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), “For centuries mathematicians have been interested in curves that can be constructed…” (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), “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), “[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