Tuesday 16 September 2014

UNIT – I NATURE AND DEVELOPMENT OF MATHEMATICS,

NATURE, CHARACTERISTICS AND OF MATHEMATICS

MEANING OF MATHEMATICS

Mathematics is commonly defined as the study of patterns of structure, chance, and space; more informally, one might say it is the study of figures and numbers. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in philosophy of mathematics.

DEVELOPMENT OF MATHEMATICS

The earliest records of mathematics show it arising in response to practical needs in agriculture, business, and industry. In Egypt and Mesopotamia, where evidence dates from the 2d 3d millennia b.c., it was used for surveying and menstruation; estimates of the value of pi are found in both locations.

CHARACTERISTICS OF MATHEMATICS
Children may exhibit feelings in insecurity, as well as fears of failure, punishment, ridicule, or stigmatizing labels. Children with math anxiety may also have a negative attitude or negative emotional reaction to math. Teachers need to provide students with experiences that they will be successful in, in order to promote a more positive attitude. They learning bridge or strategies are good ways to help prevent the early development of math anxiety.

LOGICAL SEQUENCE IN MATHEMATICS
The problem is predicting the next term of a partially specified sequence. The user shall input the rest few terms of a mathematical sequence. The expert system will rest try you understand the pattern and using the found pattern it would predict the next term.

INTEGER SEQUENCES
Integer sequences are the most commonly seen sequences. For integer sequences, it’s the addition, subtraction and multiplication operators that play the major role in Xing up in the function f. so, in order to discover the function f, we need to perform various operations on the integers that are the first few given terms of the sequence.
For example, consider the sequence 3;7;11;15;…… the way this sequence is understood is by taking the deference between adjacent terms of the sequences.
STRUCTURE OF MATHEMATICS
The focus of my presentation will be on such structural aspects of mathematics that are known or likely to cause problems or challenges for the process of learning mathematics, and hence for its teaching. I shall interpret the term ―the structure of mathematics‖ in a somewhat broad sense, by taking into account also the nature of mathematics and its characteristics as a discipline and not solely its architectural features as reflected in one or more possible construction(s) of edifice.


ABSTRACTION
Mathematical thinking often begins with the process of abstraction-that is, noticing a similarity between two or more objects or events. Aspects that they have in common, whether concrete or hypothetical can be represented by symbols such as numbers, letters, other marks, diagrams, geometrical constructions, or even words.
Whole numbers are abstractions that represent the size of sets of things and events or the order of things within a set. The circle as a concept is an abstraction derived from human faces, flowers, wheels, or spreading ripples; the letter a may be an abstraction for the surface area of objects of any shape, for the acceleration of all moving objects, or for all objects process of addition, whether one is adding apples or oranges, hours, or miles per hour.

SYMBOLISM OF MATHEMATICS
The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle-they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
The symbolism of mathematics is in truth the outcome of the general ideas which dominate the science.

MATHEMATICS AS SCIENCE OF MEASUREMENT
Mathematics and science education, including the metric system of measurement, will be strengthened throughout the system, especially in the early grades.

STRATEGIES
1. Implement the Missouri academic performance standards and frameworks for math and science.
2. Develop and implement statewide assessments aligned to the state’s content, performance, and skills standards.
3. Expand active learning opportunities through the use of technology.
4. Evaluate and disseminate effective math and science programmers.

OBJECTIVE
The number of teachers with a substantive background in mathematics and science, including the metric system of measurement, will increase by 50 per cent.

STRATEGIES
1. Ensure authentic assessment training for all teachers.
2. Increase the availability of math and science professional development activities aligned with the state’s knowledge, performance, and skill standards.

3. Institute competency-based teacher certification 

1 comment: