Pramod Maithil: A Ganak Based Game

8/3/2019 Pramod Maithil: A Ganak Based Game

http://slidepdf.com/reader/full/pramod-maithil-a-ganak-based-game 1/35

Pramod Maithil, Eklavya &

Anand Niketan School, Bhopal

Research method guidance: Dr. Anju Saigal



What

an exploration of the Ganak (the open abacus)

How

Core activity is a 3-base game based on Ganak.

Significant Outcome

With the grasp of abacus principle they were able

to make the meaning of “+” & “х” signs in the

expanded form of numbers.





What is place value system?

(an article “Place Value: Problem Solving and Written Assessment”

by Sharon R. Ross. 2002)“Our numeration system is characterized by the following four

mathematical properties: 1. Additive property – The quantity represented by the

whole numeral is the sum of the values represented by the

individual digits.

2. Positional property – The quantities represented by the individual digits are determined by the positions that they hold

in the whole numeral. 3. Base-ten property – The values of the positions increase

in powers of ten from right to left. 4. Multiplicative property – The value of an individual

digit is found by multiplying the face value of the digit by the value assigned to its position.”





In mainstream caseschildren are asked to write the numbers in

columns marked out as units, tens and

hundreds.

In the alternative approaches

Materials used in Whole number approachColor-coded 100 beads string - The Ganit mala

Materials used in place value based approachThe Diene’s block

The matchsticks bundle

How Numbers are taught?



The Material reviewused in Place Value based Approach

Strengths

It explain the base ten property of NumbersDevelops the grouping logic in place value

It explains & facilitates the algorithms very clearly

Issues

•These materials don’t follow the positional notation

system. The column are externally imposed to makesimilarity with.

Example 1345. If so, then we can write this number as 4153• Strength & need of the additive (multiplicative) composition of

numbers is simply lost. It comes exactly same in Ganak as we see

in our number system.



The Ganak as solution

‘Ganak’ is a bit modified version of roman

abacus, was used in ‘Bal Vaigyanik’ as a tool to

teach ‘decimal’ & ‘place value’

“Dr Vijay Verma even says in his article that the

Abacus was widely used other than India and

perhaps this affected the evaluation of number inthose areas” . This, at least, implies that the

Abacus is very much similar to our numbers

system.







Core activity – a 3-base game based on Ganak



























Core activity – The 3-base game based on Ganak

Naming the position

C ti it Th 3 b b d G k



Core activity – The 3-base game based on Ganak

Value of a combination of pebbles

C t l M f th St d th d



Conceptual Map of the Study method

The children enjo ed pla ing the three base game



The children enjoyed playing the three base game

and got hold of the game

They also learnt naming the boxes in order to know

the value of the combination.

All the children havelearnt to play it



The entire class was able to associate the

combination with quantity (number)



They were able to write the combination in

sequence. All selected 11 children even more could

do this for sure

They also used the name

of the boxes in order to

know the value of the

combination.

3 out of 11 did it by

counting from 1 to 56.



After pictorial

representation

they were able

to write using

Indo-Arabicsymbols as

well. All

selected 11

children were

able to writethe two base

numbers.

3 children

wrote up to 7

to 8 places of 3

base numbers.

The children designed their own game of different



The children designed their own game of different

bases by extending the part of a box and did all the

exercises which they did with 3 base game

The class was

divided in to 4

groups and all

the groups

designed theirgame.

Then to my surprise the children (8 out of 11) were



Then to my surprise the children (8 out of 11) were

now able to write the pebble combination in the form

of additive (multiplicative) composition in order to

calculate value of the number.

Continued 2



Continued ….2

Continued 3



An interesting Observation

He named the boxes

1, 5 & 25. Then he

added first 25+5+1

for the first row of

pebbles thendoubled it and then

added the unit box’s

left out pebble and

got the answer 63

Continued …. 3

Conclusion & Recommendations



Conclusion & Recommendations

It is also worth sharing that this small project was taken up in

order to learn the research methodology so this should not be seen

as cutting age research but certainly it can be treated as a pilot

study.

Although I am interested to see how the Ganak can be explored?

But I am still left with few issues/questions on the study if it is

seen as pilot study of efficacy of Ganak to teach place value.

Conceptual issues 1.The connection between the positional notation system and our

numbers seems a jump. I only assume that this understanding

will help a child to understand number batter in future?

2.Why place value should be taught?

Issues on method

1.I am unable to give justified enough rationale why did I conduct

the study in grade 6?

2.Various other factors like motivated teacher, time & syllabus

constrains and school management .

References



References

1. Harvey, G. (1998).. Writing with Sources: A Guide for

Harvard Students. Cambridge: Hackett Publishing Company Inc.

This book helped me to organize the paper and guide me where to

look for resources in the paper and the book is used contently tillthe end of the paper.

2. IGNOU AMT 01 - Teachers of primary school

mathematics Aspect of teaching Mathematics-1

3. IGNOU LMT-01, Approach to Learning 1 by IGNOU

School of science

4. “The Teaching of Place Value –Cognitive Considerations”

presented by Usha Menon

www.hbcse.tifr.res.in/episteme1/allabs/ushaabs.pdf

5. “Teaching Place Value and Double-Column Addition” by

Constance Kamii and Linda Joseph Taken from ENC Online.

6. Bal Vaigyanik class 6 chapter “Ganak ke Khel” – a

Science textbook cum workbook for Hoshangabad Science teaching

programme (HSTP)developed by Eklavya

References



References

7. RME - http://www.fi.uu.nl/en/projects/realme.html

8. About action research from net

9. The Dienes blocks

http://www.zoltandienes.com/what_is_a_base.pdf

10. Khushi Khushi classes 1 to 5 – Primary textbook cum

workbook for Prathmik Shiksha Karyakram (PRASHIKA)developed by Eklavya

11. HBCSE mathematics textbook of class 3

12. “Children Learn Mathematic” developed by the TAL

team, Freudenthal Institute (FI) Utrecht University and National

Institute for Curriculum Development (SLO), Nederland

13.chapter 1 “Early Calculation” from http://ed-thelen.org/comp-

hist/CBC-Ch-01.pdf,

References



References

14. History of computing from

www.geocities.com/paris/chateau/6110/abacus.html,

15. VSO teacher’s networks newsletter (spring 1999),

16. an article “Ganak se Ganith ki Samagh” by Dr. Vijay

Shankar Verm, published in educational bi-monthly journal

(Hindi) by Eklavya

17. www.questia.com, “Place Value: Problem Solving andWritten Assessment” by Sharon R. Ross

18. A paper Using concept mapping in the development of the

concept of positional notation system by Jean Schmittau, James J.

Vagliardo, from Proc. of the Second Int. Conference on Concept

Mapping

19. A paper “Developing the concept of the place value” by

Mala Saraswathy Nataraj & Michael O. J. Thomas, from the

proceedings of the 30th annual conference of the mathematics

education research group of Australia

Documents

Pramod Maithil: A Ganak Based Game