The Role of the Proof in Math Essay example

:: 6 Works Cited
Length: 2682 words (7.7 double-spaced pages)
Rating: Blue      
Open Document

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The Role of the Proof in Math

The notion of proof has long played a key role in the study of mathematics. It is in my opinion the role of proof that separates mathematics from the sciences and other fields of study. It is the existence of proofs that give mathematicians the confidence that their work is credible and thus allows them to continue to build upon prior work without the need to second guess what has previously been accomplished.

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.

Before discussing the virtues of proofs as a means of learning and understanding mathematics, I feel that it is first necessary to begin with a brief discussion of the functions of proof within mathematics. Following I will give a list of the functions of proof that I have comprised from three sources (Hanna [2], Knuth [3], Tucker [6]):

1.verification, the act of arguing that a statement is true

2.explanation,providing reasons for why a statement is true, which in turn
may lead to understanding

3.systematization,organizing statements and definitions into a system of
axioms, lemmas, theorems, etc.

4.discovery,creating knowledge and new results ...

... middle of paper ...

...ducation, V178 N1, pp. 35-45

[2]Hanna, Gila (2000), “Proof, Explanation and Exploration: An Overview,” Educational Studies in Mathematics, V44, pp. 5-23

[3]Knuth, Eric (2002), “Secondary School Mathematics Teachers Conceptions of Proof,” Journal for Research in Mathematics Education, V33, pp.379-405

[4]Lester, Frank K. (1975), “Developmental Aspects of Children’s Ability to Understand Mathematical Proof,” Journal for Research in Mathematics Education, V6 N1, pp. 14-25

[5]Selden, Annie and Selden, John (2003), “Validations of Proofs Considered as Texts: Can Undergraduates Tell Whether an Argument Proves a Theorem?,” Journal for Research in Mathematics Education, V34 N1, pp. 4-36

[6]Tucker, Thomas (1999), “On the Role of Proof in Calculus Courses,” Contemporary Issues in Mathematics Education, MSRI Publications, Cambridge University Press, Cambridge, UK

Click the button above to view the complete essay, speech, term paper, or research paper

Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »

This essay is 100% guaranteed.

Title Length Color Rating  
Math in Special Education Essay - There’s no denying that education is constantly changing, but what’s truly astounding is the difference that can be throughout the years in math. More is changing in math classrooms than the tools that are used. The expectations that 21st century students face are completely transforming the approach that’s being taken in classrooms across America. The United States wants to make sure its students are ready to compete on a global level, and teachers are stepping up to the plate. The National Council of Teachers of Mathematics (NCTM) has led the movement for education reform in mathematics....   [tags: math classrooms, teachers of mathematics]
:: 3 Works Cited
939 words
(2.7 pages)
Better Essays [preview]
Essay about Math Is Everywhere - What is math. If you had asked me that question at the beginning of the semester, then my answer would have been something like: “math is about numbers, letters, and equations.” Now, however, thirteen weeks later, I have come to realize a new definition of what math is. Math includes numbers, letters, and equations, but it is also so much more than that—math is a way of thinking, a method of solving problems and explaining arguments, a foundation upon which modern society is built, a structure that nature is patterned by…and math is everywhere....   [tags: real life application of the number science] 852 words
(2.4 pages)
Strong Essays [preview]
Proof Essay example - Proof Proof. What is it and why does this simple term cause such a stir among mathematics educators and mathematics students. If you were to ask a young child to prove a mathematical fact, they would be happy to show you many examples of how it works. This does not constitute a proof but it is a step in the right direction. If you were to ask a high school student or first year college student to do a proof, you will most likely be met with groans and feelings of disgust. Students at this age have probably encountered proof in a geometry class where they were expected to follow a strict format without much freedom to express proofs on their own....   [tags: Math Education Papers]
:: 14 Works Cited
3358 words
(9.6 pages)
Strong Essays [preview]
“Writing to Learn” in a Math Classroom Essay - Theory of “Write to Learn” Reading and writing are the basis of the original meaning of literacy. This definition, however, changed over time and culture. The term has expanded to include computer literacy, digital literacy, information literacy, health literacy, etc. (Vacca, Vacca, & Mraz, 2011). Nevertheless, the most important change to the term literacy is expanding the use of reading and writing. Literacy is defined as understanding, thinking and practicing the use of language in different cultural/social settings through the use of all types of media which allows people to communicate and make meanings (Vacca et al., 2011)....   [tags: Education, mathematics]
:: 2 Works Cited
891 words
(2.5 pages)
Better Essays [preview]
Understanding the Realtion Between Math and Music Essays - ... Amplitude refers to the distance from crest or trough of the wave to its equilibrium position. Garland (1995) stated, frequency is a term that describes the number of waves, or vibrations, that pass a given point per second (p. 28). It is inversely proportional to the wavelength, which is the distance of one wave cycle. Frequency can be evaluated in the pitch of a tone: a higher pitch has a higher frequency. A simple tone has constant frequency and amplitude, and its graph is similar to a sine curve....   [tags: rhythm and frequency, galileo galilei] 1308 words
(3.7 pages)
Better Essays [preview]
Essay on Math and Music: An Introduction and Mathematical Analysis - Math and Music: An Introduction and Mathematical Analysis Rhythm and Frequency To understand the relation between math and music, the primary step is to study the nature of rhythm, frequency and amplitude. Everything around us has its own pattern of rhythm, from the motion of protons and neutrons, to the beats in rock music. Rhythm is determined by the periodicity of vibration of certain object in its surrounding substance, or medium. The vibration is repeated at a constant time length, thus creating wave motion....   [tags: rhythm, frequency, amplitude]
:: 5 Works Cited
1198 words
(3.4 pages)
Strong Essays [preview]
Essay on The Benefits of Learning Mathematics - When I graduated from high school, forty years ago, I had no idea that mathematics would play such a large role in my future. Like most people learning mathematics, I continue to learn until it became too hard, which made me lose interest. Failure or near failure is one way to put a stop to learning a subject, and leave a lasting impression not worth repeating. Mathematics courses, being compulsory, are designed to cover topics. One by one, the topics need not be important or of immediate use, but altogether or cumulatively, the topics provide or point to a skill, a mastery of mathematics....   [tags: Math Education]
:: 1 Works Cited
929 words
(2.7 pages)
Better Essays [preview]
The Benefits of Music Essay - In today’s competitive society, everything and anything that makes one different from the rest is what truly counts. In every aspect of life, especially here in this the leading first world country The United States of America, we are judged by our abilities and aptitudes. Whether it be a job interview, or college application: It’s what’s on paper that is seen first by those whom can allow us to pay our bills, follow our higher education dreams, or to just be civilized human beings here in this monopoly we call home....   [tags: contributions to math and science curriculum] 633 words
(1.8 pages)
Better Essays [preview]
Essay about Women's Role in Science and Technology - Women's Role in Science and Technology Women have played an important role in the development of science and technology, but there is an insufficient number of females in those career fields. Technological change has affected the roles of women and gender role ideas. Women without doubt came a long way improving the numbers and increasing the percentages in the workforce of Science, Technology, Engineering and Mathematics (STEM) but the statistics say the numbers are still less than those of men....   [tags: women scientist, engineering, high education]
:: 2 Works Cited
1974 words
(5.6 pages)
Term Papers [preview]
Mathematical Ethics Essay - Mathematical Ethics Philosophers since antiquity have argued the merits of mathematics as a normative aid in ethical decision-making and of the mathematization of ethics a theoretical discipline. Recently, Anagnostopoulos, Annas, Broadie and Hutchinson have probed such issues said to be of interest to Aristotle. Despite their studies, the sense in which Aristotle either opposed or proposed a mathematical ethics in subject-matter and method remains unclear. This paper attempts to clarify the matter....   [tags: Math Philosophy Aristotle Papers]
:: 10 Works Cited
4154 words
(11.9 pages)
Powerful Essays [preview]