The History and Different Critiques of Critical Pedagogy

The History and Different Critiques of Critical Pedagogy The literature of critical pedagogy is very broad indeed and contains dense information. In fact, the political perspective of critical pedagogy towards the curriculum contributes much to creating abundant scholarships in the field. In addition, as many authors perceive, critical pedagogy lacks a set of definite principles; which makes the process of setting a unified definition of its premises so challenging. Still, the implementation of aspects of critical pedagogy in the classroom setting can have wide scale results on the teaching process as a whole. Hence, it is important to give a brief examination of the literature of critical pedagogy, an analysis of its core principles, and an investigation of the critique directed against its assumptions. By virtue of being critical, critical pedagogy and critical thinking share some common grounds. However, despite the existence of the critical stance in both disciplines, there are broad differences between them. One of these differences is related to the expectation of action in each discipline. In its emphasis on analysis and deep interpretation, critical thinking does not necessitate any action to achieve social change. On the other hand, the principles of critical pedagogy aim at creating a social action that comes mainly through educational practices. Another important difference has to do with the scope of interest of each discipline. Critical thinking is, by definition, individualistic and largely ignores the collective relations. Critical pedagogy, on the other hand, is more concerned with corporate action; that is why, as Burbules and Berk suggest, in critical pedagogy individual criticality is intimately linked to social criticality (55-56). Critical pedagogy might also be thought of as an extension of critical theory. Both critical theory and critical pedagogy employ their strategies with view at obliterating the hegemonic collective standards and paradigms. However, critical pedagogy is different from critical theory in the fact that it is mainly an educational philosophy that reacts towards the oppressive systems in the educational arena. The primary concern of critical pedagogy in this aspect is with issues that have to do with maintaining equal opportunities and establishing dialogical mode of discourse. As Burbules and Berk put it in the language of critical pedagogy, the critical person is one who is empowered to seek justice, to seek emancipation (50). Collins also describes the framework of critical pedagogy as being realistically involved in enlarging the sites within our institutions where genuine, noncoercive dialogue and reasonable opposition to oppressive bureaucratic controls can emerge (63). This proves that critical pedagogy involves an entirely new orientation that departs from traditional models of education and embraces a number of principles that may not be familiar in the generic pedagogical systems. The basic characteristic that separates critical pedagogy from other approaches is its celebration of social justice and emancipation. In addition, a critical approach to pedagogy is distinguished by an emphasis on dialogic interactions with view at giving equal opportunities for all voices. Critical pedagogy values the students experiences and locates these experiences at the centre of the learning process. The mission of critical pedagogy is more complex than it seems to be, and its scope encompasses a plethora of pedagogical approaches and practices. In Life in Schools: An Introduction to Critical Pedagogy in the Social Foundations of Education, McLaren points out that critical pedagogy aims at investigating, questioning and changing the relationship among different factors in the learning experience. These factors include classroom teaching, the structure of the school, and the social relations with the community. This imposes a great task on the critical pedagogue as he has to take into account a wide range of social and educational variables in his work (26-28). Critical pedagogy has its roots in Paulo Freire who is generally considered to be the inaugural philosopher of critical pedagogy (McLaren, Paulo 1). Although at first Freire dedicated his efforts to issues related to literacy in Brazil, his philosophy expanded gradually to embrace a cornucopia of social and educational issues that have been the object of criticism. In Pedagogy of Freedom: Ethics, Democracy, and Civic Courage, Freire pointed out that what he called for was not merely a pedagogical method; rather, it was a strategy of living within the educational system (67). McLaren observes that the bottom-line of Freires pedagogy is to establish a non-hegemonic approach that is based on dialogue and interaction (McLaren, Paulo 2). This clearly shows the political dimensions of Freires philosophy. Freire actually stressed the importance of incorporating social and political critiques in the curriculum. This explains why his approach promotes a liberatory form of education that emphasizes emancipation and rejects all forms of oppression and domestication. In The Politics of Education, Freire maintains that the learning process should take into consideration two essential dimensions. The first is the context of authentic dialogue between learners and educators (49). The dialogue will empower students to move toward becoming knowing subjects and they will develop a relationship with the teacher in which one knowing subject [is] face to face with other knowing subjects (49). For Freire, by employing authentic dialogue in the teaching process, education becomes pedagogy of knowing rather than an experience of narration sickness (Freire, Oppressed 57). However, Freire warns that the dialogic process should not be reduced to simple to-and-fro questions that may also become tedious and sterile. Instead, there should be a focus on creating interaction between students and teachers in problematizing knowledge. In this regard, it is the responsibility of the teacher to inspire students to move forward within this critical practice (Freire, Freedom 80). The second dimension that should be considered in the learning process is the social realities in which students live. Freire states that authentic thinking, thinking that is concerned about the world is concerned with reality, and does not take place in ivory tower isolation, but only in communication (Freire, Oppressed 64). This suggests that earning should be connected to the realities of students lives. Otherwise, by ignoring these realities, educators will be creating divisions that make difficult the construction of our ideals of change and transformation (Freire, Freedom 55). A very influential concept in Freires philosophy is that of praxis. Freires praxis, which delineates critical reflection and action, entails the application of educational practices and philosophies to create a better educational experience. To this end, students should be viewed as active participants in the teaching process and in the formulation of teaching methods. They are engaged in what Simon calls a transformative critique of their everyday lives (Simon, Teaching 60). The teachers role here resides in encouraging students to get involved in reflection on their worlds so as to assist them in engaging in critical consciousness. For Freire, the development of critical consciousness in the student can be attained by means of implementing what he called the problem-posing model of education. Freire proposed this model as a counterpart to the banking system of education dominating the educational institutions. He asserts that the banking system fosters domination and oppression, whereas the problem-posing mode promotes liberation and democracy. He goes on to claim that whereas banking education anesthetizes and inhibits creative power, problem-posing education involves a constant unveiling of reality. The former attempts to maintain the submersion of consciousness; the latter strives for the emergence of consciousness and critical intervention in reality. (Freire Oppressed 68). Freires philosophy of education was adopted and modified by various writers. The most prominent figure in this aspect is Ira Shor, who was mainly influenced by Freire. In his Critical Teaching and Everyday Life, Shor criticizes the institutionalized modes of education which involve undemocratic approaches. He demonstrates that these traditional systems have restricted students from contributing to the learning processes. He calls for implementing learning activities that are democratic in nature. These activities are set against the notions of education that students have from their previous experiences within the traditional pedagogical system. The democratic methods of teaching would change the role of students from passive to active critical subjects in which they become active participants in their own learning (111-113). Shor also pointed out some of the limitations of Freires assumptions. Examining the applicability of the Freirean philosophy, he stressed the difficulties involved in implementing the principles of this philosophy within the classroom setting. In his When Students Have Power, he strongly argues that despite the benefits gained from the implementation of the assumptions of critical pedagogy; these assumptions do not go smoothly when turned into practice in the context of classroom environment (56). However, Freire responded to this claim when he stressed the fact that his educational philosophy was not merely a collection of strategies that could be implemented in all educational environments. Rather, different educational practices should be adapted depending on each individual context. Freire acknowledged that pedagogy is influenced by ideology and since ideologies vary a lot, the existence of a single philosophy of critical pedagogy is not practical. Hence, one cannot speak of pedagogy but must speak instead of pedagogies which respond to particular necessities, interests and conditions (Gaudiano and de Alba 128). The challenges of reaching a definite conception of critical pedagogy brought about different approaches to the philosophy by many writers. bell hooks, for example, supports Freire in promoting the link between theory and practice in order for the student to be the center of the teaching process. However, she does not employ Freires concept of critical pedagogy. Rather, she has introduced what she calls engaged pedagogy. She defines it as a system that combines anticolonial, critical, and feminist pedagogies à ¢Ã¢â€š ¬Ã‚ ¦ for interrogating biases in curricula that reinscribe systems of domination à ¢Ã¢â€š ¬Ã‚ ¦ while simultaneously providing new ways to teach diverse groups of students (qtd. in Florence 10). A central feature of this model is the repudiation of the use of sophisticated language; a key feature of traditional educational methods that creates barriers between students and teachers. Roger Simon has introduced another significant approach to critical pedagogy which he calls pedagogy of possibility. In his Empowerment as a Pedagogy of Possibility Simon contends that proposing pedagogy is also proposing a political ideology. Hence, this model of pedagogy aims at enabling a particular moral project, a particular not yet of how we might live our lives together (372). He stresses the fact that such a pedagogy will require forms of teaching and learning linked to the goal of educating students to take risks, to struggle with ongoing relations of power, to critically appropriate forms of knowledge that exist outside their immediate experience, and to envisage versions of a world that is not yet in order to be able to alter the grounds upon which life is lived (375). Like Freire, Simon stresses the importance of not looking at his ideas as mere abstractions. Rather, they should be put into practice in all educational environments. Teachers who would implement the principles of the pedagogy of possibility must not expect a guideline for techniques to be adopted, but rather approach such a task strategically, locally and contextually formulating practice within an integrated moral and epistemological stance (Simon, Teaching 58). This will lead to a possibility for creating counterdiscursive activity that attempts to provoke a process through which people might engage in a transformative critique of their everyday lives (60). The complexities inherent in critical pedagogy have given rise to many critiques of its principles and assumptions. The scope of the criticism directed against critical pedagogy is so vast that it includes critiques from disciplines such as feminism, and postmodernism. It is of high importance to shed light on some these critiques directed against critical pedagogy in order to identify the potential challenges in implementing its practices in classroom environment. The first critique to be considered is that which comes from the very nature of critical pedagogy itself. Critical pedagogy inherently requires a constant investigation of its principles and practices. In this aspect, Giroux and McLaren contend that many current trends in critical pedagogy are embedded in the endemic weaknesses of a theoretical project overly concerned with developing a language of critique. Critical pedagogy is steeped in a posture of moral indignation toward the injustices reproduced in American public schools. Unfortunately, this one-sided emphasis on critique is matched by the lack of theoretical and pragmatic discourse upon which to ground its own vision of society and schooling and to shape the direction of a critical praxis (32). In her The Struggle for Pedagogies: Critical and Feminist Discourses as Regimes of Truth, Jennifer Gores critique of critical pedagogy is based on her contention that there are two distinct versions within critical pedagogy; she identifies these versions according the prominent figures who most contributed to the philosophy of each strand. The first version contributes to what she calls pedagogical practice. She suggests that Freire and Shor represent this strand of critical pedagogy which offers concrete suggestions and examples taken from their own pedagogical practice, and which is intended to help other educators (40). Gores criticism is directed against the other approach which she calls pedagogical project. This approach is represented in the contributions of many significant pedagogues, mainly Giroux and McLaren. Gore claims that their approach relies heavily on an abstract political vision and should not be called critical pedagogy, but critical educational theory (42). She goes on to argue that the major shortcoming of such an approach resides in its failure to delineate a set of practices for classroom teaching. As a result, their pedagogy might be seen to restrict its audience to those readers who have the time, energy, or inclination to struggle with it à ¢Ã¢â€š ¬Ã‚ ¦ and, in so limiting its audience, it subsequently limits its political potential (38). Essentially, Gores criticizes the fact that such critical pedagogues tend to focus on abstract theories that lack the potential for implementation. As an example, Gore cites the concept of empowerment, which is a key principle in critical pedagogy. Within the pedagogical project model, the concept of empowerment has been confined to extreme abstraction that forces teachers to be the agents of empowerment, without providing much in the way of tangible guidance for that work (Gore, What 66). Hence Gore calls for creating guidance for teachers so that principles of critical pedagogy can be translated into reality. However, Gore does not call for creating recipes for educational practices. Rather, she contends that theorists of critical pedagogy should take into consideration the context of the educational process instead of merely adhering to a unified theoretical background (Gore, What 67). As mentioned above, Freire himself rejected an essentialist view of critical pedagogy and called on teachers to adapt the learning process to the context of students experiences. In this regard, a great responsibility lies on teachers in determining the methodologies appropriate for each particular context. Similarly, Elizabeth Ellsworth employs a feminist perspective to refute any essentialist interpretation of critical pedagogy. She goes on to claim that even the term critical is a repressive myth[s] that perpetuate[s] relations of domination and hides the actual political agendas à ¢Ã¢â€š ¬Ã‚ ¦ namely antiracism, antisexism, anti-elitism, anti-heterosexism, anti-ableism, anti-classism, and anti-neoconservatism (93). She also believes that theorists of critical pedagogy have failed to launch any meaningful analysis of or program for reformulating the institutionalized power imbalances between themselves and their students, or of the essentially paternalistic project of education itself (98). Moreover, Ellsworth develops a deconstructionist critique of critical pedagogues. She claims that these pedagogues are implicated in the very structures they are trying to change (101). She criticizes the fact that much of the literature of critical pedagogy is the work of the dominant white middle class men. She goes on to argue that a relation between teacher/student becomes voyeuristic when the voice of the pedagogue himself goes unexamined (104). In his Elements of a Post-liberal Theory of Education, Bowers basic criticism resides in his claim that, in a way, critical pedagogy enforces the assumptions and values of Western metaphysics. Although he promoted the contributions of Freire and his followers, Bowers believes that Freires model emphasizes the modernist way of thinking, and thus it reinforces Western values and principles. For Bowers, all Freires pedagogy is based on Western assumptions about man, freedom, progress, and the authority of the rational process (127). He claims that the problem with Freires position is not that he advocates critical reflection but that he makes it the only legitimate source of knowledge and authority (129). Although Freires emphasis on dialogue as a basic component of the educational process has been praised as a democratic strategy, Bowers criticizes the very notion of using dialogue as a tool for emancipation. He contends that relying on dialogue in this aspect shifts the locus of authority from that of community and tradition to the individual who unifies thought and action in a new praxis (129). This focus on the individual on the expense of other collective concerns has lead to the failure of critical pedagogy in addressing issues related to ecology and the nature of the world. As he puts it, The problems of inequality and restricted individual empowerment are not nearly as important as the cultural roots of our alienation from nature. Regardless of how our agenda for social reform is framed, the bottom line has to do with reversing the global ecological deterioration we are now witnessing (159). A very important critique of critical pedagogy that should be highlighted here is that which comes from a postmodern perspective. In their Dialogue across Difference: Continuing the Conversation, Burbules and Rice explore the postmodern critique of critical pedagogy. The authors start their argument by suggesting that there are two versions of postmodernism that hold different positions relative to modernism itself (397). They call these two versions postmodernism and antimodernism. The authors suggest that a basic characteristic of postmodernism is that it goes beyond the norm but at the same time accepts the basic significance of the tradition it proposes to go beyond (397). They cite Giroux and McLaren as examples on postmodernist critics who relish some key democratic assumptions of modernism and yet go beyond them. Antimodernism, on the other hand, defines itself as the antithesis of modernism and is characterized by a strong antipathy to the language, issues, and values of modernism (398). The authors criticize this strand and assert that having deconstructed all metanarratives and radically relativized all possible values, antimodernism is left with no clear way of justifying any alternatives (398). The different positions of postmodernism and antimodernism account for the dissenting views related to the relationship between critical pedagogy and postmodernism. In this regard, some writers strongly believe that critical pedagogy is far from incorporating the premises of postmodernism. In Reflective Teaching in the Postmodern World: A Manifesto for Education in Postmodernity, Parker holds the view that many critical educational practices involve some modernist assumptions and fail to account for a genuine understanding of the process of knowledge construction from a postmodern perspective (16). Similarly, there are other feminist and postmodernist writers who assert that some strands of critical pedagogy do not address such issues which are of high importance in the field. In her Freire and a Feminist Pedagogy of Difference, Weiler explores the conflict she perceives between the modernist orientations of critical pedagogy and postmodernism. As a feminist writer arguing from a postmodern perspective, she claims that her goal is to retain the vision of social justice and transformation that underlies liberatory pedagogies (450). She suggests that the universal goals of liberation do not directly analyze the contradictions between conflicting oppressed groups or the ways in which a single individual can experience oppression in one sphere while being privileged or oppressive in another (450). Accordingly, Weiler believes that the theory that calls for the existence of universal experience of oppression does not take into account the specific contexts of the classroom experience. Hence the focal point of her argument resides in redefining the collective experience in the context of historically defined struggles (Weiler 451). In this regard, Weiler claims that Freire ignored the existence of diverse experience of oppression; hence she calls for a more situated theory of oppression and subjectivity, and for the need to consider the contradictions of such universal claims of truth or process (456). Weiler argues for a feminist-postmodern approach to confront the deficits in Freires philosophy of pedagogy. In this regard, she delineates three major issues where this process can be implemented. She names these as the role and authority of the teacher, the claims for knowledge and truth in personal experience, and the question of difference. Weiler concludes by asserting that the existence of different approaches in this arena does not necessitate abandonment of the goals of social justice and empowerment, but it does make clear the need to recognize contingent and situated claims and to acknowledge our own histories and selves in process (470). On the other side of the spectrum, there are many writers who strongly believe that critical pedagogy strongly incorporates some aspects of postmodernism. In Critical Crosscurrents in Education, Collins sheds light on this link between critical pedagogy and postmodernism as he suggests that, like critical pedagogy, postmodernist critical discourse is about the struggles for power to be heard about the empowerment of other voices' (76). In the same vein, Pinar et al. suggest that there is a possibility for developing a strand of pedagogy that engages in some postmodern principles. This version of pedagogy goes beyond the issues of oppression and suffering that are merely viewed from a class- struggle perspective (305). Other writers share the same view and contend that the philosophy of Freire and other critical pedagogues does incorporate some postmodern dimensions. Most of these writers approach this issue through dividing Freires writing into different phases, stressing that the postmodern orientations appear in his later work. Peters, for example, suggests that there are some postmodern ideas that can be clearly seen in Freires later work. These ideas include Freires emphasis on textuality, subjectivity, experience and culture in addition to his own interpretation of oppression and power (117). Similar to Peters, Roberts asserts that in order to locate the modernist inclinations in Freires writing we should look at Freires work as a whole, and not to focus on his writings during the first stage of his work. Roberts contends that Freire did promote some postmodern techniques in confronting all forms of oppression. He also highlights Freires confrontation with postmodern critics, especially in his later writing. Roberts examination of this issue concluded in his contention that Freire argues for what he called progressive postmodernism. Freire has stressed the fact that educators should challenge modern ways of thinking through becoming more tolerant, open and forthright, critical, curious, and humble (112). Clearly, the above argument proves that any attempt to come up with a clear-cut definition of critical pedagogy is utterly challenging. As mentioned above, there are multiple approaches to critical pedagogy, and there are also variables from other disciplines that are easily accommodated in this literature. All this results in creating critical pedagogies rather than one definite and universally- accepted form of critical pedagogy. These critical pedagogies are always involved in a constant process of redefinition and change, thus imposing great challenge on pedagogues in this regard. Despite these variations and challenges, teachers are always urged to go beyond the mere theoretical background of critical pedagogy. The process of theorizing without action creates no change and goes against the objectives of critical pedagogy. Teachers must promote an integrated approach of theory and practice, or what Freire called praxis. In other words, they should seriously consider the potential for implementing the premises of critical pedagogy in the teaching process. This implementation should go beyond the mere adherence to an essentialist view of a critical pedagogical methodology. Teachers should attempt, to the best of their abilities, to locate the teaching process within the realities of students lives. They should take into account the various variables, realities and experiences pertinent to students lives. Hence, they should adapt their techniques according to the specific variables pertinent to the context in which they work. The critique directed against critical pedagogy maximizes the need for this constant action on the part of teachers. In addition to adapting their educational tools to the classroom context, teachers are exhorted to encourage the involvement and empowerment of the students. Without putting the assumptions, principles and paradigms of critical pedagogy into practice, teachers run the risk of going within the traditional mainstream models of education. As Bahruth and Steiner beautifully put it: in our profession we have two choices; we can succumb to the mainstream and become programmed toward deskilling our intellect, or we can become critical pedagogues and liberate ourselves and those who choose to join in the dialogue (143).

Personal Narrative- Lost Wallet :: Personal Narrative

Personal Narrative- Lost Wallet A wallet, or purse for some, is a precious item in which most people carry things more essential than money towards everyday life. If some people were to lose that portable safe, they may be offset for the rest of that day. The person without that wallet could be cranky or depressed for a while. Maybe something of great sentimental value was in that wallet. This person could stay hold these feelings for a long time, until they find their belongings by which case they are filled with joy. I, personally, keep anything I may have interest in knowing where it is, in my wallet. I am very good about always having my wallet and never losing it...until recently. In my wallet, I store dire personal items such as my lisence and some pictures. Among other things, I have my money, like everybody else, and certificates for stores. This summer, I went to the Keys with my family. I drove down there with my wallet and took it everywhere with me, like I would any other time. Well, when someone doesn't have pockets, then it is hard to keep their wallet right next to them at all times. I was carrying my wallet out from the hotel, along with my keys, and set both on top of the car. When I figured out that I needed the keys in order to get in the car and turn it on, I took them off the top of the roof, leaving my wallet behind. I sat in the car, car door open, waiting for my dad to make it to the car so we could all go to a diving area. Once he made it to the car, without thinking, I closed the door and started the car. I had been driving about half a mile before I realized that my wallet was no longer on my body. Immediately, I pulled the car over, and the next hour or so was spent looking for my wallet. All I could think about was what I would lose if I didn't find my wallet. The week before was my birthday, and I was given $60 to Best Buy and $50 to Auto Zone. Aside from that I had $3 in cash. While walking up and down the road that my wallet flew off on, my sister found my two Best Buy cards.

RFID Technology Essay

RFID is a general term that is used to describe a system that transmits the identity data of an object wirelessly, using radio waves. This is sometimes referred to as contact-less technology and a typical RFID system is made up of three components: tags, readers and the host computer system. Tags – An RFID tag is a tiny radio device, it’s also referred as a transponder. The tag comprises of a simple silicon microchip attached to a small flat aerial and mounted on a substrate. The whole device can then be encapsulated in different materials (such as plastic) dependent upon its intended usage. The finished tag can be attached to an object, typically an item, box or pallet and read remotely to ascertain its identity, position or state. Different types of RDIF Tags available are passive and active, used as per the RDIF data read / write requirement. Readers – The reader, sometimes called an interrogator or scanner, sends and receives RF data to and from the tag via antennas. A reader may have multiple antennas that are responsible for sending and receiving radio waves. Host Computer – The data acquired by the readers is then passed to a host computer, which may run specialist RFID software or middleware application to filter the data and route it to the correct IS application as processed useful information. RFID can help hospitals to locate equipment more quickly, logistics providers to improve the management of moveable assets, brings efficiencies in the supply chain by tracking goods from the point of manufacture through to the retail stores, used as EZ card for toll-collections, remote car door access. Use of RFID technology can increase business productivity and reduce associated costs. Because of such potential benefits of RFID, many of the world’s major retailers have adopted RFID tagging for pallets and cases shipped into their distribution centers. To ensure that companies benefit from the advantages RFID provides it is important to understand how to adopt this technology. RDIF technology is been accepted by many retail chains like Wal-Mart, Tesco, Metro etc. For the supply chain and operations it provides increased levels of product and asset visibility. Retailers are looking at using the RFID technology to automatically receive shipments, and have greater visibility into the merchandize in the warehouse and on the store shelves. Few of the current Issues Facing RFID Adoption * Globally interoperable standardization problem: RFID has been implemented in different ways by different manufacturers; global standards are still being worked on. Because no global standards defined for RFID adoption, interoperability between applications or devices are not possible, which can significantly accelerate the adoption of RFID technology. * Environment: Working environment is another issue of RFID Usage. The first one is water and liquids which can absorb the radio energy signals and thereby limit range or prevent tag read/write operations altogether. Metals are another material that generally reflect radio frequency signals and deflect the radio waves, thus altering their path. The temperature of the tagged products also affected the readings. Another issue in cased by dense reader or dense tag environment are collision which cause poor read rates. Dense reader environment consist of several readers places in one closed area resulting same tag been read by multiple readers resulting reader collision. A dense tag environment involves tags placed too closely to each other resulting in tag collision because of overlap in electromagnetic waves generated by the tags interferes when being interrogated by the reader. Right type of tag/reader has to be used depending on the product, tagging level, and operational environment. The right fit is in many cases obtained through tests, which will increase read rates and accuracy. * Data management: Many conversations about RFID inevitably end up by high volume of data and data management issues that are expected to arise from tagging individual products especially in retail store environment. Data management is a key issue for any organization deploying RFID technology, and the robust middleware is required to handle that much amount of data and route it to the right database is most concerned. The right architecture is required to filter and translate RFID into useful information. Also it’s important to identify what useful RFID data should be collected and stored, which will enable easier data management and processing.

Understanding Equivalent Equations in Algebra

Equivalent equations are systems of equations that have the same solutions. Identifying and solving equivalent equations is a valuable skill, not only in algebra class but also in everyday life. Take a look at examples of equivalent equations, how to solve them for one or more variables, and how you might use this skill outside a classroom. Key Takeaways Equivalent equations are algebraic equations that have identical solutions or roots.Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation.Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation. Linear Equations With One Variable The simplest examples of equivalent equations dont have any variables. For example, these three equations are equivalent to each other: 3 2 54 1 55 0 5 Recognizing these equations are equivalent is great, but not particularly useful. Usually, an equivalent equation problem asks you to solve for a variable to see if it is the same (the same root) as the one in another equation. For example, the following equations are equivalent: x 5-2x -10 In both cases, x 5. How do we know this? How do you solve this for the -2x -10 equation? The first step is to know the rules of equivalent equations: Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation.Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.Raising both sides of the equation to the same odd power or taking the same odd root will produce an equivalent equation.If both sides of an equation are non-negative, raising both sides of an equation to the same even power or taking the same even root will give an equivalent equation. Example Putting these rules into practice, determine whether these two equations are equivalent: x 2 72x 1 11 To solve this, you need to find x for each equation. If x is the same for both equations, then they are equivalent. If x is different (i.e., the equations have different roots), then the equations are not equivalent. For the first equation: x 2 7x 2 - 2 7 - 2 (subtracting both sides by same number)x 5 For the second equation: 2x 1 112x 1 - 1 11 - 1 (subtracting both sides by the same number)2x 102x/2   10/2 (dividing both sides of the equation by the same number)x 5 So, yes, the two equations are equivalent because x 5 in each case. Practical Equivalent Equations You can use equivalent equations in daily life. Its particularly helpful when shopping. For example, you like a particular shirt. One company offers the shirt for $6 and has $12 shipping, while another company offers the shirt for $7.50 and has $9 shipping. Which shirt has the best price? How many shirts (maybe you want to get them for friends) would you have to buy for the price to be the same for both companies? To solve this problem, let x be the number of shirts. To start with, set x 1 for the purchase of one shirt. For company #1: Price 6x 12 (6)(1) 12 6 12 $18 For company #2: Price 7.5x 9 (1)(7.5) 9 7.5 9 $16.50 So, if youre buying one shirt, the second company offers a better deal. To find the point where prices are equal, let x remain the number of shirts, but set the two equations equal to each other. Solve for x to find how many shirts youd have to buy: 6x 12 7.5x 96x - 7.5x 9 - 12 (subtracting the same numbers or expressions from each side)-1.5x -31.5x 3 (dividing both sides by the same number, -1)x 3/1.5 (dividing both sides by 1.5)x 2 If you buy two shirts, the price is the same, no matter where you get it. You can use the same math to determine which company gives you a better deal with larger orders and also to calculate how much youll save using one company over the other. See, algebra is useful! Equivalent Equations With Two Variables If you have two equations and two unknowns (x and y), you can determine whether two sets of linear equations are equivalent. For example, if youre given the equations: -3x 12y 157x - 10y -2 You can determine whether the following system is equivalent: -x 4y 57x -10y -2 To solve this problem, find x and y for each system of equations. If the values are the same, then the systems of equations are equivalent. Start with the first set. To solve two equations with two variables, isolate one variable and plug its solution into the other equation. To isolate the y variable: -3x 12y 15-3x 15 - 12yx -(15 - 12y)/3 -5 4y (plug in for x in the second equation)7x - 10y -27(-5 4y) - 10y -2-35 28y - 10y -218y 33y 33/18 11/6 Now, plug y back into either equation to solve for x: 7x - 10y -27x -2 10(11/6) Working through this, youll eventually  get x 7/3. To answer the question,  you could apply the same principles to the second set of equations to solve for x and y to find that yes, they are indeed equivalent. Its easy to get bogged down in the algebra, so its a good idea to check your work using an online equation solver. However, the clever student will notice the two sets of equations are equivalent without doing any difficult calculations at all. The only difference between the first equation in each set is that the first one is three times the second one (equivalent). The second equation is exactly the same.