The Art of ReasoningPosted: August 29, 2012
Reasoning: the process of forming conclusions, judgments, or inferences from facts or premises.
There is usually more than one process or strategy in discovering a solution.
The best teaching methods take place when the teacher approaches instruction from the students’ perspective on learning, builds on their strengths and encourages them to develop their unique individual methods of reasoning.
I remember as a college student listening to the exasperation of my friend, a foreign student from Japan. My friend was majoring in business and had a real handle on mathematics. However, he became really frustrated when his math instructor insisted he use his methodical sequential steps in solving each problem. Whereas, my friend , understanding the process, came up with the same solution with lesser steps. When tested, the instructor would count each of his problems wrong unless each step matched his own. The instructor’s attitude “his way or the highway” caused undo frustration for my friend and discouraged his ability in reasoning.
Teaching is not an entity unto itself. The objective of any type of instruction is to teach students how to process the information on their own and discover their own strategies. Instruction in reasoning should encourage students to “think outside the box” rather than produce “cookie cutter” cognition. The teacher may adopt a specific strategy in discovering a solution. But what is more important is that students be given the same opportunity.
My friend’s teacher sought complete ownership of the strategy. What was more important to him was sticking to his own method with the exclusion of any further reasoning.
You can’t build upon learning without understanding the concept. Memorization of formulas and strategies without reasoning will stifle the scaffolding of future complexities in cognition.
I remember, as a second grade teacher emphasizing the concept of
“Number Sense” in mathematics; that is, encouraging a logical approach for development of strategies using number relationships. This is not a rote method in computation but rather a method that encourages students to reason and develop their own strategy in the solution process. As long as the process resulted in the correct answer, was consistent, and could be explained, the student was allowed to use it. Allowing students to verbally explain their strategy reinforces the mathematical concept.
For example, if the computation were given- 10 + 11. The student might explain his answer by using any of the following strategies:
“I know that 11 is one more than ten so I added (10 + 10) +1 and got (20) + 1 = 21”
“I know that if I add 10 to any number it will increase the number in the tens place by one more ten and the number in the ones place will remain the same.”
“I counted up from the highest number which is 11 by 10 more using my ten fingers.
After examination of all the strategies the student will decide what strategy is more efficient.
President Ronald Reagan had a plaque on his desk with the following quote:
“There is no limit to what a man can do or where he can go if he doesn’t mind who gets the credit.”
Finally, I believe there is no limit to what a teacher can do for his/her students if he/she doesn’t mind giving them the credit.