Creation of a Place Value Kit as a teaching aid for primary school children

PROPOSAL

PROJECT : Design, production, trialling and dissemination of

Place Value Kit for primary maths education

1. Summary

This is a proposal for a project by SUVIDYA, an educational resource group in Bangalore, India. SUVIDYA has been involved in many projects whose goals have been to improve the quality of education imparted in schools in several parts of India. The methodology employed by SUVIDYA involves the creation of models or teaching aids to illustrate mathematical concepts. SUVIDYA also organizes training workshops for teachers.

In the first section information about SUVIDYA like the objectives of the organization, the people behind the organization, their experience etc is provided.

The overview of the proposed project is given next followed by details like the individual tasks involved, the execution plan, the target audience, the time schedule etc. This is followed by a section on the budgetary details.

In the Appendices included at the end are previous project details.

2. About SUVIDYA

“SUVIDYA” is a trust registered with the Registrar of Trusts, Bangalore. (Registration No. 37/2000-2001, 11th May 2000). It is not presently registered with the Ministry of Home Affairs, New Delhi, under the Foreign contributions Regulations Act. However, it is possible to get prior permission from the Ministry to receive funds to SUVIDYA trust. We need about 3-4 months (after receiving confirmation from the funding agency) to get prior permission.

Legal status

SUVIDYA trust has been granted the status of wholly Charitable trust under section 12A of Income tax act and hence is exempted from payment of taxes on any grants, donations or other sums received.

SUVIDYA trust is also granted recognization under section 80G of Income tax act indicating that the donations made to SUVIDYA are exempt from Income tax in the hands of the Donors.

Trustees are: Dr.S.N.Gananath - Director

Prof.D.R.Balurgi - Professor of Physics. LVD College Raichur,

Karnataka

Dr.C.Ravikumar - Scientist & Development professional.

SUVIDYA began in 1994 as an educational initiative of SAMUHA, to promote and utilize innovative ideas in education. It was intended that the school going children in and around Jalahalli in Raichur district would be the primary beneficiaries. SUVIDYA has also committed to make available the fruits of this endeavor to anyone interested in adopting the same. Specifically, SUVIDYA has identified Math, Kannada and Science as the priority areas.

Multipurpose Algebra Kit

SUVIDYA is currently a grantee of ASHA and AID and is working on the design, developing testing and dissemination of Multipurpose Algebra Kit for children / teachers of class 7 to 10. The kits are ready for feedback and dissemination and the project is in the final stages of its completion.

3. Introduction

Increasingly, policy makers are concerned about the quality of primary education. Several programmes have now been initiated to address the issue of quality, as opposed to mere access, of primary education in government schools. Illustratively, the World Bank has supported the District Primary Education Programme (DPEP), and other bilateral funding initiatives supported Janshala, each programme running in several states of India. SIDA supported the Lok Jumbish programme in Rajasthan, In Karnataka; the central government has supported Chaitanya, an ambitious effort at teacher revitalization, involving training and teaching aids. In all of these programmes, child-centric and activity-based education is the dominant pedagogical framework. Teachers and trainers are showing far more interest in material-based pedagogy.

The result of these initiatives is that the scenario of primary school education is changing. For long it has appeared to be static; now things seem on the move, and there is a sense of excitement. In this atmosphere of greater commitment and support to quality, DPEP had a provision wherein each primary school teacher was sanctioned Rs. 500 per year, to make or purchase necessary teaching materials. Subsequently, in an informal survey of what facilities are available and availed of by primary school teachers, often money went unutilized. To the extent that any materials were purchased, expenditure was only on books. Thus, even though activity-based education is being supported conceptually, reasonably priced hands-on activity kits are not actually available in the market.

4. The proposed project

The vital role of mathematics in primary education has been adequately recognized by curriculum makers and designers. Maths is needed for abstract thinking, problem solving, logical reasoning and for developing intellectual and psychological ability of the child. In the world of development, it is a critical area of intervention (both in-school and out of-school) as it is also a life skill. Despite this, conceptual understanding is inadequate, motivation and interest are fast declining and achievement levels in maths are low. The many problems that beset teaching in primary mathematics include the uninteresting and dull presentation of material, lack of a problem-solving approach and prevalence of math phobia.

Place value is considered a difficult mathematical concept, which, in a cascading effect, leads to other problems in mathematics learning. Children do not get hands-on experience in learning about place values, resulting in a felt need for such a kit, as ascertained during our interactions with teachers, trainers and children. Suvidya intends to design, produce and test a kit consisting of 10 aids, 20 worksheets/charts and a handbook with additional information (see box for details).

Components of

Place Value Kit

10 aids

10 activities

Worksheets

Place Value Jokes

History of Place Value

Common Errors

General Information

Users’ Manual

Features of Place Value Kit

Multigrade

Multilevel

Potential to be linked to the textbook

Simple and interactive for the teachers

Several language versions

Through workshops, field-testing and feedback, primarily in rural and urban Government schools, we will refine the kit. After testing and refinement, we will liaison with the Government and NGOs for wider dissemination of the kit.

A few sampls are ecclosed ( See appendix II).This,however is a preliminary draft requiring major changes.

5. Objectives

To explore in detail, with teachers, the difficulty of place value learning amongst primary school children.
To design the kit
To produce the kit in more than one language
To trial the kit
To document the process of kit production and improvement
To disseminate the finalized kit

6. Activities and time line

1. 1	Project starts	Apr 2001
2	Design of the Kit	Nov 2001
3	Pretest the Kit	Jan 2001
4	Design the manual	Oct 2001
5	Pretest the Manual	Jan 2002
6	Obtain feedback	Jan 2002
7	Introductory workshop	Mar 2002
8	Field test	Apr 2002
9	II Worksshop/ Field test	May-July 2002
10	III Workshop/ field test	Jun-Aug 2002
11	IV Workshop / Field test	Jun-Aug 2002
12	Documentation / evaluation	Jul-Sep 2002

Although we are currently envisaging four workshops as part of the process of developing the kit, in order

to enhance the number of inputs to the kit, we will proactively be liasoning with other groups for supporting

2 to 4 more workshops.

Sl. No.	Description	Justification		Amount in Rs.
1	Materials, Labour etc to produce kit	500Kits x	500 perkit	250,000
2	Salary: Project Head 25%	5000 Per month x	18 months	90,000
3	Salary: Coordinator	6000 Per month x	18 months	108,000
4	Communication Telephone, Fax, Internet, Courier, postal	1000 Per month x	18 months	18,000
5	Rent 50% + Rent related expenses	7000 Per month x	18 months	126,000
6	Training workshops	15000 Per workshop x	4 workshop	60,000
7	Travel: Local and outstation	2500 Per month x	18 months	45,000
8	Consultancy Fee			20,000
		Sub Total =			717,000
9.	Over heads Admin etc Bank, Society, Audit, Secretarial Photocopy, Staff welfare	10% of the above			71000
9.		Grand Total =			787,000

(Rupees Seven lakhs eighty seven thousand only)

Cheque / DD may be made favouring SUVIDYA payable at Indian Overseas Bank, Jayanagar V Block Branch, Bangalore, India (A/c No. 12352) after prior permission is obtained from the ministry of Home Affairs.

A sanction letter is required to apply for prior permission.

APPENDIX - I

OUR PROJECTS

SL. No.	Project Title	Funding Agency	Date commenced	Status
1.	Maths Lab	Jawaharlal Nehru Planetarium, Bangalore	June,1994	Completed
2.	Maths corner at the Belgaum Science Centre	Karnataka Rajya Vignyana Parishad, (KRVP) Bangalore	September, 1994	Completed
3.	17 Maths labs in School Science Centres	KRVP, Bangalore	October, 1994	Completed
4.	Establishment of Maths, Science and Kannada labs in 42 government primary Schools, Raichur District, Karnata	PLAN INTERNATIONAL	June, 1995	Ongoing
5.	100 Maths labs in School Science Centres	KRVP, Bangalore	June, 1996	Completed
6.	5 Maths labs in Science Centres	KRVP, Bangalore and Sir Dorabji Tata Trust, Mumbai	June. 1996	Completed
7.	Establishment of Maths Centres in BRCs and CRCs in Belgaum, Raichur, Mandya and Kolar	District Primary Education Programme (DPEP), Karnataka	November, 1996	Completed
8.	Production and trial of Self learning low cost Geometry kits (High School)	National Council for Science and Technology Communication, Department of Science and Technology. GOI, New Delhi.	Started Mar’98 to March’99	Completed
9.	Training of trainers and teachers belonging to aided schools in Karnataka	National Education Group, South Zone (Dioceses)	Aug’98 to Nov’98	Ongoing
10.	Enrichment Programme for Maths teachers	URMUL Trust, Bikaner, Rajastan		Completed

Appendix II

Place Value kit : Draft Manual

1. Place value indicator

Materials: Opaque plastic cards / laminated thick cards, thread, 40 cards with numbers written.

Concepts: Positional value, Addition.

How to use:

1. Hold the model such that the part tied with thread is to your right. Take, for example, a 2-digit number like 71. Place the 1 in the unit’s place and 7 in the ten’s place. Now, the combined number is 71. Notice that on folding back 1 there is a 0 behind it indicating that the place value of 7 is 70. In the same way use 3- and 4-digit numbers and continue the activity.

Questions:

Can this method be used for learning and reinforcement of the decimal number system?

There are some cards with positional value. What is their use?

How does one make cards with positional values for 5^th, 6^th and higher positions?

Can this be used as a calendar?

Can this model be used in activities like addition? Try it out.

Other concepts

Rectangular shapes.

Low cost locally availabl e materials:

Boxes, Invitation cards, white papers.

2. Book of 362

Materials: The book entitled “Many facets of 362”.

Concepts: Place value, extended form of numbers.

How to use:

1. Look through the book carefully. Find out how many ways the number 362 can be

represented.

2. Each page found can be represented as a chart. Give similar numbers to the children.

Let them use these numbers in different ways. Discuss with the children the many

forms of this number.

Questions:

In what other ways can this number be represented?

Other concepts

This can be slightly changed to learn decimals. It can also be sued for fractions. The same method can be used on coins and notes.

3. Extended notation

Materials:

Thick card

Concepts: Place value.

How to use:

1. Fold the card such that the number 6375 is visibl3e to the children.

2. Unfold the card behind the number 5. Notice that 5x1 is written.

3. Ask the question “ what’s the meaning of number “7”

4. Notice 7x10 written on the fold behind the number 7. The meaning of 7 is this.

5. In the same way determine the meaning of 3 and 6.

6. In the same determine the place value of all the 4 digits.

Questions:

In the same is it possible for you to prepare the model(s) for a 2 or 3 digit number

That you like?

Other concepts:

Decimals.

Low cost locally available materials:

Paper, Chart paper, Newspapers, Calender etc.

4. Mind reading card

Materials:

Thick cards with numbers printed on them.

12 sets of 6 cards each? Laminated).

1 set of 7 cards? Not laminated).

Concepts:

Addition, subtraction, multiplication.

How to use:

There are 13 sets of cards. Each set of cards has been set with one type of design pattern. Make the sets based on that.

1. Pick up this set of cards.

2. This game is played by 2 people. Pick the first card from the set and show it your

friend.

3. Ask your friend to remember one of the numbers in the card and put it aside.

4. Now show each card to your friend asking if the card has the number.

5. If the answer is “yes” keep the card in one place and if the answer is “no” keep the

card in another group.

6. In this way after exhausting all the cards, turn and see what is written on the “yes”

group of cards. There will either be a number or some instruction. For example it may

say “sum it up” in which case the sum of all the numbers on the cards is the number

that your friend had in mind. Check this out.

7. In some cards the instruction may be “sum it up” and in others it may be “subtract”. In

such a case add the numbers first and then subtraction.

8. If the instruction is multiply one must multiply the numbers.

How to make these sets:

It is not that these sets are the ultimate ones. After playing with all of these sets you can prepare many such sets yourselves.

Pick 5 numbers. For example 4, 5, 6, 8, 3 (can be in any order).

Make a strip and write these numbers on it.

From these pick some numbers (e.g.: 4, 8, 3). Write their sum (15) in the first slot of the second row. In the second row containing 15 put a tick mark under 4, 8 and 3 as indicated in the picture.

In the same way complete the rest of the grid.

Look at number 12. Since 4 + 5 + 3 = 12 the columns with numbers 4, 5 and 3

have been ticked.

Cut out 6 cards of size 3” x 4”.

Write thus on the first card: ‘Remember any one of these numbers.’

15, 19, 11, 14, 12, 22, 4 (all numbers from the first column).

On the back of the second card write “add 4”.

On the front of the second card write all the numbers that have been ticked on the second column that are 15, 12, 4. Now the second card is complete.

In the same way prepare the cards 3, 4, 5 and 6. The way to use them has been described above.

If subtraction has to be done, the numbers in the first line in the grid must be written as

‘__’. (Substraction symbol).

The same principle can be used for multiplication.

Questions:

In a set when would more than 6 cards needed?

Low cost locally available material:

K. G. card or thin sheet.

5. Arch game.

Materials:

Arcs made of Forex sheet

Cards with numbers written on them.

Marbles.

2 wooden pieces.

Concepts: Addition

Numbers with one digit.

Numbers with two or more digits

Decimal system

Fractions

Ascending/descending order

How to use:

1. Place the arch in the middle of the classroom.

2. As indicated in the picture place the card in the elastic band.

3. At a distance of 8 – 10 feet from the arch draw a line (The distance can be modified as needed).

4. Invite a child and give him 5 marbles. Ask him to roll the marbles such that it goes into the

arches. Two rules need to be observed while doing this. The child should not cross the line.

Only one marble must be rolled in each attempt.

5. If the marble passes through arch, the number on the card above the arch will be added the

child score. The card should have maths expession whose complexity will depend on the level

of the children. larger numbers must be on the cards with the smallest arc openings and

smaller numbers on the larger arcs. (1, 10, 100, 1000).

6. This can be successfully used even in a situation where children form multiple classes are

being taught. On one side of the arch, stick cards with one digit numbers and let the children

from the first standard use this part. On another side, put cards with 2-digit numbers, and let the

children from the second standard use it.

Questions:

Can you make a model with 7 doors?

Why stick cards with smaller numbers for the arcs with larger openings? In the same way why stick cards with larger numbers for the arcs with smaller openings? Think about it.

Other concepts:

This model can be used for multiplication and subtraction.

Low cost, locally available material:

K. G. card, thick cards, carton box, cardboard. This model can be made by folding newspapers into many folds. The game can also be played by drawing pictures of the arcs on the wall, in which case the marbles will bounce off the wall instead of going in.

6. Abacus.

Materials:

Long rubber board, 36 matchsticks.

Holes in 9 rows and 4 columns.

Concepts:

Place value, decimal, addition, subtraction, multiplication, division, and different geometric shapes.

How to use:

1. Pick a single digit like 8. The child must place these 8 matchsticks in the unit position on the board. Pick a number with 2 digits. E.g.: 39. The child must place 3 sticks in the tenth position and 9 sticks in the unit’s position.

In this way pick 3 and 4 digit numbers and show the place values of the hundred’s

and thousand’s positions.

2. You can insert the sticks and then ask the children to determine the number represented.

3. Addition: Use this model to demonstrate the sum obtained on adding 35 and 2.

4. In the same way teach addition.

5. Cover up the printed place values and write tenth, unit, 1/10, 1/100 in its place. Between unit and 1/10 place a decimal point. This is like readying a decimal table. Try teaching decimal numbers with this.

6. Make a triangle using three matchsticks and a rubber band. (Look at the picture).

In the same way make other geometric figures.

Questions:

How will you change this model to teach the concept of 1000, 10000 etc.?

Can this model be used to teach the concepts of multiplication and division?

7. Subtract 8 from 13

Materials:

5 Black plastic pipes

2 Plastic lids

Concepts:

Subtraction

Addition

Units place – tenth place

How to use:

There is a difference between doing subtraction-using objects and using symbols.

Ex: Subtract 8 from 13. If this is to be done using symbols the concept of a carry over must be known. Why is carry over necessary and when is it to be used? What is its use? To learn these concepts this model would be useful.

1. Take 13 marbles and put 10 of them in a pipe. (Note: Each pipe can hold exactly 10 marbles. Only a set of 10 marbles must be put in the pipe.)

2. Tell the children “This is thirteen. This can be written as 13. This means that there are a group of 10 marbles (show the pipe full of marbles) and 3 separate ones”.

3. Ask the children “Now if 2 is subtracted from 13 how many will remain?”

4. The children will put aside 2 out 3 marbles and say 11.

5. Ask them how 8 can be removed from 13. Write this on the blackboard as well.

6. Now there is a problem. There is a need for 8 separate marbles. There are only 3 separate marbles to keep aside. What should be done now?

7. The children would have seen that there are 10 marbles in one pipe. Make them understand that if these ten are added to the 3 marbles there will be enough marbles to subtract 8. Let the children know that in such a case the pipe has to be opened. Put all the 13 marbles in a group. From these subtract 8.

Write the same thing on the blackboard also:

8. Follow similar steps for addition also. (Here one needs to make groups of 10.)

Questions:

How will you use the same model to do the following math problems?

Subtraction:

Addition:

Other concepts:

The same thing can be sued for 100 also. This can be used for cylinder and cylinder imprint.

Other ideas:

The marbles can be put in small plastic cup also. However there must be exactly 10 marbles.

One could use 10 beads strung together on a string for this activity.

Make a cylindrical shape using a sheet of paper. These can be cut into smaller pieces

and used.