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Aim & objective of teaching mathematics

The document discusses the aims and objectives of teaching mathematics. It states that mathematics encourages logical thinking and helps students discriminate between essential and non-essential information. The significance of teaching mathematics is that it develops the ability to apply mathematical concepts to daily life situations and inculcates self-reliance. The aims are categorized as practical, social, disciplinary and cultural. Objectives are directed towards achieving these aims and are specific, precise and observable goals. Bloom's taxonomy is discussed as a framework for classifying educational objectives into cognitive, affective and psychomotor domains. The revised Bloom's taxonomy changes some terms to verb forms and reorganizes categories. It also identifies different types and levels of knowledge.

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AIMS & OBJECTIVES OF TEACHING MATHEMATICS V. SURESH KUMAR ASSISTANT PROFESSOR OF MATHEMATICS RAJALAKSHMI COLLEGE OF EDUCATION THOOTHUKUDI
NEED OF TEACHING MATHEMATICS It is the only subject that encourage & develops logical thinking. Help the students to discriminate between essential & non- essentials. Knowledge of mathematics is very essential for training rational & trustworthy. Essential to face the challenges of the modern technological society. Helps to apply mathematical concepts & theorems to new situations.
SIGNIFICANCE OF TEACHING MATHEMATICS Develops the ability to transfer the mathematical type of thinking & reasoning to daily life situations. Clear understanding of laws of nature. Helps to appreciate the applications of mathematics for the scientific & technological advancement. Inculcates a good deal of self – reliance, self – confidence, tolerance & open – mindedness.
CON/- Essential element of communications. Powerful tool in the hands of the learners. Develops logical thinking & reasoning critical mind & creative imagination. Helps to think alternative methods of solving problems.
WHAT IS AIM ? Long term goal. General. Give directions for the educational process.
AIM OF TEACHING MATHEMATICS Practical aims. Social aims. Disciplinary aims. Cultural aims.
PRACTICAL AIMS Develop clear ideas. Make proficient. Make appropriate approximation. Develop mathematical skills. Understand the concepts.
SOCIAL AIMS Develop the individual to understand & participate in the general social & economic life. Help the pupil acquire social & moral values. Helps in formation of social laws & social order. Provide knowledge for adjusting with the society. Help the pupil interpret social & economic phenomena.
DISCIPLINARY AIMS Enable the learners to exercise & discipline mental faculties. Help in intelligent use of reasoning power. Develop the character through systematic & orderly habits. Help the learner to be original & creative in thinking. To help the individual to become self –reliant & independent.
CULTURAL AIMS Enable to appreciate the role played by mathematics in cultural traditions. Provide mathematical ideas, aesthetic, intellectual enjoyment & satisfaction for creative expression. Develop an aesthetic awareness of mathematical shapes & patterns in the nature.
OBJECTIVES Directed towards aims. Short – term goals. Attainable within the educational system. Steps toward the realization of the aims. Specific, precise & observable. Vary from course to course. Specific for each course originate from the aims.
Objectives Educational objectives Instructional Objectives
EDUCATIONAL OBJECTIVES Broad & philosophical in nature. Related to schools & educational system. Achieved with the help of teaching (or) instructional objectives. A dimension of learning. Worthwhileness of a pattern of learning for realizing. Level of learning to be attempted. Serve as guide posts in learning.
INSTRUCTIONAL OBJECTIVE Based on specific observable. Behavioral in nature. Measurable goal . Establishes a minimal level of attainment for judgment. Instructional objectives state both behavior is intended to be developed (Curricular aspect) & what actual behavior is developed & tested (Evaluation aspect).
BLOOM’S TAXONOMY OF EDUCATIONAL OBJECTIVES Dr. Benjamin S. Bloom & his associates in the university of chicago gave the classification of educational objectives for three domains & classification of educational objective is known as “ Taxonomy of Educational Objectives” or “Bloom’s Taxonomy”
BENJAMIN BLOOM Born : Benjamin Samuel Bloom Feb /21/ 1913. Died : Sep/13/1999. (86) Chicago. Nationality : United state citizen. Education : Ph.D in Education. Alma mater : Pennsylvania state university, university of Chicago. Occupation : Educational Psychologist. Employer : American Educational Research Association.
TAXONOMY Complex scheme for classification of phenomena or idea. Bloom’s taxonomy is an attempt to identify , define, classify & organize a comprehensive range of educational objectives into a compact & measurable structure.
EDUCATIONAL OBJECTIVE Cognitive Affective Psychomotor domain domain domain
COGNITIVE DOMAIN Bloom was identify objective & specification relating to cognitive in 1956. Stress to acquire knowledge. Development of intellectual abilities & skill.
HIERARCHY OF COGNITIVE OBJECTIVE Evaluation Synthesis Higher level Analysis Application Middle Comprehension level Knowledge Lower level
KNOWLEDGE: Ability to recall or recognize already learnt information. COMPREHENSION: Ability to organize & arrange materials mentally. APPLICATION: Ability to select & apply already learnt rules. ANALYSIS: Ability to break up a given communication into its constituent elements or parts. SYNTHESIS : Ability to produce a new communication from many sources. JUDGEMENT : Ability to judge values of materials & methods.
COGNITIVE OBJECTIVE IN BEHAVIOURAL TERMS Ex : Sol/- of linear equation with the help of graphical method. S.No Objectives Expected change in behaviour 1.1. The pupil will be able to recall 1. knowledge the linear equation. 1.2. The pupil will be able to recognize the definition of linear equation. 2. Comprehensive 2.1. The pupil will be able to illustrate equation. 2.2 . The pupil will be able to explain the graphical method. 2.3. The pupil will be able to present linear equation on graph
S.No Objectives Expected change in behaviour 3.1. The pupil will be able to demonstrate 3. Application linear eqn/- on graph. 3.2. The pupil will be able to solve linear eqn/- through graphical method. 4.1. The pupil will be able to develop skills 4. Skill to solve pbm by the use of graphical method.
AFFECTIVE DOMAIN In 1964 bloom & his associates Karthwohl & Masia explained the structure of affective domain. Development of attitude, values, appreciation, adjustment etc. Deals with emotional aspect.
LEVEL OF OBJECTIVE 1. Receiving. 2. Responding. 3. Valuing. 4. Organisation. 5. Characterisation.
PSYCHOMOTOR DOMAIN Elizabeth Simpson & R.H.Dave have formulated the objectives relating to psychomotor domain in 1972. Focus on motor skill.
LEVEL OF OBJECTIVES 1. Imitation. 2. Manipulation. 3. Precision. 4. Articulation. 5. Naturalisation
GENERAL INSTRUCTIONAL OBJECTIVES (GIOS) Non – behavioural objectives. Statement contain verb like ‘knows’, ‘understand’ etc Non – observable behaviour.
BEHAVIOURAL OBJECTIVE OR SPECIFIC LEARNING OUTCOMES(SLOS) Specific performances, which are precise & measurable. Observable behaviour.
SPECIFIC STATEMENT HAS TWO PARTS 1. The content part & 2. Behaviour modification part. The behaviour modification is described by an appropriate action verb. Ex: Recalls, Explains, Compares etc
FIVE ELEMENTS IN WRITING SPECIFIC BEHAVIOURAL OBJECTIVES 1. Performer (The student, trainer, the learner etc) 2. Action required Action – verb, Ex: Identifies, compares, classifies etc. 3. Task Include a task to be performed. Ex: Compares, the properties, explains the derivation.
4. Conditions Include any condition that may be required. Ex: Compares the properties of the given triangles. 5. Criteria for judgement: Any relevant criteria for clarity. Ex: Phenomena with two examples – Computers with speed & accuracy.
EXAMPLE FOR SLO (OR) SBO 1. The pupil recall the formula for the area of P A.V Task C equilateral triangle. J 2. The pupil selects an appropriate P A.V method/formula to solve the given problem. Task C J
Some time SLO’s have any three factors – performance, Action, Tasks. 3. The pupil list the properties of an equilateral triangle. P A.V T C 4. The pupil state Pythagoras theorem. P A.V T
EXAMPLE FOR GIO The pupil acquires knowledge of polynomial multipulations. The pupil understands the meaning of the term “Probability” The pupil applies the formula to find the area of a given quadrilateral.
REVISED BLOOM’S TAXONOMY Taxonomy of cognitive objectives. 1950s – developed by Benjamin bloom. Means of expressing qualitatively different kinds of thinking Been adapted for classroom use as a planning tool. Continues to be one of the most universally applied models. Continues to be one of the most universally applied models.
CON/- Provides a way to organize thinking skills into six levels, from the most basic to the more complex levels of thinking. 1990 – Lorin Anderson (former students of Bloom) revised the taxonomy. As a result, a number of changes were made.
CHANGES IN TERMS Six categories changed from noun to verb forms. Taxonomy reflects different forms of thinking & thinking is an active process verbs were used rather than nouns. Some sub – categories are re – organised. Knowledge is an product of thinking, the word knowledge was inappropriate to describe a category of thinking & was replaced with the word “ remembering” instead. Comprehension & synthesis are retitled to understanding & creating respectively, in order to better reflect the nature of the thinking defined in each category.
REPRESENTED IN DIAGRAM
REMEMBER Retrieve relevant knowledge from long – term memory. Understand: Construct meaning from instructional messages. Include oral, written & graphic communication. Apply: Carryout (or) use a procedure in a given situation. Analyze: Break material into consistent parts. Determine how parts relate to one another.
EVALUATE Make judgements based on criteria & standards. Create: Put elements together to form a coherent or functional whole. Re – organize elements into a new pattern or structure.
WEAKNESS OF TAXONOMY Weakness noted by bloom himself. Fundamental difference between his “knowledge” category & the other five level of his model. Intellectual abilities & skills in relation to interactions with types of knowledge. Bloom aware that there was an acute difference between knowledge & mental & intelligence operation.
TYPES OF KNOWLEDGE Bloom identified specific types of knowledge as 1. Terminology. 2. Specific facts. 3. Convention. 4. Trends & Sequences. 5. Classifications & Categories. 6. Criteria. 7. Methodology. 8. Principles & Generalizations. 9. Theories & Structures.
LEVEL OF KNOWLEDGE 1. Factual learning. Identified in the 2. Conceptual knowledge. original 3. Procedural knowledge. work added in the 4. Meta cognitive knowledge. revised version
FACTUAL KNOWLEDGE Basic to specific disciplines. Essential facts, terminology, details or elements, students must know or be familiar with in order to understand a discipline or solve a problem in it.
CONCEPTUAL KNOWLEDGE Knowledge of classifications, principles, generalizations, theories, models or structures pertinent to a particular disciplinary area.
PROCEDURAL KNOWLEDGE Knowledge that helps students to do something specific to a discipline, subject or area of study. Methods of inquiry, very specific or finite skills, algorithms, techniques & particular methodologies.
META COGNITIVE KNOWLEDGE Awareness of one’s own cognition & particular cognitive processes. Reflective knowledge about how to go about solving problems, cognitive tasks. Include contextual & conditional knowledge & knowledge of self.
Theknowledgedimension Cognitive De Re Procedural Recall Clarity Carry Out Integrate Judge Design Conceptual Recognize Classify Provide Differentiate Determine Assemble Factual List Summarize RespondTo Select CheckOut Generate ber and y ze te e
Aim & objective of teaching mathematics