Methods of teaching mathematics

Principal & Maxims Of Teaching

Love Your Parents & Profession

V.SURESH KUMARAssistant professor of mathematicsRajalakshmi college of education Thoothukudi.

Teaching PrinciplesTeaching principles, laws & maxims can be classified as1. Principle of teaching.2. General principal of teaching.3. psychological principle of teaching

General principle of teaching 1. Purposeful based Teaching.2. Child Centered Teaching.3. Experience Based Teaching.4. Activity Centered Teaching.5. Evaluation Based Teaching.

Purposeful Based Teaching Data informed learning & teaching plans are developed to provide differentiated focused teaching & open-ended learning challenges for all students.

Purposeful Teaching Involves * Efficient Organisation. * Clarity of Purpose. * Structured Lesson. * Adaptive Practice

Purposeful Teaching is in Evidence Make systematic use of literacy transition data to monitor & plan for student progress over time.Establish professional learning teams to plan, implement & evaluate comprehensive literacy programs for students identified as having potential to achieve at a higher standard.

Con/- Discuss with teachers & students preferred optimal times for time tabling of literacy intervention to maximize learning time for improving student literacy outcomes.Time table provision for at least three to five weekly sessions of explicit, intensive, literacy instruction.

Activity * Bring out students existing ideas. * Challenge some existing ideas. * Shared intellectual control. * Focus students attention on overlooked detail. * Helping students workout some of the scientific explanations for themselves. * Collecting evidence/data for analysis. * Open discussion via a shared experience.

Child Centered Teaching Active learning , student engagement & other strategies that involve students & mention learning are called learner-centered. Teaching should be child centered . Interest & liking of students given priority while teaching. Subject taught to the child as per this liking. An intelligent teacher is able to deal with this type of teaching very wisely.

Experience-Based The process where by knowledge is created through the transformation of experience knowledge results from the combination of grasping & transforming experience.

Elements* Concrete Experience. * Reflective Observation. * Abstract Conceptualization. * Achieve Experimentation.

Essential Components * Involves something personally significant or meaningful to the students . * Students should be personally engaged . * Reflective thought & opportunities for students to write or discuss their experiences should be on going learning they bring into the process .

Con/- * Students should be recognized for prior learning they bring into the process . * Teachers need to establish a sense of trust , respect , openness,& concern for the well-being of the students.

Principle of Activity (or)Learning by DoingTeacher should produce activity in each type of lesson. Types: Activity

Physical Mental

Physical ActivityTo produce activity in the body organs of the pupils.Mental activity:To activate the sense organs of the pupils.

* Every child has in born instinct of construction.* For successful teaching the teacher should make use of the pupils instinct of construction & senses to the maximum.* Pupils mind & body work together. They shows more interest in learning.

For Effective Teaching

Methods based on learning by doing* Montessori method.* Kindergarten method.* Heuristic method.* Dalton method.* Project method .* Basic method etc.

Use in school ActivitiesSchool council.Declamations contest.Various societies.Meetings.Conference.Club.Games etc.

Evaluation Based Teaching Evaluation is a wider concept than testing & measurement.Evaluation is a continuous assessment of the pupils day-to-day progress in all spheres. Helps in determining the potentialities & interest of the students.Provides information essential for an effective guidance programme.

Evaluation demonstrated as underMethods of Teaching

Objectives of Teaching

Curriculum Tools & Techniques of Evaluation

Purpose of Evaluation Purpose of EvaluationEducational Purpose Administrative Purpose Learning Curriculum Teaching Parents Society Education system

Types of EvaluationDiagnostic Evaluation.Formative Evaluation.Summative Evaluation.

Diagnostic EvaluationThis Evaluation in done in the beginning of the teaching learning process.Formative evaluation Decision Making process.Help in making changes in the curriculum, teaching strategies & the learning environment.Summative Evaluation Judgement Making process.Terminal(Final) Examination.

Classification of Evaluation

Evaluation Techniques Quantitative Techniques Qualitative Techniques Oral Written Practical ObservationAnecdotal RecordsCheck list Rating ScaleCumulative Records

Tools & Techniques of Evaluation

Tools & Technique Of EvaluationTesting Procedures Self Reporting Techniques Observational Methods Projective Measures

Testing Procedures 1. Written Tests. 2. Verbal Tests. 3. Practical Tests. 4. Performance Tests.

Self-Reporting Techniques

1. Questionnaire.2. Autobiography.3. Interview.4. Personal Diary.

Observation method 1. Anecdotal Record. 2. Check-list. 3. Rating scale. 4. Sociometry.

Projective Measures1. Association Test.2. Sentence Completion Test- SCT3. Word Association Test -WAT4. Thematic Apperception Test TAT5. Rorschach Ink Blot Test RIBT

Utility of Evaluation1. For the assessment of students performance & academic achievement.2. For the teachers for judging the achievement of objective.3. For guidance workers.4. For Educational administrations.5. For improving schools activities.6. For improving schools activities.7. For promoting co-curricular activities.

Psychological Principles of Teaching Education has transformed itself into child-oriented education . The concept of child-oriented education is the gift of psychology. Important to students abilities , capabilities , mental level , interests & age.

Important Principles1. Principle of activity or learning by doing.2. Principle of play-way.3. Principle of motivation.4. Principle of self education.5. Principle of individual difference.6. Principle of goal setting.7. Principle of simulation.8. Principle of association.

Con/- 9. Principle of readiness.10. Principle of effect.11. Principle of exercise & repetition.12. Principle of change or rest.13. Principle of feedback & reinforcement.14. Principle of training of senses.15.Principle of group dynamics.16. Principle of creativity.

Principle of Activity1.Child as a Hero in the drama of education.2. Teaching is to keep the children active in the class.

Principle of play-wayRelated to principle of learning by doing.Play is the chief activity of childhood-Froebel.It gives joy ,freedom ,contentment , inner , outer peace.

Principle of Motivation1. Satisfying the curiosity of children.2. Utilizing all the senses of children.3. Relating closely bogy & mind .4. Linking teaching-learning with life.

Principle of Self Education1.Best teaching is enabling the child learn by this own efforts.2. Teaching enable the child to work independently & without the teacher at a later stage.3.Encourage students in the development of their natural desire to work .

Principle of individual difference 1. No two children are alike. 2. Teaching to be effective must cater to individual difference of children.

Principle of Goal Setting1.Definite goal according to the standard of the each students.2. Short term of immediate goals should be set before small children .3. Goals should be very clear & definite & understand by children.

Principle of Stimulation Teaching is the stimulation , guidance , direction & encouragement of learning Burton.

Principle of AssociationIf wants to go together should be put together.Discuss at various places ideas & thing associated in a number of ways.

Principle of Readiness1. Prepare for action.2. Make the mind to participate in the teaching learning process.3. Teacher must be alive to this principle.

Principle of effectResponse is strengthened if it followed by pleasure.Response is weakened if it followed by displeasure.

Principle of Exercise or RepetitionExercise strengthens the bond between situation & response.Two subparts (i) . Principle of use. (ii). Principle of disuse.

Principle of Change & Rest Fatigue, lack of attention overcome by providing change, rest & recreation.While framing the time table that the students do not experience boredom & fatigue.Two consecutive periods of a subjects are not provided in a class.

Principle of feed-back & reinforcementPraise, grade, certificate, token money & other to incentives make the learning joy able.

Principle of training of sensesSenses are gateways of knowledge .The power of observation discrimination , identification ,generalization & application are developed through the effective functioning of senses.

Principle Of Group Dynamics1.Group behavior , changes the behavior of the members of the group.2. A suitable climate for group to be created in the classroom.

Principle of Creativity1. Provide opportunities to the students to explore things events & find cause-effect relationship .2. Creativity explored & developed to the maximum extend.

Maxims of Teaching

Maxims of teaching have been discovered, not invented, They are simply statements of the way in which teaching & learning go forward, They ensure effective &efficient teaching - An Eminent Educationalist

Introduction Distribution of the knowledge & the teacher ability , both are separateTeacher needs two things (i). The complete knowledge of the subject matters. (ii). The scientific knowledge of the teaching styles for disseminating the knowledge to the pupils.

MeaningPsychologist introduced the laws of learning , Educationists have presented their experience & decision in the form of maxims considering their laws & elements as the basis of teaching.Experience & decision ,performed in the form of maxims have been named as Maxims of teaching.

Main Maxims of Teaching (i). From simple to Complex.(ii). From known to Unknown.(iii). From seen to Unseen.(iv). From concrete to Abstract.(v). From particular to General.(iv). From whole to Part.(vii). From indefinite to Definite.(viii). From psychological to Logical.(ix). From Empirical to Rational

Con/- (x). From Analysis to Synthesis.(xi). Follow nature.(xii). Training of Senses.(xiii). Encouragement to self- study.

From Simple to ComplexTeaching is to be made successful & essential by using a maxim called From simple to complex.Teacher should be divided the subject- matter into simple aspects & complex aspect.Teacher should tell simple concept first &difficult concepts latter.

Con/- Example: (i). Drawing a straight line simple to teacher but difficult to pupils.(ii). Drawing an animals picture may be viewed by the teacher as the difficult task while it is very easy for pupils.

From Known to UnknownA good teacher bases this new knowledge on previous knowledge of students. Example: Profit or Loss - taught to the pupils by referring to the shopkeepers.

From Seen to Unseen Psychological, the pupils ranging from 6 to 14 years are at perceptual level only.Teacher use the seen or perceptual things to impart the knowledge regarding unseen or non-perceptual things.

From Concrete to Abstract The mental development of the pupils begins with the concrete objects & afterwards the gains micro words for them.Example: While teaching geography , the knowledge of mountains , lakes , rivers, & oceans or perceptual things or through their models, pictures & lines.

From Particular to general Specific examples should be presented before the pupils first and then the general laws or principles should be derived from those specific examples.Example: [Teacher wants to teach , when the solids are immersed in a liquid, They lose their weight , he should perform two experiments before this pupils , First ,the solids should be weighted in a liquid ] Pupils observed & testing from their own.

From Whole or Part Gestalt : Perceive the objects as a whole & then its parts .We gain knowledge about the Whole first & then its Parts .Ex: When we see some tree, our attention goes on the entire tree , then on its stem , branches & leaves etc Gestalt Theory

From Indefinite to DefinitePupils intellectual development proceeds from indefinite to definite. Through sense organs , gaining the knowledge regarding different objects while living in the contact of this parents , brother sister , other family members.On the basis of this gained knowledge , the gradually develops this personal concepts regarding objects.

From psychological to Logical:Psychological order: Knowledge should be presented according to the age of pupils, cursorily, needs & acquiring power.Logical order:Knowledge before the pupils dividing , it logically into various units.Presenting the knowledge logically , the pupils interest, age & acquiring power are over looked .The presentation of the knowledge in psychological order is definitely better & useful instead of teaching in a logical manner. In lower classes teach by using psychological order but logical order must be adopted as the pupils enters higher classes along with mental development.

3. In order words , we should proceed from psychological order to the logical order.

From Empirical to RationalThis maxim means to make the pupils empirical knowledge more rational , so that it becomes valid & definite. Empirical knowledge is gain by the pupil through this own observations.Examples: Freezing of water in winter & converting water into steam in summer. similarly pupils looks everyday rising up & setting down the sun.

If the question rises to the pupil about the freezing &steaming of water , they will not able to answer scientifically & logically.3. It is necessary for a teacher to make the pupils empirical knowledge more rational , it makes the pupils knowledge more true & definite.

From Analysis to Synthesis