OCW/Kosovo/Math/10/Analysis
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Year: 2011
Contents |
MATHEMATICS
For grade ten have five different plans and programs (depending on the type of gymnasiums and mathematical disciplines taught)
- High School Mathematics-Informatics
- A) Analysis of probability theory on
- B) algebra with geometry
- Gymnasium Gymnasium General and Natural Sciences
- High School Social Sciences
- High School of Languages
Part common to these five (5) plans and programs
INTRODUCTION
Mathematics for grade ten is ongoing, active recovery and extension of previous knowledge. Mathematical education allows students to gain knowledge and skills to develop understanding of physical and social world. Through mathematics students trained to analyze, describe and explain, to raise hypotheses and solve problems. Along with other materials aimed at teaching mathematics:
- Development of personality of students;
- Education for independent work habits and systematic;
- Cultivating skills abilities to think creatively and critically;
- Promoting student curiosity and encourage research in the selection of necessary information;
In particular, through the peculiar language - symbols and diagrams, aims to cultivate math skills to express themselves accurately, to organize and summarize their thoughts and communications in general. Implementing increasingly sotisfikuar of mathematics in broad areas of economy, technology and science, the chances of impact Its deep in the development of a modern society.
GOALS
The main objectives of teaching mathematics to students are:
- Activity curiosity, creativity and development of logical thinking;
- Fair description of mathematical concepts, the difference of various quantitative relations and conduct of operations correctly logical and mathematical operations in general solving tasks;
- The development of creative abilities and skills necessary for mastery of course content as receiving information with the help of successive questions, ongoing communication with students and teachers, self-confidence, reasoning and argumentation;
- Possession of new knowledge in order to apply them in problem solving situations from everyday life and other school subjects;
- Creating a solid base for paving and understood the problems;
- Build a right attitude about the importance of mathematics in developing their personality and create a clear vision about life in general;
- Acquiring the knowledge necessary to represent the basis for successful study in different directions to college education.
Methodological guidelines
As in every subject, even in mathematics, the main task of the teacher is conducting educational activities that meet the achievement of learning outcomes envisaged in the objectives. Experience has shown that the techniques, methods and strategies which ensure a productive teaching, are those that enable students to actively involved in building understanding, developing breasts Strata mathematical problem solving and skills development to apply knowledge in everyday life.In its decisions the teacher to select teaching methods, along with many factors must be taken into account:
- The nature of teaching material;
- Type of student learning;
- Level and the demands of students.
For this purpose, teaching methods and techniques should be varied to suit different styles of student learning. They should promote students' collaborative work in order to strengthen the social dimension in learning. Interactive teaching engages students in taking responsibility for gaining knowledge but also their vlerëshmërinë.
This model is defined by the following phases:
- Is defined topic or issue that is of interest to students, that makes sense and is closely related aspects of life. So mathematics from a highly abstract and theoretical subject is transformed into a meaningful subject, closely connected with life;
- The teacher encourages and encourages students to think about issues addressed in the text or about a certain problem. At this stage, they engage in various research: observe, keep records, identify problems, obtain information;
- At this stage are many questions which need clarification answered. It is important that questions be accessible to students;
- Students develop their plans to undertake research or basic research and answer more precise questions asked in the above stage;
- At this stage, students along with teacher talk about their practice-results of the investigation or solution of the problem. The teacher helps them to consider other alternatives for the results and plan further research or research. It is important that students perceive the assessment of their ideas, solutions they provide and be aware of the responsibilities that they take.
Aiming at meeting the requirements for effective learning, teaching modern methods suggested methodology the project "Teaching Critical Reading and Writing", "Teaching with student-centered" and the "interactive learning". Following are some methods we note the work.
WORKING METHODS
Schools should serve to maintain children's interest for mathematics and gradually develop it.
- The study of mathematics should not be abstract and verbal, as well as mathematics in essence acts and relations with abstract meanings. Should be offered as much as being served with the experiments, presentation graphics and real situations from everyday life;
- The way the learning of knowledge must be developed in the form of a spiral, because the actions and mathematical structures is not possible for a time and fully understood. It would be good to always relate the complexes of the small content in whole larger, so that by introducing new content learned as much as the old contents.
- Motivation is the key to learning mathematics, because it derives the artistry of the teacher. Motivating students to work steadily, as much as possible independent and systematic is a fundamental importance. It is important for content selection exercises that reinforce constantly thinking, where large - scale new questions arise. Such exercises orient productive working towards a research and raise new topics for discussion and new approaches.
- Differences in students' numerical skills can be very large. Therefore, teachers must find ways that all students progress. It is preferable that the exercise of critical thinking methods implemented by dividing students into small groups of two, four students, etc..
- Must ensure that the exercise had, to stimulate students to solve tasks in any way to yourself (original).
- The purpose of the learning of mathematics achievement is not routine, mechanical learning of facts or actions, but appropriating the foundation of matter. It should be noted that the fund of knowledge and skills acquired always be available to students.
- Since the first year teacher should not lead classes with stereotyped method of teaching with the teacher-centered, activity aside rezonuarit students in mathematics. Should be selected appropriate exercises to develop intuition to the extent sufficient to move always one step ahead.
Evaluation
Regular assessment of student progress is part of teaching and learning of mathematics and inextricably connected with them. Through this process not only determined the level of achievement of students but also vlerëshmëria the program and teaching methodology in general. Diagnosis allows assessment of student progress, planning the right of teaching, motivate students and final determinations of the results. He should focus on identifying existing knowledge of students in the wrong conceptions and learning strategies. Also provided through its valuable information, which uses mathematics teacher to review students' different abilities, their previous knowledge and learning ways to avoid mechanical facts of mathematical procedures. Teacher during the assessment should take account of program content and standards of achievement of specified by the program.
1.
Achievement level is assessed based primarily on three levels:
Level
Includes minimum accessibility, that is to say represents the minimum necessary, which should reach all students. So he represents the lower limit (allowed) the acquisition of programming content that would be expressed in percentages with 40% of the developed material. At this level should include students who solve problems with the help of teachers with a limited number of methods, the facts justify the simple math with the help of teachers and to communicate mathematical knowledge always having that support.
Level II
Presented to the limits of the results expressed in percentage (50% -80%). At this level should include students who solve problems and justify mathematical facts with limited teacher assistance, through a rather large number of strategies and methods, with some mistakes or minor shortcomings.
Level III
It is the highest level or advanced level (maximum) of pupils achieving expressed in percentage (80%). At this level should include students who solve problems and justify mathematical facts, independently. Solve mathematical problems with different methods, analyze and interpret the results obtained independently and accurately, with clear language and logical fluency.
2 .
The evaluation procedure is recommended assessment procedure conducted in accordance with established standards. It is understood that the assessment should pursue educational goals, learning objectives, assessment objectives. Assessment should be based on a significant amount of data in which these elements should be included. Types of evaluation are numerous. They should be used in accordance with the aims and objectives of the mathematics course, learning strategies and students' age requirements.
To consider the mathematics assessment can be made taking into account:
- Oral responses;
- Activity of students from the country;
- Activity during group work;
- Homework;
- Tests for group topics;
- Tests at the end of the category of content;
- Tests at the end of the semester;
At the end of final grades must be extracted which is obtained by taking the average of estimates:
- Oral evaluation - 25%
- Tests - 50%
- Assessment of the work in class - 15%
- Assessment of homework - 10%.
MATHEMATICS
5 hours per week, 185 hours per year
(Analysis of probability theory )
High School mathematics and computing
GENERAL OBJECTIVES
General objectives of teaching the theory of probability analysis to students are:
- Understand the real numbers to the community as a union of rational numbers and irrational numbers and community properties of real numbers;
- To make the difference between the community from the innumerable numërueshme;
- To implement the absolute value in solving different tasks and in shaping the meaning of ε - the surroundings of the point;
- To apply mathematical induction to prove various statements and mathematical formulas;
- Apply technologies to more complex calculations;
- To deepen the understandings of power and the root;
- Apply power properties of the root to Enforce the various simplifying algebraic expressions, algebraic rational;
- To recognize the notion of imaginary unit "i" and the notion of complex numbers as ordered pairs of real numbers;
- To adopt the geometrical layout of complex numbers;
- Understand operations with complex numbers and complex numbers rrënjëzimin;
- To implement complex numbers in solving various equations and Enforce the polynomial of degree n;
- To know the quadratic equation and its special cases;
- To recognize bikuadratik equation;
- To recognize the notion of dallorit (diskriminantës);
- To implement the Viet-it rules for solving various tasks related to quadratic equations;
- To apply quadratic equations to the solution of practical problems;
- To recognize the notion of exponential equation and inekuacionit;
- To know the trigonometric functions sin α, cos α, tgα, ctgα; in angled triangle;
- Know how the trigonometric functions of angles are 450, 600 and 300;
- To know the trigonometry in right-angled triangle;
- To know how to apply the acquired knowledge to practical tasks;
- To know the meaning of events and the space of all possible events;
- The definition of probability to understand the basic events and Composite. To recognize dependent events and independent;
- To recognize the notion of random variables, distribution, mathematical expectation (expected value), variance and standard deviation;
- Know the relevance and application of statistics to the (in) other areas;
- Understand the research methods and statistical performance.
ORGANIZATION OF THE SUBJECT CONTENTS
Construction of the content is organized in accordance with the aims and objectives of the course. Categories of course content are given in Table
no. 1
| Subject | Categories of content | Hours | Total.hours | % | Total.% |
|---|---|---|---|---|---|
| Analysis of probability theory | I. Analysis | 140 | 185 | 76 | 100 |
| II. Probability theory with statistics | 45 | 24 |
For more please download the pdf here
