Saturday, March 13, 2010
Saturday, March 6, 2010
Mathematics education
Mathematics education the practice of teaching and learning mathematics, as well as the field of scholarly research on this practice. Researchers in mathematics education are primarily concerned with the tools, methods and approaches that facilitate practice or the study of practice.
However mathematics education research, known on the continent of Europe as the didactics of mathematics, has developed into a fully fledged field of study, with its own characteristic concepts, theories, methods, national and international organisations, conferences and literature. This article describes some of the history, influences and recent controversies concerning mathematics education as a practice.
However mathematics education research, known on the continent of Europe as the didactics of mathematics, has developed into a fully fledged field of study, with its own characteristic concepts, theories, methods, national and international organisations, conferences and literature. This article describes some of the history, influences and recent controversies concerning mathematics education as a practice.
History of mathematics
The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[11] was probably that of numbers: the realization that a collection of two apples and a collection two oranges (for example) have something in common, namely quantity of their members.
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.[12] Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.
Further steps needed writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed] Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]
Mayan numerals
The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[13] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[14]
In addition to recognizing how to count physical objects, prehistoric peoples also recognized how to count abstract quantities, like time – days, seasons, years.[12] Elementary arithmetic (addition, subtraction, multiplication and division) naturally followed.
Further steps needed writing or some other system for recording numbers such as tallies or the knotted strings called quipu used by the Inca to store numerical data.[citation needed] Numeral systems have been many and diverse, with the first known written numerals created by Egyptians in Middle Kingdom texts such as the Rhind Mathematical Papyrus.[citation needed]
Mayan numerals
The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns and the recording of time. More complex mathematics did not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy.[13] The systematic study of mathematics in its own right began with the Ancient Greeks between 600 and 300 BC.
Mathematics has since been greatly extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today. According to Mikhail B. Sevryuk, in the January 2006 issue of the Bulletin of the American Mathematical Society, "The number of papers and books included in the Mathematical Reviews database since 1940 (the first year of operation of MR) is now more than 1.9 million, and more than 75 thousand items are added to the database each year. The overwhelming majority of works in this ocean contain new mathematical theorems and their proofs."[14]
Mathematics
Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns,[2][3] formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.[4]
There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".[5] Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, for example in China in 300 BCE, in India in 100 CE, and in Arabia in 800 CE, until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.[7]
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.[8]
There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions".[5] Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[6]
Through the use of abstraction and logical reasoning, mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics continued to develop, for example in China in 300 BCE, in India in 100 CE, and in Arabia in 800 CE, until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.[7]
Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and game theory. Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind, although practical applications for what began as pure mathematics are often discovered.[8]
Friday, March 5, 2010
Asian University for Women
The academic program at AUW is based on the firm belief that responsible citizens of the world must be equipped with strong skills in critical thinking, analysis, and communication. The unique "(1)+3+2" liberal arts curriculum developed at our University is composed of the following programs:
The Access Academy, a year-long pre-collegiate bridge program that provides a critical foundation in English language studies, mathematics and quantitative reasoning, and computer skills. The Academy is designed to enable students to acquire the requisite academic preparation to pursue a rigorous University education.
The combined undergraduate and graduate degree programs, taken over a total of five years: three years of rigorous training in the liberal arts and science; and two years of specialized graduate professional training.
During their undergraduate studies, students will also have the opportunity to engage in various internships with public and private organizations in countries across the region.
English is the medium of instruction in all AUW programs.
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Prof. Hilbert
Learn in mathe
a history of mathematician
Sigal and I have been back in Canada at McMaster University since January 2000. The department of mathematics and statistics, where I am based, now occupies the historic Hamilton Hall, which has recently been completely renovated to become the state-of-the-art James Stewart Centre for Mathematics. The math centre has a very friendly and open atmosphere and there are faculty representing a wide variety of areas of pure and applied mathematics. The Mathematical Biology Research Group currently includes two faculty, four postdocs, three grad students, and several undergrad research associates, and we usually have opportunities at all levels every year.
In addition to an attractive campus that borders beautiful conservation lands, McMaster has a number of features that make it an excellent place to do research in mathematical biology. Within the Faculties of Science, Social Sciences, and Health Science, there are researchers in a variety of departments with a serious interest in collaborating with mathematicians to make progress on biological and medical problems.
Apart from my current collaborations with faculty members in clinical epidemiology and biostatistics, the Centre for Health Economics and Policy Analysis, pathology and molecular medicine, and psychology, I have been discussing possible collaborations with faculty in biology, physics and astronomy, geography and geology, and anthropology. The genuine spirit of enthusiastic interdisciplinary collaboration at McMaster is outstanding.
Nearby resources at other universities and institutions in southern Ontario also provide endless opportunities for mathematical biologists. In particular, McMaster is one of the six principal sponsoring universities of the Fields Institute for Research in Mathematical Sciences in Toronto and a primary member of the SHARCNET high-performance computing consortium. Both Fields and SHARCNET have programs that provide funding for students and postdocs at McMaster.
Before returning to Canada, Sigal and I had often heard that the funding situation was much poorer than in the U.S.; however, we were pleasantly surprised by the real, current situation for new faculty members in Canada. In particular, Canadian universities can leverage very large start-up grants for new faculty from the Canada Foundation for Innovation's New Opportunities Fund. If their research interests include a health connection, faculty members in mathematical biology have more potential funding sources than other applied mathematicians, the key source being the Canadian Institutes of Health Research (CIHR).
Editor's note: CIHR is a Next Wave sponsor
Of course, not everyone who is considering a career in mathematical biology has academic research in mind. There are many other possibilities, because there is a great need for mathematically and computationally competent individuals to work on health-related problems in industrial and governmental organizations. (Examples of the latter include Health Canada and Statistics Canada.)
Some of Game
The HiLoTarget dice game is a game for two or more players. There are three versions of the game called Try for High, Go for Low, and Hit the Target. You use three polyhedra dice: A tetrahedron with four sides used to roll 1, 2, 3, or 4 An octahedron with eight sides used to roll 1, 2, 3, 4, 5, 6, 7, or 8. A dodecahedron with 12 sides used to roll 1, 2 ,3, 4, 5, 6, 7, 8, 9, 10, 11, or 12. A turn consists of three dice rolls. Each player does the following: Roll #1: Roll all three dice, choose one of the dice, and record the score on a score sheet. Roll #2: Roll two of the dice, excluding the die chosen on the first roll, choose one of the two dice, and record the score on the score sheet. Roll #3: Roll the die not choosen on the first two rolls, and record the score on the score sheet. We usually play four rounds.
This is the first of several number race games played on a set of "racetracks." In this beginner's game, each player has five racetracks, and puts a "racehorse" on the zero (0) end of each track. Each turn, a player rolls 2D6 (two 6-sided dice) and uses the numbers on the dice to move one or two horses along the track. The object of the game is to get all five horses to twelve (12). Number Race 0 to 12 describes three game variations.
This is one of several number race games. Each player has a game board that consists of four "racetracks," and puts a "racehorse" on the zero (0) end of each track. Each turn a player rolls 2D8 (two 8-sided dice, each numbered 1 to 8) and uses the numbers on the dice to move one or two horses along a track. The object of the game is to move all four horses to the sixteen (16) end of their tracks. Number Race 0 to 16 describes three game variations.
This is one of several number race games. Each player has a game board that consists of five "racetracks," and puts a "racehorse" on the zero (0) end of each track. Each turn a player rolls 2DD (two digit dice, each numbered 0 to 9) and uses the numbers on the dice to move one or two horses along a track. The object of the game is to move all five horses to the eighteen (18) end of their tracks. Number Race 0 to 18 describes three game variations.
This is one of several number race games. Each player has a game board that consists of five "racetracks," and puts a "racehorse" on the zero (0) end of each track. Each turn a player rolls 2D10 (two 10-sided dice, each number 1 to 10) and uses the numbers on the dice to move one or two horses along a track. The object of the game is to move all five horses to the twenty (20) end of their tracks. Number race 0 to 20 describes three game variations.
This is one of several number race games. Each player has a game board that consists of six "racetracks," and puts a "racehorse" on the zero (0) end of each track. Each turn a player rolls 2D12 (two 12-sided dice, each numbered 1 to 12) and uses the numbers on the dice to move one or two horses along a track. The object of the game is to move all five horses to the twenty-four (24) end of their tracks. Number Race 0 to 24 describes three game variations.
Ahoy Number Race players, Here are racetracks, two sets per page, for Number Race 0 to 12, Number Race 0 to 16, Number Race 0 to 18, Number Race 0 to 20, and Number Race 0 to 24.
REVERSE was invented by Peter Lynn Sessions and published in People's Computer Company, May 1973. Begin with a list of numbers and try to put them in order with the smallest number on the left and the largest number on the right, according to the rules of the game. REVERSE describes the standard game and suggests several variations
Grab your favorite dictionary and play WordsWorth. As you play, you'll learn about permutations of words called reverses, palindromes, semordnilaps, and anagrams. Assign a letter score to each letter in the alphabet, a through z, as follows: a = 1, b = 2, c = 3, and so on, up to z = 26. The WordsWorth of a word is the sum of the letter scores of the word's letters. Most of the play in WordsWorth is thinking: knowing words, learning more words, and devising strategies for finding answers. People are well equipped to do this type of play. Some of the play is more mundane: looking up letter scores and adding them to get the WordsWorth of a word. First grade students might start with base-10 blocks as their WordsWorth calculator, and then move on to mental math and paper and pencil math as their addition skills improve by playing WordsWorth.
This resource is part of the Investigation Backpack collection.
