sources and speak for the divine will. By liberating Muslims from the tradition of the jurists, Salafism contributed to a real vacuum of authority in contemporary Islam. Importantly, Salafism was founded by Muslim nationalists who were eager to read the values of modernism into the original sources of Islam. Hence, Salafism was not necessarily anti-Western. In fact, its founders strove to project contemporary institutions such as democracy, constitutions or socialism into the foundational texts, and to justify the modern nation-state within Islam. The liberal age of Salafism came to an end in the 1960s. After 1975, Wahhabism was able to rid itself of its extreme intolerance, and proceeded to coopt Salafism until the two became practically indistinguishable. Both theologies imagined a golden age within Islam, entailing a belief in a historical utopia that can be reproduced in contemporary Islam. Both remained uninterested in critical historical inquiry and responded to the challenge of modernity by escaping to the secure haven of the text. Both advocated a form of egalitarianism and anti-elitism to the point that they came to consider intellectualism and rational moral insight to be inaccessible and, thus, corruptions of the purity of the Islamic message. Wahhabism and Salafism were beset with contradictions that made them simultaneously idealistic and pragmatic and infested both creeds (especially in the 1980s and 1990s) with a kind of supremacist thinking that prevails until today. The predominant intellectual response to the challenge of modernity in Islam has been apologetics. Apologetics consisted of an effort by a large number of commentators to defend the Islamic system of beliefs from the onslaught of Orientalism, Westernization and modernity by simultaneously emphasizing the compatibility and supremacy of Islam. Apologists responded to the intellectual challenges coming from the West by adopting pietistic fictions about the Islamic traditions. Such fictions eschewed any critical evaluation of Islamic doctrines, and celebrated the presumed perfection of Islam. A common apologist argument was that any meritorious or worthwhile modern institution was first invented by Muslims. According to the apologists, Islam liberated women, created a democracy, endorsed pluralism, protected human rights and guaranteed social security long before these institutions ever existed in the West. These concepts were not asserted out of critical understanding or ideological commitment, but primarily as a means of resisting Western hegemony and affirming self-worth. The main effect of apologetics, however, was to contribute to a sense of intellectual self-sufficiency that often descended into moral arrogance. To the extent that apologetics were habit-forming, it produced a culture that eschewed self-critical and introspective insight, and embraced the projection of blame and a fantasy-like level of confidence. In many ways, the apologetic response was fundamentally centered on power. Its main purpose was not to integrate particular values within Islamic culture, but to empower Islam against its civilizational rival. Muslim apologetics tended to be opportunistic and rather unprincipled, and, in fact, they lent support to the tendency among many intellectuals and activists to give precedence to the logic of pragmatism over any other competing demands. Invoking the logic of necessity or public interest to justify courses of action, at the expense of moral imperatives, became common practice. Effectively, apologists got into the habit of paying homage to the presumed superiority of the Islamic tradition, but marginalized this idealistic image in everyday life. Post-1970s Salafism adopted many of the premises of the apologetic discourse, but it also took these premises to their logical extreme. Instead of simple apologetics, Salafism responded to feelings of powerlessness and defeat with uncompromising and arrogant symbolic displays of power, not only against non-Muslims, but also against Muslim women. Fundamentally, Salafism, which by the 1970s had become a virulent puritan theology, further anchored itself in the confident security of texts. Nonetheless, contrary to the assertions of its proponents, Salafism did not necessarily pursue objective or balanced interpretations of Islamic texts, but primarily projected its own frustrations and aspirations upon the text. Its proponents no longer concerned themselves with coopting or claiming Western institutions as their own, but defined Islam as the exact antithesis of the West, under the guise of reclaiming the true and real Islam. Whatever the West was perceived to be, Islam was understood to be the exact opposite.
Of course, neither Wahhabism nor Salafism is represented by some formal institution. They are theological orientations and not structured schools of thought. Nevertheless, the lapsing and bonding of the theologies of Wahhabism and Salafism produced a contemporary orientation that is anchored in profound feelings of defeat, frustration and alienation, not only from modern institutions of power, but also from the Islamic heritage and tradition. The outcome of the apologist, Wahhabi and Salafi legacies is a supremacist puritanism that compensates for feelings of defeat, disempowerment and alienation with a distinct sense of self-righteous arrogance vis-à-vis the nondescript "other" -- whether the other is the West, non-believers in general or even Muslims of a different sect and Muslim women. In this sense, it is accurate to describe this widespread modern trend as supremacist, for it sees the world from the perspective of stations of merit and extreme polarization. In the wake of the September 11 attacks, several commentators posed the question of whether Islam somehow encourages violence and terrorism. Some commentators argued that the Islamic concept of jihad or the notion of the dar al-harb (the abode of war) is to blame for the contemporary violence. These arguments are anachronistic and Orientalist. They project Western categories and historical experiences upon a situation that is very particular and fairly complex. One can easily locate an ethical discourse within the Islamic tradition that is uncompromisingly hostile to acts of terrorism. One can also locate a discourse that is tolerant toward the other, and mindful of the dignity and worth of all human beings. But one must also come to terms with the fact that supremacist puritanism in contemporary Islam is dismissive of all moral norms or ethical values, regardless of the identity of their origins or foundations. The prime and nearly singular concern is power and its symbols. Somehow, all other values are made subservient. <!-- / message -->
Why can’t everyone think with numbers? Why do some children learn math readily, handle money and time concepts with ease, retain information from year to year, and think with numbers effortlessly? What cognitive processes do some have that others do not?
Mathematics is cognitive process-thinking-that requires the dual coding of imagery and language. Imagery is fundamental to the process of thinking with numbers. Albert Einstein, whose theories of relativity helped explain our universe, used imagery as the base for his mental processing and problem solving. Perhaps he summarized the importance of imagery best when he said, “If I can’t picture it, I can’t understand it.”
For the people who “get” math, the language of numbers turns into imagery. They use internal language and imagery that lets them calculate and verify mathematics; they “see” its logic.
Imaging is the basis for thinking with numbers and conceptualizing their functions and their logic. The Greek philosopher Plato said, “And do you not know also that although they [mathematicians] make use of the visible forms and reason about them, they are thinking not of these, but of the ideals which they resemble…they are really seeking to behold the things themselves, which can be seen only with the eye of the mind?”
The relationship of imagery to the ability to think is one of the preeminent theories of human cognition. Allan Paivio, author of the Dual Coding Theory (DCT) and a cognitive psychologist, stated, “Cognition is proportional to the extent that mental representations (imagery) and language are integrated.” Research from the 1970s and into the 1990s has validated Dr. Paivio’s work as a viable model of human cognition and its practical, as well as theoretical, application to the comprehension of language (Bell, 1991). Dr. Paivio believes that in order to think and understand, humans must be able to simultaneously generate imagery and corresponding language to describe that imagery.
Mathematics is the essence of cognition. It is thinking (dual coding) with numbers, imagery and language; reading/spelling is thinking with letters, imagery and language. Both processes, often mirror images of each other, require the integration of language and imagery to understand the fundamentals and then apply them. Dual coding in math, just as in reading, requires two aspects of imagery: symbol/numeral imagery (parts/details) and concept imagery (whole/gestalt).
Numeral Imagery
Visualizing numerals is one of the basic cognitive processes necessary for understanding math. For example, we image the numeral “2” for the concept of two. When we see the numeral “3,” we know that it represents the concept of three of something: three pennies, three apples, three horses, three dots. If someone gives us two pennies for the numeral three, we have a discrepancy between our numeral-image for three and the reality (concept) of three. The first imagery needed for math is the symbolic (or numeral) imagery that represents the reality of a number concept.
What does numeral imagery look like? Here’s one example. Cecil was very good in math. He could think with numbers, arrive at answers in his head, and mentally check for mathematical discrepancies in finance or life situations easily. He explained this ability, “I just visualize numbers and their relationships. Certain numbers are in certain colors, and the number-line in my head goes specific directions.” Not only could Cecil visualize numerals and concepts, both types of imagery, but he also had an unusual talent for color imagery. He assigned colors to specific numbers!
“What color is the number 14?” he was asked. His eyes went up, and in all seriousness, he said, “Light blue.” Similarly, number 3 was reddish pink and the number 88 “kind of a purple.” Quizzed again months later, Cecil assigned the same colors to the same numbers. Chronological relationships appear in our minds on a number line, the days of the week, the months in the year. Imagery is our sensory systems’ way of making the abstract real. It is a means to experience math.
Concept Imagery
While imaging numerals is important to mathematical computation, another aspect of imagery is equally important: concept imagery. Understanding, problem solving and computing in mathematics require another form of imagery--the ability to process the gestalt (the whole). Sometimes children or adults can visualize the numerals, the parts, but cannot bring those parts to a whole, just as they can sometimes visualize individual words but cannot bring those words to a whole to form concepts. Mathematical skill requires the ability to get the gestalt, see the big picture, in order to understand the process underlying mathematical logic.
“Concept imagery is the ability to image the gestalt (whole),” Bell (1991). Concept imagery is basic to the process involved in oral and written language comprehension, language expression, critical reasoning and math. It is the sensory information that connects us to language and thought.
The ability to create mental representations for mathematical concepts is directly related to success in mathematical reasoning and computation. However, because some children do not have this imaging ability, they are often mislabeled as not trying, unable to retain information, or having dyscalculia (the inability to perform arithmetic operations).
Manipulatives May Not Be Enough
Joanie’s second grade class covered a review of recognizing numbers, addition, subtraction, and even some multiplication. They worked a lot with concrete manipulatives and Joanie was doing well at the end of the year. But her third grade teacher complained that Joanie didn’t know anything about numbers. Concrete experiences-manipulatives-have been used for many years in teaching math (Stern, 1971). However, like Joanie, many children and adults have often experienced success with manipulatives, but failure in the world of computation (NCTM, 1989; Moore, 1990; Papert, 1993). They have what has often been described as “application problems.”
Joanie’s second grade class had spent a lot of time with manipulatives. Some of the children moving on to third grade continued to “think with numbers.” Their experience with manipulatives became part of their mental deposit of imagery. Like a bank deposit, these images could be drawn upon at will. However, not all children create mental imagery as they work with concrete manipulative. For these children, the process of turning the concrete experience into imagery must be consciously stimulated.
On Cloud Nine® Math Concrete to Imagery to Computation
Arnheim (1966) wrote, “Thinking is concerned with the objects and events of the world we know…When the objects are not physically present, they are represented indirectly by what we remember and know about them…Experiences deposit images.”
Numbers can be experienced and the relationships between them can be made concrete by using manipulatives. What appears abstract can be experienced and imaged to concreteness. Math’s roots are in the realm of the concrete, and imagery is the link to mathematical processing, retention, and application.
To develop concept and numeral imagery, the On Cloud Nine® math program (developed by the authors) integrates and consciously applies imagery to the cognitive process of computing and conceptualizing math and mathematical principles. As individuals become familiar with the concrete manipulatives, they are questioned and directed to consciously transfer the experienced to the imaged. They image the concrete and attach language to their imagery. The integration of imagery and language is then applied to computation. Individuals develop the sensory-cognitive processing to understand and use the logic of mathematics.
The program moves through three basic steps to develop mathematical reasoning and computation using: 1) manipulatives to experience the reality of math, 2) imagery and language to concretize that reality in the sensory system, and 3) computation to apply math to problem solving. On Cloud Nine® manipulatives serve two purposes: 1) to concretize numbers and mathematical concepts, and 2) to serve as a base for establishing imagery.
When asked to add the numbers 3 + 2, children who are drawing on their vault of images may see 3 apples and 2 more oranges to show 5 pieces of fruit. Others may draw on an image of a number line and place their mental finger on the 3 as a starting point. The “+” tells them to move forward and the “2” indicates how many places. They know the answer because they can “see it” in their mind’s eye. These children may look up as they access their images (defocusing). Children who don’t seem to have a vault of images may say things like “I don’t remember that one.” They need explicit instruction in imaging the concrete and applying that imagery to the computation.
How does imaging as a conscious process work? The On Cloud Nine® math program begins with numbers in isolation—numeral imagery. A student is asked to view the written numeral, and then it is taken away. The student must demonstrate the “number” underlying the numeral by showing how many cubes represent that number. The student sees, says, and writes the number in the air. The goal is for the student, when she sees the numeral, to immediately create an image of the formation of that number and the value behind it.
The process continues with experiencing the number line, first as a concrete manipulative, then as a flexible mental image. “Show me where you see the number 15?” “What’s the number one step up from that?” “Is the 3 close to the 15 or quite far away?” “What number is closer to the 15 – the 10 or the 5?” Students develop a number line they carry with them in their vault of images. These students can access their vault of images at will. Conscious imagery and the ability to simultaneously create images and verbalize these imaging—dual coding—are continued as children are taught addition, subtraction, word problems, multiplication, division and more advanced math.
On Cloud Nine® math integrates and consciously applies imagery to the cognitive process of computing and conceptualizing math and mathematical principles. Children image the concrete and attach language to their imagery. The integration of imagery and language is then applied to every aspect of mathematical computation.
All children can develop the sensory-cognitive processing to understand and use the logic of mathematics. In every aspect of math, children can have access to what becomes an innate bank vault of imagery for memory and computation.
Nanci Bell, owner and director of Lindamood-Bell Learning Processes, is the author of two books on imagery as the base for language processing. KimberlyTuley, the director of operations for Lindamood-Bell is a trainer and consultant in the application and refinement of Lindamood-Bell® programs. Bibliography Aristotle. (1972). Aristotle on Memory. Providence, Rhode Island: Brown University Press. Arnheim, R. (1966). Image and thought. In G. Kepes (Ed.). Sign, Image, Symbol. New York: George Braziller, Inc. Bell, Nanci. (1991). Visualizing and Verbalizing for Language Comprehension and Thinking. Paso Robles: NBI Publications. Moore, David S. (1990). On the Shoulders of Giants: New Approaches to Numeracy. Steen, L. (Ed.). Washington, D.C.: National Academy Press. Papert, Seymour. (1993). The Children’s Machine: Rethinking School in the Age of the Computer. New York: Basic Books. Paivio, Allan. (1981). Mental Representations: A Dual Coding Approach. New York: Oxford University Press.
Stern, Catherine and Stern, Margaret B. (1971). Children Discover Arithmetic. New York: Harper & Row, Publishers, Inc.
Why can’t everyone think with numbers? Why do some children learn math readily, handle money and time concepts with ease, retain information from year to year, and think with numbers effortlessly? What cognitive processes do some have that others do not?
Handwriting Analysis Speed Learning video by Bart Baggett
In today's highly competitive and ever-changing world it is extremely important to acquire the ability to explain your point of view, your contention as well as the gist of the topic you are familiar with. Whether you intend to become a teacher or have chosen other career path, it is imperative, even indispensable for many careers to develop good communicative skills. During your study at the University you might be assigned with several types of written assignments that help you to develop and enhance communication skills. I would like in this article to focus on two of them, expository essay and persuasive essay. In spite of the fact that the structure, style and some other elements of these writing projects are similar, there are some notable differences between them.
The main purpose of expository essay is to teach you to develop communication skills by learning how to acquaint your reader or listener with the knowledge that you possess. Depending on the subject you are assigned with, your expository essay should include factual information which should be backed by reliable, trustworthy and up-to date evidence. It might be advisable to write in the third person in this type of the written assignment. Try to avoid using of such words as "I", "we" or "our "as much as possible. In this way your expository essay would fit more to the standards of the educational institution set for this type of the essay. Also, remember as this is a factual essay you should avoid explaining your point of view or contention on particular subject, as in this case your attitude must be defended. The essay, where your contention is stated and defended is named "persuasive essay", I will deal with it later. Let us examine how the expository essay should be composed. First you must state your thesis. One should bear in mind that it must not be too broad as the length of expository essay is usually short. Your sentences should be written in easy to read, logical and coherent style. All facts should be backed up by evidence. One should restate the thesis in the last final paragraph of the essay. If you follow these simple rules you will be bale to compose the expository essay that meets the requirements set by your tutor.
In contrast to expository essay, persuasive essay should not only provide your reader with your contention, it should back it up so the reader understands why your point of view is better than the contentions of your opponents. Whereas the main purpose of expository essay is to explain the facts of view, the aim of persuasive essay is not only to explain your point of view, but to convince the reader that your point of view is right. The plan of your persuasive essay might be similar to expository one; however, it is advisable to include in the body of your assignments several important elements. First, one should consider strong and weak point of your argument and the contention of your opponents. Second, your contention in this type of the essay should be backed by the up-to date and trustworthy evidence in order to convince e your reader that information provided by you is reliable. In this way it would be easy for you to learn how to persuade even the most skeptical persons.
About the Author
Keith Adams has been working as a leading editor at BestEssayTips.com - Essay Writing Tips for more than three years. Her professional interests relate to composing various types of essays such as persuasive essay and expository essay.
After taking the time to research, find, and a storage unit "Rent> a storage unit is time to start moving their extra belongings in it. Before you start throwing things from the back of your car your storage unit stop and think about the disaster that could be done. If you do not take the time to properly organize your new storage unit will be creating only a big fuss of items will be cleaned later. How your storage unit started in the right direction will save much time and energy in the future.
The first step for the organization of items in your storage unit is cleaning the unit out. This may seem ridiculous, but that will make all the difference in the world. Remember, unless your storage facility is brand new people probably have used their storage unit before. It is not uncommon for items that are left behind in an old storage unit and if not take the time to clean your property that is mixed with trash left by others.
Even if there is no property usually is in the best interest of an owner of the new storage unit for cleaning the storage unit carefully. This will help you avoid putting all boxes and containers down on spills, dirt and other messes. The best way to clean a new storage unit is carefully sweep all dirt and dust from the walls, while removing any insect nests or spider webs. Where possible try to vacuum the floor and then replace the cover Protecting the floor to help keep their insurance.
Once your new storage unit has been thoroughly cleaned can begin to place Larger items furniture and appliances inside the unit. Always make sure that no furniture or appliances leaned against the wall of the building. Try to keep at least an inch of empty space around the walls of your unit. This will help air circulate, which will help keep your storage area cool. When all the furniture and major appliances are in the storage unit carefully covered with plastic or furniture covers that will help protect of the elements.
Boxes placed in storage all should be about the same size. This will make it much easier to stack boxes initially and then put them back on if you ever need to move or remove any items from storage . Make sure all the boxes are carefully labeled in detail. You never know when it will take all storage or will need some storage and without labels that will be playing a guessing game very frustrating. Labels should be on all sides of the box so you can easily see what you are looking for without change of boxes and furniture out of his way.
When you start stacking boxes in the storage unit to try to stack on top of furniture and appliances whenever possible. This will help you make the best use of your space. Avoid stacking boxes too high because you do not want to suffer an injury from falling boxes that have been too high for anyone to easily. If you are organizing a storage unit that is owned or if you plan to be frequently access to the boxes in place in a way that makes it easy for you to access.
After he managed to store everything you plan on storage unit to write a basic inventory list the number of boxes, furniture and appliances that are stored in the unit. Keep this information in a safe place with any insurance policy you purchased storage and contact information for the enterprise storage unit. This information is not to be very detailed but if you do want a detailed list that includes the contents of each box and then start keeping an inventory list when packing instead of waiting until everything in your storage unit.
Owning or renting a storage unit is a great way to get your house in order while not losing sight of some of their favorite belongings. With only a little effort and determination you can make your title = "storage unit"> storage unit is maintained as organized and well as their own, newly ordained, home.
About the Author
Simply Self Storage - What Could be Easier than Simply?
Simply Self Storage is the largest privately owned self storage company in the United States and Puerto Rico. We own and/or operate over 228 facilities with over 16.1 million square feet of storage space.
How to Stay Motivated While Writing Your Great Book
Here is a list of some activities that can help you stay motivated while writing your great book. Create some of your own.
1. Surround yourself with enthusiastic people with a positive attitude. Phone them when you need to be uplifted. Or send them an email and ask for their enthusiastic encouragement.
2. Your favorite music. It should be soft, easy listening, classical, upbeat, or some type of music that doesn't distract you from writing.
3. A well-organized, clean work area. Un-clutter your desk and you will un-clutter your writing life. If you are a natural disorderly person and insist that you can't work any other way, then, okay, that is you. Be sure to evaluate and assure yourself that your cluttered work area is really working for you.
4. Develop a plan for your book. Create a Table of Contents and you will know where you are going. You are less apt to get stuck when you write your book.
5. Limit distractions as much as possible. It means that dogs, cats, children, doorbells, phones, etc., must be avoided during your writing time. Even loved ones and friends must honor your writing time. Make an agreement to be with them after your SCHEDULED writing time is done.
6. Attend a Writers Retreat. You will be with others who are writing a book. You will motivate each other, get some terrific ideas to help you write and publish your book, and gain some new friends. Writers Retreats are a great way to boost your motivation and get the book done.
7. Get in The Zone - The Ultimate Energy Booster
Once all the "motivating factors" are in place there is no stopping you from your writing endeavor. You can do it.
When we have enthusiasm while writing, we are in The Zone. We have positive energy, which is actually a feeling of mild ecstasy. And when we have this feeling, we can do anything. We feel like a super hero. We have supreme confidence in our abilities and are totally immersed in what we are doing. We have to write during this time. We have total concentration and we speed through anything that gets in our way.
Write passionately about the things you love - something you believe with all your heart and soul. That is how you keep your enthusiasm. That is how to stay motivated.
Copyright 2008, Joan Clout-Kruse.
About the Author
America's Book Coach, Joan Clout-Kruse, helps entrepreneurs and business professionals write a biz book that will get them recognized as an expert, attract more clients and boost their income. Claim your Free audio and tips on writing your great book at http://www.WriteMyBizBook.com
3015 Cookson Elgin, IL - Large 4-5 BR semi-custom home in Providence subdivision.
Improve your Children's Education by Getting Online and Using the School of the Internet
Now days everyone that has a computer with an internet connection has their own personal tutoring service available for free in their own home. Parents have a free homework helper available anytime, day or night. Gone are the days when the entire family struggled to help their child with an impossible homework question posed by the teacher. Every piece of information is at our fingertips.
Both children that attend a local school or are involved in home schooling, can benefit and enhance their education by having access to the internet. Any information you can think of seems to be available on the internet. If your child needed to research a project for homework they would have no problem finding the relevant information. You simply type what you want into a search engine like google and it will show hundreds, if not thousands of pages matching your search words. For example I have wanted to find about about pronouns, verbs, adjectives, etc.. All I had to do was type in "what is an adjective" or "definition of a verb" or "example of a pronoun".
Children at the preschool age can also participate in activities which are not only fun, but extremely educational as well. Websites such as the Barbie web site or the Disney web site can help with your child's mouse skills, co-ordination, listening skills and improve reading skills.
You can also download free trial software from Schoolhouse
Technologies that generates and prints maths worksheets, find a words, and more. These programs are very easy to use and the kids love them.. They will be nagging for more worksheets because most children enjoy completing them.
There are also web sites for making crafts, learning to spell, downloading educational games, writing poetry, reading music, designing web sites, and much more..Visit a website that I designed with no training other than the internet.Free Computer Education
Any child or adult can learn about absolutely anything on the world wide web. Go and give it a try!! Notes:If your children are going to use search engines to browse the internet you will need a net nanny or filter to stop inappropriate pages from coming up in the results.
About the Author
Mitz Pantic writes articles for a number of websites. Go to the Free Computer Education website to see more articles
Choosing the right writing curriculum for Home Schooling
When choosing a writing curriculum to home school your children, you will want to consider a few things. It is not a bad idea to sit down with the members of your family who will be acting as teachers and go over a few questions. For example, will you want a home school curriculum that is structured or do you prefer something that you can take from but not completely follow? Will your style of writing instill a sense of confidence in your children by letting them express themselves in their writing? Do you want to be a hands on teacher or allow your children to learn on their own with the tools you provide? Would you like to have the support of others to help with grading and lesson planning? Is writing important to you, or would you prefer to concentrate on other subjects?
These are just a few starter questions to get you thinking about how you want to teach, which will help you narrow down your choices for home school writing curriculum. You can always visit the websites of the programs you are considering and look at reviews and read information about them to do comparisons. Here are a few writing curriculums that are popular:
Braver Writer - Written by a mom who home schools as well as a professional writer. It is an extremely structured writing curriculum that instills confidence in your children and makes them comfortable about their writing.
Institute for Excellence in writing - One of the most popular writing curriculums for home schooling. It is based on classical education so will be the most like teaching from a regular school curriculum. It has assignments that help develop writing skills and is also very structured.
WriteShop Incremental Curriculum - Used for middle and high school students, this writing curriculum does not focus on overall writing, but rather one specific skill. Everything is included in the program, lesson plans, teacher's aides and instructions for grading. It is less structured than others even with all that is included.
Write at Home - A good choice if you are looking for an online program. Your children can take workshops and classes to improve their writing. Tutors are also available. This is a great option for those parents who are new to home schooling.
Writing Standards - Also very popular with home schooling parents. All grades are covered so can be used for families with children in varying grades.
Writes Source - Although this is not a formal curriculum, many children enjoy it. It has great resources for parents and children and comes in varying levels.
As you can see, there are many choices when it comes to home school writing curriculum. Your best resource for making the decision is to talk to other parents who home school their children. They will be able to give you valuable information on what has worked for them, and what has not. You can also find information on the Internet, and resources for home schooling parents. If you are able, get involved in a home school group where you can meet other parents and children. You may not make the best choice your first time around, but the beauty of home schooling is you can try again until you find something that works for your children.
There are numerous benefits to home schooling and choosing the proper home school curriculum for your child, including math, science, and a writing curriculum too. For more information about Home School and Curriculums, please do visit our site - http://www.homeschoolcurriculum.org/
Does Your Home School or Gifted Child Need Professional Writing Tips from a Published Author?
Would you waste money on an opera ticket for this guy?
'Of course I love opera,' he said, foot tapping restlessly.
Research has shown that the old adage is true: Actions (such as a foot tapping) do speak louder than words. So when we write, we should 'show' with actions, not 'tell' with words.
Kids like to state outright: 'Michael was in a bad mood.' However to make it convincing they should actually show Michael in action.
List what a teenager would do if he came home annoyed:
* Slam the front door
* Throw his bag into the bedroom
* Kick off his shoes
* Head to the kitchen - and the fridge
* Complain there was no food.
So now you have the ideas, it's easy to put this all together into a paragraph.
She was just powering down the computer when the door slammed. Michael was home.
'Hi,' she called. 'How was school?'
There was a grunt, barely heard, and then the sound of a bag hitting the bedroom floor hard. Not good. She sighed and headed into the kitchen. Michael was already there, staring with slumped shoulders into the open fridge.
'Darn,' he said, shoving the door shut hard. 'There's never anything to eat in this house!'
She took a deep breath and counted to ten before she replied.
Showing, (not telling) takes longer to do, but it brings characters to life and is far more convincing too.
Ask your kids to brainstorm about 20 things that 'show' a Dad hates gardening.
e.g. the weeds are 30 cm tall.
e.g. he goes off to the hardware store - and takes 4 hours to get back.
When the list is long and interesting, get kids to pick a few things and write a paragraph to 'show' exactly what Dad feels about gardening.
I often give younger kids an opening sentence as it helps them to focus.
'What great weather we've got for the working bee,' said Mum, pulling on her gardening gloves.
They can ignore this of course if they have a better idea.
To reinforce the skill, students can do this every morning for a week. Here are some sample topics:
A teacher is about to get married.
e.g. Her nails are always painted so she can flash the ring around.
Opening sentence: 'Now, next term I won't be here of course,' said Miss Bettersley...
A parent and a kid are always fighting about playing computer games.
e.g. Kid flicks the screen off every time the parent comes in.
Opening sentence: 'How did the Maths test go?' I was barely home from school and Mum was on my back again.
The new neighbours are a pain.
e.g. The radio plays loud sport every weekend in their back garden.
Opening sentence: 'Hey Mate, can you turn the footy down a bit?' yelled Dad over the fence.
A girl thinks a guy is really hot, but is too shy to tell him. (Or vice versa)
e.g. She stammers and mumbles when they talk.
Opening sentence: 'Isn't that Ken over there?' asked Shelly.
Remember the chunking concept. Don't get kids to write a whole story, just one paragraph.
(c) Jen McVeity, National Literacy Champion.
About the Author
The fun Seven Steps to Writing Success program, by successful author, Jen McVeity, is in 900+ schools. Suited to the home school curriculum & gifted children, it has rapidly increased students' writing skills and enjoyment. Visit http://www.sevenstepswriting.com for top writing tips and activities - more in the free Parent Newsletters. Click on 'Sample' tab for a free Story Starters Worksheet.
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