The post How Children Can Learn Mathematics From Daily Lives appeared first on The Progressive Teacher.

]]>Research has shown that most of the children have the ability to learn and be proficient in it. If approached correctly, mathematical concepts and ideas can be made graspable even before starting with any formal primary schooling.

How can operating with numbers be a fun activity and an entertaining experience and can be learnt from daily lives?

Professor Robert H. Lewis writes, ‘Mathematics is not about answers, it’s about processes’. If we understand how Mathematics can be used in our day to day lives, we would be able to grasp it. We can apply mathematics to everyday applications for ease of understanding. Whether it is about organising competitions, number games or exciting puzzles, Mathematics is everywhere!

Children as young as age one can enjoy learning numbers through fun educational games. Motivating, innovating and creating a fun and practical context for learning is one of the best ways to increase the interest of a student in a course. Applying these tactics to mathematics, which is considered by many as boring or difficult, allows the young ones to learn in a fun and dynamic manner, while developing skills and competencies that are a part of academic goals.

There are many everyday situations that demand the knowledge of mathematics. Applying mathematics in the context of everyday activities helps students understand concepts that are otherwise difficult to assimilate and understand. Every day, students should be made to solve numerical problems, not necessarily academic in nature. The idea is to encourage the use of mathematical thinking without the students perceiving it as an academic activity. For example –

- Buying daily items- Ask your child to look for a product with the lowest price to review the concepts of major and minor. You can even be specific here and tell them to purchase say two packets of biscuits for each member of the family. Here, the concept of multiplication can be made clear to him.
- Money- Ask the children to read the amount on the bill, take out the total amount to be paid, calculate the change to be taken.
- Kitchen- While preparing a recipe, children can help in the task of measuring or weighing ingredients. This can help them to review and understand fractions. A good idea is to allow children to cut slices of a pie, cake or pizza. This would help them comprehend things better without the fear of failure.
- Playing- Children, though unconsciously, already apply their number skills in many games. Understanding the concept of mathematics is possible if learning is integrated in a fun and motivating environment. In many games, without even realizing, children are already training their brains to deal with numbers. Monopoly, snakes and ladders and a lot of other games that require the use of a dice are a perfect opportunity to review the concepts of addition, subtraction along with mental calculations. Other games like sudoku, magic tricks, tambola also contribute to learning mathematics in a fun way. Moreover, some puzzles, coupled with different ways to construct geometric figures, help students understand the practical applications of geometric concepts.

Today, the use of new technologies is emerging as one of the most effective ways to motivate maths learning. On the web, we can find many games for children of all ages to play and learn mathematics in a technological environment. Games with calculators, mathematical puzzles and challenges are some activities that can be easily found on the web. These games serve the purpose of learning and are engaging and interesting for children.

Brain games are another way to raise the motivation level of children by making them independent and confident of finding solutions to problems. Such games help in developing the ability to concentrate and to think critically. For example, a number chain game can be very helpful in sharpening the memory of a child. Such games are a good exercise for enhancing the overall personality of a child. The more the application of the brain, the more the child becomes active and smart to face difficult and complicated challenges. And this is what is exactly required for Mathematics!

*Yuvraj Krishan Sharma, is the co-founder of KOMPANIONS (a Gurugram based Ed-Tech-Sci start-up that works in the areas of AR, VR, MR and gamification in education) and is a spirited and creative person at heart. He has a flair for innovation and is always excited in the creation of ‘NEW’. Yuvraj is an education enthusiast and has spent a considerable amount of time inside classrooms with learners of varied intelligence. An accomplished facilitator and a persuasive speaker, Yuvraj has a way with children and young adults and keenly explores newer ways to develop future skills in the learners of today!*

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]]>A cyclic number is like a snake chasing its tail. When you multiply a cyclic number with another number, the product has the same digits as the cyclic number. And these digits are in the same order as the original number.

Take for example, 142857.

Write it like a snake chasing its tail:

Now let us multiply it by 4: 142857 × 4 = 571428

Now in this number 571428, the head is 5 and the tail is now 8:

In the same way, if you multiply 142857 with any number between 2 and 6, the body of the snake stays the same. But the head and tail changes:

142857 × 1 = 142857

142857 × 2 = 285714

142857 × 3 = 428571

142857 × 4 = 571428

142857 × 5 = 714285

142857 × 6 = 857142

The other interesting idea in this is that you don’t actually have to do the arithmetic to get the answer. There is a very simple trick to figure out where the head of the number is and where the tail.

Say, you want to find the answer to the multiple of 6:

Step 1: Take the digit at the unit’s position ? 7.

Step 2: Multiply 6 with 7 ? 42.

Step 3: Look at the units place of the product from step #2? 2.

Step 3 tells us where the tail of the snake is. The snake ends at 2. So the head of the snake must be the number after 2 (because the snake is eating its tail, remember?) ? 8.

And the answer….magically…. is 857142.

Remember this works only when multiplying the cyclic number with multiples between 2 and 6.

That was easy. Now let’s look at a really large cyclic number. This one has 96 digits:

010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567

Now I know that the first digit is 0 and some of you may argue that it’s technically a 95 digit number. But stay with me and watch the magic.

As with 142857, the trick works only with certain multiples. This time the range is larger and the trick works for all multiples between 2 and 96.

The steps to find the tail of the snake work the same way as above::

Step 1: As earlier, take the digit at the unit’s position ? 7.

Step 2: Multiply 7 with your chosen multiple.

Step 3: Look at the units place of the product from step #2 and this is the tail of the snake.

So if the multiple is 23, the tail of the snake is at 1 [ 3 X 7 = 21 ]. But 1 figures 10 times in our long snake. So which one is it?

The answer is in Step 4: The head of the snake is the same as the tens digit of the multiple. So the head is at 2 (from the multiple 23). Can you spot the breakpoint in the old snake? Remember the tail comes before the head in the old snake. So look for ‘12’.

010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567

The answer of Big Snake X 23 =

237113402061855670103092783505154639175257731958762886597938144329896907216494845360824742268041

Want to check this? Try www.wolframalpha.com.

What happens when we multiply with a number less than 10? Then the head of the snake is at 0.

There is an additional rule that you must remember: When the multiple has either 8 or 9 in the units place, change Step 2 to this: Multiply 7 with your chosen multiple and add one to it.

Why this Kolaveri Di?

Say the multiple is 68.

Step 1: Digit at unit’s place ? 7.

Step 2: Multiply 7 with your chosen multiple ? 7 X 8 = 56.

Step 3: Tail: Look at the units place of the product from step #2? 6.

Step 4: Head: The head of the snake is the same as the tens digit of the multiple: 6

So the split point is 66. But the big snake has no 66 in it.

So add Step 4a: Add one ? 6 + 1 = 7.

So the split point is 67.

Old snake:

010309278350515463917525773195876288659793814432989690721649484536082474226804123711340206185567

Old snake X 68:

701030927835051546391752577319587628865979381443298969072164948453608247422680412371134020618556

Was that fun?

Try this yourself: What is the number if you multiply the 96 digit snake with 51?

B D Bhargava was born in Ajmer, Rajasthan in 1932. He graduated from Ruia College Bombay (now Mumbai) and did M Sc ( Pure Maths) from the University of Bombay. He retired as Secretary Marketing from L.I.C. Central Office in November 1990. Now 84 years old he lives in Agra. He loves recreational and innovational work involving words and numbers. He has developed the world’s largest dictionary of Bacronyms – where a word is described in a sentence comprising words that start with the letters of the original word, in sequence.

His work was displayed at the Taj Literature Festival in Agra in February 2013, and has been featured in numerous publications throughout the world. He has also developed many extensions of magic squares and cubes.

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]]>The post The Purpose of Mathematics appeared first on The Progressive Teacher.

]]>Responses:

1. Students dislike ‘word problems’

2. Students forget what they learnt in the previous class

3. Students get bored and want to know why they have to ‘do this’

I am very sure you will get the same responses. It could be that all of these responses do not come from each teacher but put together these would be the set of challenges teachers face in the teachinglearning of Mathematics. In my interactions with teachers across the country, it’s been the same rabbit that comes out of the same hat, every time; and I have no accomplice in the audience.

There is no magical mystery to this poser actually. The truth is that over the past several decades we in India have not really changed our approach to Mathematics. When we talk of ‘approach’ what we mean is what do we see as the purpose of Math, what are the salient features about the subject that need to be identified as core and how then do we address these areas as we design the teaching-learning programme.

Up to a few decades ago schools were still a product of the industrial age. Only the more advantaged students attended schools that educated them as future academic, cultural and organisational leaders. That system does not meet the needs of today that requires not merely mathematically literate workers but employees who understand the complexities and technologies of information- age communication, who can work cooperatively in teams and who can solve open-ended problems. Hence, as students engage with a math curriculum in school, problem solving should not be a distinct topic but should permeate the entire programme and provide the context in which concepts and skills can be learned.

That is why in any credible mathematics programme, problem solving forms a central core. For a student to understand that there is a situation that is begging a solution, to even know just that and to start thinking about solutions, sharing their thinking and approaches with other students and teachers and working out strategies is how the mathematical thinking process should evolve. The problem can be very simple or extremely complex. Mathematics then develops as a tool to solve that problem. The problem is at the centre, not the math.

Sadly, our math curricula mostly put problem solving at the end of a concept after all the maths is done. Chapter-ends in many textbooks have a section called problem solving; alienated as it were from the main part of the chapter. Let us look at an example:

Sania eats a fourth of a cake for breakfast. Her brother eats a fourth as well. How much cake do they eat all together?

This is a very simple ‘direct’ word-problem. However many third graders may not be able to solve it. They can write one-fourth, they can shade one-fourth in diagram but they fail to understand how to proceed in applying the concept. This is most often because they have not been taught how to visualise math concepts. The way they have been taught is: This is the symbol of a fourth (some teachers erroneously and mostmisleadingly call it ‘one by four’): ¼,

The top part is called the numerator; the bottom is called the denominator and so on. So then ¼ + ¼ = what? A student brought up in the ‘problem solving is central’ approach would be, on the other hand, able to feel the problem, see the situation, and intuitively know and be allowed to opine that one fourth and one fourth is two fourths just like one chocolate and another chocolate is two chocolates.

The salient features of effective mathematics learning are concept development and skill development. Both go hand in hand while an assessment for learning and an assessment of learning follow closely.

The ability to visualize is essential to mathematics. Mathematics is one of the most concrete subjects, especially so in the foundation years and middle years. That is why activities that grow out of problem situations are valuable. This leads to effective and deep concept development. Students who develop a deep understanding of concepts have a lifelong retention of them and are able to apply them with ease in any relevant situation.

To be able to ‘do’ math mentally or otherwise falls under skill development. The learning outcome of any mathematics session should be a skill no matter how short the session is. To illustrate and explain this further let us look at a case of a teacher taking a 30-minute class on adding fractions. The teacher should be able to walk into the session (and also actually out of it having accomplished the mission) with the desired learning outcome well defined in advance and in writing e.g.

By the end of this session my students will be able to add ‘like fractions’ by demonstration, orally and in written mathematical symbols.

What is also key is frequent, effective and informal formative assessment. Every classroom session should contain at least two to three opportunities to informally assess the students’ understanding of the concepts that are being studied. For example, a task asking students to show by drawing and writing a story how three fourths of the cake might be consumed could be given. The focus is still on the problem and mathematical thinking is required for this. The students’ work will give a very good indication to the teacher on how well the concept has gone down and whether or not the teacher can proceed; if not, the teacher moves towards a plan to ‘re-form’ the students understanding of the concept.

When problem solving becomes an integral part of instruction, and concept and skill development evolve out of that, students gain confidence in doing mathematics, engage with it at a superior level developing persevering and inquiring minds. There is also much deeper retention and hence greater and more permanent enjoyment for teacher and student alike. No mystery, no magic and no ‘problem’! Game over.

**Sarita Mathur** is a free-lance education consultant offering services to schools, both rural and urban, in India and abroad. An alumnus of St. Stephen’s College, Sarita has a degree in Mathematics, Education and a post-graduate degree in Operations Research. She started her career with the India Today group as Assistant Manager Marketing and then after a period of 12 years went on to join the education sector. The Mathematics background and her well-honed sense of systems and processes had her institutionalize several long lasting and important changes as Principal of The Shri Ram School placing it firmly on the map as a progressive and leading school of India. Sarita has served as a consultant on the International curriculum of the CBSE and also serves as advisor/ consultant to several curriculum companies, schools and start-up ventures. She is currently actively engaged with Scholastic India and the Shiv Nadar Foundation.

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]]>Teaching of Mathematics, particularly at the school, level is gradually becoming a challenge. The reasons could be many but I would like to discuss this under four major heads.

**Teaching Tools:**Gone are the days when the textbook published by the board was the only teaching tool available. Perhaps this was one reason why there was immense scope for a teacher to explore experiment and discover alternatives for better learning. To what extent do the teachers of the 21st century have scope to evolve? The answer is not much. Why? It is because of the resources easily available in the market and the role of a teacher is to ensure that learning happens with the optimum use of the available resources. Now the task would have become easy if there had been just two or three tools.But with more than five tools placed before the teacher to be used, the process becomes ineffective. Some of these tools include Textbooks, Workbooks, Activity Books, Graded Worksheets, Lab Activity Material Kits, Smart Boards, Customised Modules for individualised learning, Mental Maths Kits, etc. With no choice before a teacher to choose the best among these, there is every reason for a teacher ending up in a state of confusion losing interest in the profession.**Students:**Teachers being digital immigrants teaching digital natives, they will always face conflict when it comes to the choice of teaching-learning tools. Students prefer to work with technology whereas the teacher is a strong believer that Mathematics can be better learnt through written practice. Then, the only option left before the teacher is to become competent in the use of technology. However, till then do you think s/he would be spared? The answer is a NO in the majority of cases. There are some who are determined to take up the challenge, but the rest prefer to work in an environment where there is scope for them to ensure learning through conventional ways.**Parents:**Parents play a very crucial role in the professional journey of a Mathematics Teacher. How? They can either make or break the journey. It is an accepted fact that majority of the parents are concerned about their child’s performance particularly in Mathematics. Whatever may be the reason they prefer that the child should go for coaching. This is where the problem lies. On the day of PTM – it is a very common statement heard from the parents – our child is doing well in the tuition classes but we don’t understand what goes wrong in the school. Howsoever much the teacher may try to convince the parents, it becomes a losing battle. Incomplete work by the student is secondary for a parent but work left unchecked becomes the first priority. With students and parents being more important stakeholders for an organisation than a teacher, it goes without saying that the teacher has to accept the fact that s/he is defeated not by the people but by the purpose.**Management:**It is quite obvious that a teacher has to abide by the rules and regulations laid down by the Management. However here are a few questions for all the people involved in facilitating the journey of a Mathematics Teacher –- Have the teachers been given adequate freedom to be flexible in approach or have they become robots just to execute the plans mechanically?
- To what extent are the teachers involved in the selection of teachinglearning resources / tools?
- Have they been provided with ongoing training and mentoring?
- Is the monitoring process of the performance of a teacher scientific?

It is high time we spend quality time on addressing these practical difficulties of a Mathematics Teacher in the classroom. Everyone should make it a point to be one with the teacher. The Coordinators and Subject Heads are expected to demonstrate not just once but a number of times the multiple ways of effective teaching instead of giving mere advice. Only then can we multiply the joys and divide the sorrows of a Mathematics Teacher. Let us begin to patiently listen to the difficulties experienced and thus come out with solutions which add strength and subtract the hassles.

**P V Satya Ramesh** is working as a Post-Graduate Teacher in Psychology at the Shanti Asiatic School, Ahmedabad., where he teaches Mathematics up to Class X and Psychology to Classes XI and XII. He is M Sc in Psychology, M Phil in Counselling Psychology, B Ed, and a UGC NET qualified teacher. He has published value based articles oriented towards counseling all the stake holders in the arena of education in a number of educational journals. He has a strong belief in the ancient Indian Value System. He strives to inculcate courage in young minds and teaches them to always stand for what is right. He works in the direction of providing his students an environment which promotes critical thinking and ways to express their point of view without fear.

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]]>Does your child have trouble with anything to do with basic arithmetic skill? Does he have less understanding of numbers? Does he find it difficult to memorise arithmetic facts? Has he always got stuck in understanding quantity? If your child is facing these problems persistently, chances are he may have dyscalculia. But hold on, don’t get scared because his disabilities can be remediated, unlike a few years ago when even the diagnosis of a child with dyscalculia could have been altogether a very tough task, let alone handling it the way it should be. Thanks to the huge success in the research and development taking place in this field, today dyscalculia is probably just a matter of getting some professional help for diagnosis and intervention.

**What is dyscalculia?**

Dyscalculia is a type of learning disorder. As per American Psychiatric Association, dyscalculia is a specific learning disability that affects the normal acquisition of arithmetic skills in spite of having normal intelligence. Children with dyscalculia face difficulties in understanding number concepts, manipulating numbers and recalling basic mathematical facts. They usually show dislike of or anxiety towards maths. It has been observed that children with dyscalculia can also have dyslexia, another learning disorder, where a child has difficulty reading and writing.

Studies looking at the percentage of dyscalculics who are also dyslexic differ wildly in their estimates from 17% to 64% (Badian, 1999; Gross-Tsur et al., 1996; Lewis et al., 1994) but the relationship between them is still unclear. There might be many reasons – like neurological defect, poor working memory, genetics, poor teaching and unsuitable learning environment or even math-phobia – that cause a child to have difficulties in doing mathematics. But a study says dyscalculia might be caused by a difference in brain function or in brain structure, more specifically the right parietal lobe. Some of the common mathrelated problems a child with dyscalculia may face include:

- They find it difficult to memorise basic number facts. Number facts are basic procedures, rules or formulae which a child find difficult to recall.
- In spite of having good concepts of mathematics, they often end up committing errors because they misread signs, forget to carry digits, put digits in wrong place or make mistakes in carrying numbers, or don’t write digits clearly enough. Sometimes they perform operations in wrong direction.
- They often make mistakes while copying sums from either classroom board or from textbooks.
- They face difficulties in doing multi-step and complex maths problems. They face difficulty in switching between different steps in a complex maths problem. They often forget what they are doing in the mid of solving a maths problem.
- Solving word problems is a tough task for them. They get confused with the language of the problem and are unable to understand the direction or explanation.

**How can you help a dyscalculia child?**

Dyscalculia can affect any children including those who are profoundly gifted, of mediocre intelligence, or those diagnosed with a mental retardation. Most students diagnosed with dyscalculia feel frustrated and de-motivated to doing maths. So it is the responsibility of parents and educators to help these children overcome their weakness – after all, some research of over 30 years has already proved that the brain can be ‘customized’ by experience, understanding and learning. Teachers and parents can incorporate certain strategies to help these children to succeed in mathematics.

- An important thing for parents, teachers and special educators is to communicate with each other and decide on a common curriculum. They should follow a similar instructional approach.
- Teach them basic concepts using concrete objects, like allowing them to explore number concepts by counting the number of dishes on the dinner table or by subtracting pencils from a pencil box. Using real-life situations helps them to learn in more effective ways. Use more and more visual and auditory examples for better understanding.
- Encourage dyscalculic children to visualize math problems, especially word problems, by drawing.
- Complex and big problems should not be given at the initial stage. Educators should break down big math problems into smaller parts and gradually build on them with time.
- Encourage them to review the work after completing the task and modify it if necessary.
- Allow dyscalculic children to use a calculator. Calculators help them to overcome the difficulties in performing basic computation.
- Learning through play like dice game, business game or card game benefits dyscalculic children.
- Use different learning strategies for arithmetic calculations like if a child has problem in memorizing multiplication tables, he can be taught other ways to solve a multiplication problem. For example, 6 x 4 can be solved by adding 6 + 6 + 6 + 6.
- Use specialized materials like graph paper which makes it easier for a child to keep track of numbers when doing arithmetic calculation.

If a child has dyscalculia that does not mean he will fail in maths or cannot move up the academic ladder.

Dyscalculia is a recognized learning disability, so schools will make accommodation for dyscalculia students. Children with dyscalculia can be helped with remedial programmes as mentioned above, but of course the sooner the remedial programme starts, the better chance they have of overcoming their dyscalculia.

**Mausumi** is currently associated with an intervention therapy clinic in Delhi for special needs children. She is also associated with a Bangalore-based online counselling start-up where she gives her expert advice and guidance to students and parents. She has more than 6 years of hands-on experience in handling children and adolescentrelated issues as well as parent counselling. Her interest area is educational psychology. She deals with children having academic and behavioural issues. She is also an avid blogger. An M.Tech in Computer Science, Mausumi did her Certification in Child Guidance course – and Masters in Psychology later on. She worked as a software engineer at Tata Consultancy Services (TCS) for a couple of years before changing her career to a completely different field. Her desire to help young people, especially children, motivated her to change her career.

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]]>**‘A brilliant scholar might not become an excellent teacher but an average one would definitely outshine because he/she knows where the shoe pinches.’**

I am very sure about it because I am an example. I was just about average during my school days in Mathematics. Starting from the year 2003, when I actually started school teaching, I found a kind of apprehension in the students and very poor attitude towards the subject, which was basically due to lack of understanding of the subject and realising its importance in day to day life.

Most Math classes start with ‘Here’s the new formula for today; here’s how you derive in values; here’s the correct answer’. The problem is, there’s no attempt to motivate the learners whereas the motive must be to trigger curiosity, involvement and ownership of the students. The students have little say in what the topics are and the exact response is expected from everyone. It’s not surprising there is little enthusiasm for such ‘one size fits all’ approach. A very effective way to engage students is to get them involved into something that involves the topic.

Teaching would be really powerful if the activity they do is related to other interesting activities of the day. This helps students work out the bigger picture and make connections between what they are taught and what they need to know.

**Teaching with humour is an effective medium of learning and teaching too.**

I would just like to share one or two of my classroom experiences with you all. When I was teaching LCM to class VI (a class which faces a transition from V to VI) I thought let me make them do it in a play-way method: for the LCM of 2, 3 and 5, they were divided into three groups, the first was to clap at multiples of 2, second at 3 and third at 5. Then I started the counting; when I reached number 30, the whole class clapped together and everyone was surprised. Then I explained the reason behind clapping together was actually the LCM of 2, 3 and 5 i.e. 30. Also, while teaching students to multiply decimals, what I noticed was that most of the time they forgot to account for decimal place value. To help them remember the decimal point, I thought of using the decimal dance. I had read about it somewhere but I was not sure how effective it was going to be.

On the chalk-board I worked out the product of the number. Then I simply exaggerated the motion of counting decimal places. I also made a large white arch under each digit until I accounted for the correct number for the decimal places. By this method, students remembered to account for decimal place value after multiplying decimals. It had really worked and some of my colleagues also tried using this technique in their classrooms and found it successful.

These types of classroom innovations make a particular concept clear and develop interest in students to grasp and understand the concept.

- It creates long lasting memory / co-relation of a concept.
- In teaching, language as a technique can be an effective medium by the teacher to develop word power.
- Role-play and scenario analysis based teaching is also long lasting in the minds of learners.

With certain techniques in the modern world we can use various Multimedia Tools in our classrooms.

- slide based
- icon based
- movie based
- book based

This would bring very high impact on the minds of the students about a concept. It creates clear understanding and improves innovative thinking.

In the end I want to say that if we introduce this wonderful subject Mathematics in a different and interesting way and make the students realise its importance, they would definitely love the subject and once they start loving it, learning takes place automatically.

**Yaman Gauhar** ia a dedicated teacher and facilitator with an extensive experience of ten years in the field of school teaching. He is always ready to take up challenges and responsibilities. An avid programmer and organizer, he also takes initiative to enhance the quality and methods of teaching in the classroom. A master trainer of ALOHA, specially designed for children’s scientific brain management techniques, he has also attended several workshops for innovative teaching ideas. He possesses excellent communication skills with command over multiple languages. He easily builds connections with students and works hard for their overall development.

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]]>Mathematics, an exact science related to measurements, calculations and discovering relationships derives its name from ‘Ganita’ a Hindi word connoting the science of calculations. It is basically a science of reasoning.

**SIGNIFICANCE OF MATHEMATICS :**

Mathematics is a subject of great educational value and plays a vital role in our lives:

a) It has many practical applications and is needed at every stage of life. People can get along without their mother tongue but not without mathematical calculations. A person belonging to any class of society whether wealthy or poor, has to use the knowledge of mathematics in one form or the other.

b) The study of mathematics disciplines the mind and develops our reasoning power.

c) Mathematics has helped in transmitting and enriching our culture. It has helped in the development of various subjects and occupations.

d) Mathematics has great vocational value. It finds extensive application in all vocations like agriculture, accountancy, banking, business, engineering, carpentry, tailoring, surveying, etc.

e) Mathematics has immense aesthetic value. There are interesting riddles and paradoxes in mathematics. Various symmetric designs by the great mathematician Ramanujan offer great pleasure.

f) Mathematics teaches economy in matter of time, money, speech and thought.

g) Mathematics requires unique thinking. There is no scope for cramming. Solving mathematical problems is nothing less than making discoveries and hence develops one’s creative bent.

**QUALITIES OF A MATHS TEACHER:**

Teaching mathematics is not an easy job. A maths teacher has to bear in mind many factors visa`- vis the children with individual differences, aims and objectives of Maths, selection of teaching methodology, etc. Besides having command over the subject and knowledge of methods of teaching, a maths teacher must be well versed with diverse ways of applying Mathematics in other subjects, vocations, life, etc. This makes teaching of Maths momentous and motivating for the students. A mathematics teacher should be an innovative thinker. He/ She must be able to suggest alternatives to certain procedures or rules to his/her students so as to give wings to their creative thinking.

**DEFECTS IN TEACHING OF MATHEMATICS AND REMEDIAL MEASURES:**

It is quite surprising to observe the way mathematics is being taught nowadays as it does not help in the realisation of the educational value of the subject. Sometimes students do not become adept even in elementary Arithmetic.

a) The lack of purpose in teaching and learning of Mathematics is a major cause of incompetency in the subject. When the teacher does not know what he must develop in the students through his teaching, how can he select suitable subject matter and learning activities? Even the students do not know the rationale for which they are studying the subject; they just study it mechanically. The teacher should remember the aims and objectives of the subject and should plan his teaching accordingly.

b) Most of the teachers generally cling to traditional methods of teaching Mathematics. They generally follow lecture method and dogmatic methods making their teaching often dull, droning and only verbal. The teachers should espouse suitable methodology like heuristics, problem solving, analytic and inductive methods, etc. These methods stimulate the pupil’s thinking and reasoning power, develop their insight into the subject, eventually leading to better retention of knowledge.

c) One of the greatest ills of present day teaching practices is that the teachers and students feel that the examination is the ultimate goal. So all their efforts are directed towards this goal. The teacher’s efficiency and pupils’ achievement should not be measured only by the results of examination. They should feel that examination is a means to an end and not the end in itself.

d) Our present day teaching is teacher-oriented and subjectdominated. Teachers choose methods of teaching which suit them. These may or may not suit all the pupils as there are individual differences. The curriculum framers of mathematics should construct curriculum keeping in view the interests, level and achievement of pupils at a particular stage. Individual differences in pupils should be kept in mind.

e) Mathematics teaching is generally verbal and abstract. The work becomes tedious, monotonous and desiccated especially to those who are not mentally mature. The children do not understand much at the abstract level and hence their learning is not thorough in the absence of concrete means. The pupils find no opportunity to apply the knowledge in real life situations. The teachers should adopt concrete means and encourage practical work in mathematics especially while teaching small children.

Practical and project activities makes the study of the subject interesting to the pupils. They should be given real problems to solve so that they get opportunities to apply their knowledge to various real life problems.

f) Though in mathematics there is enough scope for correlation, yet the teachers generally isolate its teaching from other subjects and life. There are interrelationships among various branches and also among the topics of the same branch of the subject, but these are not pointed out. Lack of correlation makes the subject appear dry and abstract; learning is also not effective. The teacher should try to link his teaching with various topics or facts of other subjects and fields. The possibilities of correlation should be thoroughly explored.

Keeping in mind the aforementioned facts, we as teachers should transcend from traditional teaching to collaborative learning in order to incorporate maximum students’ participation in day to day learning of Maths.

**Pardeep Wadhwa**, M.A., B.ED is an Academic Coordinator in Delhi Public School Sonepat. He has 15 years of teaching experience and has been a Maths teacher in secondary classes. He has been awarded in 2014 by the Rotary club of Sonepat for his contribution to academics. It has been a great achievement for DPS Sonepat to get 100 % marks in analysis of evidences of assessment-X-Term 2 – 2015- 16 from RO Panchkula under his guidance. He has also been appreciated by the Honourable Minister of Human Resource and Development, Ms. Smriti Zubin Irani for the stellar performance of his students in secondary school examination-2014-15 of CBSE.

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]]>**Vedic Mathematics**

** – Smart way of doing Mathematics**

We all believe that our brain works faster than the world’s fastest computer. But the million dollar question is how to use this potential? How to really become as fast as a computer? Let’s unveil the Human Calculator in you.

And that’s where the knowledge of smart techniques helps us – which I call “adding smart work to your hard work”. Using these smart maths techniques, popularly known as ‘Vedic Mathematics techniques’, a student can do most of the calculations mentally, without using pen and paper, in one line. The process boosts confidence in one’s ability to tackle mathematical problems, which is necessary for a sustained interest in Mathematics.

Vedic Mathematics is the world’s fastest method of mental mathematics. The history of Vedic Mathematics dates back to the golden age of India, where calculations were done mentally. There was perfect coordination of both right and left parts of the brain. The capacity of the mind was used by every individual up to 100 percent. In due course of time, mind power and mental calculations reduced. A need was felt to document the knowledge of that time for future generations, when different Vedas were being written. With time, that knowledge also got scattered. But it is the result of intuitive work of Late Swami Shri Bharati Krishna Tirthaji, the Shankaracharya of Puri, who presented a glimpse of the high tech methods used in earlier times in the form of a system now popularly known as ‘Vedic Mathematics’. He, through his eight long years of research on Vedas, has presented 16 formulae and 13 sub-formulae which cover a wide range of mathematical operations from arithmetic to analytical cones.

Generally in seminars and workshops, when I calculate long numbers in front of students and teachers, they don’t believe how I arrive at the right answers like a computer. It seems magic to them! But when I tell them the techniques for those calculations, it’s difficult to keep them on their seats. They start answering the questions out of excitement and joy. That is why, I call this system ‘Math-E-Magic’.

“It’s magic until you understand it, And it’s mathematics thereafter.”

Let us take a glimpse of this magic world.

Example 1:

Find the square of 35.

Using the old traditional method, there is no other way of finding the square of 35 other than multiplying 35 by 35. But by using the Vedic Maths Technique, the answer can be directly given as 1225.

**Want to know how?**

For finding the squares of numbers ending in 5, the answer comes in two parts: LHS(Left hand side) and RHS(Right hand side)

Example 2:

75^{2} = 7×8/5^{2} = 5625.

So , you see, instead of struggling through long cumbersome steps of working, answer to difficult sums can also be given in a single and simple step of work by the Vedic Method.

Not only squares, other calculations like long multiplication, division, finding square root, cube, cube root, fraction and much more can be computed easily.

No doubt, the students are required to do the calculations using formulae and identities taught in school and have to show the method also, but these techniques should be introduced in classroom teaching which can help them to recheck their answers in no time.

These techniques are highly useful while answering MCQ’s and while appearing in various Olympiad and other competitive exams where they are required to give answers in seconds. Also students develop an interest in numbers and calculations, thereby helping them to get rid of maths phobia.

In a nutshell, we can say that owing to its very special and universal features, these smart techniques convert the dry and tedious maths into a playful and joyful subject, which children enjoy learning with a smile.

For more such techniques read our book How to Become a Human Calculator?’ and for online vedic maths videos visit our website: www.aditisinghal.com or email: mvedica@gmail.com

Aditi Singhal*Aditi Singhal, founder of Dynamic Minds Group, is an International memory trainer, author, Motivational speaker, counsellor and Vedic Maths expert par excellence. She has to her credit Guinness World Record for teaching Largest Maths Lesson and three records in The Limca Book of Records for memory & fastest calculation. She has also been awarded – “The Best Memory Trainer” by the India Book of Records. She had a dream to make calculations simple for all. Hence she authored a book – How to Become a Human Calculator?*

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