Importance of Mathematics in Everyday Life
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The National Council of Teachers of Mathematics (NCTM) was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally.
NCTM holds annual national and regional conferences for American teachers and publishes four print journals. Its published standards have been highly influential in the direction of mathematics education in the United States and Canada.
The NCTM does not conduct research in mathematics education, but it does publish the Journal for Research in Mathematics Education, which is the most influential periodical in mathematics education research worldwide and the fourth most referenced educational research journal of any kind. Summaries of the most important findings in mathematics educational research as regards current practices can be found on their [http://www.nctm.org/news/content.aspx?id=8468 website].
The NCTM also publishes three other print journals for elementary, middle school and high school teachers of mathematics.
NCTM has published a series of math Standards outlining a vision for school mathematics in the USA and Canada. In 1989 NCTM developed the Curriculum and Evaluation Standards for School Mathematics followed by the Professional Standards for Teaching Mathematics (1991), and the Assessment Standards for School Mathematics (1995). These math standards were widely lauded by education officials, and the National Science Foundation funded a number of projects to develop curricula consistent with recommendations of the standards. Several of these programs were cited by the Department of Education as "exemplary". On the other hand, implementation of the reform has run into strong criticism and opposition, including parental revolts and the creation of anti-reform organizations such as Mathematically Correct and HOLD. These organizations object especially to reform curricula that greatly decrease attention to the practice and memorization of basic skills and facts. Critics of the reform include a contingent of vocal mathematicians and some other mathematicians have expressed at least some serious criticism of the reformers in the past.
In 2000 NCTM released the updated Principles and Standards for School Mathematics. PSSM is widely considered to be a more balanced and less controversial vision of reform than its predecessor.
Post World War II Plan
In 1944 the NCTM created a post war plan to help World War II have a lasting effect on math education. Grades 1-6 were considered crucial years to build the foundations of math concepts with the main focus on algebra. In the war years, algebra had one understood purpose - to help the military and industries with the war effort. Math educators hoped to help their students see the need for algebra in the life of an everyday citizen The report outlined three strategies that helped math educators emphasize the everyday usage of algebra. First, teachers focused on the meanings behind concepts. Before, teachers were expected to use either the Drill or the Meaning Theory. Now, teachers gave students purpose behind every concept while providing an ample amount of problems. Second, teachers abandoned the informal technique of teaching. This technique was popular during the 1930s and continued during the war, and in essence depended on what the students wanted to learn, based on their interests and needs. Instead, math teachers approached the material in an organized manner. The thinking was that Math itself had a very distinct organization that could not be compromised simply because the student was uninterested in the matter. Third, teachers learned to adapt to the students by offering the proper practice students needed in order to be successful After the sixth year, seventh and eighth grades were considered key in ensuring students learned concepts, and were increasingly standardized for all pupils. During these years, teachers verified all key concepts learned in the previous years were mastered, while preparing students for the sequential math courses offered in high school. The army credited poor performance of males during the war to the men forgetting math concepts; it was recommended that reinforcing past concepts learned would solve this problem. The Report lists the organization of the topics that should be taught in these years. â€œ(1) number and computation; (2) the geometry of everyday life; (3) graphic representation; (4) an introduction to the essentials of elementary algebra (formula and equation).â€� At the same time, these years were meant to help students gain critical thinking skills applicable to every aspect of life. In middle school, students should gain maturity in math, and confidence in past material In ninth grade, the NCTM expressed the need for a two track curriculum for students in large schools. Those who have a greater desire to study math would go on one track, studying algebra. Those who did not have a large interest in math would go another route, studying general mathematics, which eliminated the problem of students being held back Finally, grades 10-12 built math maturity. In the tenth year, courses focused on geometry through algebraic uses. The eleventh year focused on a continuation of more advanced algebra topics. These topics were more advanced than those discussed in the ninth grade. However, if the student took an advanced algebra class during the ninth year, then he took two of the semester classes offered the twelfth year.
1989 Curriculum and Evaluation Standards for School Mathematics
The controversial 1989 NCTM Standards called for more emphasis on conceptual understanding and problem solving informed by a constructivist understanding of how children learn. The increased emphasis on concepts required decreased emphasis on direct instruction of facts and algorithms. This decrease of traditional rote learning was sometimes understood by both critics and proponents of the standards to mean elimination of basic skills and precise answers, but the NCTM has refuted this interpretation.
In reform mathematics, students are exposed to algebraic concepts such as patterns and the commutative property as early as first grade. Standard arithmetic methods are not taught until children have had an opportunity to explore and understand how mathematical principles work, usually by first inventing their own methods for solving problems and sometimes ending with children's guided discovery of traditional methods. The Standards called for a de-emphasis of complex calculation drills.
The standards set forth a democratic vision that for the first time set out to promote equity and mathematical power as a goal for all students, including women and underrepresented minorities. The use of calculators and manipulat
The invention and ideas of many mathematicians and scientists led to the development of the computer, which today is used for mathematical teaching purposes in the kindergarten to college level classrooms. With its ability to process vast amounts of facts and figures and to solve problems at extremely high speeds, the computer is a valuable asset to solve the complex math-laden research problems of the sciences as well as problems in business and industry. Major applications of computers in the mathematical sciences include their use in mathematical biology, where math is applied to a discipline such as medicine, making use of laboratory animal experiments as surrogates for a human biological system. Mathematical computer programs take the data drawn from the animal study and extrapolate it to fit the human system. Then, mathematical theory answers the question of how far these data can be transformed yet still preserve similarity between species. Mathematical ecology tries to understand the patterns of nature as society increasingly faces shortages in energy and depletion of its limited resources. Computers can also be programmed to develop premium tables for life insurance companies, to examine the likely effects of air pollution on forest productivity, and to simulate mathematical model outcomes that are used to predict areas of disease outbreaks. Mathematical geography computer programs model flows of goods, people, and ideas over space so that commodity exchange, transportation, and population migration patterns can be studied. Large-scale computers are used in mathematical physics to solve equations that were previously intractable, and for problems involving a third dimension, numerous computer graphics packages display three-dimensional spatial surfaces. A byproduct of the advent of computers is the ability to use this tool to investigate nonlinear methods. As a result, the stability of our solar system has been checked for millions of years to come. In the information age, information needs to be stored, processed, and retrieved in various forms. The field of cryptography is loaded with computer science and mathematics complementing each other to ensure the confidentiality of information transmitted over telephone lines and computer networks. Encoding and decoding operations are computationally intense. Once a message is coded, its security may hinge on the inability of an intruder to solve the mathematical riddle of finding the prime factors of a large number. Economical encoding is required in high-resolution television because of the enormous amount of information. Data compression techniques are initially mathematical concepts before becoming electromagnetic signals that emerge as a picture on the TV screen. Mathematical application software routines that solve equations, perform computations, or analyze experimental data are often found in area-specific subroutine libraries which are written most often in Fortran or C. In order to minimize inconsistencies across different computers, the Institute of Electrical and Electronics Engineers (IEEE) standard is met to govern the precision of numbers with decimal positions. The basic configuration of mathematics learning in the classroom is the usage of stand-alone personal computers or shared software on networked microcomputers. The computer is valued for its ability to aid students to make connections between the verbal word problem, its symbolic form such as a function, and its graphic form. These multiple representations usually appear simultaneously on the computer screen. For home and school use, public-domain mathematical software and shareware are readily available on the Internet and there is a gamut of proprietary software written that spans the breadth and depth of the mathematical branches (arithmetic, algebra, geometry, trigonometry, elementary functions, calculus, numerical analysis, numerical partial differential equations, number theory, modern algebra, probability and statistics, modeling, complex variables, etc.). Often software is developed for a definitive mathematical maturity level. In lieu of graphics packages, spreadsheets are useful for plotting data and are most useful when teaching arithmetic and geometric progressions. Mathematics, the science of patterns, is a way of looking at the world in terms of entities that do not exist in the physical world (the numbers, points, lines and planes, functions, geometric figuresâ€”â€”all pure abstractions of the mind) so the mathematician looks to the mathematical proof to explain the physical world. Several attempts have been made to develop theorem-proving technology on computers. However, most of these systems are far too advanced for high school use. Nevertheless, the non-mathematician, with the use of computer graphics, can appreciate the sets of Gaston Julia and Benoit B. Mandelbrot for their artistic beauty. To conclude, an intriguing application of mathematics to the computer world lies at the heart of the computer itself, its microprocessor. This chip is essentially a complex array of patterns of propositional logic (p and q, p or q, p implies q, not p, etc.) etched into silicon . see also Data Visualization; Decision Support Systems; Interactive Systems; Physics. Patricia S. Wehman Devlin, Keith. Mathematics: The Science of Patterns. New York: Scientific American Library, 1997. Sangalli, Arturo. The Importance of Being Fuzzy and Other Insights from the Border between Math and Computers. Princeton, NJ: Princeton University Press, 1998.
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Answers:They're important for giving a pretty good estimate of the pH of a solution. How can they be used in everyday life? Well people normally don't go around carrying a bunch of acid/base indicators with them. They're used more for academic purposes. I guess they could be used for things like pools and rain water...
Answers:The government uses prime numbers to hand out stipends, that way there is always a remainder which they can collect back. :) Prime numbers are also good for encryptions because to hack it a common method is to use addition subtraction, and other elementary operators which can be difficult with prime number codes. Prime numbers are essentially a novelty. What is the use of 6? or 12? or 18? They are just numbers that fall into a certain category. Someone recognized their similarity and it applies to only mathematical models.
Answers:Algebra is used frequently in everyday life, but we don't often think about the fact that we are using algebra. If you are trying to figure out how many packages of hot dog buns to buy for a party, you are using algebra. Planning a budget for a road trip based on gas prices and gas mileage - using algebra. As for why it's being taught as early as Kindergarten (yes, those old problems Square +1 = 2, what goes in the square? - algebra!), it's to develop algebraic thinking. Thinking about algebra means thinking in a unique way in which numbers combine not just in a forward 1+2=3 but also in a 3-2=1 or 2+1=3 way and so on. The sooner we introduce students to this form of thinking the more successful they will be with any type of logic problem presented to them, not just algebra. However, I agree with you about calculators. It is important to teach students how and when to use calculators. It is also important to teach students how to estimate so they know if they made a mistake leading to a wrong answer on a calculator. Calculators can only be as good as the people using them.
Answers:Culinary use ------------------- Magnesium chloride is an important coagulant used in the preparation of tofu from soy milk. In Japan it is sold as nigari ( , derived from the Japanese word for "bitter"), a white powder produced from seawater after the sodium chloride has been removed, and the water evaporated. In China it is called "lushui" ( in Chinese). Nigari or Lushui consists mostly of magnesium chloride, with some magnesium sulfate and other trace elements. It is also an ingredient in baby formula milk. Use as an anti-icer ----------------------------- A number of state highway departments throughout the United States have decreased the use of rock salt and sand on roadways and have increased the use of liquid magnesium chloride as a de-icer or anti-icer. Magnesium chloride is much less toxic to plant life surrounding highways and airports, and is less corrosive to concrete and steel (and other iron alloys) than sodium chloride. The liquid magnesium chloride is sprayed on dry pavement (tarmac) prior to precipitation or wet pavement prior to freezing temperatures in the winter months to prevent snow and ice from adhering and bonding to the roadway. The application of anti-icers is utilized in an effort to improve highway safety. Magnesium chloride is also sold in crystal form for household and business use to de-ice sidewalks and driveways. In these applications, the compound is applied after precipitation has fallen or ice has formed, instead of previously. The use of this compound seems to show an improvement in driving conditions during and after freezing precipitation yet it seems to be negatively affecting electric utilities. Two main issues have been raised regarding the anti-icer magnesium chloride as it relates to electric utilities: contamination of insulators causing tracking and arcing across them, and corrosion of steel and aluminium poles and pole hardware.