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Matematico Deductive Theory Of Rote Learning Vs Critical Thinking

Is critical thinking in the classroom more important than rote memorization?

Now, at the beginning of the 21st century, almost all information can be gleaned from the Internet, so long as you ask the right questions on Google. So is there any point in having students memorize facts? Instead, students could spend their time learning to ask the right questions, which requires critical thinking skills.

The American educational arena is certainly stressing the importance of teaching critical thinkingskills. Common Core standards emphasize the importance of critical thinking. Students must be able to read text, grapple with the meaning of the text, challenge and verify or refute its accuracy, and use the information in meaningful ways.

In discussions with teachers, I often hear that they are very concerned with their students’ abilities to make distinctions between fact and fiction when searching the Internet, which is essential to knowledge acquisition. We would not want students to think that Dallas is the capital of Texas just because someone decided to be funny on Wikipedia. The ability to distinguish between fact and fiction requires both critical reading and critical thinking skills.

In addition to developing the skills to use the Internet effectively, students must develop the skills to adapt. Today’s kindergarten students will graduate from college in 2029. We do not know the knowledge and skills that students will need to possess in order to succeed in this future world. Therefore, teachers cannot successfully impart 2029 knowledge and skills to students in today’s classrooms. Instead, the best that we can do is help students adapt to different kinds of environments. Adaptation requires critical thinking skills.

It’s clear that an argument can be made for the importance of teaching critical thinking skills in schools. However, what is the argument in favor of teaching knowledge and skills that do not require critical thinking?

Consider the numerous subjects that today’s adults learned in school that did not require critical thinking skills. For example, learning multiplication tables involves rote memorization. Learning geography may involve simple recall. Quick. What’s the capital of your state? Students can obviously learn to answer this question very simply. They might even spend hours memorizing the capitals of every state and country. This is engaging, but it represents low-level thinking. As another example, learning to spell does not require critical thinking in most situations.

When I was in graduate school, my friends nicknamed me E.D. Hirsch, Jr. You may recall Hirsch’s book series on what common knowledge students should possess at every grade level. Most of the members of my graduate school cohort emphasized the importance of critical thinking. I certainly did not disparage its importance. However, I think I would lack something as an individual if I did not know that Austin is the capital of Texas, as I wait in the Austin airport for a flight. I hope that there are no spelling mistakes in this post, though I know spell-check cannot always catch the difference between there and their.

Rote memorization can be essential to successful participation in social, business, and civic life. A well-known American broadcaster once said that if she were trying to get a job today she would try to learn as much about as many things as possible. The best job candidates know as much about as many topics as they can learn. The reason for this is simple: one never knows what topic an interviewer is going to want to discuss. People should be prepared with as much information about sports, history, music, dining, and everything else as possible. Schools can promote this kind of knowledge by exposing students to a wide array of different topics. Simple exposure, however, does not require critical thinking.

Within science, there are certain pieces of information that all students should know. Can you imagine how lost an individual would be if he/she did not know how to identify the different parts of the body? People who know sophisticated terms for various bodily functions will feel much better when speaking to polite audiences in certain situations. (This situation is particularly meaningful to me this week as I was in the emergency room last week passing a kidney stone.) These words must be learned and memorized. Nobody is going to Google synonyms in the middle of conversations just so that they do not have to use slang terms.

Of course, the challenge is in determining which facts and ideas people must know. E.D. Hirsch tried to do this for himself. I would argue that communities must come up with these lists for themselves. A single author cannot impose a body of knowledge on anybody else.

Unfortunately, the school year is only about 1,100 hours long. Consequently, students cannot spend an unlimited amount of time learning simple information and how to think and read critically. However, I do not believe that learning to think critically necessarily precludes the opportunity to learn simple information. The best curricula scaffold learning so that students have something meaningful to think about. Students can read facts, in engaging text, and then be challenged to think about them in critical ways. I think that the best curricula include both rote learning and critical thinking.

What do you think?

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"By heart" redirects here. For other uses, see By heart (disambiguation).

Rote learning is a memorization technique based on repetition. The idea is that one will be able to quickly recall the meaning of the material the more one repeats it. Some of the alternatives to rote learning include meaningful learning, associative learning, and active learning.

Versus critical thinking[edit]

Rote methods are routinely used when fast memorization is required, such as learning one's lines in a play or memorizing a telephone number.

Rote learning is widely used in the mastery of foundational knowledge. Examples of school topics where rote learning is frequently used include phonics in reading, the periodic table in chemistry, multiplication tables in mathematics, anatomy in medicine, cases or statutes in law, basic formulae in any science, etc. By definition, rote learning eschews comprehension, so by itself it is an ineffective tool in mastering any complex subject at an advanced level. For instance, one illustration of rote learning can be observed in preparing quickly for exams, a technique which may be colloquially referred to as "cramming".

Rote learning is sometimes disparaged with the derogative terms parrot fashion, regurgitation, cramming, or mugging because one who engages in rote learning may give the wrong impression of having understood what they have written or said. It is strongly discouraged by many new curriculum standards. For example, science and mathematics standards in the United States specifically emphasize the importance of deep understanding over the mere recall of facts, which is seen to be less important. The National Council of Teachers of Mathematics stated:

More than ever, mathematics must include the mastery of concepts instead of mere memorization and the following of procedures. More than ever, school mathematics must include an understanding of how to use technology to arrive meaningfully at solutions to problems instead of endless attention to increasingly outdated computational tedium.[1]

However, advocates of traditional education have criticized the new American standards as slighting learning basic facts and elementary arithmetic, and replacing content with process-based skills. In math and science, rote methods are often used, for example to memorize formulas. There is greater understanding if students commit a formula to memory through exercises that use the formula rather than through rote repetition of the formula. Newer standards often recommend that students derive formulas themselves to achieve the best understanding.[2] Nothing is faster than rote learning if a formula must be learned quickly for an imminent test and rote methods can be helpful for committing an understood fact to memory. However, students who learn with understanding are able to transfer their knowledge to tasks requiring problem-solving with greater success than those who learn only by rote.[3]

On the other side, those who disagree with the inquiry-based philosophy maintain that students must first develop computational skills before they can understand concepts of mathematics. These people would argue that time is better spent practicing skills rather than in investigations inventing alternatives, or justifying more than one correct answer or method. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong foundational skills. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject. Thus, these people believe that rote learning is an important part of the learning process.[4]

Eugène Ionesco commented upon rote learning in his play "The Lesson".[5]

By nation and culture[edit]

While the system is widely practiced in schools in Brazil, China, India, Pakistan, Malaysia, Singapore, Japan, Romania, Italy, South Korea, Turkey, Malta, and Greece, it has been criticised by numerous academics.[6][7][8][9][10]

In computer science[edit]

Rote learning is also used to describe a simple learning pattern used in machine learning, although it does not involve repetition, unlike the usual meaning of rote learning. The machine is programmed to keep a history of calculations and compare new input against its history of inputs and outputs, retrieving the stored output if present. This pattern requires that the machine can be modeled as a pure function — always producing same output for same input — and can be formally described as follows:

f() → () → store ((),())[11]

Rote learning was used by Samuel's Checkers on an IBM 701, a milestone in the use of artificial intelligence.[12]

See also Memoization.

Learning methods for school[edit]

The flashcard, outline, and mnemonic device are traditional tools for memorizing course material and are examples of rote learning.[13][14][15][16]

See also[edit]


External links[edit]

  1. ^Understanding the Revised NCTM Standards: Arithmetic is Still Missing!
  2. ^National Council of Teachers of Mathematics. "Principles and Standards for School Mathematics". Retrieved 6 May 2011. 
  3. ^Hilgard, Ernest R.; Irvine; Whipple (October 1953). "Rote memorization, understanding, and transfer: an extension of Katona's card-trick experiments". Journal of Experimental Psychology. 46 (4): 288–292. doi:10.1037/h0062072. 
  4. ^Preliminary Report, National Mathematics Advisory Panel, January, 2007
  5. ^Ionesco, Eugène. The Bald Soprano & Other Plays. New York: Grove Press, 1958.[page needed]
  6. ^Feynman, Richard; Leighton, Ralph (1985). Surely you're joking, Mr. Feynman!. New York: W. W. Norton. ISBN 0-7861-7728-4. 
  7. ^Jones, Dorian (2007-03-21). "Turkey: Revolutionizing The Classroom". Deutsche Welle. Retrieved 2008-08-12. 
  8. ^Feynman, Richard; Robbins, Jeffrey (2005). The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman. New York: Basic Books. ISBN 9780465023950. 
  9. ^Bean, John C. (2011). Engaging Ideas: The Professor's Guide to Integrating Writing, Critical Thinking and Active Learning in the Classroom (2 ed.). John Wiley & Sons. p. 384. ISBN 978-1-118-06233-3. 
  10. ^Mulnix, J. W. (2010). "Thinking critically about critical thinking". Educational Philosophy and Theory. doi:10.1111/j.1469-5812.2010.00673.x. 
  11. ^Ming Xue; Changjun Zhu (25 April 2009). A Study and Application on Machine Learning of Artificial Intelligence. Artificial Intelligence, 2009. JCAI '09. International Joint Conference on. pp. 272–274. doi:10.1109/JCAI.2009.55. 
  12. ^"Rote Learning". 
  13. ^Preston, Ralph (1959). Teaching Study Habits and Skills, Rinehart. Original from the University of Maryland digitized August 7, 2006.
  14. ^Cohn, Marvin (1979). Helping Your Teen-Age Student: What Parents Can Do to Improve Reading and Study Skills, Dutton, ISBN 978-0-525-93065-5.
  15. ^Ebbinghaus, H. (1913). Memory: A Contribution to Experimental Psychology, Teacher’s College, Columbia University (English edition).
  16. ^Schunk, Dale H. (2008). Learning Theories: An Educational Perspective, Prentice Hall, ISBN 0-13-010850-2.

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