MATHGUIDE FOR ALL YOUR MATHEMATICS NEEDS

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

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

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

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REFERENCE : CBSE 11 GRADE BOOK

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.     

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  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

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

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        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

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