Observing a mathematics lesson

Observing a mathematics lesson Introduction: The world in which we live is mathematical. In our everyday activities we need mathematics for instance; there is need in everyone for mathematical thinking as well as problem solving in the workplace, at home, when in a shopping spree, etc. In a world of such kind, you notice that those who comprehend and can operate mathematics will have immense opportunities that others lack. In fact, mathematical proficiency opens avenues to productive prospects. Conversely, lack of mathematical competency closes those doors. Usually, learners have varied abilities, interests and more fundamentally, needs. Yet each learner requires mathematics in his or her individual life, be it at home, in the workplace, and even in further study. All learners deserve a chance to appreciate the power and splendor of mathematics. Students should learn a new collection of mathematics nitty-gritty as well as higher level critical-thinking handiness which are critical to problem solving. These permits them to work out fluently, interpret and to unravel puzzles innovatively and resourcefully. The objectives of this lesson is to enable instructors establish suitable strategies employable in problem solving and appropriate forms of mathematical assessment and further the correlation between problem solving and learners achievement. In the lesson, the standards in mathematics with regard puzzle solving are also looked at, as well as problem solving and assessment in an inclusive setting. In the lesson, several standards put down by the National Council of Teachers of Mathematics (NCTM) were addressed. The NCTM declares that students need to develop a range of strategies for solving problems, such as using diagrams, looking for patterns, or trying special values or cases (NCTM, 2000, p. 7). These teaching strategies allow learners to comprehend with ease abstract mathematical concepts and make these concepts realistic to learners perception. According to Hanson et al (2001), if all learners are going to gain knowledge of these strategies, then these strategies should be imbedded in and most importantly be taught across the curriculum. Beside strategies standards, NCTM also establishes the standards for mathematics assessment to help in enhancing learning of mathematics and modeling and shaping teacher instruction. As a result, learners need to use assessments as a part of the reflecting process and work together in partnership with the teachers to determine the direct ion of learning in mathematics (Hanson et al, 2001). The teacher did discriminate instruction within a diverse classroom into mainly high achievers and the low performing learners. In this case, the teacher exposed low achievers to basic skills with limited exposure to operate higher-level problem-solving skills which were left for the higher performers (Grouws Cebulla, 2000). These low performing learners according to Grouws Cebulla, (2000) need to be exposed to more challenging curricula which provide first hand experience. For instance, rather than handing learners a worksheet, a more interesting puzzle might relate to an investigation of classmates involving the kinds of pets they have. From that basis, the class could create graphs depicting data, find partial comparisons (introduction to ratios and probability) and percents. Technology was not used in the instruction of the math lesson. For more effectiveness and probably efficiency, technology can be incorporated into this lesson. For instance, the teacher can make use a graphing calculator. This will offer learners an opportunity to collaborate and discuss the puzzles to establish the solution, as they would in a real world situation. Teaching mathematics needs a lot of reference lists. Teachers habitually have reference lists posted in their classrooms during lessons to which students can make reference when faced with a problem-solving situation. Mathematical problem solving indeed is a multifaceted cognitive activity which involves numerous processes as well as strategies (Montague, n.d.). Stages involving Problem solving are twofold: representation of the problem and problem execution. In the lesson, the teacher used pictures or manipulative objects. Pictures and objects do help make the problems as well as concepts more real and concrete to students as nearly all mathematics concepts are abstract. Modern theories on teaching techniques discourage competition and instead promote collaborative learning. Competition as a teaching strategy demotivates and demoralizes the underperformers. As a teacher, I would reorganize the classroom to accommodate more learner-learner interaction. Placing learners into cooperative learning and problem solving situations will promptly increase the interaction between the high-performing and low-performing students with the target of bridging the learning gap. Moreover, I would employ use of alternative assessments like portfolios and hands-on projects in order to improve strengths and weaknesses of each individual mathematics students. I would also include modifications like slowing the pace of instruction, reducing the process of estimation from problem solving, using flip charts of the involved processes and strategies, and finally teaching from known to unknown, concrete to abstract and from simple to complex. Conclusion: Mathematical problem solving can best be taught by employing cooperative learning technique. Students should be provided with the processes, stages and strategies that make mathematics problem solving simple to learn. Teachers should also consider providing real life mathematics situations to challenge students, and students will begin to appreciate the necessity and essence to be excellent problem solvers. References: Grouws, D. Cebulla, K. (2000). Improving Student Achievement in Mathematics. Geneva, Switzerland: International Academy of Education International Bureau of Education, Educational Practices Series -4. Hanson, et al (2001). Should standard calculators be provided in testing situations? An investigation of performance and preference differences. Applied Measurement in Education, 14(1), 59-72. Montague, M. (n.d.). Math problem solving for middle school students with disabilities. The Access Center. National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics.

Social Norms of Income Distribution

During the period between 1929 and 1953, the United States occupational pay ratios and earning inequality is declined, mainly across World War II (Ober 1948, Phelps Brown 1977, Williamson and Lindert 1980, Goldin and Margo 1922b). The evidence showed that the condition of income inequality was occurrence in that period. Moreover, the problem of income inequality is declined. But, the problem of income inequality is existed. The government cannot spread the income distibution evenly. Many reasons obstructed the income distribution evenly. In my discussion, I concentrate to explain five reasons to influence the income distribution in the United States in the 20th century. Changing in social norms is related to the income distributions. Many people think that women represented a cheaper alternative for employers. Their jobs were viewed as temporary to be abandoned in favor of marriage and a home. High turnover combined with a large pool of replacements in any occupation will tend to depress wages, but it also means there is no incentive to provide career opportunities or invest much effort to train persons for more responsibility. Consequently, women tended to fill the more specialized and lower-paying work, while men moved into the new office manager roles. The fact is that clerical, service, and sales work does not yield significant financial returns to people with more formal education or longer work experience (Bibb & Form, 1977). In large part, this is because most of these are low ceiling careers, lacking in meaningful promotion opportunities for higher paying positions. The jobs have been filled advantageous position by one sex or the other. The point is strongly influencing the income distributions. The point of the unionization is related to the income distributions. Unions have improved wages and benefits, increased job security, and protected workers from discriminatory managerial decisions. Male workers are more likely to be members of trade unions, thus enjoying the advantages of collective bargaining for wages and earning more than women (Flaherty & Caniglia, 1992). Overall, women are about half as likely to be union members as men. Rinehart wrote,  ¡Ã‚ § This accommodation to capitalist power was formalized in what is known as the post  ¡V World War II compromise forged in the midst of the intense class struggles of the 1940s. This settlement between labor, big capital, and the state featured the establishment of a new industrial relations system and stipulated a set of trade  ¡V off. Unions were legally recognized and accorded organizational security. ¡ (P.184) Changing in the education level of the population is related to the income distribution. In the U.S, the financial return to a university or college degree also declined during the 1970s. One explanation of this phenomenon was the substantial increase the proportion of the population going to university, particularly the entry into the labor force of the  ¡Ã‚ § Baby-Boom ¡ generation during the 1970s (Welch 1979). Freeman (1976, 1980) argued that the demand for educated workers also declined, so that not all of the change in relative earnings could be attributed to temporary developments on the supply side. Dooley (1986) concluded that the entry of the large baby ¡Vboom cohort during this period did lower earnings growth for this group, but that this demographic effect could not account for the observed harrowing of earnings differentials by level of education. Dooley ¡s results thus suggest that demand  ¡V side forces may also have played a role. Changing in the age structure of the population is related to the income distribution. The shapes of the earning streams reflect the main key factors which is earnings increase with age but at a decreasing rate. This concave shape reflects the fact that individuals generally continue to make human capital investments in the form of on-the-job training and work experience once they have entered the labor force. This job experience adds more to their productivity and earning s early in their careers due to diminishing returns to experience. However, to the extent that education increases productivity, individuals with the same amount of work experience but more education will earn more, perhaps substantially more. Migration is related to the income distribution. Economic theory predicts that the forces of competition would serve to reduce pure regional wage differentials so that they reflect compensating differences, short-run adjustments, or noncompetitive factors. Those forces of competition were the movement of capital from high- to low-wage areas, and the movement of labor from low- to high-wage areas. Empirical evidence tends to verify the implications of migration as a human capital decision. In a recent study, Osberg, Gordon, and Lin (1994) explore the determinants of interregional and interindustry mobility of individuals in the Maritimes. Using the 1986-87 LMAS, they find that younger individuals and those with higher expected wage gains are more likely to migrate. As well, the process of migration tends to reduce the regional disparities that induce the migration decision. In conclusion, the five reasons are influence the income distribution in the United States in the 20th century. The social norms show that the income inequality is happened between men and women. The unionization shows that the unions have a power to improve the wages and benefits for their members. In this situation, the income inequality is happened between union ¡s members and non-unions members. Although the demand for education workers was declined, education people still earn more than the uneducated people do because they have an expertise knowledge and experience. Migration is benefits for the young individuals. They can have a chance to prove themselves. Therefore, the movement of migration decreases the regional disparities.

Top Examples of Research Paper Outlines Guide!

Top Examples of Research Paper Outlines Guide! Academic writing really needs a particular format. Formatting a research paper is not a simple undertaking. Plagiarism is definitely from the question. It's possible to also describe the range of your research. You don't have to be concerned about privacy. Additionally, among the vital purposes of an outline is to clearly convey the relation between the thesis and every one of the topic sentences. Essays may look very dull sometimes. Completing an MLA outline will guarantee your research paper format is accurate. The MLA format stipulates the vital guidelines for effectively writing an essay based on the MLA standards. Don't forget about valid references and suitable citation according to the necessary paper format. Essay outline for college plays an important function. College students should use a suitable numbering for unique sections. Essay outlines shows you that even if you aren't an expert writer, you are still able to make a great essay. Know how your essay is going to be evaluated. Correct all errors that you could spot and enhance the general caliber of the paper to the best of your ability. Demonstrate the way your input develops and distends the current works. On the flip side, you might write from a worldwide perspective and examine sustainable cities around the world. The maturation of a powerful and independent neighborhood government is accented in Mexico (states are split into free municipality). Why don't you drop in today and let our crew of experts assist you with your research papers. In the event the structure of the chief body has many levels, it is preferable to use different numbering styles. If you take a close look at research paper outline examples, you will observe we have several approaches to present the major body. Construct the human body and the abstract. Bear in mind that the chief goal of the research paper is to clearly show your abilities to work on your own and demonstrate the scope of your knowledge on several different topics. The guide covers its primary elements and gives valuable examples. In order to start outlining the research paper, determine why you're researching the subject. To get started researching local problems, head straight to local newspapers and internet sources. With essay outline, essays will avert writer to get off topic or jumping from 1 argument to a different argument that doesn't relate with what it is you are discussing. Writing research papers is a wearying procedure, and even more so if you don't have a predetermined topic. It is not just merely a compilation of related literature that could support the argument you are trying to raise, the findings you are trying to get, or the question you are trying to answer. Writing a research paper may look as a mission impossible if you've never had th e chance to work on this kind of assignment. Now you know how to begin your research paper, you're probably thinking about how to keep going. After reading the thesis, there ought to be no doubt precisely what the research will be about. To compose a great research proposal on local government, it would be helpful to get familiar with free examples research paper topics on the matter. For this reason, you might have to look for good topics for high school research papers on the internet.

Gay Marriage Should Be Legalized - 938 Words

Gay marriage is in fact a controversial topic that many people feel strongly about. I believe that gay marriage should be legalized without being penalized by people who disagree with it. I will, within reason, explain to you why gay marriage should be legalized and argue against Karlee’s essay about why gay marriage shouldn’t be legalized. The first thing Karlee talks about in her opposing essay is, â€Å"Children of same-sex couples, biological or not, need both a mother and a father in their life.† In an article on Sciencedaily.com, Do Children Need Both A Mother and A Father? it mentions that, â€Å"...there is almost no social science research to support this claim.† Another great point it includes is, â€Å"...the researchers found no evidence of gender-biased parenting abilities†¦ noting that very little about the gender of the parent has significance for children’s psychological adjustment and social success.† As said in the article, children with same-sex parents â€Å"do as well on average as children raised..:† by opposite gender parents. Another thing I will point out in Karlee’s paper is the statement she mentioned, â€Å"Those children will hunger for a mother like figure and a father-like figure.† Although that may be true, if one were to a sk a kid, would you trade your parents? Their immediate reaction would be normal because no matter the gender, parents are parents. Children will love their parents, they’ve been there for them through everything, no matter what.Show MoreRelatedShould Gay Marriage Be Legalized?1313 Words   |  6 PagesCredit – Should gay marriage be legalized? Marriage is considered to be the rite of passage from an religious point of view, it is considered as holy matrimony before the eyes of God. Attraction between individuals of the same sex has been a topic of debate. However, over the past few years gay individuals made a decision to our grievances of oppression despite receiving tremendous critics from the public. Initially, gay marriagesRead MoreShould Gay Marriage Be Legalized?935 Words   |  4 PagesThere is a lot of controversy about gay marriage and whether or not it should be legalized in certain states that haven t yet legalized it. My opinion on this topic is that it should not be legalized for various reasons. 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Previously legalizing gay marriage was out of the question, but as times has changed and more liberal politicians have gained office to reflect th e views of today’s society. One of the reasons that LGBT people fight for the right to marry because married couples receive more protections and advantages in