Major Idea of Teaching Mathematics

Upon reading the framework, it is evident that the major idea of teaching mathematics in California public schools revolves around the development of a balanced instructional program that not only provides students with an enabling environment to become proficient in basic computational and procedural skills, but also to continuously develop conceptual understanding of the mathematical concepts and become proficient in problem solving.Advertising We will write a custom critical writing sample on Major Idea of Teaching Mathematics specifically for you for only $16.05 $11/page Learn More As indicated in the framework, teachers should aim to achieve a balance between these three concepts (proficiency in computational and procedural skills, attainment of conceptual understanding, and proficiency in solving new or perplexing problems) if they expect their students to be competitive in mathematics (California Department of Education, 2006). The concepts are in terrelated; hence teachers must strive to come up with methodologies and strategies to deliver them to mathematics students according to the standards of a particular grade level. As indicated in the framework, â€Å"when students apply basic computational and procedural skills and understandings to solve new or perplexing problems, their basic skills are strengthened, the challenging problems they encounter can become routine, and their conceptual understanding deepens† (California Department of Education, 2006 p.5). Consequently, it is suggested that the major idea of teaching mathematics to students in California public schools entails connecting their skills, conceptual understanding, and problem solving capability to develop a network of mutually reinforcing components in the curriculum that are intrinsically aligned with the standards depending on grade level. Examples of Teaching Strategies From the framework, it is clear that no single strategy of instruction is the b est or most appropriate in all contexts, and that teachers have a wide choice of instructional strategies including â€Å"direct instruction, investigation, classroom discussion and drill, small groups, individualized formats, and hands-on materials (California Department of Education, 2006 p.5). As one of the approaches to teaching, direct instruction is not only skills-oriented but the teaching practices it adopts are essentially teacher-directed.Advertising Looking for critical writing on education? Let's see if we can help you! Get your first paper with 15% OFF Learn More In teaching algebra and functions to grade six students, for example, a teacher can use small-group, face-to-face instruction to demonstrate to students how to solve linear equations and develop algebraic reasoning at each step of the process by breaking down the instructions into small units, sequencing them deliberately, and teaching them in an explicit manner. Although teachers can use this st rategy to ensure that Grade six students are able to use their computational skills and conceptual understanding to solve problems in algebra through explicit, guided instructions, the strategy nevertheless limits student’s creativity and active exploration. The other teaching strategy is investigation, whereby teachers play an active role in guiding students to identify a topic of interest, explore the current knowledge on the topic, frame the topic into manageable questions, gather appropriate information, analyze and synthesis the information, take action on the findings, and reflect on the outcomes found. This strategy could be used to teach geometry to grade six students as it does not only facilitate an explicit understanding of geometric concepts, including raising students’ levels of geometric thinking, but also motivates students by presenting mathematical topics in an enjoyable and interesting manner that challenges their intellectual development. Reflection Overall, upon reflection, I have learnt that no single method of instruction is the best or most appropriate in all situations, it is important to balance the concepts of computational and procedural skills, conceptual understanding and problem solving capability when teaching mathematics, in mathematics instruction, new skills are developed almost exclusively on previously learned skills, methods of assessing students for mathematics comprehension should be context-specific. These learning outcomes can be implemented in real-life classroom situations by coming up with a well formulated framework that does not necessarily follow a linear order to ensure students benefit from the mathematics lessons taught in class, and also by proactively aligning instruction with assessment. Reference California Department of Education. (2009). Mathematics framework for California public schools: Kindergarten through grade twelve. Retrieved from https://www.cde.ca.gov/Advertising We will wri te a custom critical writing sample on Major Idea of Teaching Mathematics specifically for you for only $16.05 $11/page Learn More This critical writing on Major Idea of Teaching Mathematics was written and submitted by user Teagan Cantrell to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Advantages of Bilingual Children.

Advantages of Bilingual Children. "Bilingualism is to intelligence as food is to human fitness....A simple statement about bilingualism and intelligence is as impossible as prescribing one simple food for human survival" (Baker 1). For 30 years experts have had ongoing discussions concerning the bilingual child and his mental abilities relating to intelligence and education. Originally, experts believed that a bilingual person could not be an intellectual, since he/she was carrying two or more languages in their head. Consensus has changed considerably over the past three decades, with the development and use of new testing. Children with bilingual ability offer an opportunity for researchers to explore the connections between language and thought (Bialystok Cognitive 643). Bilingual children have advantages in education, due to cognitive development, divergent thought, and mental flexibility.Cognitive ability relates to mental activity, such as thinking, remembering, learning, or using language. Research demonstrate s the differences in cognitive functioning between monolinguals and bilinguals.Category:Educational researchAnalysis and control are language components that develop later in monolinguals than in bilinguals (Bialystok Cognitive 636). These abilities refer to representation and selective attention in language that aid in comprehension and understanding. Adults who speak two languages in childhood are profoundly affected in their cognitive development (Bialystok Cognitive 643).This advantage can be manifest itself in several ways. The majority of field researchers conclude that this ability allows bilinguals the advantage of diversity and flexibility in cognition to a significant level over monolinguals (Latham 79). Gonzalez proposes that bilingual children naturally develop cognitive representation verbally, non-verbally, and symbolically (230). Truly bilingual students surpass monolingual students on many intelligence tests, both verbal and nonverbal (Latham 79). Language fluency is determined by listening, speaking, and reading abilities (Rosenberg 1).However, since levels of bilingualism exist, the affect to cognitive development is correlative (Latham 79). In a study conducted by Ellen Bialystok, both...

Puerto Rican Culture Essay Example | Topics and Well Written Essays - 750 words - 1

Puerto Rican Culture - Essay Example In my naivety, I had thought that Americans were very sophisticated people who lived harmoniously with one another. I never, not for a single second, thought that I would experience some of the worst discriminations in my life. I never thought that I would have to work several times harder to prove myself than other American kids had to. The realization that life in the U.S was not as rosy as I had been made to believe came as a shocker to me. In Colombia I had been grown used to the closeness of the people. Everyone was each other’s keeper, so to speak. I had very many companions back in Colombia because the sociability of the people makes it easy to make new friends almost every day (Waters and Ueda 216). However in America, the situation was quite different. First of all, I did know much English when I fast landed in the US, so communication was a big problem. I did not have to wait for long before I realized what it meant to be a Colombian American living in New York. Discrimination followed me almost everywhere I went. My ethnicity made me a subject of resentment from both white and African Americans (Olson and Olson 116). I did not consider speaking Spanish to be wrong, but to Americans, it was objectionable. Many regarded American Colombians to be illegal immigrants which was sometimes true. However, my mother had ensured that she had all the right papers before coming here. This of course did not stop other people from lumping us together with illegal immigrants. As such it was very hard for us since my mother, who also knew very limited English, could not get a good job. Colombian immigrants could only get casual jobs, and these did not pay well enough (118). It is a well documented fact that America is a highly fragmented society (Flores 19). This identity fragmentation affected me greatly when I was new in the country. I started very slowly in school since I could not communicate very well. In my school everyone was grouped

Working in Teams Research Paper Example | Topics and Well Written Essays - 1750 words

Working in Teams - Research Paper Example This paper describes the work in team and compares it with individual work. Teamwork has lately become one of the most essential ways in which work is being organized as organizations are increasingly delegating work responsibilities to work groups rather than individuals. Structural changes at the workplace such as the implementation of teams are more likely to increase efficiency while encouraging workers to work harder and smarter. Working in teams does yield better results over the efforts of any one individual because when a group of people works together actively, all their skills are harnessed effectively, thereby leading to the achievement of a common purpose. Individuals in the group are more confident about their abilities and are more willing to contribute their ideas because they will be enriched through the team member’s input. Unlike teams, individuals working on their own are often under pressure to perform that they may end up making simple mistakes that could easily avoided when working in teams. The team players can tolerate twice as much pressure as individuals working independently in rowing games. This analogy can as well be extended in a general team context, to explain that the pain threshold of individuals working in teams is much higher than that of independent workers, and this enables them to overcome challenges that come with work. In that respect, working in teams increases individuals’ competence to handle tasks as the members often build each other’s capacity with the sole purpose of enhancing the overall group performance.

The Right to Property Essay Example for Free

The Right to Property Essay Every person in this worls has the right to own a property according to availability of the same. This ownership is founded on his right to live and survive. However, the ownership of a property is subject to certain things that may be out of control of the person. These pertains to the inherent right of the government to act on every matter relating to its subjects. Based on principles and concepts, the ownership of property is very intricate as it involves complicated processes in the political system. Different countries do not have the same rules relating to property rights. As such, one rule may not be applicable to other people. However, no matter how complicated the processes may be, each individual with respect to his morals, nature, needs and other important factors may basically hamper the inherent right of every government to exercise its power. It is true that the government has the power govern the people based on the need of governmental existence, however, these right has its limitations. As every person is also entitled to his right to live a good life, these natural rights actually protect a persons property from any intervention from the government no matter what kind of intervention it may be. Ownership comprises the right to possess, the right to use, the right to manage, the right to the income of the thing, the right to the capital, the right to security, rights or incidents of transmissibility and absence of terms, the prohibition of harmful use, liability to execution, and the incident of residuarity. All these things may simply be understood on the right of every person to enjoy his property, a right to own or possess the same, the right to even destroy it and the right to exclude other people from its use in line with applicable laws. This is in line with the interplay of fact of ownership by a person and the right of the government to subject every person under the rule of law. The right to possess means the right to be put in exclusive control of a thing and enjoy the thing itself according to his will including the right to remain in control. It also include the claim that others should not without permission, interfer the exercise of ownership. The right or liberty to use at ones discretion has rightly been recognized as a cardinal feature of ownership and the fact that, as we shall see, certain limitations also occur. There is a need to follow this limitation in order to make the society harmonious. If we fail to do the same, the use of property without fundamental laws to follow will cause so much trouble in the political system. The right to manage is the right to decide how and by whom the thing owned shall be used. This decision shall rest from the discretion of the owner of the property. As such, he has the right to transfer or let other person use his own property. We should know that ownership has never been absolute. It has been subject to incidents of ownership as the prohibition of harmful use, liability to execution for debt, to taxation and to expropriation under the exercise of the inherent right of the government on eminent domain through public authority. Emphasis on the social aspect of ownership has, however, varied from age to age. Those sacred and inviolable rights, which, according to the Declaration of the Rights of Man, no one could be forced to cede except for public necessity have become, in French law for instance, liable to expropriation on grounds of public utility and subject to a general doctrine forbididng abuse. According to the liberal conception of ownership, there is a sharp distinction between 3 government and ownership. Though, in a loose sense, the said has the right to exercise the power of eminent domain over at least theland comprising its territory, this does not carry with it rights to possess enjoyment or even to alienate it, so that the sense in which the state is owner is very loose indeed. The interest of the state, according to this conception is confined to power of expropriation and a minimum of restrictive regulation, together with the expectancy of acquiring property as legally vacant or by escheat in some instances (Honore 113). This will give us the idea that the state can only hold a property of a person under the exercise of expropriation and other regulations that the government are required to implement. Another concept that is widely related to ownership and use of private property is socialism. Socialism has led to a revised view of the relation between government and ownership, at leat as regards some important types of property, such as land and business. This will mean, pertaining to practice, that the owners privileges of using and powers of managing a thing a she wishes have been curtailed and that the social interest in the productive use of things has been affirmed by legislation. In the negative, this process has meant that, in the interests of health and comfort, many substances cannot be used at all or can only be used in certain ways. For example, the sale of drugs is automatically controlled as it is harmful to the people, only smokeless fuel may be used in certain areas and garden hoses may not be used at certain periods. Such situations multiplied a thousand fold, have come to seem so natural that we hardly realize that the social interest in the use of things, the conservation of resources and in the details of manufacturing processes in a modern, though it is also a primitive, conception. 4 Now, another thing will be added to explain what has been expounded earlier. Positive control by the state shades into prohibition. The positive duty to exploit ones property in a socially beneficial way, as opposed to the prohibition of a harmful exploitation, has not been generally imposed as its implications fully worked out. It has something to do with the prohibition to use properties that may cause nuisance with other people or anyhting that will do bad things against other persons. A different form of state control is exercised by drawing a distinction between different types of ownership. The difference lies, of course, in the right of government officials to interfere in the management of the former categories and in state regulation of income rights deriving from the property, also in differing rules about alienation. In this way, the sphere of operation of ownership in the liberal sense is narrowed and a form of state participation in management substituted in the remaining sphere. These differences may be seen in the actual interplay of the implementation of property laws. Another form of social control consists in the exercise by officials of the management of things in ther private ownership of the state. Such arrangements present the form but not the substance of ownership in the liberal sense. Management and enjoyment are actually divided and political control, directly or indirectly, is exercised over the allocation of resources and the uses to which the thing owned is put. The nationalized industries in the United Kingdom folow this knid of pattern control. The next social control may be exercised by a restriction on the type of thing that is subject to ownership by persons other than the state, a sin the Russian building lease, where the building is owned by a private individual, the land remaining in state ownership. In effect, this restricts the privileges of the building owner in the general interest. 5 For us to understand the details on how government exercise of power was hampered by the natural rights of man to own different kinds of property, we will illustrate it by giving a concrete example. We will view a scenario that was given by Waldron when for instance a person owns a car. When a person owns a car, he has the legal capacity to use it in a certain way (Waldron 27). But it is true only in some circumstances. The owner of the car is not at liberty to drive it on the footpath or to drive it anywhere at a speed faster than seventy m. p. h. There is no liberty to drive it also without a license from the authorities because that would be illegal. The owner of the car has also the right not to let them use car without permission. However, the use of the car should not be a nuisance to his neighbors or should be in a good condition. As such, he may be liable to damages if it rolls into his neighbors fence. We should remember that these rights, liberties and duties are the basic stuff of ownership. But legal relations can be changed. If the person owns a car, he is in a position to change them. He has the power to sell it or give it to somebody else, in which case all the legal relations change. He has to take on the duties and limited rights of a non-owner of the car and someone else take son the rights, liberties, duties and powers of ownership. Or perhaps he lends or hires the car, that invokes a temporary and less extensive change in legal realtions. He can even bequeath the car in his will and testament so that someone else will take over his property rights when he dies. These are his powers to change his leagl situations or relations and that of others if he is the owner of the car. Finally, she may also, in certain circumstances, have his own legal position altered in relation to the car for instance, he is liable to have the car seized in execution of a judgment summons for debt.

Fear :: essays research papers

FEAR ?@   Ã‚  Ã‚  Ã‚  Ã‚  Recently, earthquakes have hit many places like, Kobe, Greece, Turkey and Taiwan. Moreover, some scientists predict that a huge earthquake will hit the Tokai area and it will have enough power to destroy the Tokyo area. I fear earthquakes for 3 reasons: anticipation of disaster, being on the point of death in the rubble, and becoming injured or sick. First, when any size earthquake hits, even a small one, I feel fear because my mind says, ?gSomeday there will be huge earthquake?h. Actually, a huge earthquake has not come yet, but psychologically I feel fear. For example, a few days ago an earthquake hit Tokyo. It was small but my heart beat so quickly during and after the earthquake that I could not do anything because I was so scared.   Ã‚  Ã‚  Ã‚  Ã‚  When a huge earthquake such as the Kobe earthquake occurs, many buildings and houses will be destroyed. At that time, I give full scope to my imagination that I will be buried under rubble. Actually, being buried under rubble is most frightening to me because I could become weaker and weaker and finally die. I am frightened not only of being buried under rubble but also of being surrounded by fire or poisonous gas. Being surrounded by fire or poisonous gas, I could feel heat or breathe with difficulty and could know I am going to die. If an airplane crashes or a bomb explodes most people will die instantly, so people usually do not feel pain or fear. However if I am buried under rubble or surrounded by fire and poisonous gas I will feel pain or have difficulty in breathing and I will not die quickly. So it is an agonizing death filled with fear.   Ã‚  Ã‚  Ã‚  Ã‚  After the earthquake happens, many problems will occur; for example, there will be a problem of supply with goods or temporary dwellings. However, the most frightening problem is disease. After an earthquake, there are sanitary problems. If some diseases spread among the people, it will be difficult to cure the diseases because there will be almost no medical supplies and almost no food.

Critical Thinking Essay

The four keys to a sound decision making are recognizing that the person is actually facing a very important decision. Then it would be followed by consideration of the possible alternatives. After doing so, one will need to evaluate these alternatives and would finally need to act with discipline to be able to choose the best possible alternative. Such decision making process was present in my life during my fourth year in high school wherein I would have to finally pick a college course. My parents want me to become an ordinary businessman. I, on the other hand would want to enter the military school. I weigh between the two alternatives of which would be my best choice. I believe that doing something that I have no enthusiasm would not likely to benefit me. In the end, I chose to persuade my parents into letting me go to the military school instead of the other way around. Knowing what alternative it is that one really wants and believes to be the best. Having an alternative that is proven to work and that would yield more benefit than the other/s is the one alternative that shall be chosen. In my case, I chose what I really want over the alternative of following the advice or the wants of my parents. It serves me well and I am happy that I made such decision. 7. Briefly describe the early decision making years (2-11 years of age) and the adolescent decision making years (12-17 years of age). Now review in your mind your recollections about your life as an adolescent. Ask yourself the following questions .a. Can you identify some ways in which you were influenced by the media as an adolescent? Elaborate. In the adolescence years, most of my decisions were roughly based on how I want others to treat me and see me. Since the adolescence period is a time wherein individuals try to find themselves and create their own identity advertisements have been really influential. One of the things that I remember about being influenced by the media was through promotions of white and lean is handsome or beautiful. As far as I can remember there have been television advertisements that promote being good looking in the concept of having more muscles. Television shows mostly have leading actors who are muscularly built and dressed ruggedly. The view on how to measure success was also influenced by the media. I grew up reading articles about rugs to riches stories and what have inspired this people. I tried to imitate their actions, nevertheless, as far as my character is concerned, I am different person in a different neighborhood with a different capability and attitude in life; although, those stories had got stuck in mind up until today. b. Can you identify one bad habit you formed as a result of poor adolescent decision-making? Elaborate. One bad habit that have formed in me resulting from a poor adolescent decision making would be attempting to rebel from my parents. During those years I felt as if my whole world is being so much manipulated by my parents. I guess, that’s how people usually think when parents started being over protective during those years when everyone else is trying to have a good time. As a usual adolescent I tried to sleep over, drink alcohol, and skip classes, smoke cigarette and marijuana. Those kinds of things seem to be the natural things to do. Then here comes my parents shouting at me telling me to straighten my life or else I would not be receiving anything from them. I felt so sick about how they treat me. It seems like I am still a little baby who cannot decide on his own. Thus, I have decided to run away from home. After a week, I have seen what life is without my parents. I mean, at first it is an overwhelming sense of freedom and success. Afterwards you will find everything lousy. Your life would seem to have no direction and you will realize, â€Å"I should have listened†. c. To what extent did your decisions during adolescence reflect an attempt on your part to gain recognition and acceptance from other adolescents? My decisions during my adolescence reflected my attempts on gaining recognition and acceptance from my peers when I run away from home just to go with them on a road trip. My parents have been so against my friends, since they are the kind of people who indulged on so much smoke and liquor. Disobeying my parents and prioritizing my friends over my studies have been my best attempt for them to accept me. They lived their lives that way and I believed that time that in order for me to have friends, I must try to be like them. It did work, but I then understand that I should just be myself and real good friends would stick with me. 8. The text lists seven steps to sound problem solving. Identify a situation from your own experience where you have applied those steps. List how you applied each and how they impacted your ability to solve that particular problem. I have been able to apply the seven steps of problem solving in my life during my stay hear in Iraq. My goal in being here in Iraq is to serve my country. However, there have been several issues that seem to denote that I am doing something that is wrong. Since, there are so many people who believe that soldiers in Iraq are unnecessary or that soldiers in Iraq are being used by the American government to express its hegemonic capacities. It is not that I do not have faith or trust to the government of America but since I, as a soldier have experience seeing people cursing us on behalf of the American government, I decided to make some research regarding the views of people especially of those who are residing here in Iraq about the American government and how they see it as a threat and why. Depending on the various information and opinion that I have collected in the internet and through other people I have inferred that generally the people with a communist or Marxist background and those who have an affinity or sympathy with the actions and principles of the Jemai Islamia view the United States government as a modern colonizer. I decided that in short term I could talk people out of such idea by presenting them with logical explanation. However, I figured out it would be dangerous since peoples beliefs and philosophy is deeply embedded in their consciousness; a consciousness that was formed by experience and constant reinforcement of ideological beliefs. It would be hard to talk to them and convince them to believe other wise. A long term action I could do is to create blogs or article in the internet that would voice out the interest and opinion of the people who are actually involved in the rehabilitation of Iraq in order to explain better about what is the need for soldiers and America to continue supporting the Iraqi government. In order to do this I have talk about some of my friends and sort of interview them regarding the matter. They believe that it is a good idea to create articles that would voice out our side of the issue. This article would better be available to other people who would like to know a holistic view of the story. The strategy that I decided to apply is to send emails to my friends and relatives to view a discussion panel on the internet. This panel would be focused on the war in Iraq and would generate the views from different people. However, it would be hard to promote the site. So I am still thinking of other strategy. One of my fellow soldier decided that we should create a book that would reflect our experiences here in Iraq. I guess that will be a better alternative. But it would take a long time from now since we don’t have enough time and resources to do a book at the present moment. 9. Provide a personal example for each of the two forms of irrational problem solving. Discuss how these were irrational and what you might have done differently? Thinking irrationally follows from not being able to reason out, it is doing something out of sheer habit or false belief. Egocentric thinking or solving a problem based on selfish or self-centered view often results to negative effect. As when a person is thinking only of personal wants, such wants may not be the same wants that other people like. If so, one would be imposing his wants and others might hate him for that. Also, in problem solving when a person acts according to his emotions he would not think about other people and would only think about a solution that has personal bias. Such solution may not be good for a long term or for a group of individuals and thus, it is more likely to fail than to succeed. If a person is jealous, the person would not think about the reason why things happened, instead the person would view things in accordance to how the person feels things are going. There are certain decisions that might not have been done if jealousy was set aside. Another irrational problem solving is doing what you are told without critically examining the reasons for a certain action. For instance you are told that you should go to church and believe in Christ since you are a child. If you would just believe what others tell you and not think about them in a more critical manner. When you have a problem regarding your religion or someone offered you a counter argument, such things might ruin or shatter your faith, since you cannot reason it out. References Paul, R. and Elder, L. (2006). Critical Thinking. 2nd ed. Person Prentice Hall. Richardson, B. (2006). Theme of the Month: The Tyranny of the â€Å"Fifth Constraint†: Taking Your Thinking Off Autopilot . allPM. com. Retrieved on November 24, 2007. Retrieved from the World Wide Web: http://allpm. com/modules. php? op=modload&name=News&file=article&sid=1580&mode=thread&order=0&thold=0.