Group work
Question: Developing math-lab in school (concept of math-lab in school, objective of math-lab, type of math-labs, and type of materials: manipulative, visual, audio-visual, literature and electronics and use of math-lab in teaching mathematics).
‘Guidelines for Mathematics Laboratory in Schools
The document aimed at providing detailed guidelines to schools with regard to the general layout, physical infrastructure, material and human resources, etc for a Mathematics Laboratory. Besides, the document included a list of hands-on activities and projects, detailed procedure to be followed for carrying out these activities and the scheme of evaluation. In the meantime, the Board had issued two circulars to all its schools with regard to establishing Mathematics Laboratory and introduction of the scheme of internal assessment in the subject. Given on the basis of performance an individual work, project work and continuous assessments.
What is a Mathematics Laboratory?
Mathematics Laboratory is a place where students can learn and explore mathematical concepts and verify mathematical facts and theorems through a variety of activities using different materials. These activities may be carried out by the teacher or the students to explore, to learn, to stimulate interest and develop favorable attitude towards mathematics. In addition to issuing directions to its affiliated schools to take necessary action in this regard, a document on ‘Mathematics Laboratory in Schools – towards joyful learning’ was brought out by the Board and made available to all the schools. The document primarily aimed at sensitizing the schools and teachers to the concept of Mathematics Laboratory and creating awareness among schools as to how the introduction of Mathematics Laboratory will help in enhancing teaching – learning process in the subject from the very beginning of school education. The document also included a number of suggested hands-on activities.
With the objective of strengthening the concept further, the Board brought out another document
Need and objective of Mathematics Laboratory
Some of the ways in which a Mathematics Laboratory can contribute to the learning of the subject are:
• It provides an opportunity to students to understand and internalize the basic mathematical concepts through concrete objects and situations.
• It enables the students to verify or discover several geometrical properties and facts using models or by paper cutting and folding techniques.
• It helps the students to build interest and confidence in learning the subject.
• The laboratory provides opportunity to exhibit the relatedness of mathematical concepts with everyday life.
• It provides greater scope for individual participation in the process of learning and becoming autonomous learners.
• It provides scope for greater involvement of both the mind and the hand which facilities cognition.
• The laboratory allows and encourages the students to think, discuss with each other and the teacher and assimilate the concepts in a more effective manner.
• It enables the teacher to demonstrate, explain and reinforce abstract mathematical ideas by using concrete objects, models, charts, graphs, pictures, posters, etc.
•To provide readily accessible rich manipulative materials.
•To develop physical involvement in order to add new ideas to their cognitive structure.
•To make children experience with real – world embodiments of mathematical ideas.
•To emphasis on learning by doing.
•To provide children with opportunities to discover and understand mathematical concept through their active involvement in solving problems
•To make children to think, to look for patterns and ask questions.
•To develop an attitude of inquiry.
Type of Mathematics Laboratory
There are four different types of mathematics laboratory exist in practices:
(i) Decentralize or classroom Mathematics Laboratory;
A decentralize laboratories provide a good situation to promote the teacher in classroom. This is ideal because the teacher is responsible for all areas of curriculum and for a major portion of the time a child in school. It is also allows the children and the teacher to use material when ever thy need arises. A variation can be adopted when it is expansive to supply all teachers with the materials or when it is desirable make use of any special talents of teachers. In this situation, several teachers join and cycle the class for mathematics instruction into one room. The teacher for that room, which is equipped with the laboratory, is then responsible for the mathematics instruction for all the children in the cycle.
(ii) Centralized Mathematics Laboratory:
Centralize laboratory is used in many school where participation all children from all class or from certain class also. Share the facilities of the laboratory for part of their mathematics instrument. The ideal program should have especially trained teacher in the room full time to instruction to the children with the aids of regular teacher. In this situation the Mathematics Laboratory teacher could do the scheduling take care of the materials. Creates activities and use his specials talents to help all the students.
(iii) Roving or movable Mathematics Laboratory:
The movable laboratory is useful; when a school cannot afford to buy materials and does not have room for central laboratory. The materials are carefully itemized and placed in containers for easy assembling by the teachers. The containers for a particular topic have all necessary materials to allow the child to investigate the related problems freely. All the objects are then put on a large movable cart, and a schedule is created to allow access. The teacher who gets the laboratory during a certain period can quickly layout the containers and produce an instant mathematics laboratory in the room. Children can drive many benefits from participation in mathematics laboratory.
(iv) Team-room Mathematics Laboratory:
Team-room laboratories were created, as schools become equipped for team teaching. The most distinguishing feature of this type of laboratory is that it is in constant use by the children, and only a small number of them attend the laboratory at a given time. Children are in sight of a teacher at all times.
Type of Mathematics Materials
Teacher uses an instructional aid to communicate a new idea, and to add meaning and interest to verbal instructional. Teaching materials help for the student and teacher to clarify the instruction and about mathematics knowledge. In mathematics teaching without materials there is no meaning to achieve the mathematical knowledge. There are many types of mathematics materials exist in practices. Mainly mathematics materials are given below:
(i) Manipulative Materials
Manipulative materials are objects or things that the pupil is “able to feel, touch, handle, and move. They may be real objects which have social application in our everyday affairs, or they may be objects which are used to represent an idea” Manipulative material appeal to several senses and are characterized by a physical involvement of pupils in an active learning situation. Hence, not all teaching aids or instructional materials are manipulative materials.
Manipulative materials provide tools for problem solving. When a child has an aid to solve problem that is always available in the mathematics laboratory, his self-confidence is increased, because he does not need to depend on the fallibility of this memory. Unorganized way of using manipulative materials fails to attain important goals of mathematics instructions. Children should not learn merely to manipulate objects. Children should use this manipulation of objects as a means of learning important mathematical process, principles, and skills. The use of manipulative materials is not an end in itself, and care must be taken that they do not become ‘seductive shibboleths’.
Several types of manipulative materials such as chart, model, puzzle, tan-diagram, geo-board and other manipulative materials are available for mathematics teaching. In mathematics, manipulative materials are the physical object or things that the students are able to fill, touch handle and move. Many of materials for teaching mathematics at school levels can be made locally by students and teachers for class room use.
(ii) Audio, audio-visual, and electronic materials
Mathematics teachers can make good use of films, filmstrips, power point, videotapes and over head projector as well as traditional equipment such as flannel boards and chalk board. The overhead projector has becomes increasingly popular. With it, to prepare the teacher can project his writing on the screen, use previously prepared transparencies, use of variety of commercial transparencies now available. Facility accurate broad walking the teacher can use stencils for chalkboard drawings and graph. These audio, audio-visual, and electronic materials are new dimensional to meaningful mathematics learning.
(iii) Literature, textbook, and symbolic Materials
A large section of readable materials are interesting books, pamphlets, reference books, journals, curriculum. Materials and other in mathematics are available for students and teacher. These materials add enrichment, broaden the mathematical background of students and stimulate. Curiosity in new ideas, internet also, provides verities of literatures in mathematics.
Uses of Mathematics Laboratory
1) Students do experiments with numbers and geometrical shapes and try to generalize these patterns.
2) Students do most of their calculations with the help of scientific calculators.
3) Students draw graphs of large number of functions with the help of scientific or graphic calculators and try to become familiar with graphs of all the functions they usually deal with.
4) Students solve real life problems with real data because complex calculations are no longer a major consideration.
5) Students express their answers to mathematics problems in decimal numbers and not in symbols and have a good idea about their magnitudes.
6) Students get practice in estimating orders of magnitudes and obtaining approximate answers when exact answers are difficult to find.
7) Students make charts and models to illustrate mathematical ideas.
8) Students do almost all the work themselves, of course under the guidance of teachers, but the students are active all the time and are involved with what they are doing.
9) The creativity of students is allowed free play.
10) Students solve graphically equations involving all types of functions.
11) Students are free to discuss among themselves and with the teachers; in fact students and teachers form joint investigating teams.
12) Students find areas and volumes of both regular and irregular solids.
13) Students undertake projects both in mathematics and its applications.
14) The concepts and theorems are not given to the students; these arise naturally from their investigations.
15) Interfaces between algebra, geometry; probability; calculus etc are freely investigated and discussed.
16) Attempts are made to interpret every symbolic solution.
17) The process of mathematics is emphasized much more than the product of mathematics.
18) Students are encouraged to find alternative solutions and alternative methods of solving problems.
19) Students enjoy learning mathematics.
Conclusion
Teachers who have been trained through a behavioral model had no knowledge of methods such as cooperative learning and guided exposure method. Therefore, these methods are less preferred to teach mathematics through traditional methods, such as educational conference, the lecture-demonstration methods. Mathematics and its usefulness have given less importance in the continuing education level. The majority of serving teachers lack knowledge of mathematics in the laboratory after the teaching mathematics in secondary school. Most teachers have received training in using Mathematics Laboratory to teach math. The use of mathematics materials to teach math and to provide theoretical knowledge of mathematics in a Mathematics Laboratory has resulted in positive reinforcement for students. The use of mathematics laboratory materials was not in the curriculum of continuing education degree. This is why mathematics teachers were not aware of the use of Mathematics Materials to teach math. Mathematics Laboratory used in mathematics has provided practical experience taught math.
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