Calls for Change in High School Mathematics Essay Example for Free

Calls for Change in High School Mathematics Essay Mathematic educators, parents and students are calling for proper changes in approaches to learning mathematics in high schools. The need to improve learning of mathematics in schools is highly recognized and underlined. Thus, the National Council of Teachers of Mathematics published the Curriculum and Evaluation Standards for School Mathematics that offered recommendations for high school mathematics reform. In addition, the Conference Board of the Mathematical Sciences in their official report ‘The Mathematical Sciences Curriculum K–12: What Is Still Fundamental and What Is Not’ stresses the importance of new topics and techniques in the secondary schools. New approaches should develop new learning techniques that would be discrete from statistics, mathematics, and emphasis on algebra and geometry should be properly re-assessed according to different abilities and needs of students who are taking mathematics course in the secondary school and high school respectively. The need for change and innovation is generally driven by emergence of advanced computing technologies that offers excellent opportunities for school educators to replace manipulative traditional techniques with more complex realistic problem-solving techniques. In its turn, the National Science Board Commission issued a report ‘Educating Americans for the 21st Century’ challenging courses in algebra and pre-calculus and stressing the importance of developing integrated mathematical sciences curriculum in the secondary school. Researchers argue that new curriculum will positively affect students’ achievement outcomes in the secondary and high schools. To make changes more effective teachers are required to understand the advantage of curriculum’s full scope and its consequences; students are required to support the expectations of classroom environment. The Core-Plus Mathematic Project is newly developed curriculum for high school mathematics. Of course, the Core-Plus Mathematic Project or CPMP curriculum is a matter of debates and controversies as not everyone admits the need of high school mathematics reforms. Nonetheless, the CPMP curriculum is worked out with assistance of mathematics education researchers, instructional specialists and classroom teachers. Moreover, the curriculum is shaped by empirical evidence gathered from students and teachers who are willing to participate in field testing. In particular, organization of mathematics curriculum should be interpreted in terms of teaching and assessment recommendations and should follow the standards set in the above-mentioned reports. New mathematics curriculum is a three-year mathematics course for high-school students who are allowed to take the fourth year to prepare for college mathematics. Newly designed curriculum differs from more traditional approaches as new curriculum encourages students’ understanding of mathematics – statistics, probability, algebra, geometry, trigonometry and discrete mathematics. Learning mathematics is developed in focused units that combine fundamental ideas with mathematical habits of mind. It means that new curriculum stresses the need to connect function, data analysis and symmetry with recursive and visual thinking. In contrast to traditional approaches to mathematics, new curriculum emphasizes the role of mathematical modeling and problem-solving instead of simple calculus. Researchers say the primary goal of curriculum improvement is to enhance students’ understanding and comprehension of key mathematical processes and concepts, to enhance student’s ability to use mathematical concepts in real-world problem-solving. Graphic calculators should enhance students’ understanding and abilities to solve authentic problems. Improved instructional materials encourage active teaching and learning processes that will primarily focus on problem situations, abstraction and analysis. Oral and written communication, reasoning with ability to represent, and conceptual understanding are highly appreciated and encouraged. All courses centre on mathematical reasoning and thinking with abilities to develop formal proof. Additional fourth year course will allow to keep students, who prepare for college mathematics, despite whether their undergraduate program is based on calculus. Students interested in mathematics are encouraged to be accelerated into the fourth course year. Today, many researches are focus on identifying whether new curriculum meets its specific goals. In particular, they try to reveal whether the learning outcomes based on new patterns of mathematics learning process differ from outcomes based on more traditional curriculum. During the past eight years researchers conducted various studies to examine mathematical achievement in classroom with CPMP curricula. Research studies have revealed that performance of CPMP students is much better than that of students with traditional interpretation of mathematical representation. It means that problem-solving and recursive thinking appear to be more effective in learning mathematics than simple understanding of key concepts of processes. Further, CPMP students are characterized by higher grade results at the end of the years than students with traditional approach to mathematics. Summing up, recent researches have indicated that CPMP students perform better than students with traditional curriculum. CPMP students are characterized by better abilities to interpret mathematical representation and calculation, to measure conceptual understanding and to recognize the importance of problem-solving. CPMP students are better in probability and statistics, algebraic manipulative skills, etc. Nonetheless, researchers argue that student’s success in college mathematics doesn’t fully depend on CPMP curriculum. Other factors, as, for example, student’s attentiveness, readiness to participate in learning process, self-awareness, classroom environment, play their important role in student’s high school mathematics performance. With guidance from educators, researchers and teachers, curriculum developers will be able to build on stronger patters of student outcomes. References Schoen, H. L. , Hirsch, Ch. R. (2003). Responding to Calls for Change in High School Mathematics: Implications for Collegiate Mathematics. The Mathematical Association of America Monthly, February, pp. 109-123. Available on-line from http://www. jstor. org/stable/3647770 .

Rates of Reaction :: GCSE Chemistry Coursework Investigation

Whether the strength of Hydrochloric acid will affect the speed of the rate of reaction when reacting with Magnesium Ribbon. I want to find out whether the strength of Hydrochloric acid will affect the speed of the rate of reaction when reacting with Magnesium Ribbon. Variables There are two important independent variables in my investigation the first of which is the concentration of the Hydrochloric Acid used during the investigation. The concentration of the acid will partly determine how fast the reaction takes place, if we put some of the magnesium ribbon into the HCL at 2molar then it might have simply dissolved within a few seconds and then I would not have had time to record down any decent enough results to plot a graph with. The other important independent variable that will affect the speed of the rate of reaction is the length of magnesium ribbon. We need to put enough Mg Ribbon into the HCL so that it doesn’t run out straight away but also so that the experiment stops by itself once the gas syringe has filled up. The reasons for choosing these two independent variables are that it would be too hard to try and find a catalyst for this experiment; a catalyst is a substance that increases the rate of a chemical reaction without being consumed in the reaction. Finding a catalyst for this particular experiment could take months never mind the amount of time we have been given for our experiment. The independent variable that I will change is going to be the hydrochloric acid, we will use 50ml of HCL at the following molarity concentrations; 2molar, 1.6molar, 1.2molar, 0.8 molar and 0.4 molar. I have decided to experiment with these different strengths of molar because I think it will give a wide set of results to put into a graph. The dependant variable I shall be measuring will be the time it takes for the magnesium to completely react with the hydrochloric acid, I shall record the times for each concentration of hydrochloric acid three times so that it makes it a fair test. To ensure the investigation is fair we will use the same length of magnesium ribbon for all the different strengths of hydrochloric acid and the length will be the one that we picked out from the preliminary experiments. Another way in which we will keep the investigation fair will be to carry out an experiment at each concentration of hydrochloric acid three times so that we can then get hopefully around the same outcome from each experiment, and if there are any anomalies we can try to explain why they happened.

Ethical Egoism

Ethical egoism, in my belief, is not the moral theory that men should follow or live by. Simply put, my belief stems from the multiple inconsistencies and contradictions that are inherent in the said normative system. Self-interest and self-preservation, although very valuable, are not, in my opinion, the primary factors that should drive a man’s life. It is because, I believe, by purely following one’s own interests, man fails to consider the greater picture, that being the peace and harmony in society.More importantly, I believe that man can be driven by other desires and motives in his moral actions. Hobbes’ assertion is that man should use his power to preserve himself and to do what he must in order to satisfy his own interests. His fundamental assumption regarding the nature of man is that man is an agent of self-interest who is prepared to harm others in order to obtain what he believes is best for him. Furthermore, Hobbes states that man is governed by hi s own reason and that every man has the right to everything. Such statement is what Hobbes calls the fundamental law of nature.However, Hobbes believes that if it is in the self-interest and preservation of one’s life to enter into a covenant with another, man is bound to abide by such covenant. Contracts are reached when both parties feel that it is in their best interests to enter and agree to the terms. Breaking a covenant or a contract is considered unjust in Hobbes’ view. Hobbes’ idea is that man must submit to certain moral rules out of fear of conflict which is to his best interests. Basically, Hobbes suggested that a human being acts morally because it is in his self-interest to do so.There have been various philosophers who have raised arguments and objections against Hobbes’ views. One of such philosophers is H. A. Prichard. In Prichard’s point of view, there is no need to whether self-interest and morality run in parallel with each other . Instead, he suggests that human beings have reasons other than self-interest to act morally. One such reason is the innate desire in humans to do the right thing. Prichard suggests that having motives other than self-interest allows us to determine whether an individual who has done something moral deserves praise or not.Without the presence of other motives, self-interest will be the only driving factor and thus, will remove any possible distinction between two persons committing the same moral act. Brody’s argument with regards to the basis of morality on self-interest is that human beings can have other motives for being moral. Admitting that all actions are based on the satisfaction of a certain desire, Brody states that humans may have desires for something else other than his own well-being. Brody believes that selfish motives are indeed a possible source of moral actions.However, he asserts that this does not mean that all moral actions stem from selfish motives alon e. In other words, egoism is not clearly established as the sole source of morality. My belief that ethical egoism is not the correct moral theory agrees with Brody’s assertions. Aside from the points that Brody has raised, I believe that ethical egoism fails to consider the possibility that men act not for their own interests alone. The interests of another person may drive the man to act morally especially if such a person is deeply valued. For instance a parent may act morally not for her own interests but for that of her children.Ethical egoism fails to consider that human nature includes certain emotions that are driving factors of one’s actions. Emotions or feelings such as love, care, and affection are also possible motives for actions. These have not been taken into account by ethical egoism. Thus, it is my personal belief that ethical egoism is not the correct moral theory. Reference: Arthur, John. 2005. â€Å"Morality, Religion, and Conscience. † In Ar thur, J. (Ed. ) Morality and Moral Controversies: Readings in Moral, Social, and Political Philosophy. Upper Saddle River, N. J. : Pearson Prentice Hall.

How To Measure Mass Using a Balance

Mass measurements in chemistry and other sciences are performed using a balance. There are different types of scales and balances, but two methods can be used on most instruments to measure mass: subtraction and taring. Key Takeaways: Measure Mass Using a Balance A balance or scale is an instrument used to measure mass in the science laboratory.One common method of measuring mass is to tare the scale and measure the mass directly. For example, this is how people weigh themselves.The other common method is to place a sample into a container and measure the mass of the container plus sample. The mass of the sample is obtained by subtracting the mass of the container. Proper Use of a Balance Before using a balance, its important to take some preliminary steps. This will help ensure you get the most accurate and precise measurement. Be sure you understand how to use a balance before taking mass measurements.The balance should be clean and free of debris.The balance should be on a level surface.Never place a sample directly on the balance. You should use a weighted boat, weighing sheet, or another container to hold the sample. Some chemicals you may use in a lab could corrode or otherwise damage the surface of the weighing pan. Also, make certain your container will not chemically react with your sample.If the balance has doors, be certain to close them before taking a measurement. Air movement impacts the accuracy of mass measurements. If the balance does not have doors, make certain the area if free of drafts and vibrations before measuring mass. Mass by Difference or Subtraction If you place a container full of sample and weigh it, youre getting the mass of both the sample and the container, not just the sample. To find the mass: mass of sample mass of sample/container - mass of container Zero the scale or press the tare button. The balance should read 0.Measure the mass of the sample and container.Dispense the sample into your solution.Measure the mass of the container. Record the measurement using the correct number of significant figures. How many this is will depend on the particular instrument.If you repeat the process and use the same container, do not assume its mass is the same! This is particularly important when you are measuring small masses or are working in a humid environment or with a hygroscopic sample. Mass by Taring When you use the tare function on a scale, you are making certain the reading starts from zero. Usually, there is a labeled button or knob to tare the balance. With some instruments, you need to manually adjust the reading to zero. Electronic devices do this automatically, but require periodic calibration. Zero the scale or press the tare button. The scale reading should be 0.Place the weighing boat or dish on the scale. There is no need to record this value.Press the tare button on the scale. The balance reading should be 0.Add the sample to the container. The value given is the mass of your sample. Record it using the proper number of significant figures. Sources of Error Whenever you take a mass measurement, there are several potential sources of error: Air gusts may push the mass up or down.Buoyancy can affect measurements. Buoyancy is directly proportional to the air volume that is displaced and is affected by air density changes due to temperature and pressure fluctuations.Condensation of water on cold items may increase apparent mass.Dust accumulation can add to mass.Evaporation of water from damp items may change mass measurements over time.Magnetic fields may affect components of the scale.Temperature changes can cause components of the balance to expand or contract, so a measurement taken on a hot day may differ from one taken on a cold day.Vibration may make it difficult to obtain a value, as it will fluctuate. Is It Mass or Weight? Remember, a balance gives you a mass value. The mass would be the same whether you measured it on the Earth or on the Moon. On the other hand, the weight would be different on the Moon. While its common to use the terms mass and weight interchangeably, they are only the same values on Earth! Sources Hodgeman, Charles, Ed. (1961).  Handbook of Chemistry and Physics, 44th Ed. Cleveland, USA: Chemical Rubber Publishing Co.  pp.  3480–3485.Rossi, Cesare; Russo, Flavio; Russo, Ferruccio (2009). Ancient Engineers Inventions: Precursors of the Present. History of Mechanism and Machine Science. ISBN 978-9048122523.