dear user you know what is mathematics?
What is Mathematics?Home Page |
A Tidbit of HistoryMathematics as a formal area of teaching and learning was developed about 5,000 years ago by the Sumerians. They did this at the same time as they developed reading and writing. However, the roots of mathematics go back much more than 5,000 years.Throughout their history, humans have faced the need to measure and communicate about time, quantity, and distance. The Ishango Bone (see ahttp://www.math.buffalo.edu/mad/ Ancient-Africa/ishango.html andhttp://www.naturalsciences.be/expo/ishango/ en/ishango/riddle.html) is a bone tool handle approximately 20,000 years old. Figure 1 The picture given below shows Sumerian clay tokens whose use began about 11,000 years ago (seehttp://www.sumerian.org/tokens.htm). Such clay tokens were a predecessor to reading, writing, and mathematics.Figure 2 The development of reading, writing, and formal mathematics 5,000 years ago allowed the codification of math knowledge, formal instruction in mathematics, and began a steady accumulation of mathematical knowledge.Mathematics as a DisciplineA discipline (a organized, formal field of study) such as mathematics tends to be defined by the types of problems it addresses, the methods it uses to address these problems, and the results it has achieved. One way to organize this set of information is to divide it into the following three categories (of course, they overlap each other):
Even within the third component, it is not clear what should be emphasized in curriculum, instruction, and assessment. The issue of basic skills versus higher-order skills is particularly important in math education. How much of the math education time should be spent in helping students gain a high level of accuracy and automaticity in basic computational and procedural skills? How much time should be spent on higher-order skills such as problem posing, problem representation, solving complex problems, and transferring math knowledge and skills to problems in non-math disciplines? Beauty in MathematicsRelatively few K-12 teachers study enough mathematics so that they understand and appreciate the breadth, depth, complexity, andbeauty of the discipline. Mathematicians often talk about the beauty of a particular proof or mathematical result. Do you remember any of your K-12 math teachers ever talking about the beauty of mathematics?G. H. Hardy was one of the world's leading mathematicians in the first half of the 20th century. In his book "A Mathematician's Apology" he elaborates at length on differences between pure and applied mathematics. He discusses two examples of (beautiful) pure math problems. These are problems that some middle school and high school students might well solve, but are quite different than the types of mathematics addressed in our current K-12 curriculum. Both of these problems were solved more than 2,000 years ago and are representative of what mathematicians do.
Problem SolvingThe following diagram can be used to discuss representing and solving applied math problems at the K-12 level. This diagram is especially useful in discussions of the current K-12 mathematics curriculum.Figure 3 The six steps illustrated are 1) Problem posing; 2) Mathematical modeling; 3) Using a computational or algorithmic procedure to solve a computational or algorithmic math problem; 4) Mathematical "unmodeling"; 5) Thinking about the results to see if the Clearly-defined Problem has been solved,; and 6) Thinking about whether the original Problem Situation has been resolved. Steps 5 and 6 also involve thinking about related problems and problem situations that one might want to address or that are created by the process or attempting to solve the original Clearly-defined Problem or resolve the original Problem Situation. Click here for more information about problem solving.Final RemarksHere are four very important points that emerge from consideration of the diagram in Figure 3 and earlier material presented in this section:
|
No comments:
Post a Comment