Mathematics

Kayla Reed
7/13/08
IDST 4114
Prof. Augustine

Worksheet for Researching Disciplines

Name of Discipline: __ Mathematics____________________________

Discipline Subject Matter: The Study of Mathematics and its Relationship with the Field of Education

Definition of Discipline Mathematics: is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them.

Sub-Fields within a Discipline:
Algebra: A branch of mathematics in which symbols, usually letters of the alphabet, represent numbers or members of a specified set and are used to represent quantities and to express general relationships that hold for all members of the set.
Geometry: The mathematics of the properties, measurement, and relationships of points, lines, angles, surfaces, and solids.
Calculus: The branch of mathematics that deals with limits and the differentiation and integration of functions of one or more variables.
Trigonometry: The branch of mathematics that deals with the relationships between the sides and the angles of triangles and the calculations based on them, particularly the trigonometric functions.



Research Methods: A research method that people who study Mathematics are Standardized Tests and Assessments. These help teachers determine their effectiveness in conveying the information to the students.

Key Concepts:
· Key Concept #1: Education enlarges your possibilities. Education gives you a base of choices and increased power, as shown in Figure 1-3. First, through different courses of study, it introduces you to more choices of career and life goals. Second, through the training you receive, it gives you more power to achieve the goals you choose. For example, while taking a writing class, you may learn about careers in journalism. This experience may lead you to take a class in journalistic writing that teaches you about reporting. Down the road, you may decide to work on a newspaper and to make journalism your career. Looking back, you realize that two classes you took in college changed the course of your life. (2)
· Key Concept #2: Education gives you tools for lifelong learning. You learn facts while you are in school, but more importantly, you learn how to think. While some of the facts and figures you learn today may not apply to the world of tomorrow, your ability to think will be useful always, in everything you do. (2)
· Key Concept #3: Education improves your employability and earning potential. Learning additional skills raises your competency so you can fulfill the requirements of higher-level jobs. In addition, having a college degree makes an impression on potential employers and makes you eligible for higher-salaried positions. (2)


Leading Theories:
Leading Theory #1: Behaviorism: Behaviorism is a theory of animal and human learning that only focuses on objectively observable behaviors and discounts mental activities. Behavior theorists define learning as nothing more than the acquisition of new behavior (3)
Leading Theory #2: Social Cognition: The social cognition learning model asserts that culture is the prime determinant of individual development. Humans are the only species to have created culture, and every human child develops in the context of a culture. (1)
Leading Theory #3: Cognitive Psychology: Cognitive psychology is the branch of psychology that studies mental processes including how people think, perceive, remember, and learn. As part of the larger field of cognitive science, this branch of psychology is related to other disciplines including neuroscience, philosophy, and linguistics. The core focus of cognitive psychology is on how people acquire, process, and store information. There are numerous practical applications for cognitive research, such as ways to improve memory, how to increase decision-making accuracy, and how to structure educational curriculums to enhance learning. (1)

Key Books/Seminal Texts:
Key Book/Seminal Text #1: “101+ Great Ideas for Introducing Key Concepts in Mathematics: A Resource for School Teachers” by: Alfred S. Posamentier and Herbert A. Hauptman
Why is it important? This book is important because it engages students with the great ideas in Mathematics compiled by two of the greatest minds in mathematics. From commonly taught topics in algebra, geometry, trigonometry, and statistics, to more advanced explorations into indirect proofs, binomial theorem, irrationality, relativity, and more, this guide outlines concepts and techniques that will inspire veteran and new educators alike.
Key Book/Seminal Text #2: “Teaching Mathematics: A Sourcebook of Aids, Activities, and Strategies” by Max A. Sobel and Evan M. Maletsky
Why is it important? This book is important because it addresses the art of teaching mathematics while also providing specific aids and activities in arithmetic, geometry, algebra and probability and statistics for use in the classroom.
Key Book/Seminal Text #3: “The Language of Mathematics: Making the Invisible Visible” by Keith Devlin
Why is it important? This book is important because it reveals the vital role mathematics plays in our life to understand who we are and the world we live in. It shows how mathematics is more that just numbers by providing us with the eyes to recognize and describe the hidden patterns of life that exist in the physical, biological, and social worlds without, and the realm of ideas and thoughts within.


Key Thinkers and Practitioners:
Key Thinker #1: Kurt Gödel (1906-1978) turned the lens of mathematics on itself and hit upon his famous "incompleteness theorem" — driving a stake through the heart of formalism
Key Thinker #2: Ludwig Wittgenstein (1889-1951) was an Austrian philosopher who worked primarily in the foundations of logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. His influence has been wide-ranging and he is generally regarded as one of the twentieth century's most important philosophers.
Key Thinker #3: Alan Mathison Turing (1912-1954) was an English mathematician, logican and cryptographer and provided an influential formalisation of the concept of the algorithm and computation with the Turing machine.
Key Practitioner #1: Pythagoras, (580-500 B.C) whose name was bestowed upon the famous Pythagorean Theorem, was both a philosopher and a mathematician. Although he was not the first to discover the basic properties of right triangles, he founded a branch of philosophy and mathematics that effected Greek society long after his death. They believed that the basic properties of number theory (whole numbers, perfect numbers, ratios, etc.) reflected the true nature of the universeKey Practitioner#2: Euclid, (300 B.C) one of the greatest geometers ever. Euclidian geometry bears his name, and he is responsible for compiling its fundamental list of postulates.
Key Practitioner #3: Archimedes of Syracuse (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and the explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name.

Professional Academic Journals:
Academic Journal #1: Global Journal of Mathematical Sciences: Theory and Practical: This is an international journal of high quality devoted to the publication of original research papers from pure and applied mathematics with some emphasis on all areas and subareas of mathematical analysis and their broad range of applications. Areas and subareas of interest include (but are not limited to) approximation theory; statistics; probability; fluid mechanics; Fuzzy mathematics; transport theory; mathematical biology, including population dynamics; wave propagation; special functions; algebra and applications; combinatorics; coding theory; fractional analysis; solid mechanics; variational methods; financial mathematics; asymptotic methods; graph theory; fractals; moment theory; scattering theory; number theory and applications; geometry of Banach spaces; topology and applications; complex analysis; stochastic process; bifurcation theory; differential equations; difference equations; dynamical systems; functional differential equations; numerical analysis; partial differential equations; integral equations; operator theory; Fourier analysis; matrix theory; semigroups of operators; mathematical physics; convex analysis; applied harmonic analysis; optimization; wavelets; signal theory; ultrametric analysis; optimal control; fixed-point theory and applications; reaction-diffusion problems, discrete mathematics; automata theory
Academic Journal #2: Applied Mathematics and Information Sciences: a journal of applied mathematics reporting research on the information science structures that describe fundamental processes of computational and numerical methods for exploring these structures.

Professional Academic Associations:

Professional Academic Association #1: American Mathematical Society:
The AMS provides information to further mathematical research and scholarship. Included on this server is a preprint archives with links to other preprint archives, information on publications published by the AMS, carrer development resources for mathematicians, searchable Combined Membership List, information on meetings and conferences and links to other Mathematics Information Servers. (http://e-math.ams.org/)
Professional Academic Association #2: The Mathematical Association: The Association exists to bring about improvements in the teaching of mathematics and its applications, and to provide a means of communication among students and teachers of mathematics. (http://www.m-a.org.uk/)