Wiki source code of LearningArithmeticinthe21stCenturyStocktonBurton

Last modified by Holger Dick on 2010/09/09 14:22

Content · Comments (1) · Attachments (3) · History · Information

Hide line numbers

 1: The course of action that we would recommend is that Boulder Valley Schools introduce calculators only after the students have developed a solid mathematical foundation for carrying out arithmetic. We feel it is essential for students to learn the “nuts and bolts” of arithmetic in order for them to be capable of grasping more complicated mathematical concepts. While calculators may be a powerful tool that is often used in the work force, the introduction of calculators to those who do not yet understand the computations they are trying to perform will “produce adults who cant do basic arithmetic, doomed to wonder through life in a numeric haze.” (Gelernter)
 2: 
 3: “... We must not ignore one of the primary reasons we teach math~-~-it trains the mind. It promotes logical and rational thinking skills and discipline. It requires using learned information to proceed to the next level of information, whether it be dealing with numbers or ideas. These types of thinking skills are imperative if students are to be able to function as thinking, intelligent, contributing members of society: the ultimate goal of education.” ( Ayers)
 4: 
 5: The primary idea of education is not the rote repetition of processes or memorization of facts, instead the intent is to develop students into individuals who understand the underlying concepts of a given field. The use of calculators early on as a supplement to arithmetic ability will effectively separate implementation from cognition. While some may not see a need for full understanding of mathematical concepts, the effort put into such understanding greatly improves a students ability to grasp other abstract subject matter.
 6: 
 7: Its common sense that you do not want to ask someone to use a tool with out making sure that first they know how to use it. The essence of a math problem can not be “addressed?, conquered” by developing an algorithm to sequentially push buttons on a calculator. Knowledge (especially in math) needs to be extensible. Linda Starr states this point by saying that calculators “encourage students to randomly try a variety of mathematical computations without any real understanding of which is appropriate and why. Basically, what is the use of knowing different functions and mathematical processes if you cannot decipher when each one is appropriate?
 8: 
 9: Though some may argue that frustrated students are easily discouraged and often lose interest in mathematics, the solution is not to introduce calculators and thus a false sense of ability, but to expect better and more adaptive pedagogical practices from the instructor.
10: 
11: Victor Guskov makes this argument:
12: 
13: Both my experience (32 years in the classroom) and my investigations (20 years of studies) shows that pupils with unsteady elementary mental computational skills (addition and subtraction within the limits of 20, multiplication and division within the limits of 100) have great difficulties while learning the other basic topics of arithmetic and algebra. In other words they are doomed to poor progress in school math. Even calculators cannot help them
14: 
15: Calculators, though they are such a powerful tool in the work force, ultimately stunt mathematical development of cognitive problem solving when they are introduced to students at such a young age. The end result of such early exposure to calculators is demonstrated by the picture below.
16: 
17: [[image:output_html_m7cc32e39.gif||height="398" width="443"]]
18: 
19: 
20: 
21: 
22: Works Cited:
23: 
24: {{id name="citation"}}{{/id}} Starr, Linda. "Educators Battle Over Calculator Use". Education World. 9/5/10 <http:~/~/www.educationworld.com/a_curr/curr072.shtml>
25: 
26: {{id name="citation1"}}{{/id}} Guskov, Victor. "The Hazard of Using Calculators at School". EZINE. 9/5/10 <http:~/~/ezinearticles.com/?The-Hazard-of-Using-Calculators-at-School&id=195066>
27: 
28: {{id name="citation2"}}{{/id}} Ayers, Nancy. "Calculators and Calculating Devices". Witchita State University. 9/5/10 <http:~/~/www.math.wichita.edu/history/topics/calculators.html>.
29: 
30: {{id name="citation3"}}{{/id}} Gelernter, David. "Calculators and Calculating Devices". Witchita State University. 9/5/10 <http:~/~/www.math.wichita.edu/history/topics/calculators.html>.
31: 
32: 
33: Authors:
34: 
35: Burton, Jacob C
36: 
37: Stockton, Aaron E