Open book learning versus rote learning

       What is rote learning?

     Rote learning is the concept that you will memorize a procedure by endlessly repeating it until you “understand” it.  Some believe this is the only way to truly understand a topic in mathematics.  It is the “practice makes perfect” paradigm.  The rote learning idea is that understanding is derived from memorization and recall over time.  [edit:(9-24-2015) As we learn more about the human brain and the way it carves and hones pathways, we begin to see the the role of rote learning. We have come to learn that rote memorization of key concepts tends to in a way  free up "ram" ,working memory, in our brains. With key concepts being stored in long term memory, our brains are able to process higher level logic faster. ] Understanding means to comprehend or to grasp the meaning of. Students with good memories will just simply memorize the formulas and recall them on demand at test time, and the teacher will believe they understand the concept and move on.  Students who do not have great memories will struggle and get frustrated while trying to memorize the formulas. We can single them out in an attempt to give them extra help to understand, which in some cases actually embarrasses the students. [edit:(9-24-2015) A strategy to overcome singling out students with poor memory, is to implement a small section on memorization techniques. Proper application of memorization strategies can also teach concentration and focus techniques. (link 'www.psychologytoday.com')]

 Embarrassment even in the smallest amount begins a psychological impairment on a child’s ability to learn. No matter how we approach the situation singling out one student or even multiple students can impair learning.  Now I am sure there are some very exceptional teachers with the amazing ability to approach a student to find out why they are failing with minimal impact. Unfortunately, not all teachers can do this; it is a talent of charisma that we just simply cannot teach everyone. We are now left with the question: How do we give the children that need this extra attention help without singling them out? We first need to remove the extra pressure of rote learning exercises. We can do this by utilizing Open book learning approaches.

                           What is open book learning?

Open book learning takes away the pressure of having to cram for a test. Relieving a student’s stress will create a better atmosphere of learning. In introductory courses, having a system based on pure open book examinations can cause some problems of students not studying or reading the material before the test. To alleviate this problem you can implement both open book and closed book exams.  The exams need to be structure for whether it is open book or not. For the open book tests do not put in direct information that can be simply copied. Present the questions where the students will have to apply the knowledge rather than recall or look them up and simply copy it from the book. Keep it random as well don’t let the students know what kind of test they are going to be having, so you don’t discourage study.

                      Don’t be one sided.

               

Stay flexible and implement all of these strategies together. The mechanical rote learning approaches should stay limited to introductory courses. Rote learning should never be the pass/ fail in math education.  A final examination should be on concepts and understanding not recall of facts that anyone can look up.  

The purpose of education is career preparation.[edit:(9-24-2015) The purpose of education goes far beyond career preparation. It is the cornerstone of human development and understanding our world. While career preparation is a tangible by-product of education, it is not the 'sole' purpose.]   An engineer can still build a great bridge even if they have to look up a formula. However; if they don’t have a conceptual understanding of what to look up or how to look it up they won’t be an engineer for long. 

Knowledge versus Intelligence

    



       Math is something people use everyday, although it can be difficult at times to use effectively. Mathematics education has been in need of a major overhaul for some time now. Too often, mathematics educators have fallen into a habit of teaching only one way to do things. In some cases, educators are unaware of multiple ways of teaching mathematics.

     There is too much emphasis on memorization, and not emphasis on logic. In classrooms many days are often spent memorizing one task or method of calculation, or one formula. or in some cases many formulas.This task can make math quite overwhelming. The goal here should be to ensure that students understand the concept, rather than just to be sure that they can memorize a bunch of formulas. Unfortunately, this is not the case.

      Logic is the foundation by which mathematics is built. All of the theorems, formulas, and rules that we use today are the result of the mathematicians starting with the very basics of numbers and building upon them by using logic. If we were to learn how to logically arrive at new theorems and formulas in mathematics, we would possess a greater understanding of mathematics as a whole. This means that educators should encourage students with an interest in finding new ways to approach a problem. After all, we would not have any of the great discoveries of math processes today, if we did not first look for an alternate way of using formulas and numbers. However, students are graded on their ability to memorize and regurgitate facts and formulas, and not on their ability to think and understand.

           Rote memorization is simply a method that will increase knowledge. It is more important to increase a person’s intelligence. Often people confuse knowledge and intelligence as the same thing, however, they are two very different things. Merriam Webster defines knowledge as the sum of what is known: the body of truth, information. They also provide the definition of intelligence as the ability to learn or understand or to deal with new or trying situations: reason; also: the skilled use of reason, the ability to apply knowledge to manipulate one's environment or to think abstractly.

      First, we will examine the definition of knowledge. The definition of knowledge shows us that knowledge is simply a quantitative measure of what we have memorized or experienced. From the definition of intelligence, we can conclude that intelligence is a qualitative measure of our ability to understand and to gain knowledge.

        Ole Roemer, the first person to calculate the speed of light, accomplished this through use of his intelligence not his knowledge. His knowledge did play a hand in his ability to make the calculations. However, without his ability to reason or to think abstractly he would not have made this exciting and profound discovery. As you can see knowledge and intelligence are both extremely important, but knowledge can be obtained by anyone.

        Just because a person doesn't know the definition of a word doesn't mean they're not intelligent, it just simply means that particular word is something they have not been exposed to. However, an intelligent person knows they can simply open a dictionary and find the definition of the word they are unfamiliar with. Also, an intelligent person will not only understand that definition but deduce the proper way to use the word.