аЯрЁБс>ўџ HJўџџџGџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџьЅС7 јП3bjbjUU "F7|7|/џџџџџџlрррррррєЈ
Ј
Ј
Ј
М
,єч,є
(fhhhhhh$ 3fрxррЁxxxррfxfxюxfррfш
№txOЦєДЈ
Ж.ffЗ0чfфfxєєррррйMath Workshop Summary
Jodo Gyan, based in Delhi, conducted a 2-day Math workshop on activity based learning of mathematical concepts. The concepts can be applied for multiple levels based on the extent of usage of tools –, be it for pre-primary, primary or middle school levels.
Hyderabad
Feb 6-7, 2006
9:00 am - 5:30 pm
St. Anns Retreat cum Seminar center (St. Anns Generalate),
Nagarjunanagar Colony, Tarnaka, Hyderabad
Language of Communication: English.
Translation into the local language was provided. Telugu at Hyderabad
Cost involved
Rs. 200/- per participant for daytime attendees (includes lunch and refreshments)
Rs 250/- per participants for attendees staying at the venue (includes lunch, refreshments and accommodation)
People who participated
Maximum 3 teachers could participate per school in each workshop
Rebecca (from Prashanti Kutir; Belaku Project; she stays in the Belaku orphanage, helps with the childrens studies and also takes care of the bridge school) along with Anjamma and Rajamma, teachers from the pre primary centers went to the Learning Network's Math workshop held at Hyderabad. Anita who organized the workshop too mentioned that they were very happy and receptive with the workshop contents. They enjoyed the experience immensely.
Goal
The training imparted to them should help them well at the Belaku and PPC centers.
About the workshop:
The workshop format was demonstrative, interactive and hands-on. Participants would be using teaching-learning aids developed by Jodo Gyan for understanding various mathematical concepts.
Topics Covered: Spatial sense and Geometry, Measurement, Early Numbersense, Number & Number Operations, Place value and Algorithms, Algebra,Fractions, Puzzles
Session details
First Day
Introduction
The participants were asked to form pairs choosing a new person from a different organization and introduce each other to the larger group. The rest of the day we had many activities. Some of the activities are described below
Activity 1
Started with dividing into smaller groups of 6-7 people and the rangometry kit was given to try out different creative patterns, which can be made from a childs perspective. We were also asked to think of what concepts could be taught using rangometry. The participants listed the following teaching shapes, colors, interrelationship between shapes, patterns, tiling, generalizations, manipulation of shapes etc.
Activity 2
Two people in each group sat back and back. One person made a pattern with the rangometry pieces and gave verbal instructions to the person sitting behind on how to make the pattern he/she had made. Neither of them was allowed to see what the other person was making. 2 observers observed the whole process. After this exercise participant shared difficulties, problems and what they found worked. A few things came up communication is very important in teaching/learning/doing. To communicate effectively we need to start from where the other person is, common grounds of understandings of shapes is important for communication, many people associate shapes with various images they have seen around them, step by step commands is essential, number of pieces to be used needs to be specified.
After this, the origin of angles from the Egyptian system and the value of angles in circle triangle, square and hexagon was explained. The link between square numbers and geometry was explained. A pattern of sum of odd numbers will bring square numbers was explained with an example.
Activity 3
Concept of 1-1 correspondence and reinforcement of number concept was done by canceling each line with respect to the rolling of dice and by a clap. This activity also made the tactile feel of numbers, which would be a strong base for later math concepts. Pre-addition was explained through a story of frog named matku and the flies sitting on the pebble. The usage of landmark of known and comfortable numbers with respect to addition was taught with an example.
Other Teaching Materials shown
Ganita Rack for counting, manipulation and flexibility to transact numbers was taught with a story of shopping, counting in doubles, partitioning and sharing concept
Ganit Mala understanding of numbers, reinforcement of number and its relationship between each other, jumping forward counting, reverse counting, volunteer thinks and number and participants by asking questions more or less guesses the target number by moving the clip in the ganit mala.
Second Day
Activity 1
Jodo blocks were given to the respective groups and were asked to make some patterns and find out what concepts could be taught through them. Participants mentioned the following - Number counting, Operations- addition, division, multiplication, subtraction; Patterns, Concept of units and tens, Eye hand coordination, Development of motor skills, Teach colours, Shapes, Volume, Long and short, 1-1 correspondence
A story about people getting in and out of the bus to reach home was told to depict how the concept of addition and subtraction can be taught using the blocks.
Activity 2
The groups were asked to make a rectangle with various dimensions with 48 jodo blocks namely (6*8,12*4,16*3,24*2,48*1) which helped us to understand the concept of factors and also the prime numbers were explained focusing on the patterns that can be generated using prime and odd number of jodo blocks.
Activity 3
Concept of odd and even through jodo blocks. Use 2, 4, or 3, 5 jodo blocks and build a pattern with two rows of jodo blocks. One can visually see the difference in the pattern between odd and even numbers. Looking at the pattern one can see that a set of numbers give a smooth even surface while another set of numbers do not. And then we can name the numbers that give smooth surface as even numbers and the other set as odd numbers. Commutative property of the addition was beautifully explained which would form as a base for algebraic operations.
Activity 4
The concept of perimeter and areas was described. We were asked to make all possible patterns using 4 jodo blocks. The tactile learning of feeling the outside border of any pattern was facilitated which taught the concept of perimeter.
At the end of trying different patterns it was found that square shape pattern has least perimeter for a fixed area (i.e. fixed number of blocks).
Activity 6
The concept of estimation was taught by drawing a figure for e.g. a mango and filling the inner space with jodo blocks and simultaneously the meaning of areas was also re-in forced.
Activity 7
The least common multiple (L.C.M) was explained so explicitly and vividly thro a story of two boys who get into two different trains going to the same destinations and are trying to get back together, but one train stops every 2 stations, while the other stops every 3 stations. So we were finding out what are the possible stations where they would be able to meet (finding common multiples) and then finding the first station where they could have met. (Least common multiple)
Activity 8
The ganith mala was hanged with number catchers made of wood, which could be used to do multiplication easily.
Activity 9
The Dienes block was distributed which gave us an idea as to how units, tens, area, decimals, additions, subtractions and percentage can be taught with interest.
Activity 10
Lastly the concept of fractions was taught with distributing different shapes of foam with quarters, half. 3/4th and whole and different activities were given to make some whole etc
various combinations were explored to get the idea of equivalent fractions, smaller and bigger fractions, how to add two fractions, subtract two fractions, etc.
Conclusion:
A feed back form was distributed with questions to get the feel of the workshop and how better can it be done and what are the suggestions, which could be incorporated. A very well presented show for learning the basic concepts of maths.
About Jodo Gyan
Key expertise
Mathematics, Resource Group, Elementary, Middle School, Primary, Upper Primary, Training, Learning Aids, Teaching Aids
Geographical Location
New Delhi
Languages
English, Hindi
Philosophy/Beliefs
Jodo Gyan is a self-supporting not-for-profit organization working in the area of activity-based education since 1998. Jodo Gyans efforts arise from the conviction that quality education can be provided to our children only by linking their thought processes with their own experiences. The focus is to provide complementary services for the formal education imparted in schools by developing/making available materials and modules for activity based learning.
In Jodo Gyan we combine the spirit of non-profit motive with the decision to face the challenges of the market. Jodo Gyan itself is a learning organization with a vision of promoting human cooperation, autonomy and accountability.
Work Description
The objective of Jodo Gyan is to support the development of educational materials based on actual classroom experiences, mainly in the area of science and mathematics. We have designed some educational materials based on our own experiences of the teaching-learning process and we produce them with the participation of community members in Shakurpur, a resettlement colony in northwest Delhi.
In case of mathematics, we have drawn on research by late Hans Freudenthal and his colleagues at the University of Utrecht. We also make available various innovative educational materials and teaching practices from different parts of the country developed through the creative activities of organizations such as Navnirmiti and Eklavya.
We make a small contribution to the education of children in Shakurpur and we collaborate with similar organizations working to promote activity based education in other parts of India. Ours is a modest attempt to support the challenge that our teachers and parents face in providing quality education to our children. We reach out to children, parents and teachers of Delhi through schools and community organizations, display and demonstrations and fairs in schools and community centers to promote changes in classroom practices and joint-activity between parents and children.
Resources Available
- Various learning aids for mathematics Jodo Kit, Jodo Cubes, Mathemat, Puzzles etc.
- Various learning aids for science Bamboo microscope, Bug viewer etc.
- Regular Teacher Training Programs
Contact Information
Jodo Gyan
E/12-13, Shakurpur
Near Britannia Chowk
Delhi 110034
Contact persons: Shaji, Usha Menon
Phone: (011) 27102820
More information is available at HYPERLINK "http://www.learningnet-india.org/" \t "_blank" http://www.learningnet-india.org/
Jodo Gyan draws upon the latest mathematical research to develop creative educational materials and methodologies for teaching and learning mathematics. Jodo Gyan has recently worked with the Delhi government to set up mathematics laboratories in Delhi Municipal Schools and is changing the face of math learning. About Learning Network
The Learning Network explores various approaches towards holistic learning. This network helps learn about new perspectives and strengthen existing efforts. It is a resource for interested groups, educators and parents seeking meaningful approaches to education. The network members have a special emphasis on making quality education & resources available to economically poor sections.
Visit us at www.learningnet-india.org or email us at HYPERLINK "mailto:info@learningnet-india.org" info@learningnet-india.org
About Goodbooks Teachers Center
Goodbooks Teachers Center, Chennai was set up 2003 with an aim to provide a forum for sharing ideas, problems & solutions in education & create a positive, pro-active space that will enable teachers to upgrade & update their skills. The centre organizes workshops for teachers & contains a collation of learning aids & books.
Write to goodbuks@vsnl.com for more details.
More information at www.goodbooksindia.com
ЕЮа!/я№I
c v 3
4
9
;
J
Ш
Щ
н
э
ј
ЂЁГP\!"іырбУрОрбырыГЄГыыГыГыГыГы}v}vnvnvnvnf5OJQJ^JOJQJ\^JOJQJ^J5OJQJ\^J0J5CJOJQJ\^J0J5>*CJOJQJ\^J5>*OJPJQJ\^JaJOJPJQJ^JaJ0JPJ0J5OJPJQJ\^J0J5>*OJPJQJ\^J0JOJPJQJ^J0JCJOJQJ^J5>*OJQJ^J(*9LДЕк !/я№IJ b c w x ;
м
н
§§§§§§§§§§§§§ћ§§§ћ§§§§§§§§§§§3§н
э
ю
ј
љ
щъѕ
Ё
НОлмчЗИзЁЂЎЙYZћќ§§§§§§§§§§§§§§§§§§§§§§§§§§§§§ќ9:Emnop{iќ§ОПЪЌИ( ) 4 з и ф ;"<"H"7#§§§§§§§§§§§§§§§§§§§§§§§§§§§§§"Юы ' R!T!8#I#J#--Э-Ю-я-№-ё-1/2/7/8/N/P/1
1<1=1>1X1Y133љёљёщёљсљжЫМЫМЏМЄЫЄЫЄЄЫМЫМЏМЫљ#jOJPJQJU^JaJ0J5>*CJOJQJ\^JOJPJQJ^JaJ0JOJPJQJ^JaJj0JCJOJQJU^J0JCJOJQJ^J5>*OJQJ\^JH*OJQJ^J5OJQJ^JOJQJ\^JOJQJ^J!7#8#9#I#J#X#Я#а#ц#№#ё#ћ#
$$$ь%э%д&е&ц&p(q(У)Ф) ,
,,u,О,т,§ћћ§љ§§љ§§љ§§љ§§§§љ§§§§§§љ§§§т,у,ї,--)-6-Y-o-p-ї-P/ж0з0Z1[1{1Т2№233§ћ§§§§§§§§§§§§§љ§§§§ 1hАа/ Ар=!А"А# $ %АяDаЩъyљКЮЊKЉinfo@learningnet-india.orgрЩъyљКЮЊKЉDmailto:info@learningnet-india.org
i8@ёџ8NormalCJ_HaJmH sH tH B@B Heading 1$@&5>*OJQJ\^J>@> Heading 2$@&5OJQJ\^J<A@ђџЁ<Default Paragraph FontFg@ЂёFHTML TypewriterCJOJPJQJ^JaJ.U@Ђ. Hyperlink>*B*phџ ўOЂ bodytextўOЂ!title1/Fџџџџ*9LДЕк !/я№IJ bcwx;мнэюјљщъѕ Ё НОл
м
ч
ЗИзЁЂЎЙYZћќ9:Emnop{iќ§ОПЪЌИ()4зиф;<H789IJXЯац№ёћ
ь!э!д"е"ц"p$q$У%Ф% (
((u(О(т(у(ї())))6)Y)o)p)ї)P+ж,з,Z-[-{-Т.№.//0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"3 н
ќ7#т,3!"3)Э)я)-=-X-/XTџXџ/1ѓњџА$Л$Ћ%Е%К%С%^(f(#)()G)L)N)R)S)X)/Eq~L&Z&/333йкя№№J:;ннЗЗnp89Jn)[-///џџrestricted usercC:\Documents and Settings\restricted user\Desktop\arlu updates mar 06\teacher training workshop.docџ@ дР/p@џџUnknownџџџџџџџџџџџџGz џTimes New Roman5Symbol3&z џArial5&zaџTahoma?5 z џCourier New"q№аhЈЃFTУЃІNаи&R!№ ДД20Г/@№џџrestricted userrestricted userўџр
ђљOhЋ+'Гй0`ЈРЬм є
(
4@HPXфssrestricted userestNormaltrestricted user23tMicrosoft Word 9.0@Tх
@
:ЊРLЦ@№ёwOЦаи&ўџеЭе.+,љЎDеЭе.+,љЎ,шhp|ЄЌД
МЩфuicRГ/
Title< 8@_PID_HLINKSфAє_'"mailto:info@learningnet-india.orgZX"http://www.learningnet-india.org/
!"#ўџџџ%&'()*+ўџџџ-./0123456ўџџџ89:;<=>ўџџџ@ABCDEFўџџџ§џџџIўџџџўџџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџRoot Entryџџџџџџџџ РF0ЗxOЦKData
џџџџџџџџџџџџ$1Tableџџџџџџџџ,WordDocumentџџџџ"FSummaryInformation(џџџџџџџџџџџџ7DocumentSummaryInformation8џџџџџџџџ?CompObjџџџџjObjectPoolџџџџџџџџџџџџ0ЗxOЦ0ЗxOЦўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџўџ
џџџџ РFMicrosoft Word Document
MSWordDocWord.Document.8є9Вq