Solving Problems with Metaphor “Problems are often open-ended, paradoxical, and sometimes unsolvable, and require investigation before one can come close to a solution” (Zeitz x). When problems in a field can be defined as “open-ended, paradoxical, and sometimes unsolvable,” (Zeitz x) one might be able to reasonably assume that the field is difficult to conceptualize. Problem solving is a field of mathematics specifically designed around solving mathematics-related problems in competitions. Unlike the academic competitions seen in movies like “Mean Girls” or on trivia shows like “Jeopardy,” math competitions like The William Lowell Putnam Mathematical Competition are more akin to taking a test, where contestants write out proofs to complex …show more content…
These questions can range from trivial mind benders to full-length proofs, so preparation becomes a key element for success in the field. One useful text to help students new to the field prepare is “Art and Craft of Problem Solving” by Paul Zeitz, and this text will be the primary source for metaphors to be referenced in this essay. But why would there be any need to find metaphors in a mathematics textbook? Well, similar to other complicated fields, problem solving relies heavily on metaphor to explain certain concepts because, as Zeitz states in the prologue of his textbook, “Some branches of mathematics have very long histories, with many standard symbols and words. Problem solving is not one of them” (Zeitz 3). In fact, at least in the case of Zeitz, metaphor is a necessity for imparting an understanding of problem solving concepts on readers because some of these problem solving concepts are so abstract. As such, an understanding of metaphor is extremely useful in the understanding of the heuristics for solving a problem, analyzing metaphors which are naturally involved with word problems for the intended direction of the problem, and understanding the common theorems and other tools …show more content…
Because of the abstract nature of the theorems that need to be taught and the problems that need to be understood, it is extremely difficult to learn these topics without metaphor, as metaphor allows the students struggling with problem solving to relate the concepts they don’t understand to elements of real life, elements ranging from the conceptual metaphor Arithmetic is Object Collection to chess boards or maps. Without metaphor it would be extremely hard to introduce new students to even the idea of problem solving, where even the shorter problems actually take more than three or four steps as opposed to the common single step problem that frequents calculus and pre-calculus classes. As can be seen through the heavy involvement of metaphor in Zeitz’s Art and Craft of Problem Solving, metaphor is an integral part of the education of the problem solving process, particularly for understanding the heuristics of problem solving, analyzing the metaphors involved with word problems to find the intended direction for solving the problem, and certainly in understanding the common theorems that are useful tools for
“Metaphor.” Dictionary of World Literature: Criticism - Forms - Technique. Ed. Joseph T. Shipley. New York: Philosophical Library, 1943. 377-8.
In the book, the author has used several metaphors to make the book to be more interesting for the readers of the book. Additionally, the author of the book has used metaphors to bring about some of the meanings in the story. This has made it easy for the readers to be able to understand what they are reading. In conjunction to this, the author has used the metaphors to bring out the character traits of some characters like Janie and Joe in the book. Therefore, it is through metaphors that the book has been very interesting and easy to understand.
... relationship in one problem that doesn’t appear in others. Among all of this, there is such vastness in how one person might approach a problem compared to another, and that’s great. The main understanding that seems essential here is how it all relates. Mathematics is all about relationships between number and methods and models and how they all work in different ways to ideally come to the same solution.
The education of students is lacking in substantial curriculum designed to help students decipher the metaphors that we encounter so often.
Metaphors, according to Professor George Lakoff, are a way to think and reason about life. They are not a unique way to speak about it, but a common way to talk about life experiences since they are a reflection of our thought processes (1986). This became immediately apparent to me when I began looking for metaphors commonly used. It took some time to find any because they were pervasive of my thought system that I did not even notice many phrases around me were metaphors. Those phrases were not “poetic or rhetorical” way of talking, but a normal usage for those around me to express their thoughts (Lakeoff, 1986, p.216). The metaphor that came up several times on my search was history as roots. This metaphor allows us to think about life in a certain way and it holds particular implications for our interpersonal communication.
As well, metaphors exists everywhere. They influence the way we process information in our minds. Without the idea of comparison in order to achieve a better understanding of material, everything would be abstract and the way we perceive the information would be completely
In the book Metaphors We Live By, authors George Lakoff and Mark Johnson address the traditional philosophic view denouncing metaphor's influence on our world and our selves (ix). Using linguistic and sociological evidence, Lakoff and Johnson claim that figurative language performs essential functions beyond those found in poetry, cliché, and elaborate turns of phrase. Metaphor permeates our daily experiences - not only through systems of language, but also in terms of the way we think and act. The key to understanding a metaphor's effect on behavior, relationships, and how we make sense of our environment, can be found in the way humans use metaphorical language. To appreciate the affects of figurative language over even the most mundane details of our daily activity, it is necessary to define the term, "metaphor" and explain its role in defining the thoughts and actions that structure our conceptual system.
It is important to understand that in real life experience can connect to so many things. A book is not just a book, a book is a pathway that allows the mind to make connections. A couple chapters can be describing one’s childhood as a whole book can make a person reminisce about their young adulthood. Authors are not using metaphors accidentally but on purpose. Some authors write books, but some may think they are writing to them. They are retelling somebody’s story that happen in their life. These great metaphors is a key that opens up a door to millions of
Based upon this observation, it becomes natural to ask the questions pertaining to the use of proof in learning and understanding mathematics. If the concept of proof is so important to the field of mathematics, then is it possible that by writing proofs and studying proofs that an individual will be better equipped to understand the mathematics for which the proofs pertain? And if this is possible then when should a person be first exposed to proofs and at what level? In this paper I will give my views pertaining to these questions, as well as, a few more of my views pertaining to some other topics related to these questions.
Solving problems is a particular art, like swimming, or skiing, or playing the piano: you can learn it only by imitation and practice…if you wish to learn swimming you have to go in the water, and if you wish to become a problem solver you have to solve problems. -Mathematical Discovery
It has been shown that metaphors are made of consistent part which are strongly attached to one another. The previous terms have also been analyzed based on their similarities and differences as well as problematic aspects concerning
I am a person who has always had a profound passion and fascination for areas requiring an analytical approach. Right from early days at school, Mathematics has intrigued me. The most challenging of all problems were my favorites and obtaining solutions to them would leave me with a sheer feeling of ecstasy. I always did and always would thrive on solving the most challenging problems. With a compelling desire to excel, hard work became my second nature. My aspiration for a technical career prompted me to take up one of the most coveted undergraduate program in Computer Engineering at SR Engineering College, the best of such institutions. My own systematic & methodical towards finding a solution to any problem best suits this field.
Mathematics teachers teach their students a wide range of content strands – geometry, algebra, statistics, and trigonometry – while also teaching their students mathematical skills – logical thinking, formal process, numerical reasoning, and problem solving. In teaching my students, I need to aspire to Skemp’s (1976) description of a “relational understanding” of mathematics (p. 4). Skemp describes two types of understanding: relational understanding and instrumental understanding. In an instrumental understanding, students know how to follow steps and sequential procedures without a true understanding of the mathematical reasons for the processe...
A somewhat underused strategy for teaching mathematics is that of guided discovery. With this strategy, the student arrives at an understanding of a new mathematical concept on his or her own. An activity is given in which "students sequentially uncover layers of mathematical information one step at a time and learn new mathematics" (Gerver & Sgroi, 2003). This way, instead of simply being told the procedure for solving a problem, the student can develop the steps mainly on his own with only a little guidance from the teacher.
Furthermore, the relationship between the metaphorical linguistic expressions and the conceptual metaphors can be understood in the following way: the linguistic expressions (ways