PREFACE

Mathematics has always been governed by rigour and logic. A result has to be proved in order to be accepted. This make it difficult for the average students and boring for the bright ones. Now there is awareness ,that as a solution to this , together with the formal method of teaching mathematics, the presentation of mathematics through some nonformal methods might help. One of the methods that is getting more and more popular is the ‘hands-on’ method, where we use mathematical teaching aids and perform activities. Although this is only verification and not a proof, it helps the student to see and understand the result easily. While many school boards have now made experiments and activities compulsory in their syllabi.

The concept of Mathematics resource center is an attempt to make selected models available to schools and teachers so as to facilitate their wider use. The Resource center contains a set of teaching aids , which have been carefully selected based on the topics covered in the syllabus for standards 1^st to 10^th and puzzles are also meant for students of that level, from the point of view of understanding and logical thinking. We also kept user manual containing a detailed description of each of the models and its use. For convenience , the models, both teaching aids as well as puzzles, have been arranged in the resource center, according to the mathematical category they belong to.

We hope the resource center will be useful and our vision shape into reality. We have tried to pass on our experience of hands-on teaching and learning methods to the teachers. All suggestions and comments are most welcome. We are sure they will go a long way in improving our future endeavors.

Vikas Sharma

Program Consultant ( Maths and Science)

CSPC-TATA TRUSTS

Coastal Salinity Prevention Cell (CSPC) was established in 2008 as a joint initiative of the Aga Khan Rural Support Program India (AKRSPI), Tata Truss and Ambuja Cement Foundation (ACF). Our aim is to improve the quality of life of the rural coastal communities of Gujrat through socio-economic development programmes which sustain the fragile environment.

CSPC largely works with its partner organisation, the local and state Government, Research agencies and Community Organisations.

VISION

Evolve Sustainable approaches for prevention and mitigation of salinity ingress, whilst enhancing livelihood resilience of communities affected by salinity in coastal villages.

Education program ,Okhamandal block, Devbhumi Dwarka

The program interventions were designed to meet the following objectives:

To improve the quality of age appropriate literacy (both oral and written) and numeracy skills in Primary Schools

To improve the quality of numeracy and science skills in Upper Primary Schools

To use available computers and internet infrastructure to improve learning outcomes in Maths and Science, Digital literacy and Life skills

Engagement with Teachers in the overall process of improvement in the learning levels

To improve the overall perspective of the community on education and enable them to take decisions on a day to day basis that are facilitative of their children’s education

To influence the department at a local level to ensure sustainability of the practices beyond the tenure of Trusts interventions

In a study to improve education levels in three blocks of three different districts of the Saurashtra region of Gujarat-Junagadh, Jamnagar and Amreli. In the year 2013-14 identified Okhamandal block with distinctly lower literacy rates than the state average. Further , the study also highlighted that education of the students of the region was adversely affected on account of migration for economic reasons. This became the evident reason for us to initiate interventions in education in Okhamandal block of the Devbhumi Dwarka district of Gujrat.

As part of a new project that was initiated in the district, government teachers were trained on library component and efforts were initiated to set up resource centres at DIET, Jamnagar.

The attendance level of students across the centres surpassed 70% average. Average attendance of last year was 67%.

Key Achievements of Education Initiatives

Development of foundational skills of literacy and numeracy in 20 schools and (930 students)

Activity based learning in Science and Maths for approximately 820 students in 20 Upper Primary Schools.

Start with my favourite line-

“Every student can learn mathematics and every student should learn mathematics.”

Manipulative skills in mathematics cannot be obtained by doing a large number of drill-sums. These cannot be obtained only by understanding the structures of the systems under consideration. Drill very often impedes the learning process since it makes learning monotonous and it makes the subject look trivial. Thus the intellectual content of school arithmetic is very little and rebellion of the children against arithmetic, which is very often ascribed to the difficulty of the subject, is really against the triviality of the subject.
The best way to teach mathematics is to let the students recreate mathematics for themselves. Mathematics is learnt by doing it rather than by listening passively to it. Students should be helped to discover as much of mathematics as possible themselves. The teachers’ role is to help the students in discovering mathematics. Mathematics should be taught not as a finished product but as an evolving discipline.
The philosophy and nature of mathematical thinking should influence and be influenced by thinking around us. In mathematics we have to consider all possibilities, in life also neglect of any possibility leads to errors. Mathematics teaching should aim at producing citizens who are rather precise in language, who are strong in their logical reasoning, who are not passive learners, who can detect fallacious reasoning, who can argue in depth, who have an appreciation for intellectual aesthetics and who have the willingness and ability to climb intellectual mountains.
The unity of mathematics should be emphasized throughout. Every opportunity should be taken to point out how different mathematical concepts illuminate one another and how these relationships give great power to mathematics.
Discussion of unsolved problems will show mathematics as open-ended discipline.
Teaching of mathematics should be integrated with the other subjects, as far as possible, especially in schools.
The teacher should encourage questions both inside and outside the class rooms and he should not appear annoyed even if the questions are not relevant.
The teacher should not be over anxious to help a student who is struggling with a problem. The student may have to muddle around on a problem before it becomes clear to him. The muddling process is the core of creative thinking. The teacher may give hints but should not deny the students the chance to think.
Creativity is the heart and soul of mathematics. Curiosity and creativity are key-stones in mathematics.

Mathematics Resource centre

Theme- to shift Perspective and pedagogy from algorithm approach to mathematical reasoning

The basic idea is to improve quality of mathematics education and provide better learning experience for children in schools through improving the capacities of –

Teacher’s perspective on mathematics education
Content knowledge
Appropriate pedagogic approaches that work given the child’s context and developmental stage.

This requires regular academic engagements with teachers and this cannot be achieved just though training or workshop alone.

Multimode-

Workshop
Discussion
Seminar
Melas

Resources-

The space and material required (books, teaching learning materials etc.)Which enables academic engagements with teachers
A team is regularly working in and around the centers for

Enable facilitate academic engagements
Calendar of activities, regular informal events etc.

At Resource Centre–

Workshop

Metric Mela

Voluntary forum

Seminar

One day event/TLM

Resource centre

T.L.M
Number system, Fraction, Geometry, Kit

(Concept note and FAQ)

Puzzle corner
Reading (Sandarbh, Learning curve, Right angle, Pull out)
E- resources –web link, videos, e-books
Games ( concept note and FAQ)
Print rich environment
Stories and Poems
Movie (zero ganit ka hero, nil bate sannata etc.)
History of mathematics (mathematicians)

A Month of resource centre-

Focus TLM
Mathematician of the months
Games of Month
Reading and books of the month
Movie /Video of the month
Stories and poem of month

Rationale:

Mathematics has always been an important subject in the school curriculum and important aspect of life in societies. Changes have been taken place in school mathematics in the past two to three decades. These changes have brought about a near revolution in the content, methods of instruction of mathematics. Demand has grown for teachers to make mathematics teaching more imaginative, creative and interesting for pupils as per the nature of the subject. Excellence in teaching mathematics is the desired goal for teachers. Professional development (affecting the beliefs, attitudes, knowledge, and practices of teachers in the school) is central to achieving this goal.

TLM list

Number system-

42. Angle Machine

43. Factor circle

44.Electric circuit

45. Pythagoras theorem 1

46.Pythagoras theorem 2

47. 360 degree angle protractor

48. Maths colony

49. Division Machine

50. Eat that apple Puzzle

51. Alpha magic square

52. Protractor 180 degree

53. Real numbers

54. Pascal triangle

55. T – puzzle

56. Match stick puzzle

57. Fraction peacock

58. numbers tree

59. Numbers tree

60. Ascending of fractions

61. Numbers puzzle (1-8)

62. Fraction wall

63.Division strategies

64.Tessellation kit

65.Rangometry

66.Number sticker

67.Number catchers

68.Math mat

69.Maan card

70.Jodo straw

71.Jodo Block

72.Ganit mala

73.Fraction kit

74.Decimal maan kit

75.Currency

76.Decimal kit

Note–

TLM 1 to 41- From Vikram A Sarabhai Community Science Centre, Ahmedabad

TLM 42 to 63- Prepared at CSPC office

TLM 64 to 76- From Jodo gyan , Delhi

Books for Resource centre

S.no.	Title	Author	Publisher
1	Ganit Ka Pehla Kadam	Krishna Mohan	Maitryee
2	dainik jeevan me ganit	R.M. Bhagwat	NBT
3	Ganit ke khel	Rajrishi Raman, Devendra Prasd Verma	Vaani
4	Ganit mei Paheliya	D.D. Sharma	Gyan Ganga, Delhi
5	Bhaskaracharya	Gunakar Mule	Rajkamal
6	Saral ganit(kalan or falan sidhaant)	Rakesh Pathak	Vaani
7	Saral ganit(bijganit)	Kishore Chand Jaiswal	Vaani
8	Ganit sabke liye(jaimiti)	Anuradha k. Ramchandan vagovaski	Arunodya
9	Ganit sabke liye(trikonmiti)	Anuradha k. Ramchandan vagovaski	Arunodya
10	Ganit Sabke liye(Ankganit)	Anuradha k. Ramchandan vagovaski	Arunodya
11	Ganit shurwati gatividhiyan	Madan Lal, Bhagwan Singh	Vaani
12	Ganit ka gadbadjhala	Vipin Bihari Saxsena, Prabodh Mishra, Satish Kanoongo	Vaani
13	rupantar kalan	Dr. Braj Mohan	Vaani
14	Vedic bijganit	Vrendra Kumar, Shailendra Bhushan	Granth Academy, Delhi
15	Ganit Gatividhiyan(ginti talika k jadu)	Dr. R. P. Singh	Vaani
16	Maya varg	Dr. Braj Mohan	Vaani
17	Ganitiya Kosh	Brajmohan	Vaani
18	Ganit ka Itihaas Chitravali	Shakulntala, Brajmohan	Vaani
19	Aadhunik Ganit Part 1 to 5	S.P Nayar & Jaideep Agarwal	Peetambar
20	Everyday Math Demystified, 2nd Edition	Stan Gibilisco	Mc Graw Hill
21	Practice Makes Perfect: Fractions, Decimals, and Percents	Erin Muschla	Mc Graw Hill
22	Beginning & Intermediate Algebra	Andrea Hendricks,Oiyin Pauline Chow	Mc Graw Hill
23	Practice Makes Perfect Basic Math	Carolyn Wheater	Mc Graw Hill

Mathematics and Mathematics TLM

Vikas sharma

Mathematics is frightening, children are afraid of mathematics, mathematics is a difficult subject, etc. The sentences we hear about mathematics. This approach, which is of great importance, allows children to go without mathematics, whereas in reality they did not even go to mathematics.

Knowing children continue to do math in life, play children, introduce themselves to their environment, eat food, fight in children etc. In every work of children, there is math.

The teachers and the elders must understand that mathematics is not merely a concept which is to be filled with learning through a position, but its miracles are relevant in every field of life.

In today’s environment, there has also been another heavy responsibility on mathematics. To keep children calm and calm Of course, today’s children are fast flowing in every way but many capabilities of the same generation of equally important ones have also vanished. These include being calm down, reading a book, or being absorbed in such a process which takes time to complete and does not get instant gratification like Maggie noodles. Nowadays the problems of instant life are solved by mathematics.

Mathematics works to create a better personality. Arguably creates a balance in creativity, imagination, creativity, imagination, and daily life.

In all the methods of teaching of mathematics, such as synthetic, analytical, arrival, incorporation, inductance, RME, sports law and problem solving method, etc., two methods which I personally do not like are those by behavioralism and business. It is not logical to take the concept of concepts and concepts without intimacy, without knowing it. I myself have taught most of the mathematics by these two methods.

There is no need for more TLM for mathematics orbit. The clarity of the teacher becomes the most important TLM for the communication of the teacher and his vision and the purpose of mathematics. Teachers can identify children in their language with interesting mathematics. They are story-parts, in which there are characters with whom children can have a vibrant relationship.

The teaching of mathematics cannot be done with suppression, because due to inadequate understanding, the problems which are born in the first year only, the teacher has to suffer later.

Small-small objects are helpful in teaching mathematics, such as skeletons-stones, small wooden pieces, leaves, cards, matchboxes. It is important to keep in mind that we only use tangible objects in mathematics teaching so that children can reach intangible consonants and abstract thinking reflexes.

The clock in the classroom, the calendar itself has interesting TLM. Who cooperate in compiling comprehensive concepts of mathematics. The black board of the class also plays the role of a strong TLM. Children’s involvement is very important in this. Expecting more TLM than the market, T.L.M. has more significance in preparing TLM than with the teacher’s children in sports. Children want to hear their views heard by others.

Other TLM teaching cards which can be deposited at different places according to the concept of the subject and the concept. Materials, Flash cards, trunks, rods, puppets, curtains, masks etc. needed to organize work-books, activities.

Mathematics is not a water tank, but it always keeps the flow in it, with its flow, it runs on many ideas, techniques and innovations.

Nature of Mathematics and its relation with school education

Amitabh Mukherjee

Background

In all school subjects, mathematics is such that its status is unique – but contrary to it. On one hand, it is considered an essential part of school education. Starting from Class 1, Class 10 is taught as a compulsory subject. It is often considered a type of criterion that accordingly: the same person is educated, who comes to mathematics. On the other hand, it is considered to be the most scary in school subjects, and because of this, the fear of fear and failure in the students is pervasive. Even those adult people who have successfully passed the school round can be heard saying: “I have never understood mathematics properly at school.” (While some of us did the science of Delhi University in 1992 If we started the School Mathematics project in the Education and Communication Centre then our motive was to treat this fear. For the recent situation, you have the position of National Focus Group formed on Mathematics Education Action Paper can read this URL http://www.ncert.nic.in/html/pdf/schoolcurriculum/position_papers/Math.pdf)

The paradox described above produces many questions. Some of them are: What is math and why should we teach it to school? Is the problem coming up with school math in relation to the nature of mathematics, or is it taught, or is there anything to do with both of these things? Can all children read mathematics at a certain level? What kind of mathematics should we teach in school? And how should you teach?

It may be ambitious to try to answer all the questions above, perhaps even daring. In this article, I will pay attention to some of the changes made in the last five decades about school maths, and their impact seen in India in the last few years.

Mathematics for all

Regarding the context of Universalization of Primary Education (UEE) in any contemporary discussion about school mathematics, it is important to keep in mind. Today, UEE appears to be an achievable goal rather than a distant dream. The next stone universal secondary education (USE) of the mile will also definitely become a major part of the academic agenda in the coming decade. So when we talk about school math, then we are talking about something which is addressed to all schoolchildren.

Can everyone learn mathematics? Fifty years ago, the answer was clearly ‘no’. Even today, we can hear adult people say something about children that they will never be able to learn mathematics. In this regard, the position paper described above gives a clear view of how UEE / USE expectations are answered:

‘Our approach to excellent mathematical education is based on two beliefs that all children can learn mathematics and all children should learn math. Therefore it is imperative that we provide all the best mathematical education of the children.’

After this the question arises, what kind of mathematical education will meet the needs of all children? In order to answer this, we need to get some clarity about the objectives of mathematics education.

“Knowing that all children are studying mathematics up to the eighth grade (and even up to tenth), the main purpose of school math teaching cannot be to create a mathematician.”

The aim of the school’s mathematical education

Knowing that all children are studying mathematics up to the eighth grade (and even up to tenth), the main purpose of school math teaching cannot be to create a mathematician. And in the same way it cannot be helpful in generating a scientist or engineer, although mathematics is very important and special place in reference to these areas. Then what is the purpose of school mathematical education? The position paper says:

Simply put, the only main goal – the mathematization of the child’s thought processes.

In other words, the goal is to learn to think about the world in the language of mathematics, and to develop such thinking which is typical mathematical. On the other hand, in the last five decades, there are some different things to look at while running courses and textbooks in the country. It appears that ‘university education’ or perhaps ‘IIT education’ has been dominated by the subject matter and style of school mathematics. So there is no wonder that went to school in the past and there is no love for this subject in the mind of most students going to school today.

What is math?

If the main goal of mathematics education is to make mathematical thinking, then it is necessary to have a brief agreement on what is the mathematics created from the key. If you ask a common person the question “What is math?” Then it is more likely that you will get quick answers “add, subtract, multiplication, parting”. (And on thinking or asking, people usually add algebra and geometry (geometry) and add them to these points.) These actions are definitely an important part of mathematics, but only mathematics or mathematical thinking Cannot be defined. I will not try to give any definition; Rather, I will give you some examples of mathematical thinking-

“The door is between me and the wall.”

“There are about fifty toffee in the jar.”

“This glass is tall but narrow. There will be less water than a wide mug. “

“Nineteen and fifteen is … one less than twenty and fifteen … i.e. thirty-seven.”

“If you go by road you will take about fifteen minutes to reach the station, but a shortcut That is where you will reach ten minutes. “

At first sight it will appear that there is no evidence of mathematical thinking in the first statement. But spatial relationships for school-age children such as ‘above’, ‘below’, ‘in between’, ‘beyond’ are an important part of mathematization.

Mathematization of thinking is not a complete or one-diminishing event. During and after school life, even children and adults, mathematization continues. On the other hand, there may be many things in our courses that students learn without any associated processes, and hence they cannot contribute to the ‘basic education’ of mathematics. Here are some examples of things that, if they do not get the support of appropriate class processes, they are finally taken away.

“To divide anything by m / n, you have to multiply it by n / m.”

“The value of the smallest equation of a and b is equal to the number coming on when b is multiplied by a to a bar, dividing the number coming from the greatest consonant of a and b b.”

“The area of all the triangles with the same plane and height is equal.”

Problems of abstraction

Little kids learn about the world playing with things. Therefore, they also introduce mathematics in this manner. But with mathematics, even abstraction exists in the first grade. Look at this sentence taken from the lowest level of school math:

“Two and two make four together.”

This statement is about two and four, which are intangible elements. There is something similar in bicycle wheels, socks and two apples: a property which we can call ‘two-water’. “Two apples and two other apples make up four apples”, it is a statement about the physical world, which can actually be tested in contrast to the abstract statement given above.

Martin Hughes’s 1986 book “Children and Numbers” has many conversations with children, showing that even before the children started to go to school, “there was a surprisingly good knowledge about the number” is”. But this knowledge does not express in the formal language of mathematical organs. It may be that a child correctly calculates the number of bricks placed in a box, and tell that if it has eight bricks, then adding two more will total ten bricks. But after asking this abstract question from this child, she will not find anything “how many are eight and two?”

This type of experiment has been done by many other people later and their outcomes are similar. Their implications for classrooms is that activities to be done with solid objects should be done before using the formal, abstract language commonly used to express mathematical content. Apart from this, special attention should be given to our classical activities on informal-to-formal changes.

Composition of mathematical knowledge

Since the basic elements of mathematics are abstract, we may have to think whether their existence is objective and independent of the human brain, or they are the brain’s produce. This is an issue on which philosophers have been debating at least from the time of philosopher-mathematician René Descartes (1596-1650). For example, are the numbers really ‘somewhere’ or they are only in our brains? Bertrand Russell, the essence of the different situations of this topic, has been presented in his very readable short book “Introduction to Mathematical Philosophy”. Here, I will get away from this discussion for a long time and draw attention to a slightly different aspect of the issue, an issue that is directly related to the class.

After the work of Piazza, Vygotsky and others, it is now generally accepted that children do not passively acquire knowledge. Instead, each student actively creates knowledge for itself. The process of knowledge-building involves reconciliation and behaviour with the outside world as well as other people. So, there is no point in whether mathematical elements have any objective existence: we all have to go through the process of building them for themselves.

Although Piazza did not care much about school mathematics, his work directly influenced the mathematical study of the early period. For example, Constance Kami has argued that small children do not find arithmetic, but re-invent them. For the first time, this will be contrary to the claim that children of pre-school age have good knowledge of mathematics or at least numbers. However, there is no contradiction in this, if we look at the fact that children are already filled with various types of mathematical references before they enter the school.

Is mathematical knowledge unique?

Before we turn to the meanings of these ideas for classes, we have to solve this issue so that which mathematics should be taught. Should the choices of our courses be determined only by the framework of mathematical knowledge? If yes, then is this structure unique and universal? If this question is placed in front of a professional mathematician then the possible answer would be an obvious ‘yes’. But, we must remember that members of the mathematical research community are a self-defined limited social group. As has been argued earlier, the purpose of school math education is not to get membership of this elite group for the students.

TLM

1.Angle Machine

This teaching learning aid is used in geometry for understanding

Alternate interior angles
Vertical opposite angles
Corresponding angle
Interior angle on same side

2.Factor circle – This teaching learning aid is used for understanding of Factors.

3.Electric circuit -This teaching learning aid is used for assessment and practice of concepts.

4.Pythagoras theorm 1

This teaching learning aid for visulaising Pythagoras theorem.

5.Pythagoras theorem 2

This teaching learning aid for display Bhaskarachay proof of Pythagoras theorem.

6. 360 degree Protractor

This teaching learning aid is used in geometry for understanding angles and its measurement.

7. Maths Colony

This teaching learning aid display about geometrical shapes.

8. Division machineThis teaching learning aid for understanding concept of division and its algorithm.

9.Eat That Apple Puzzle

10.Alpha Magic Square

This is a special magic square , Numbers , english name of those numbers having number of alphabets and count those alphabets – all follow Magic square rule!

11.Protractor 180 degree
This teaching learning aid is used for teachin angles and its measurement.

12. This teaching learning aid dispay understanding of Real Numbers.

13. This teaching learning aid shows various pattern of Pascal Trianlge.

14. This teaching learning aid is famous mathematical puzzle for logic.

15. This is an interesting puzzle of Matchsticks.

16. This teaching aid is for fraction uderstanding , what is the total of this peacock in fraction ?

17. This teaching aid is for learning counting specialy concept of zero.

18. This teaching aid is used for concept building of fraction

19. This is an interesting game of numbers. (1 to 8)

20. This is an important teaching aid of fracion learning.

21. This charts shows how we can divison to our students differently.

22. Mathemat – This teaching learning aid is multipurpose aid that can be used to learn various concepts at all levels of elementary mathematics.

23.Jodo Straw– The secret of Jodo is in the unique and original connector, a vectorial connector vertex whose arms can be bent to take any direction in space.

24. Jodo cubes– These colourful blocks are fantastic multipurpose blocks that can function in myriad ways as a teaching aid and as a toy.

25. Number Sticks –It has been seen that many children see numbers only in terms of digits and they do not think about quantities represented by the numbers. Therefore it becomes imperative to give enough counting experience to children.

26. Number catcher– This teaching aid is used along with Ginmala.

27. Fraction Kit-Fraction remains a major hurdle in the teaching of elementary mathematics. Children need to participate in appropriate activities to dispel this misconception. This fraction kit suits this objective.

28. Ganit mala – This teaching learning aid is for Number system- counting, addition –subtraction, multiplication, factors, LCM/HCF etc.

29. Decimal kit –There is tendency to confuse decimals with whole numbers with which they are already familiar. This teaching learning aid is to help children understand the decimal notation and related place value by combining use of contexts and materials.

30.Rangometry- Rangometry is a real treasure trove for children. Here shapes and colours combine together to form beautiful rangoli patterns. And also hidden in them is a whole world of geometry.

31. Place value cards- This teaching learning aid is used for understanding of place value writing.

32. Place value card (Decimal)- This teaching learning aid is used for writing decimal numbers.

33. Currency notes- This teaching learning aid is used for place value understanding and in number system.

34. Apollonius’ theorem- This mathematical model is used to verify Apollonius’s Theorem.

35. This is a teaching aid to verify this algebraic identity.

36. This model is a teaching aid and is used to verify the given algebraic identity.

37. Tessellation Kit- A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Tiling which go on repeating leaving any space in between are also called tessellations. These shapes help children in developing interest in geometry.

38.Rectangular geoboard- This is a teaching aid used to verify the properties of lines, angles and different polygons and the results regarding their measures and areas.

39. Circular Geoboard- This is a teaching aid and is used to verify various properties of a circle. It is a rectangular board with nails fastened equidistantly on a circle, its centre and some more outside it.

40. Construction –ellipse –This model is a teaching aid for the construction of an ellipse. Actually the soft-board that is given for a parabola can be used for this construction also.

41. Binary converter-This model is a teaching aid which can be used to convert decimal representation of a number into binary representation.

42. 4*4 colour puzzle- This is an interesting puzzle.

43. Pegboard puzzle- This is a mathematical puzzle.

There are 11 pegs on a board with five white and five black counters arranged at the two ends of board; in the puzzle you have to interchange the positions of the white and black counters by observing puzzle rules.

44. Number strips-This teaching aid is used understanding counting order.

45. This model is a teaching aid and is used to verify the given algebraic identity.

46. This model is a teaching aid used to verify a cube plus b cube algebraic identity.

47. These teaching aids is used to verify area of trapezium, area of Rhombus, Area of triangles, area of parallelogram.

48. Soma cube- There are very few puzzles or mathematical pastimes which are as interesting as the Soma cube. It consist of seven pieces of different shapes .

49.Tower of Brahma- puzzle All the discs are on one of the pins with the larger disc always below a smaller one. The problem is that all the disc have to be transferred to either of the pins in a minimum number of moves.

50.This mathematical model is a teaching aid used to verify Pythagoras’ Theorem.

51. This model is a teaching aid for verification of the following property of intersecting chords of a circle.

52. This model is a teaching aid for the verification of the following to the Pythagoras.

Corollary: In a right triangle BAC, if AD is the perpendicular to the hypotenuse BC, then AD² = BD. DC.

53. This mathematical model is used to verify the angle bisector theorem in a triangle.

54. This is an interesting puzzle.

55. This book is for mathematical puzzles.

56. This mathematical model is a teaching aid used to verify the Pythagoras’ Theorem.

57. This model is a teaching aid used to verify the above identity.

58. 5*5 colour puzzle and an interesting game

59. Parking puzzle- This is a mathematical puzzle.

60. Tangram – An exciting and Challenging game to keep you questioning, exploring and discovering for hours.

61. This is a challenging mathematical puzzle.

62. These teaching aids is used for verify area of quadrilaterals.

63.Interlocked loops Puzzle

64. Crazy cubes

65. Disc – Divisible by Seven

66. Fraction strips–

67. Make a cube-

68. Board of geometrical shapes.

69. Numbers game (1-8)

70. Dodecagon and Square

Display work-1

DIET faculty Dr. Surbhi observed the resource centre and appreciated this effort

Display is all about Perspective, Content and Pedagogy of Maths .

1.This display shows large number which you can imagine.

2.This display is about different behaviour of geometry in different space – Euclidean ,Non-Euclidean and Hyperbolic space.

Vitruvian Man is Leonardo da Vinci’s own reflection on human proportion and architecture, made clear through words and image. The purpose of the illustration is to bring together ideas about art, architecture, human anatomy and symmetry in one distinct and commanding image.

4. Maths is used every single day in a plethora of different ways despite its ambivalent response by a lot of disgruntled students (and adults).

In an attempt to break maths down and explain its uses (and necessity), explains how all maths is related and how it can be applied to real world problems

5.Mathemtical modelling of Pi

6. We get aims of education and other values from our constitution.

7. Aims of Maths education from NCF -2005.

8. What is Abstraction in mathematics?

9.Different perspective towards Maths education-

10.Perspective of learning

11.Maths is everywhere, here is maths of our Planet.

Note for Number System TLM

Positional Number System

Vikas sharma

Mathematics scattered in our lives, when children and teachers seem to be dull and cumbersome with it , this becomes a very serious question how to enjoy living with it.

Mathematical curriculum is not only disappointing for those who oppose it, but also does not present any challenge for talented children. Problems, exercises and evaluation methods are mechanical and repetitive and have been strongly emphasized in computation. It has not been given place for mathematical areas such as local thought. (NCF 2005)

Concept of resource centre strategies to combat this question –

Place value

Mathematical concepts are abstract, in an idea form, which is an understanding of human. Mathematical concepts progress further with the foresight of some proven beliefs which are themselves proven, or with the consistency of reasoning on those that cannot be proven.

Number knowledge is one of the basic understanding of the world of mathematics, the difficulties further increase due to the absence of this, but this weakness also becomes the first step in making distance from mathematics.

Number understanding consists of three main dimensions – number of names, picture of number, meaning of meaning or understanding. Creating an understanding of the meaning of the name and the picture, requires great mental retention. Like 5, the picture can be easily displayed by adding 5 to the name of 5 but it is all about joining the wire with understanding of the amount of 5. That is why it is necessary to start number knowledge with great restraint, proceed with understanding with the intangibility of numbers, with a number of numbers from 1 to 9, should carefully reach the understanding of 0 after the long work. In terms of zeroes as a double understanding number and in the context of positional values, the number is moving towards the most important aspect of knowledge – understanding the positional values in the ten based number method.

The understanding of the Place values has been made by deciding the long mathematical journey of many civilizations, with the understanding of its concept, mathematical problems of elementary classes are associated with it –

Seeing 15 to be made of 1 and 5, which makes 15 and 51 large numbers and a small number of confused

Comparing the number of digits on the basis of numbers, such as 303 and 0303, the number of 4 digits is bigger

Write one hundred five to 1005 or read 1005 to one hundred five

Confused about the place values of numbers like 343 left to the left, three hundred or three hundred etc.

These problems make the operation worse and the standard methods do not even give the understanding of the place values to solve the operation, such as adding 35 to 25, adding 5 in 5, then adding 2 to 3, standard methods, the child’s mental There is no synergy with methods like adding 25 and 35, adding 20 and 30, then joining 5 and 5, joining the ten earlier ones, reaching 50 + 10, 60.

Therefore, there is a need to create a strong base of understanding of local values at the initial level, as well as the need to understand the mathematics of operations before reaching standard methods.

The understanding of the place values can be started from the concept of counting in the group, counting ten numbers initially in small groups like group of 2, group of 3, then see the group of two ten in 20 , See the group of 3 to 30 in 30 To understand this understanding, understand a game.

Introduction to Dean’s Block

The whole class will be included in different ways, by sitting in front of the two groups of two children, watching the other children, the teacher will be involved in the score of the children’s score and the commentator. The names of all the four groups will be written on the board, the units will be placed in the middle of a lot of children (pearl or counter) dean’s block, 2 more children will be in the role of bank, who have units of dean’s block, hundreds Will be flat.

One of the four groups will throw the dice first, pick up the number of units it will get, similarly the next group will move and respectively, the units will get equal number of points.

Important Rule – As soon as a group has ten units, they will collect them in the bank and take ten strips (ten) of the same, after having ten stripes, they will collect one flat (hundredths) by depositing them in the bank.

Teacher’s Role – The teacher will play the role of commenter for the whole class, asking the number on the dice to speak to the louder person and speak to everyone. As soon as 5 comes to the dice, he will ask, what will come, will tell you in the table, correcting the correctness of the group or not accurately. The table unit, the tenth and the hundredth column, will be made of columns.

As the game progresses, the group units will be replaced by tens, the tens will be changed in hundreds, the time frame will be set before the start of the game, when the group completes the units, tens, and hundreds Tell the teacher to match the table, all of them – their numbers will be looking on the board as if a group has 4 units, 5 stripes and 2 flats. The students will share their names in their table with the number of 254 in the number of two hundred, five tenths and 4 units. If there is no one, he will also be given an emphasis on Zero writing. Before writing the unit on the right in the number and then multiplied by 10 on every left side, pre-preparation of mathematics can also be started through this game.

Note for Fraction TLM

Vikas sharma

Reference: Mathematics capacity building workshop at CSPC office with Learning assistant

(Based on memory, important points of the session)

Today we discussed about fraction and it’s TLM. Fraction has been remained challenging topic for both students and teachers. It was seen anyone can do operations on fraction easily but making its visuals produced difficulties. E.g. – gives ½ when ask for 1/3. We mostly see two whole number in one fraction number like 2/3, we see 2 as numerator and 3 as denominator, and here we lost the quantity sense of fraction number which is an important phenomenon in dealing with fractions. It take time to develop meaning of fraction numbers.

In counting we have definite interval between two numbers but it is not in decimal/fractions. Here we go for measurement. Dealing with fractions multiplying and division relatively easy than addition/subtraction.

We can use term Ordered pairs for fraction. Numerators and denominators in a definite order make a pair that is fraction.

Fraction can be shown on number line and each fraction has a definite point on number line.

One meaning of fraction is represent a part of a whole. Whole can be a thing or group of things. It is necessary in any condition to represent in fraction that it’s all part must be equal.

In a proper fraction numerator is smaller than denominator and in improper fraction numerator is always greater than denominator. Improper fraction can be also written in the form a whole and a part, In this case it is changed in mixed fraction. Each proper and improper fraction has many equivalent fractions.

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CIRCLE SQUARE STRIPS

We can make three type of material (TLM) by using circle, square and strips for Fractions (Ordered pairs). Circle roll, no other type of material roll, children can enjoy seeing whole while roll. On the other hand square model is advantageous for multiplication and for division chocolate-chip model can be useful. Fraction T.L.M must be proportional while in whole number T.L.M can be both proportional and non-proportional.

We make circles for ½,1/3,1/4,/1/5,1/6,1/8,1/9,1/10 not for 1/7 because of these have divisibility property with 360.We make it one set on Ivory sheet and 1 set on card board.

Ivory sheet material along with card board use to understand it in both ways as part of whole and equal part from the whole as following-

With Ivory sheet With card board

Above activity is helpful to make meaning of fractions. another activity is give a person material that is made by card board from his back ,by touching with his hands he can try to tell what part of fraction it is , starting this activity with ½,1/4,1/3 and later on after practicing ¼,1/5/,1/8 etc. ,to differentiate among 1/5,1/6,1/8,1/9 need a good familiarity with these materials.

Another activity is to make whole with the use of more than on unit fraction. As-

½+ ¼+ 1/8+ 1/8 =1

1/2+ ¼+2/8 = 1

Fraction scale is another T.L.M that we made from 10” *2” ivory sheet. We use its both side and its 4 edges as shown in picture-

A4 size paper has unique advantage on other sizes of papers. It has 297 mm *210 mm .It is √2:1.

It is suggested by many to use paper folding materials but problem remained it only 2, 4, 6,8,10 possible denominator. A4 size is easily available and above problem is simplified here. 210 is divisible with2, 3, 5 and 7. It is possible to make material with denominator 7.

One of use fraction scale is to make fraction wall. It produce meaningful visuals in the minds of children if they watch it daily in their classrooms. For making 1/9 we can use following construction-

Divide A4 sheet (length ) in to 3 equal part, draw the diagonal of first part ,now draw bisector of first part, join another diagonal point to mid-point (top to bottom),now draw perpendicular on intersecting point. This length is 1/9.

This can be proved with the similar triangle properties, we can take an idea from above picture.

Fraction wall –

Some application of fraction wall-

As part of whole increasing, their size on fraction wall decreasing. This help making visuals in the mind of children.

Understanding of Equivalent fraction

Addition /subtraction of equivalent fraction

Addition of same denominator like ½ +1/3 can be seen 3/6 +2/6 easily.

The difference between sizes of ½ to 1/3, 1/3 to ¼ .1/4 to 1/5 ………is decreasing.

When we were making these material we did so many mistakes and had so many confusion in spite of all instruction was already written on white boards or told us so we should take care with our expectations with children.

There is a claim that Indian Mathematics is not really Mathematics since it was not axiomatic, it was related to the world whether in calculation of planet positions or dimensions of the sacrificial pyre, it was not really logic since it was explicitly related to the empirical and so on.

Indian Mathematics was explicitly engaged with the natural world and is in some sense grounded upon the nature of our cognition as well as the nature of the world. It was more about doing and in a sense closer to the constructivist paradigm. A famous example is the Indian mathematicians’ pragmatic acceptance of square root of 2 (as something that is used in construction, for example) as against its rejection by the Pythagoreans on idealistic grounds.

Another one uniqueness is the way Indian mathematics written, it is written in poetic form and less use of modern symbols and more appeal to common mass and give insights to use this form in teaching maths to develop interests among learners.

Here is list of 14 great Indian mathematics date back from Indus valley civilization to modern times.

Lagadha (c 1300 B.C): The earliest mathematician to whom definite teaching can be ascribed to, and who used geometry and elementary trigonometry for his astronomy.

Baudhayana (c 800 B.C): He is noted as the author of the earliest Sulba Sutra which contained several important mathematical results; the now known Pythagorean theorem is believed to have been invented by him.

Yajnavalkya (c 800 B.C): He lived around the same time as Baudhayana and is credited with the then-best approximation to pie.

Apastamba (c 500 B.C): He lived slightly before Pythagoras, did work in geometry, advanced arithmetic, and may have proved the Pythagorean Theorem. He used an excellent approximation for the square root of 2 (577/408, one of the continued fraction approximants).

Aryabhatta (476-550 C.E): His most famous accomplishment was the Aryabhata Algorithm (connected to continued fractions) for solving Diophantine equations. The place-value system was clearly in place in his work and the knowledge of zero was implicit in Aryabhata’s place-value system as a place holder for the powers of ten with null coefficients.

Daivajna Varâhamihira (505-587 C.E): His knowledge of Western astronomy was thorough. In 5 sections, his monumental work progresses through native Indian astronomy and culminates in 2 treatises on Western astronomy, showing calculations based on Greek and Alexandrian reckoning and even giving complete Ptolemaic mathematical charts and tables.

Brahmagupta ‘Bhillamalacarya’ (589-668 C.E): His textbook Brahmasphutasiddhanta is sometimes considered the first textbook “to treat zero as a number in its own right.” Several theorems bear his name, including the formula for the area of a cyclic quadrilateral: 16 A2 = (a+b+c-d)(a+b-c+d)(a-b+c+d)(-a+b+c+d).

Bháskara (c 600 – c 680 C.E): He was apparently the first to write numbers in the Hindu Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata’s work. Bhaskara’s probably most important mathematical contribution concerns the representation of numbers in a positional system.

Mahavira (9th-century A.D): He is highly respected among Indian Mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle; rhombus; circle and semicircle. He asserted that the square root of a negative number did not exist and gave the sum of a series whose terms are squares of an arithmetical progression and empirical rules for area and perimeter of an ellipse.

Sridhara (c. 870 – c. 930 C.E): He wrote on practical applications of algebra and was one of the first to give a formula for solving quadratic equations and gave a good rule for finding the volume of a sphere.

Madhava of Sangamagrama (1340-1425 C.E): He did work with continued fractions, trigonometry, and geometry. Madhava is most famous for his work with Taylor series, discovering identities like sin , formulae for , including the one attributed to Leibniz, and the then-best known approximation.

Srinivasa Ramanujan Iyengar (1887-1920 C.E): He produced 4000 theorems or conjectures in number theory, algebra, and combinatorics. Because of its fast convergence etc.

Prasanta Chandra Mahalanobis (1893-1972 C.E): He is best remembered for the Mahalanobis distance, a statistical measure. He made pioneering studies in anthropometry in India. He contributed to the design of large scale sample surveys.

Satyendra Nath Bose (1894-1974): As an Indian physicist, specializing in mathematical physics, he is best known for his work on quantum mechanics in the early 1920s, providing the foundation for Bose-Einstein statistics and the theory of the Bose-Einstein condensate.

https://youtu.be/F-fbqD2ucqo Video link for above article.

Reference- Learning curve article of BS Rishikesh and Sundar Sarukka, Wikipedia, Quora,various you tube channel and google searches and google images.

-By Vikas sharma

General Websites

http://www.mathforum.org)

http://www.cimt.plymouth.ac.uk

http://www.mathcats.com

http://www.counton.org

http://illuminations.nctm.org

http://www.shodor.org/interactivate

http://www2.gisd.k12.nm.us/GMIWebsite/IMathResourc

es.html

http://mathematics.hellam.net

http://www.mathsnet.net

http://nlvm.usu.edu/en/nav/vlibrary.html

http://www.primaryresources.co.uk/maths/maths.html

http://www.proteacher.com/100000.html

http://www.trottermath.net/contents.html

http://www.msteacher.org/math

http://recmath.org/Magic%20Squares

http://www.shyamsundergupta.com

http://www.woodlands-junior.kent.sch.uk/maths/brokencalculator/

index.html

http://durham.schooljotter.com/coxhoe/Curriculum+Link

s/Numeracy

http://www.mathplayground.com/Algebra_Puzzle.html

http://mathbits.com/MathBits/AlgebraTiles/AlgebraTile

http://www.worldofteaching.com/mathspowerpoints.html

http://www.mathsisfun.com

http://www.coolmath4kids.com

http://www.mathplayground.com/Calculator_Chaos

.html

(http://www.wordwizz.com/pwrsof10.html)

MathBitsNew07ImpFree.html

http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles

MathBitsNew07ImpFree.html

http://www.cyffredin.co.uk/

http://library.thinkquest.org/3288/fractals.html

http://www.shodor.org/interactivate/activities/Tessellate

http://www.mathsphere.co.uk/resources/MathSphereFre

eGraphPaper.html

http://www.korthalsaltes.com/

http://www.mathpuzzle.com/

http://www.johnrausch.com/PuzzlingWorld/contents.html

http://www.cut-the-knot.org

http://www.delphiforfun.org/Programs/Indices/projectsI

ndex.h

http://www.10ticks.co.uk/s_dailyPuzzle.aspx

http://www.archimedes-lab.org/index_teachers.html

http://www.pedagonet.com/brain/brainers.html

http://www.gymnasiumforbrain.com

www.thinks.com

S.no. Name of the Publisher Website

Children’s Book Trust

Eklavya

Flipkart

Macmillan Publishers

National Book Trust

National Council of Educational Research and Training

Navnirmiti

Scholastic India Publishing

Pratham Books

School Zone Publishing www.schoolzone.com

Vidya Bhawan Society

Digantar Khel Kud Society

Homi Bhabha Center for Science Education, Mumbai

The Mathematical Sciences Trust Society

www.childrensbooktrust.com

http://eklavya.in/

www.flipkart.com

http://international.macmillan.com

www.ncert.nic.in

www.nbtindia.org.in

http://www.navnirmiti.org/index.html

www.prathambooks.org

www.scholasticindia.com/publishing.as

http://www.mstsindia.org/

www.hbcse.tifr.res.in

www.vidyabhawan.org

Some NGOs working in the area of Math Education

Eklavya, Bhopal

Homi Bhabha Centre for Science Education, Mumbai

Jodogyan, Delhi

Navanirmiti, Mumbai

Shishu Milap, Vadodara

Suvidya, Mysore

Vidya Bhawan Society, Udaipur

Sr . N0.	Topic	You tube Video link
1	Maths TLM टोपी बनाना संग कहानी Geometry shapes learning activity	https://youtu.be/KR1pHO2FkoE
2	Maths TLM- Activity for learning type of angles , Best Geometry Activity /TLM	https://youtu.be/8aeft-7LzOA
3	Maths TLM- Addition and subtraction of integers counter game NCERT activity	https://youtu.be/Q8VabGFGC0Y
4	Maths TLM working model Integers additions and subtractions game	https://youtu.be/1NXAVBWBHcc
5	गणित के TLM- Division Machine for Primary classes	https://youtu.be/p3Mrf_oULzo
6	Area and perimeter story telling NCERT activities Maths TLM for primary classes	https://youtu.be/qrKz2B6PpKE
7	कवि की सूझबूझ और बादशाह अकबर भिन्न पढ़ाने के लिए कहानी maths TLM NCERT story	https://youtu.be/hGNO3Gv2N-w
8	गणित के TLM- खेल climb and ladder game primary teaching maths fun	https://youtu.be/SZRNt6sbx6g
9	गणित के TLM algebraic expression and identities geometrical proof with paper cutting	https://youtu.be/sEaXrZQ0Nt4
10	angle sum property of triangle – Inductive and deductive proof (Hindi) Maths TLM	https://youtu.be/czKbuCjmHM4
11	Maths TLM Teaching fraction using Strips, concept, equivalent fraction and operations	https://youtu.be/c-sZazpf_gA
12	गणित के खेल : खेल बोर्ड ( गिनती पढ़ना व् लिखना सिखाने की गतिविधि) Maths TLM/Project	https://youtu.be/Wzd3uiL0SIU
13	origami for kids – 2 shandaar topi Maths tlm कागज का मुकुट learning with fun	https://youtu.be/TPXiLI6UC1w
14	MATH FAIR 1 : Child centered activities, best pedagogy tool for learning, MATHS TLM and Project	https://youtu.be/xV3JGimrKR0
15	AREA AND PERIMETER : RELATIONSHIP ,ACTIVITY TO UNDERSTAND AFFECT ON PERIMETER CHANGE WITH AREA TLM	https://youtu.be/rzUtTiQ44yA
16	अब पहाड़े रटना नहीं How to learn multiplication table with easiest way tricks part 2 Maths TLM	https://youtu.be/6uoDmLCyqPg
17	Maths TLM place value writing using TLM ARROW CARDS (Number system)	https://youtu.be/A8CJ_pSG6FM
18	गणित के खेल Tinkering mathematics 2 सोचने समझने की गतिविधियाँ models for maths /TLM and Projects	https://youtu.be/qK4kqu8HvN8
19	गणित के खेल – Maths TLM/Project chess board puzzle pattern activity, Tinkering activities	https://youtu.be/uawjJ5WcvO0
20	Area of triangle Activities with 3 models Maths lab TLM Verify formula	https://youtu.be/9AxEfMYLz6M
21	( a cube – b cube )Geometrical explanation and derivation of Algebra identity	https://youtu.be/D53n8fQV95c
22	Maths TLM: Activity for Verify AD²= BD×CD ,AD ⊥ BC	https://youtu.be/87C5IwIs9fU
23	Maths TLM : To verify Sum of first n natural numbers Activity math lab	https://youtu.be/w4ZQnqP7Aos
24	Maths TLM: Tower of Hanoi or Tower of Brahma or Lucas’ Tower When will this world end?	https://youtu.be/JMVGyplkoEk
25	Maths TLM: Binary converter machine	https://youtu.be/pDRMmvx3tTk