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PIAGET'S THEORY OF COGNITIVE DEVELOPMENT
STAGES OF COGNITIVE DEVELOPMENT Piaget identified four stages of cognitive development 1. Sensori-motor stage - Children learn through their five senses, goal-directed actions and object-permanence. They experience ego-centricism and fail to understand others' point of view. 2. Pre-operational stage - This stage covers 2-7 years of age. Children are able to do one step logical problems, develop language but still continues to be ego-centric 3. Concrete stage - This stage occurs during 7-11 years of age and develops logical thinking and concrete ideas in the children but they still struggle with abstract ideas. 4. Formal operational stage - This stage spans from age 12 to adulthood. Children think about abstract concepts. Thinking, reasoning, planning, problem solving abilities are developed. Educational Implications of Piaget's Cognitive Development Theory 1. Teacher must consider maturation level of the students in order to know what and how to teach. 2. Adequate amount o
VYGOTSKY SOCIAL LEARNING THEORY
IMPORTANT QUESTIONS RAISED 1. How people learn in social context? 2. How as teachers we have to create active learning communities? ASSUMPTIONS 1. We learn through our interaction and communication 2. Social environment influence learning 3. Teacher should create a learning environment to maximize learner's ability to interact with each other through discussion, collaboration and feedback 4. Culture is primary factor for knowledge construction SOCIAL LEARNING METHODS 1. Collaborative learning 2. Group work 3. Discussion based learning 4. Challenging tasks for students 5. Conduct small research and share results USE OF VYGOTSKY THEORY IN EDUCATION 1. Central to the theory is ZPD (Zone of Proximal Development) which uses social interaction with more knowledgeable others to move development forward. 2. Teacher (more knowledgeable) should provide assistance to the student, engage him in activity and use explaining, modelling and guided practice in the classroom. 3. Theory uses scaffol
BRUNER'S CONTRUCTIVISTIC THEORY OF LEARNING
Highlights of the theory 1. Leaning is an active process in which learners constructs new ideas or concepts based on present or past knowledge. 2. Learner selects information, construct hypotheses and make decisions, relying on cognitive structures (mental model) to do so. 3. Cognitive structures provide meaning and organisation to experiences. 4. Teacher and students should try to engage in active dialogue and try to discover principles. Major aspects of theory According to Bruner instruction should address four major aspects 1. Pre-disposition towards learning - curiosity, willingness, exploration 2. Structured knowledge - structured for easy understanding. 3. Sequence - in which material should be presented - sequencing should move from enactive (first-hand, concrete), to iconic (visual, representative ), to symbolic (descriptions in words or mathematical symbols). 4. Nature of reward and punishment ( reinforcement /motivation ) Principles of Constructivistic Theory 1. Read
FINDING AREA OF TRIANGLE PRACTICALLY IN MATHEMATICS LAB
REQUIRED MATERIAL CARDBOARD SCISSORS PHYSICAL BALANCE / DIGITAL SPRING BALANCE PROCEDURE Cut the cardboard into triangular shape. Measure the weight of this triangular cardboard with the help of spring balance. Note down the weight on a notebook. Now measure a piece 1 cm x 1 cm from somewhere within the triangular cardboard and cut it. Measure the weight of this piece with the spring balance and note it on the notebook. Then comes the calculation part. Suppose Weight of triangular lamina = x gm Weight of 1 square cm of lamina = y gm Now Using Unitary Method y gm is the weight of 1 square cm of lamina 1 gm is the weight of 1/y square cm of lamina x gm is the weight of x/y square cm of lamina. Therefore Area of Triangular Lamina = Weight of whole lamina / Weight of 1 square cm of lamina. Verify by finding area of triangle by Heron's formula. Use this activity method to find areas of different plane figures and verify by using universal formulae.
KNOW YOUR QUADRILATERAL
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PROPERTIES OF TRIANGLE
TRIANGLE AND ITS PROPERTIES Let A, B, C be three distinct non-collinear points. The figure formed by three line segments AB, BC, CA by joining these non-collinear points A, B, C in pairs, is called Triangle. PROPERTIES OF TRIANGLE 1. Sum of angles of a triangle is 180 °. This property is called angle-sum property of triangle. 2. In a triangle the exterior angle is equal to the sum of opposite interior angles. Therefore, exterior angle is always greater than each interior angle. 3. The sum of any two sides of the triangle is always greater than the third side. www.mathguide.org/e-book.html https://www.amazon.com/dp/B01HPVX3X2 https://plus.google.com/u/0/communities/117574624236201347536 https://twitter.com/ amitkd1234
OBJECTIVES OF TEACHING MATHEMATICS
INSTRUCTIONAL AND BEHAVIOURAL OBJECTIVES Instructional Objectives 1. These are the statements of measurable learning that is intended to take place as a result of instruction. 2. These are set according to the level of students in a particular class. 3. These are classroom objectives unique to each course or subject. 4. These are derived from the terminal behaviour which the students are expected to display as a consequence receiving instruction. Behavioural Objectives 1. These are the objectives in terms of behaviour of the students. 2. These are description of observable student behaviour related to learning. 3. Behavioural objectives should identify the following (i) Learner - for whom the objectives are written. (ii) Behaviour - targeted for change. (iii) Conditions - under which the behaviour will be performed. (iv) Criteria - for the acceptable performance of behaviour to occur. EXAMPLE TOPIC - PYTHAGORAS THEOREM I. COGNITIVE OBJECTIVES 1. To state
CORRELATION OF MATHEMATICS WITH OTHER SUBJECTS
Mathematics correlates with almost all school subject. Sciences uses mathematics the most. Even the Fine Arts use mathematics to some extent. Mathematics has characteristics like symmetry, similarity, originality, generalization and verification. All these characteristics make mathematics very usable, practical and versatile. Relation of mathematics with science, economics and fine arts is covered in this text Relation of Mathematics with Sciences 1. Physics - (i) The numerical derivations of many Laws of science are provided by mathematics. (ii) Newton Laws of Motion, Gravitational Laws, Boyle's Law, Charles Law etc. require mathematics for practical understanding. (iii) All measurements, units and measuring devices depend upon mathematics. 2. Chemistry - (i) Chemical equations, balancing of equations (ii) Atomic number, atomic and molecular mass, atomic mass units, radii of atoms and molecules. (iii) Chemica
QUADRILATERALS
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CIRCLE - AREA
ACTIVITY TO FIND AND UNDERSTAND AREA OF CIRCLE Divide into sixteen parts and arrange these parts as shown. You get a near rectangle with length equal to half the circumference ( πr ) and breadth equal to radius (r). Therefore Area of circle = Area of rectangular figure = length x Breadth = πr 2 NOTE : If we increase the numbers of divisions of circle in such a way that measure of arc on each part becomes a straight line then we can get a perfect rectangle. Division into sixteen parts make it easier to explain.
PLACE OF MATHEMATICS IN SCHOOLS
Mathematics is an important school subject. It helps to develop logical reasoning in the students. It trains the brain to use logic to solve problems. I will enlist the points that make place of mathematics in schools permanent 1. Mathematics help in mental exercise and sharpen our mental faculties 2. Mathematics helps in understanding other subjects especially sciences 3. Mathematics has a very high practical value. It is used enormously in our daily life 4. Mathematics prepares us for future occupations like banking sector, commerce, architecture and almost in every occupation 5. A good teacher can make mathematics very interesting Some arguments that go against mathematics are 1. Difficulty of the subject 2. Not significant correlation with other subjects like music, fine arts, languages etc. 3. Very basic arithmetics is used in most occupations 4. Even illiterate person without any knowledge of mathematics could carry out daily calculations 5. Sometimes mathematics class b
VALUES OF TEACHING MATHEMATICS
Introduction On one hand a teacher would say that mathematics is a valuable subject that's why it is a compulsory subject in schools. On the other hand students would say mathematics is tough and boring, so it should not be compulsory. Compulsory or not, mathematics is still very important and valuable school subject. In understanding science and scientific facts, mathematics is required. For understanding business and commerce, mathematics is required. For buying and selling, mathematics is required. Thus practical life would be impossible without mathematics. Values of Mathematics 1. Practical Value - The day starts with a wake up alarm on a table clock. It's 5 O' clock and time to get up. I go out to get a cup of tea/coffee and spend money. I work all day to earn money. I prepare my weekly/monthly budget. I get my clothes stitched according to my body structure and size. I eat a balanced diet. I make saving for my future life. All these instances
CONSTRUCTIVIST APPROACH AND MATHEMATICS
CONSTRUCTIVIST APPROACH AND MATHEMATICS Constructivist approach means that all the knowledge is created from the basic previous knowledge and experiences of the students. The stress is on construction of knowledge by the students with their active participation and involvement in the teaching learning process. The teacher create situations for the students to act constructively. Constructivist approach develops critical thinking in the students and motivate them. The students are engaged in inquiry, activities, imagination, discovery, hypothesizing solutions and reflection. According to Audrey Gray, the characteristics of a constructivist classroom are as follows: the learners are actively involved the environment is democratic the activities are interactive and student-centered the teacher facilitates a process of learning in which students are encouraged to be responsible and autonomous.( http://ccti.colfinder.org/sites/default/files/constructivist_teaching_methods.pdf )
PROPERTIES OF REAL NUMBERS
PROPERTIES OF REAL NUMBERS www.mathguide.org/e-book MATHGUIDE E-BOOK AMAZON www.mathguide.org/e-book
RATIONAL AND IRRATIONAL NUMBERS IN TERMS OF DECIMAL REPRESENTATION
www.mathguide.org/e-book MATHGUIDE E-BOOK AMAZON RATIONAL AND IRRATIONAL NUMBERS IN TERMS OF DECIMAL REPRESENTATION
MATH PROBLEM SOLVING
SOLVING A PROBLEM OR PROBLEM SOLVING IN MATHEMATICS I have a problem, I want to solve it. Say the problem is - Who Shaves the Barber? To solve this, do I need mathematics? The answer is No. I just need to ask the barber and the problem will be solved. Lets take another example. I want to go on a vacation for 5 days. For that I have to take a leave, select a place for vacation, check how much money is required, check booking dates with hotel, decide mode of transport and make a time-plan of visits to different places during vacation. Now the question arises, "Do I need mathematics?" The answer is Yes. Money required, dates, distance to travel and time-plan need mathematics. This is the real life example of problem-solving in mathematics. For this you have to think, plan, reason out, apply logic and solve the problem systematically. Writing solution and finding solution are two different scenarios. Writing a solution means solving a problem without th
QUADRATIC EQUATION - NATURE OF ROOTS
QUADRATIC EQUATION - NATURE OF ROOTS This second degree equation in one variable has two roots (solutions). These roots could be calculated by using factorization or using quadratic formula. It is very important to note that roots of quadratic equations depend on the discriminant and nature of roots could be understood by solving the discriminant. For more Visit www.mathguide.org/e-book MATHGUIDE E-BOOK AMAZON
MASTERY LEARNING MATHEMATICS
IMPORTANT POINTS TO NOTE 1. MASTERING MATHEMATICS CONCEPTS BY REPETITION 2.NO SEGREGATION AND ALL STUDENTS WORK TOGETHER FOR MASTERY 3. MASTERING SPECIFIC CONCEPTS FIRST THEN MOVE TO BROADER CONCEPTS GOTO MASTERY LEARNING MATHEMATICS REFERENCE https://in.finance.yahoo.com/news/top-performing-asian-countries-mastery-171300479.html
SOLVE THESE EQUATIONS
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LOGARITHMS - CHARACTERISTIC AND MANTISSA
LOGARITHMS - CHARACTERISTIC AND MANTISSA MATHGUIDE E-BOOK MATHGUIDE E-BOOK AMAZON
REAL NUMBER LINE - POINTS TO REMEMBER
REAL NUMBER LINE - POINTS TO REMEMBER MATHGUIDE MATHGUIDE@AMAZON
BOOSTING CONFIDENCE OF KIDS TO LEARN MATHEMATICS
BOOSTING CONFIDENCE OF KIDS TO LEARN MATHEMATICS 1. BE FLEXIBLE - Mathematics seems to be a difficult subject because teacher lacks flexibility in the class. Different kids learn in different ways. Some students need more examples, some are shy to ask and some are lazy to practice. Teacher needs to leave his traditional ease and be more innovative and flexible in attending needs of different learners 2. FUNDAMENTALS - Students lack fundamental concepts and skills in mathematics. Basic computation skills, mathematical tables, arithmetic operations, skill in drawing geometrical shapes are missing. They don't know the use of mathematical symbols and notations. Teachers need to work on these aspects. 3. PRACTICAL APPROACH - Make mathematics practical. This means to make students connect mathematical problems to their daily life. Students need to live mathematics and not learn mathematics. Measuring lengths and breadth of notebooks, cutting various mathematical shapes, counting and div