Mamikon's Calculus Paper Research Example | Topics and Well Written Essays - 1500 words

Mamikon's Calculus - Research Paper Example II. Description of Mamikon’s Approach Mamikon’s method utilized shapes in order to get his points across about the ways that calculus could be approached. According to Pritchard (2003), Mamikon Mnatsakanian came up with a visual method of solving calculus utilizing shapes, which befuddled the Soviets; later on, he got his Ph.D. in physics (pp. 38). Of course, giving students linear and curved objects would be just one way to demonstrate how a calculus problem is set up. According Tom Apostol and Mamikon Mnatsakanian’s article in Haunsperger (2007), â€Å"For centuries mathematicians have been interested in curves that can be constructed†¦Ã¢â‚¬  (pp. 120). Mamikon’s idea was that if young people—even very young children—could use manipulatables in order to see how shapes can form and change based on volume or linear adjustments, they would be able to innately understand principles that come directly from calculus. In this regard, it is so important to have exposure to complex math problems as early as possible in order to stimulate a child’s mind. This is not to say that very young students should be forming the geometry proofs proving energy equals mass times the speed of light squared. On the contrary, the math that children should work on, in terms of problems, should be guided with visual aids and shapes or drawings that would further explain some complex concepts. III. Three Examples Having the students find a simple derivative would be a good place for them to start in learning more about the world of calculus. According to Alsina and Nelsen (2006), â€Å"In calculus, one [important piece of information] is the area under the graph of a function† (pp. 16). First, they could start of with a very simple equation, like f(x) = x^2. Then, what they could do next is find the derivative. The equation would be f’ (also known as f prime) = 2x. Next, the next step would be having a derivative of 2. And then the integer would become zero, finally. So, this is just one way in which some of the rules of derivatives could be simply explained on the board with graphs and a formula instead of having to go through the rules of the derivatives, which are pretty self-explanatory once you see how it’s done. Graphs help greatly in this regard. According to Larson and Edwards (2008), â€Å"[L]ine segments give a visual perspective of the slopes of the solutions of the differential equation† (pp. 256). The second example that would be given would be more geometry than anything else, and more of an introductory calculus problem. In order to find the hypotenuse of a triangle that the kids would cut out, they would have to take the sin of the angle equal to the opposite over adjacent lengths and then solve the problem. The third project that kids could work on would be to correctly calculate the time that it would take for a fish tank to fill up by taking measurements of the speed of the water, the measurements of the tank, etc. They would then use a calculus formula in order to figure out the answer by plugging in the numbers. This could be used to fill up a fish tank and then add new fish to the tank as a class project. IV. Lesson Plan for Students (With Accommodations for Diverse Learning Styles) Lesson Plan Components for a 5th-Grade Calculus-Focused Math Class Resources. Blackboard or whiteboard, construction paper, fishtank, water, hose, scissors, pens, pencils, colored pencils, and calculus

Effects of Bullying on Student Attendance Dissertation

Effects of Bullying on Student Attendance - Dissertation Example Written permission from each student’s parent or guardian is required prior to the student participating in the study. The parents will be provided with the following background information: â€Å"Bullying is a serious problem in our schools that requires more study and attention. The incidence of bullying has been linked to poor school attendance. The purpose of this study is to determine whether there is indeed an association between bullying and poor attendance at school. In order to conduct this study, we are asking for permission to interview your student to determine whether he or she has issues with bullying. Fifty to one hundred students in grades four to six will be interviewed. If our study shows a relationship between bullying and attendance, we hope that more resources will be allocated towards working to resolve the problem of bullying in the schools.† Interview questions with the students will not involve asking them directly if they believe they are bullied. Rather, the interviewee will ask specific questions regarding whether the student has had certain feelings and experiences. Many times the student does not realize that he or she is a victim of bullying, especially if it is a combination of seemingly minor incidents and it is non-physical. The questions will be asked in a conversational way, so the children do not feel threatened by the procedure. Through a supportive conversation, the following information would be asked of them: