GIFTED & SLOW LEARNERS IN MATHEMATICS

       “A person showing consistent extraordinary achievement in a productive field is a genius/Gifted.”

                                                                                                                                                --Having Hersit.

      “A genius is extraordinary in his productive proportion, rate and quality.” ---R.N.Tylor

                                                                                                             

     “Genius children show remarkable achievement in music, arts, leadership, and expression  

           Consistently.”   ---Weeti

                  A Student is considered as mathematically gifted student, if he shows consistent remarkable interest and achievement in mathematics.

Identification of Gifted students in mathematics

1. Gifted student picks up things rapidly and easily.
2. A gifted student is quick in grasping, relationships, making generalizations and drawing conclusions.
3. He puts intelligent questions in class.
4. He is able to solve those problems which are of a higher standard.
5. He shows originality in solving problems.
6. He possesses a  good power of imagination, thinking and reasoning.
7. He is a liking to work at abstract levels and does not like simple practical work.
8. His achievements are remarkable in various achievement tests.
9. His assignment work is of good standard.
10. He is always alert and actively participates in teaching learning process.

Enrichment Programme for Gifted Students

1. An enriched syllabus to provide for extensive and intensive study.
2. They should be encouraged to enrich their knowledge by the study of supplementary readers, reference books and general literature from the library.
3. They should be allowed to do their independent study in the library.
4. For teaching such gifted children the teacher should use heuristic, analytic, problem solving, project or discussion method.
5. They should be told the history of the development of various topics and about the contributions of renowned mathematics.
6. Gifted students be encouraged to actively participate in various activities of Mathematics club.
7. Gifted students be encouraged to apply mathematical facts for solving their day to day problems and should be told about the practical, cultural and disciplinary values of the subject.
8. Gifted students be asked to organize seminars, exhibitions etc. concerning Mathematics.
9. They should be asked to work on some useful projects either independently or collectively.
10. They should be told that there is enough scope for research work in mathematics.
11. The work of such gifted students should be duly appreciated by the teacher.
12. Special coaching be arranged for such students.

            In a subject like Mathematics providing individual attention assumes a greater role because of the intricate skill involved and the vigorous mental and disciplinary qualities in build in the very nature of the subject.                                                               

       The identification of the mathematically gifted is as important as nurturing their mental abilities and skills to acquire a high level mathematical thinking ad reasoning.

        The unique characteristics exhibited by the gifted students will help the teacher in identifying them. However, the teacher has to carefully follow their academic and other performance consistently for a long time before he identifies them as gifted.

          The nurturing of gifted children in mathematics, first of all, requires their identification. The following points should be taken into account while classifying the students as mathematically gifted or mathematically weak.

1.       Opinion of other subject teachers.

2.       Students’ score on mathematics aptitude test, mathematics achievements test and intelligence test.

3.       Students’ past performance in mathematics in the previous classes.

4.       Students’ score on inventories like Interest in mathematics. Attitude towards mathematics.

5.       The report of a properly planned interview.

6. The opinion of the teacher himself based on the day-to-day observation of the child’s behaviour.

Characteristics of the Mathematically Gifted

General Characteristics:

1.       Has excellent memory, good vocabulary, broad attention span, and high reading ability.

2.       Makes associations readily and retains them indefinitely.

3.       Recognizes similarities and differences quickly.

4.       Has a relatively mature sense of values.

5.       Pursues interest with tremendous energy and drive.

6.       Uses his spare time productively.

Special Characteristics:

1.       Frequently impatient with drill and details that he thinks are not important.

2.       May be reading mathematics books years ahead of his age.

3.       Recognizes patterns readily and enjoys speculating on generalization.

4.       Prefers to think oin higher levels of abstraction.

5.       Classifies particular cases as special cases of more general situations with relative case.

6.       Follows a long chain of reasoning, frequently anticipating and contributing.

7.       Frequently asks profound questions.

SLOW LEARNERS IN MATHEMATICS

     In the functioning of school and teaching learning process every teacher encounters the problems of slow learners especially of mathematics in reality. Such children don’t desire any benefit through generalized instruction. Facial expressions, indifference and incapacity to respond to simple questions are sure indications of retarded learning.

    Slow learners generally do not respond to the lessons meant for that class and are incapable of achieving even to level below that of a year. The general I.Q of a child is between 85 and 155. According to the studies of CirilBirt the I.Q of a slow learner is below 85. Burton Hall identifies a slow learner as a low achiever to the generally accepted educational levels.

            When a student is found to lag behind other students in his class we call that particular child as backward.

Identification of Backward Students

1. To identify students with low I.Q teacher may carry out intelligence tests.
2. To find, if a student is slow in picking up facts, teacher can put up few oral questions and observe the responses given by the students.
3. Teacher can also know about the level of understanding of a student by observing their faces. Whenever a student fails to understand some important details his face bears a blank look.
4. The score of a student in an achievement test also points to the position of the student. The score of a backward child is generally low.
5. A backward child is not able to do written work in a finished style. He generally does things in a haphazard manner.
6. A backward student would prefer to be seated on a backbench or in corners.
7. A backward student is generally irregular in doing his homework.
8. A backward student may not be very regular in attending the class.
9. A backward student is likely to remain passive for most of the time in the class.

Identification of Slow Learners

Ø  Intelligent Quotient is below 90.

Ø  Has little Drive.

Ø  Has short span of attention.

Ø  Has weak association memory.

Ø  Is a poor reader.

Ø  Has difficulty with abstractions.

Ø  Is not logical in thinking.

Ø  Lack of imaginations.

Ø  Is unable to detect his own errors.

Ø  Has little power to transfer training.

Ø  Is not creative in his thinking.

Characteristics of slow learners

1. Slow learners have limited cognitive capacity. They fail to dope with learning situations and to reason abstractly. Rational thinking becomes practically impossible. They have the capacity to succeed in rote-learning. These children show interested in learning where relationships are clearly demonstrated. With regard to retentive memories they require more practice and revision in comparison with normal children.

2. One of the pertinent characteristics of slow learners is poor memory. It occurs due to lack of concentration, it is impossible to say how much a child can learn and retain although he is motivated externally and internally. Experimental evidences reveal that very often the dull children can recall facts about their local cricket team as well as its players.

3. Classroom situations include distraction and lack of concentration of slow learners. This typical behaviour is also associated with poor motivation. Again different studies also report that when the learning material are presented through concrete situations, the slow learner’s concentration and attention do not differ significantly from that of a normal child.

4. Inability to express his ideas through language is another significant characteristic of a slow learner. A slow learner also lacks imagination and foresight. He faces difficulty to foresee consequences in the future.

5. In developing societies, has slow learners invite social as well as educational problems. Of course, some dull children are very poor in scholastic achievements in the school. Their performance is not satisfactory. But some children who come from sophisticated homes show good performance, because they get help and encouragement from home. This is only possible at the primary stage of education. But at the secondary stage, the frustrations and failures come from different sources. The children develop an attitude of resentment towards the authorities and create problems. This kind of attitude may lead to anti-social behaviour in the future.

CAUSES AND REMEDIES:

1. Physical causes:

            Backwardness may be due to some physical causes such as poor eyesight, hearing defect or any other physical ailment which do not allow the child to concentrate on studies. Remedy of all these causes lies with the physician or doctor but some sort of physical exercise may also help the child.

2. Lack of interest in the subject:

            Interest is the basic factor in teach mathematics subject some of the students have little or sometimes no interest for learning mathematics. In some cases the students are forced to learn mathematics due to over enthusiasm and ambitions of the parents such students generally develop a sort of disinterest, apathy or sometimes hatred towards the subjects and in the long run turn into so called backward in the subject.

Therefore it is essential that the children should be given proper opportunities for the essential motivation to learn mathematics. All efforts should be made to make the subject interesting and meaningful by correlating it with their natural interests and basic needs.

3. Mental Disability:

           The mental disability may be inborn or caused by environmental factors. The child may have low I.Q, mental conflict, inferiority complex, feeling of insecurity, anxiety, tension, fear, nervousness, maladjustment etc. Many of these mental disorders can be successfully tackled by a competent teacher with a conscious effort. Attitude of affection, sympathy and kindness can go a long way in this regard.

4. Lack of Mathematical ability:

         Certain abilities like abstract reasoning, numerical ability, spatial ability, arithmetic reasoning, and computational ability are prerequisites for success in mathematics. Slow learners may lack proficiency in one or more of these abilities. The teacher will have to test proficiency of slow learners on these abilities and necessary training programmes should be implemented to improve the skills and abilities.

5. Inappropriate Learning Experiences:

       The inappropriate learning experiences provided in the mathematics class could lead to confusion resulting in misconception of the basic mathematical concepts. The teachers should plan the learning experiences which are simple and relevant for the slow learners to achieve the objectives and get the concepts clear and clarified. Remedial teaching has to be done in such cases where the slow learners need them. Remedial teaching has to be planned in such a way that learning experiences provided would be different and would meet the special needs of the slow learners.

6. Irregular Study Habits:

       Mathematics is a subject of logical sequence. Higher order concepts depend upon low order concepts. Rules and formulae are statements of relationship among these concepts. Therefore a student with irregular study habits will find it hard to understand and apply the mathematical laws and principles. The teacher should help such students to plan their study time properly and make them more regular and systematic. Drill and review also could help them in improving their performance.

7. Teacher’s Indifference:

       Many a time the mathematics teachers become impatient and show indifference to the slow learners who are slow in grasping mathematical ideas and concepts. Moreover slow learners may not be able to perform the mathematical tasks at the same rate as their counterparts in the class. This could result in frustration among the slow learners leading to low achievement.

         A Teacher could take more interest in the slow learners and understand their levels of learning. This will definitely boost up the self-confidence of the slow learners.

8. Ineffective method of Teaching:

          The group of methods of teaching are not very effective for the slow learners because their rate of learning, levels of achievement and level of understanding are not the same as the other students in the class. The teacher has to give special attention to the needs of the slow learners. In the case of slow learners, methods of individualized instruction like Programmed Instruction, Computer Aided Instruction (CAI) and use of learning packages and modules could yield better result and facilitate effective learning. The teacher should also give individual attention to the slow learners in clarifying their doubts, in stimulating and in directing their thinking. This will enthuse in them a sense of well-being, trust and confidence in the teacher.

9. Practice and Drill:

       The slow learners need more concrete experiences for effective learning and more drill and practice for longer retention. The teacher has to provide them with such opportunities which would result in meaningful learning.

10. Lack of facilities at Home:

       When the child does not have adequate time and facilities for learning at home, it may lead to backwardness. The teacher can help such students by arranging supervised study, where the child can learn under the supervision of the teacher. In this connection the teacher can seek the help of the gifted children.

11. Family Background and Home Environment:

        The uncongenial atmosphere at home, the negative attitude of the parents towards the subject, the pressure of the parents and so on could adversely influence the students’ performance in mathematics. A teacher could deal with such children with patience and sympathy. The teacher has to change the attitude of the parents and students by interacting with them in a more meaningful manner.

12. Irregular School Attendance:

        The irregularity in attendance causes a serious problem for mathematics learning as it creates a wide gap in the student’s understanding of mathematical concepts. Mathematics being a sequential subject, the understanding of a concept depends upon an earlier concept. Once the link is lost, the learning becomes more complex and difficult. The teacher has to look into the causes of irregularity in attendance and help the students in the best possible ways.

13. Lack of Individual attention:

            Proper learning in mathematics needs individual attention. Individual differences are bound to exist.

                The need is to pay proper individual attention of the proper time the teacher should take care that each of the student in his class understandings the basic concepts clearly. He should be helped in solving the problems independently. His homework should be regularly supervised and the difficulties, if any, should be individually solved.

14. Lack of proper educational guidance:

            Sort of affair needs careful educational guidance to the students in the choice of subjects and courses. In this way children should be help in making right educational choices through the properly arranged guidance services at the school and community so that no child may develop into a backward child in learning mathematics on account of the lack of educational guidance.

SOME USEFUL CLASSROOM TECHNIQUES FOR SLOW LEARNERS

1.       Provide an opportunities for the class to learn through several senses at a time such as seeing, hearing, manipulating dramatizing and doing.

2.       Have daily routine, with surprises, as routine gives them a feeling of security.

3.       Frequent changes of activity are necessary because slow learners have a short span of interest. Provide variety within a period.

4.       Never put a child on the spot for an answer if he is dull.

5.       Give these pupils immediate satisfaction by checking their work as they do it.

6.       Make each daily lesson complete in itself so that the slow learners can learn it easily.

7.       Never penalize a slow child by forcing him to work longer at mathematics than his brighter peers.

8.       Always prepare pupils for verbal problems. One or two thought problems each day are more effective than a long test at one time.

9.       Always make directions clear by writing them on the blackboard.

10.   Do not try to force slow learners to do mathematics when they are not really interested.

11.   Try to think of new ways to review concepts.

12.   Break content into small repetitive steps and give easy exercises for immediate reinforcement.

13.   When a question is asked, break the questions into a number of simpler questions.

14.   Do not insist on verbal definitions and statement of rules if there are evidences that the child has understood the idea.

15.   Always introduce a new relationship with the simplest arithmetic or algebra possible so that the pupil can concentrate on concept itself and not get frustrated by tedious computation.

16.   If there are several approaches to a new concept, use one per lesson to avoid confusion.