Stephen M. Montgomery

Psychology 115A Section 13

December 4, 2000

Methods of Effective Learning

What does it mean to learn? Has a student who memorized a list of vocabulary words for a test, then proceeded to forget them 15 minutes after the end of the exam, learned anything? Is memorization sufficient, or does learning entail a much deeper set of abilities? It is fundamental to understand that knowledge builds vertically, and its growth is therefore dependent upon a solid, broad foundation of facts and skills. However, in acquiring a breadth of knowledge, it is important not to sacrifice depth of understanding for the sake of simply knowing more facts by rote. Since knowledge is primarily disseminated through school, it is important for America to reevaluate its educational system for the purpose of discovering better methods of teaching children.

Most everyone would like to be considered an expert in at least one if not many fields of knowledge. What makes an expert? The National Research Council has outlined six key concepts which separate an expert in a particular subject from a novice. Experts notice meaningful patterns of information, organize that information efficiently, use context to narrow the base of information necessary to solve a particular problem, retrieve knowledge fluently, are potentially efficient teachers, and can adapt and extrapolate their knowledge to situations they have not explicitly experienced previously (Bransford, Brown, and Cocking 31-48). Experts do not necessarily complete tasks more quickly than novices. In fact, the expert often spends extra time analyzing and examining the problem at a greater depth, therefore increasing his chances of arriving at a more correct answer. Experts excel at any type of problem which requires critical thinking, analysis, and use of multiple domains of knowledge.

In determining the ways in which we attain a high level of proficiency and skill in a particular domain, it is helpful to consider a personal experience I had with calculus. It is universally accepted that calculus is an advanced, abstract subject which requires roughly equal amounts of memorization, practice, and critical thinking techniques. I began to learn calculus as soon as I was taught to count to ten. That is, I became extremely adept at manipulating the basic, concrete numbers which would later be applied in a more abstract manner. Later, I learned the four basic numerical operations of addition, subtraction, multiplication, and division. At first, I practiced the basic operations extensively to improve my ability to recognize patterns. With time, I was able to increase my short-term memory capacity by "chunking" pertinent information (Bransford, Brown and Cocking 32-33). For example, instead of looking at the operation 12 x 8 and having to multiply 2 x 8 to get 16, and multiply 10 x 8 to get 80, and finally add 16 and 80 to produce the answer 96, I was able to look at the problem and simply know that 12 x 8 equals 96. This chunking technique is cumulative, so it made solving more complex problems like 12 x 81 and 120 x 8 simpler. Additionally, obtaining knowledge in subjects other than mathematics is vital to success in calculus. English or Greek letters represents variables in higher levels of mathematics, and many problems are written in paragraph format, instead of in numerical notation. This makes literacy as important as numerical manipulation in acquiring knowledge of calculus. Finally, when I enrolled in Advanced Placement calculus during my senior year of high school, my teacher continued to expand my knowledge base by introducing both the new calculus theorems and a variety of problems which forced me to use previous knowledge in new ways and learn the unfamiliar calculus concepts proficiently enough to be able to apply them to a variety of situations. The result of a year of practice and study was that I had enough broad and deep knowledge of the subject to pass a comprehensive calculus test whose questions I had never previously seen.

The process of learning complex abstract subjects like calculus begins at a very young age. The methods of learning which are emphasized by our parents and teachers during the first years of life have a profound impact on our capacity for learning later in life. It has been proven that even infants possess rudimentary concepts of physical and biological properties, number, and language (Bransford, Brown, and Cocking 84-95). Children also develop multiple strategies for solving the same problem. The more strategies a child is endowed with, the more problems he will be able to successfully solve. It is clear that a variety of problem solving techniques must be emphasized almost from birth in order for a child to be prepared for the myriad challenges and opportunities he will face once he enters school.

Questions are also key to a young child’s development. Even questions that require only a single yes or no answer force a child to practice and refine cognitive skills. The questions need only address tangible aspects of a child’s environment, not conceptual matters. I, as most children do, learned about colors, animals, shapes, and sounds from questions adults asked me every day. At first, I didn’t know the answer, and the adult would provide it for me. Later, the adult would not give me the whole answer, but give me a clue which would help me determine the correct response. As I became more familiar with the objects in question, I began to answer on my own. I had advanced through my zone of proximal development, or the zone between the tasks which one can complete alone and which one can complete with assistance (Bransford, Brown, and Cocking 80-81). Eventually I began to ask questions of my own, which further enhanced my early knowledge. In this way, I developed tools necessary for critical thinking before ever enrolling in Kindergarten.

Knowledge acquisition is a social, cumulative process. It begins when we are born and never truly stops. In acquiring knowledge, children take data from their environment and from human interactions and try to conceptualize it in the best way they can. The more methods of expressing ideas we instill into our children, the more types of problems they will be able to effectively solve. Additionally, we must be careful of the context of the examples and stories we tell children (Bransford, Brown, and Cocking 62-63). When material is overly contextualized, children often have difficulty applying knowledge to other types of problems. For example, a child who can perform a complex division problem in a classroom setting may experience difficulty in trying to determine the batting average of a baseball player, given the player’s number of hits and at-bats. Although both problems involve the same long division techniques, the child who is accustomed to only working problems in mathematical notation and who has little knowledge of baseball may not recognize that division is involved in the solution to the baseball problem. When children must work a variety of problems and are empowered with a multitude of strategies with which to solve them, the idea of context is neutralized and children are much more likely to be able to transfer knowledge effectively across domains. The challenge facing America’s teachers and parents is to expose children to the most problem solving techniques possible, to best develop both their knowledge base and their ability to extend that base to unfamiliar situations.

Works Cited