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.

Essay --

A wedding is exciting, especially if it’s your own. However, the actual preparations could dampen that sense of eagerness and anticipation. In extreme cases, working out the details, such as invitations and the bridal car (http://carrentgoa.com/wedding-cars/) can turn the â€Å"lucky lady† into a bridezilla. Don’t take the fun out of your special day before it’s even begun. Avoid these costly wedding planning mishaps. Mistake No. 1 - Going all out on the jewellery It’s tempting to have more than one sparkler as you walk down the aisle. If the bling is worth half of your budget, think again. Remember, everyone’s attention will already be focused on you. The bride is the star of her own wedding, after all. Choose a key accessory to match the cut of your dress and slip on that lovely engagement ring (http://abcnews.go.com/Nightline/diamonds-decoded-experts-guide-buying-engagement-ring/story?id=19630519). †¢ Ice Envy diamond rings (http://www.iceenvy.com.au/) – these exquisite jewellery pieces are created by a master artisan and has gemologist approval. Mistake No. 2 - Asking all your friends to be part of the wedding party Sometimes, being engaged makes you want to shout it from the rooftops. That’s great! But it doesn’t mean everyone who hears about it should automatically be part of the wedding party. If your (and your intended hubby’s) finances are limited, the money should be spent on where it’s most needed. Bridesmaid bouquets and dresses can get expensive. Determine the number of people in the wedding party by your budget, not your contact list. If you really think about, individuals whom both of you are really close to might not be more than dozen. Having known you since childhood or seen you through every relationship cris... ...have so many things to attend to, there’s no time to practice your â€Å"blushing bride† look. Let a professional take over. Discuss with the stylist the look you want to achieve. †¢ Red October (http://www.redoctoberhairandbeauty.co.uk/) – experienced unisex hairdressers in Lancashire. Mistake No. 6 – Having decorations that are too elaborate Decor is necessary to liven up the venue. But avoid going overboard. The cost of wall hangings and rope lights can add up. Stick to the essentials (e.g. fresh flowers). These sources may come in handy. †¢ Tynte Flowers (https://www.tynte.com/) – an online florist shop where customers can get fresh bridal bouquets. †¢ Mystique Events wedding aisles (http://www.mystiqueevents.com.au/white-wedding-aisles-melbourne) – decorative solutions that add beauty to the venue for the nuptials. Find additional references on these web pages:

Labor Relations Essay

With each of these scenarios also give the type of employer, the history of the worker at that company, the incident which arose, why it was a clear violation of employer policy, and what would be the likely result of arbitration of this issue if the employee acknowledged his wrong doing but asked to keep his job. Explain the reasoning for our considered outcome. When an employer has to discipline a unionized employee there are four steps to the grievance (infraction) procedure. In the first step the employee is given the grievance in an informal oral manner so a quick resolution can be made, and before a written record is established. The second step in the grievance procedure is to present the grievance to the industrial relations representative or (IR). The IR representative is familiar with the union’s contract and decides on a disciplinary action or if the grievance involves an employee discharge then the union will take it to step three. In step three the employee has union representation and the grievance is most likely settled at this step, if an agreement cannot be made then step four is the last chance to resolve the grievance or it goes to arbitration. Arbitration is a quasi-judicial process in which parties agree to submit unresolved disputes to a neutral third party for binding settlement. [ (Labor Relations, 10th Edition, 2009) ] (pg. 490). When an employee repeatedly breaks the rules and has been disciplined the union, employer, and employee write up a last chance agreement (LCA). This is an agreement drawn up by all parties stating that if the employee has another grievance violation within a certain amount of time the employee will be terminated. The type of employer that my three employees work at is a security company. The security company has hired all three as security officers and upon hiring they were informed of the company’s rules and the grievances that are imposed if the rules are not followed. All three employees have acknowledged the rules, and have signed a document stating that they understand the rules and the disciplinary actions taken if they break the rules. John, an officer at the security company, has never had any disciplinary actions against him since he started working for the company and has been a great employee thus far. John was involved in an incident while on duty with the company patrol vehicle. He has had an accident in the patrol vehicle and has run into a parked car while patrolling the parking lot. It is mandatory that if an employee is involved in an accident with a company vehicle while on duty a drug test is taken and if the drug test shows that John was under the influence (which he was) then that is grounds for immediate termination of his employment. John knows that this is a clear violation of company policy and has requested his union representative. If this disciplinary grievance goes to arbitration the likely result would still be the termination of John’s employment with the security company. The reason for my considered outcome is John was under the influence of drugs while on duty. There is a no tolerance policy for drug use especially while on duty, he could have done a lot more damage and very easily could have injured an individual in the process. Bill, an officer at the security company, has had issues with his behavior and attendance since he started working for the security company three months ago. It has affected his performance on the job and he has had two disciplinary actions against him in three months time. Company policy states that if an employee has three disciplinary actions in a 90 day period that is grounds for termination. Bill has just showed up late again for work and this will be his third grievance for the 90 day period. Bill admits his tardiness and swears that he will not be late again if he is given another chance to improve his attendance. Bill goes to arbitration and the likely result of the arbitration will be that Bill, the employer, and union will draw up a last chance agreement (LCA) for Bill to sign and abide by for a specific length of time. If Bill violates that agreement then it is automatic grounds for termination of his employment at the security company. The reason for my considered outcome of this scenario is because this is the most realistic way a company would handle this kind of disciplinary problem with an employee. Usually if an employee has had three disciplinary actions in a 90 day period that shows a pattern of undesired work behavior and the employer is going to want a last chance agreement to put an end to the undesired behavior. Bob, an officer at the security company, has been employed by the company for almost two years. Bob had a disciplinary action against him the second month of his employment with the security company. The infraction was a complaint of sexual harassment against one of his female co-workers at a previous job site. The complaint was investigated and Bob admitted to saying some inappropriate comments to his co-worker. The security company has a strict no tolerance policy on sexual harassment, but because Bob has admitted his wrong doing and the co-worker accepted his apology, Bob was permitted to stay employed with the security company and was put on a last chance agreement which he completed with no further issues. My considered outcome for this scenario was a bit light considering what Bob’s disciplinary action was for. The reason I considered giving Bob a second chance is that he acknowledged what he had done wrong and apologized to the co-worker that he had offended. Bob completed his last chance agreement he had made and has not had any other grievances since then. Bob probably did not think what he had said to his fellow co-worker would offend her like it did, and because it did he watches what he says and talks about while at work so he does not make the same mistake twice. Reference Fossum, J. A. (2009). Labor Relations (10th ed. ). New York, NY: McGraw-Hill Irwin.

3 Common Types of Phrasal-Adjective Hyphenation Errors

3 Common Types of Phrasal-Adjective Hyphenation Errors 3 Common Types of Phrasal-Adjective Hyphenation Errors 3 Common Types of Phrasal-Adjective Hyphenation Errors By Mark Nichol One of the most ubiquitous categories of error in written composition is failure to provide a visual clue to readers that two or more words preceding a noun are temporarily functioning as a single unit of information. After each of the sentences below, a discussion explains one of several types of such mistakes, and revisions demonstrate correct usage. 1. This new work will represent one of the highest profile projects. The basic phrasal adjective consist of two words combined to modify a noun, and the basic error in the use of phrasal adjectives is to omit a hyphen, which is often (but not always) necessary: â€Å"This new work will represent one of the highest-profile projects.† (Exceptions include terms listed in the dictionary as open permanent compounds, such as â€Å"income tax.†) 2. The agency recommends removal of the four-business day limit. Another type of hyphenation error with phrasal adjectives is hyphenating only the first and second words in a three-word string that modifies a noun. Here, the sentence is revised to reflect that the reference is to a limit of four business days, not a day limit of four businesses: â€Å"The agency recommends removal of the four-business-day limit.† 3. This guide includes a special supplement on the first of its kind regulation requiring certification and screening programs. Errors also occur when a writer fails to acknowledge that an entire phrase- which, like other phrasal adjectives, needs no hyphenation in isolation (For example, in â€Å"This regulation is the first of its kind†)- requires the connective symbols in before-the-noun mode: â€Å"This guide includes a special supplement on the first-of-its-kind regulation requiring certification and screening programs.† Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Punctuation category, check our popular posts, or choose a related post below:100 Mostly Small But Expressive InterjectionsDriver License vs. Driver’s LicenseOne "L" or Two?

The Importance of Planning in Self-Publishing

The Importance of Planning in Self-Publishing Fiction writers are sometimes divided into â€Å"plotters† and â€Å"pantsers† depending on how much advance thought they put into the development of their novels. The â€Å"plotters† like to work everything out in advance. They may develop elaborate outlines, timelines, character portraits, diagrams of pivot points in their story, and know, even before they strike the first key, exactly what the story is and how it will develop. â€Å"Pantsers† get their name from â€Å"flying What about self-publishers? They can also be divided in terms of how they approach the publication of their books. Consider: Planners As soon as a planner gets going, they have specific dates for all their events. An author may have booked the blogs on which she’ll be appearing during her book launch several months away. She might locate vendors for the services she’ll need, set up a publishing company, and get all her â€Å"ducks in a row.† Although all this preparation is impressive, planners may be driven Free Spirits Free spirits approach publishing with a less structured approach, and are more concerned with the task in front of them, not with future events. A free spirit author may be so absorbed Although it sounds slower, these authors may be more open to serendipitous meetings and spur of the moment inspiration. Although they dont get the benefits of advance planning, they may have more fun in the process. Questions Arise Most people think that a book is a simple, commonplace object - words on a page, one page after another until you reach the end. What’s complicated about that? But then, when you decide to publish yourself, the picture becomes murkier. You begin to realize there are many decisions that go into making a book. The questions start, and never seem to stop:   Hardcover, paperback, ebook?   How big a book?   Where to sell, and for how much? Then it gets even more confusing:   What should I do first?   How long will it take?   How do I stay on track? Planning to Succeed Many authors are also teachers, business people, retirees, consultants, electricians, military, lawyers, doctors, and so on. They have expertise in their own field, but they don’t know how book publishing works. They have no grasp of the whole book publishing process. Ideally, you could have an expert sitting next to you as you plan your project to explain all the steps and when to do them. Thats a great solution, and some authors end up hiring a book shepherd or publishing consultant. But only a few do that. Most try to figure it out Understanding the sequence of events in publishing a book should be your first task when you decide to self-publish. So if youre thinking of publishing your own books, educate yourself first. Nothing will repay you as much as getting clear in your mind about how the process of turning a manuscript into a book works in the real world. Youll soon be a publishing pro yourself! NOTE FROM HOPE:  A new software program automates scheduling and tracking tasks for book projects. Its called  Book Planner  . A one-year subscription makes a great holiday gift for your favorite indie-publisher! Im a rabid fan of Joel Friedlander products, and this is a great way to jumpstart your own writing.

CULTURAL AND ETHICAL VALUES Essay Example | Topics and Well Written Essays - 750 words - 1

CULTURAL AND ETHICAL VALUES - Essay Example All rational actions carried out by men will always aim at achieving something good. There is a hierarchy to the end as the end point or purpose of some actions could lead to the beginning of a totally new action. The ends in the hierarchy might themselves vary in their value; however, the ultimate end is valued on its own measure and that which is sufficient and completely good. People might do things for the sake of achieving something else and this chain would continue, but Aristotle feels that every human being would definitely possess one supreme goal in life and all the other tasks which one undertakes would lead towards this goal. Aristotle then goes on to explain what, according to him, is the ultimate goal in human life that is over-all happiness in one’s life. The Greek word â€Å"eudaimonia† provides a close enough explanation to what Aristotle views as ultimate good. Eudaimonia stands for eternal and ever-lasting peace and happiness and whether a person has truly led a eudaimoniac life can be ascertained only after the end of one’s life. His argument for stating that ever-lasting happiness is the final goal in a human’s life is that every action performed by man is only to achieve happiness, which alone can make a man self-sufficient. Aristotle further explores the means to achieve happiness. He believes that every human possess a characteristic activity much like the animals and this activity would ultimately help one to achieve a state of eternal happiness. According to him, this characteristic activity possessed by every human is the power of reasoning, which when used in t he correct manner will help a person to achieve a happy life. It is this unique ability that distinguishes mankind from other animals and is the key that would lead each of us to our ultimate goal. In other words, he believes that the power to achieve the final goal lies within the reasoning capability of the individual and the degree to which the goal is

Gays in the Military (Equal Employment Opportunity) Essay

Gays in the Military (Equal Employment Opportunity) - Essay Example This policy also lawfully pertains to military personnel. It’s simple, the government does not allow discriminatory practices in hiring therefore gays must be given equal access to all military jobs whether in a combat or non-combat role. However, the issue of gays in the military is far from simple and a topic of heated debate. The main argument against it concerns privacy and troop morale while the argument for is based on defending the uniquely American concept of personal freedom that the troops are fighting to protect, among other objectives. Some suggest that bigotry and ignorance are the root causes of the opposition to gays serving their country, that troop morale is just an excuse used to deny American citizens their civil liberties. Others believe homosexuality to be an immoral lifestyle choice which, if tolerated, would tarnish the proud, well-deserved iconic image the U.S. Armed Forces has spent centuries to earn and diminished the effectiveness of the men and wome n in uniform. This discussion examines the debate in a historical context specifically the ‘Don’t Ask, Don’t Tell’ policy, the Constitution and the Founding Fathers’ viewpoint on personal liberties as well as the opinions of those who inspired the Founders, both pro and con as it pertains to this issue. It also addresses the issue of homosexuality itself, an important consideration because if it is indeed a choice, in the same way drinking and driving is a choice, then it would not be covered under federal employment discrimination laws. The opinions and reasoning’s of those against gays in the military will be reviewed and subsequently debunked while the harmful effects to the security of the U.S. by banning gays are illuminated. The ‘Don’t Ask, Don’t Tell’ policy was enacted soon after President Bill Clinton assumed office in 1993. Clinton initially sought to end the military’s ban on admitting gays entirely with no