Mathematics

Math has been developed to aid human understanding .More the math associated with a subject, better is our quantitative understanding of the subject. Calculus is a great tool in this regard. If we look at individual tools of mathematics they may fail to be useful. But when different branches of mathematics are used together they will definitely help in all subjects. One more thing â€Å"If we don’t use a tool doesn’t mean that it’s useless, There are many things that can be done with it but we don’t require it in everyday life so we just don’t use them.† Specifically looking at examples :-   1) Minister  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   : one of his main job is campaigning. He should campaign more in areas where he has chances of winning than in areas where he is sure to win. This can be found out by survey of last elections, general notion prevailing among people that time. He must also campaign in areas where there’s high probability of people turning up for his lecture and for voting. When he becomes minister, he has to look for the development of the region. This involves all branches of mathematics. His long term aims, promises etc. Fore most is to manage the funds available. Suppose he decides to construct a bridge or flyover or any such Infrastructure project, he has to think of funds for construction. If he keeps some toll tax than how much should he keep? This can be decided by how many people would use it everyday? How much he is targeting to collect? Inflation etc.etc. This all are determined using calculus. 2) Kindergarten teacher : She has to look on child’s growth. Some child can catch things fast. It’s not needed to spend a lot of time on them. Teachers should concentrate more on average child. Also it is sure that not everyone will understand all the things. So teacher has to do some calculations as to when be the right time to move to next topic. If she plots a graph of ‘how many people have understood versus time.’ Definitely she would get a Gaussian curve. This will come handy for subsequent classes. She can ask some simple question to all students and carry out this survey. Also, marks scored by students will have a Gaussian curve shape. Now suppose she has to convert it some other grading standards. (Example from a scale of 100 to relative grading of scale of 10).It would be good for her to know of calculus. She can figure out How much area (integration) is covered by the above mentioned graph?   How much percentage of people are present in which area? What is the average grade she wants to keep etc. etc. These are some of things which directly come to my mind. Tell students to think more in this line and they will surely find out more uses. Or better still put some enthusiastic calculus teacher in the above post for a day and He/she will think of a 100 more uses. Someone may argue that they are specific cases but remind them that jobs not only require to be proficient in everyday work but of special cases also which are likely to be encountered. Mathematics The most common error committed by students is the sign error.   Consider, for example the following instance.   A seventh grade teacher is to provide instruction in the multiplication of signed numbers. The teacher walks through the room, observing progress of each student as they work on a number of sample problems at their seats. The teacher notices that several students consistently make the following error: (-5) x (-6) = -30. One misconception is that the students think that signs do not matter.   In solving these kinds of problems, they tend to disregard the number signs.   This might be because of lack of knowledge of the concept.   The teacher may not have given the importance of number signs.   In this regard, the teacher should give the reason why they should not disregard number signs.   This will help students be more careful in solving numbered signs because they know its importance. Another is that some students tend to believe that since the sum of two negative numbers is a negative then their product might also be a negative number.   Students may overlook the details on the difference between adding and multiplying negative numbers.   The teacher, for this matter, may have not emphasized or given a thorough detail on multiplying a negative number.   This misconception can be diminished if the teacher gives the difference between adding and multiplying negative numbers.   This will help students to keep in mind that the product of two negative numbers is NOT a negative number since they know that multiplying two negative numbers is different from adding two negative numbers. There are many other underlying causes on why students commit this common error.   One major reason is because teachers often overlook the details and skip the important ones.   This error may be reduced if teachers emphasize on the details especially the importance of what they are doing. SOURCES: Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing Mathematics for Teaching. American Educator. Conference Board of the Mathematical Sciences. (2001). The Mathematical Education for Teachers. Providence RI and Washington DC: American Mathematical Society and Mathematical Association of America. Misconceptions in Mathematics: Calculations with Negative Numbers.  Ã‚   Retrieved November 1, 2006 Patterns of Error. (2002).  Ã‚   Retrieved November 1, 2006, from http://math.about.com/library/weekly/aa011502a.htm Schechter, E. (2006). The Most Common Errors in Undergraduate Mathematics.  Ã‚   Retrieved November 1, 2006, from http://www.math.vanderbilt.edu/~schectex/commerrs/#Signs Yetkin, E. (2003). Student Difficulties in Learning Elementary Mathematics. ERIC Digest.  Ã‚   Retrieved November 1, from http://www.ericdigests.org/2004-3/learning.html