# Mathematics, why it is more than just 1+1!

By Jayana Desai,

Have you ever felt that math is nothing but numbers, calculations, constructions and formulas?  Have you ever asked yourself how will math help you in anyway or does it play any role in your daily life? If you are still wondering then read further because you’ll be surprised what miracles math can do to you and how it will help you in your academics as well as daily life.

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The only way to learn mathematics is to do mathematics” – Paul Halmos

Why is mastering the core fundamentals of math important? How can learning and practicing math exercises help children strengthen their math skills? How does math help children assess their knowledge?

Answering the whys and hows of mathematics may be as complex as the Merriam-Webster Definition of Mathematics: “The study of the science of numbers and their operations, interrelations, combinations, generalizations, and abstractions and of space configurations and their structure, measurement, transformations, and generalizations.” However, like any mathematical problem, we need to break down the whys and hows to fully understand what is being asked and to reap the benefits of studying math.

Why is mastering the core fundamentals of Math important?

When I think about the core fundamentals of math, I think about addition to determine the sum of two numbers or subtraction to calculate the difference of two numbers. I think about the memorized multiplication facts to simplify repeated addition or the use of division to split parts or groups equally. While these basic math concepts solve math problems, they also teach children basic life skills to be successful in everyday life. This revelation came to me as a teacher while teaching 1st and 2nd grade math. The most important concept I learnt is that math is directly connected to real life. The development of mathematical skills transforms to the development of life skills.

So, let me share the 5 skills that children develop in everyday life while doing math:

Number sense – Through math, children build their knowledge of numbers and their relationships and connections. They also develop the use of numbers in their physical and social worlds.

Assessing knowledge – The “use what you know” strategy in math is a great example of how children reflect on the knowledge or information they have in their memory, which leads to building off their prior knowledge, and applying their knowledge to interpret, identify, and solve math problems.

Problem solving – Whether it is a simple addition problem or an algebraic equation, math is all about problem solving.

Critical-thinking – Studying math provides children with the opportunity to think critically and creatively to generate strategies that will solve math problems.

Communication – Though discussing math may not be a normal practice, children should be encouraged to share their approach and reasoning when solving math problems.  By talking about their thought processes, children are strengthening their communication skills.

Now take a step outside the classroom and into the real world and you will see that these skills are needed everywhere- at a food store buying groceries, qualifiers for a candidate seeking a job, conversing with a friend about a problem, or a leader guiding the way and making a difference. These skills are the cornerstones to living life.

How can learning and practicing math exercises help children strengthen their math skills?

They say, ‘Practice makes a man perfect’ and this is no different for math. By encouraging children to continuously practice math exercises, children are reinforcing and deepening their learning of mathematical concepts as well as further strengthening their skill set. They are also becoming more comfortable and confident with math and learning to enjoy doing math. Thus, in addition to the above skills, practicing math will:

• Help children see patterns
• Lend to making connections with math
• Support children’s ability to apply basic math skills to complex math concepts (i.e. x + y to y = m x + b)
• Help children recognize the relationship between math and real life

Therefore, children should make the effort to take a few minutes of their time each day to do math exercises. Doing math will only have a positive impact on their learning of math.

How does Math help children assess their knowledge?

Working out math problems can help children see the progress they are making across a wide-range of skills. Thus, doing math on a regular basis can help children:

• See their learning of concepts and formulaic procedures evolve
• Recognize their knowledge of different strategies and appropriately use strategies for problem solving
• Observe their use of patterns and connections when doing math
• Check if their answers are reasonable
• Determine if they are clearly expressing their thought processes and ideas
• Comprehend the challenges they are facing in learning math

In a nutshell, doing mathematics is pivotal to our daily lives both inside and outside the classroom. Children will cultivate life skills and build self-confidence as well as develop a love for the subject. So, do not put off math any longer – take out a pencil and paper or switch on your computer and start solving math problems!

An avid professional in the field of International Education, Jayana Desai hung up her investment banking heels of 13 years to pursue her dream of educating children. She holds a Master’s degree in International Education from New York University, Steinhardt. She has taught children at the primary grade level in both India and in New York. Her passion for educating children can be seen in the curriculum materials she develops, as well as in her love for teaching yoga to children. Being able to empower children with knowledge through positive learning experiences is Jayana’s goal. She would like them to be able to develop their body and mind, while bringing joy to their lives. Prior to her experience in Education, Jayana worked at two prestigious Investment Banks- JP Morgan and Lehman Brothers. She held various leadership positions in managing strategic, global-scale initiatives.

Learnhive is a leading provider of technology based learning solutions for K-12 students, parents, and tutors. Our goal is to make curriculum based learning more effective and fun. We specialize in providing after school learning solutions for students and parents. Our flagship product, Personal Concept Tutor™ gives students the flexibility to learn concepts at their own pace using a wide variety of materials and resources suited for their individual needs. Our technology is compatible with multiple device formats such as desktops, laptops, tablets and smart phones to make learning more fun, interactive and available to students anywhere and at anytime. Signup for free to access the learning materials (lessons and exercises).

# How To Beat the Fear of Learning History

By Ranjani Sastry,

Is writing a history answer a nail-biting finish for your children? Does your child feel that the subject history is beyond his/her understanding? Well, not anymore. Here are some tips for your long-awaited queries on how to study a subject full of dates, events, names and achievements. This detailed article will give you an insight into some innovative ways of learning the subject faster and smarter.

Photo Credit: http://www.sxc.hu/photo/1207518

Falling in love with history: It’s more than a subject of past, or dead and dry collection of facts.

We agree that history is a dry study of past or a collection of facts. Let us put it this way: One of my students expressed his views about the subject history as – ‘Ma’am, these are mere stories about dead people!’ Children are sure to get bored staring at the text book for long hours and trying to memorize what happened and who was involved. I think if you are a teacher or a parent of a student who finds it difficult to read and learn history, then it surely adds to your stress during examinations. But, it shouldn’t because why should you take stress when there is a solution for it. It is very important to generate interest in the child during the initial stage before taxing them to memorize for the sake of general knowledge into their little brains. All they have to do is have the will and love for history which will in turn generate interest.

Here are some sure-fire strategies to make history a fun subject. Let me explain by categorizing a student into age-wise groups:

1. For Children till 4th Grade

2. For Children up to 10th or 12th Grade

3. For those who are really interested in history and still read more about it

### Generating Love for History through your childhood stories:

It is important to tell your child stories of your childhood or your family history. These stories should have a moral lesson to teach and have a third person point of view. They should connect with your child’s feelings but not your perceptions about the event or life. You must be selective and choose what is worth telling. Initially, you must intrigue them to understand your past and your family bonding, likewise you can also generate interest in kings, kingdoms, and wars from the past. Wait for the child to ask questions to you.  Slowly, this may kindle their interest in learning about other happenings and events. This is called ‘transfer of learning’ in psychology. Children understand concepts better when those are connected with a story. There are many analogies you can browse through, or search for key words and events and create a ground for understanding them. This is just one way of making them interested in history. If family stories is not their kind, introduce them to all the fun stories from the past about their “liking.” This shall create a great interest.

### Strengthening the power of different ways of questioning:

While reading historical facts, if you develop the questions of ‘Why’, ‘How’ and ‘For What reasons’, then you will sharpen your skills of reasoning. History provides this power of reasoning and logic.

### The sense of ‘I’:

When you want them to learn about character sketches like: Akbar the great, Abraham Lincoln, Mahatma Gandhiji and other personalities, try to use the ‘I’ approach. For instance, If you want them to remember, ‘In South Africa Gandhiji organized (1907) his first Satyagraha [holding to the truth], a campaign of civil disobedience.’ Put it this way –ASK THEM TO BECOME THE CHARACTER AND SPEAK- ‘In South Africa I organized (1907) the first Satyagraha [holding to the truth], a campaign of civil disobedience.’ It shall create a great impact initially and they might have to unlearn the ‘I’ while writing it down which is very important. It creates a better picture and they can memorize it in a better way with ‘I’ creating its magic! Try once with difficult-to-remember paragraphs.

### Imagining Cartoon characters:

Your children may have a fondness for cartoon characters. You can create actions like – wearing a crown while teaching them about king, action of putting veil on face while talking about queen and creating a drama stage in their study room while you teach them about characters. This shall definitely create an interest in them, likewise, they will learn to memorize names and events in a better way.

For Children up to 10th or 12th Grade

Students in to the middle or higher grades, have the compulsion to learn social studies. Even if it is their top most in the list of favorite subjects, these tips and tactics are going to be of great help to your children.

Photo Credit: http://www.sxc.hu/photo/278748

As students graduate to a higher grade, the pressure to learn many more lessons increases. Like in mathematics, you cannot forget the formulas taught in previous classes to perform better; similarly in history, you cannot forget the events been taught to you previously, for you to learn the current lessons better.

All you need to do is, take the page of a current lesson and read a paragraph, recall about the similar topic or the person who taught you. If you read about events – question the cause of the event and try to recall two important things:

1. WHY IT HAPPENED?               &               2. WHAT WERE THE EFFECTS?

Can’t recall? That’s absolutely fine! Google it. Read some relevant information. Read the questions given behind the lesson. ‘When’ and ‘Who’ are all questions that are fine. But, you must search for questions starting with ‘WHY’ as ’Why’ is connected with curiosity and anything you searched for with curiosity always stays with you. When you start answering the ‘WHY’ questions, you cannot deny the answers to ‘What’, ‘Who’ and ‘When’. Try this out and try some more mnemonics and local mapping technique and plotting on paper to recall better. I’ve observed that my students have no problem in remembering things but, the problem is in recalling. Why is it that during exams you tend to forget? It happens because in math, there are easy ways to remember sequence of formulas or theorems; but in history it is not so. In history, there are multiple people involved in an event and some lessons have biography sketches of leaders and prominent personalities. If you have observed, history is a fact that events have reasons. Only reading will not help, but questioning what you are reading and writing with a flow and rationalizing it will certainly help. Moreover, by questioning you answer to yourself and you will remember well.

### Reference to the Context:

You can take one paragraph, read the topic thoroughly until a new topic starts; take one prominent line you feel is very important in the paragraph which is the best found cause for the event in the topic. If you are reading about personalities, take one simple line, a trait or work they did and draw a mind map on a paper. Once you generate this connection between their personalities, their work, you know their actual sketch of character! Later, read aloud their birth dates and parent’s name and their early life as a child.

### Making Points:

There are many instances where you have points numbered as 1, 2, and 3 which helps you to remember easily. Jot down your points. Read each point aloud, close the book and recall the number you gave to that point. Repeat this for all points. You will surely remember those points. You can do this for all subjects. While remembering wars and some freedom struggle movements like ‘Quit India Movement’ or ‘Simon Go Back’, you can enact these to your parents and teachers. You can use your imagination and learn.

In history, you need confidence to prove your points and to do this you need to remember right facts and figures, therefore, more than ‘why’, you need to ask ‘who’, ‘when’, ‘where’, and ‘what’. These questions are equally important.

For those who love history and want to delve deeper into it:

### Chalking out Strategies:

There are strategies to go about in history and learning about it. You can revive the Doordarshan serials, watch YouTube videos, read historical books and biographies by some amazing authors. If an author has written about an event or a historical figure, then try reading an article written by another author on the same fact. This may give you a different perspective. This could make things more interesting to you and might help you to get your own ideas without getting biased or judgemental . Nevertheless, you must read books of authors who have already done some research before writing down. They must have also referred to some other articles and books in their cross reference sections.

Photo Credit: http://www.sxc.hu/photo/1219898

To friends and readers who are still struggling with reading, learning, understanding and remembering the vastness of the knowledge that history accounts for, you can think about this –

2. What exactly do you like in history?

3. Are you reading for a career in architect, archaeology or paleontology?

It depends on what you are reading history for. You will find that you can interpret history from any point of view i.e. social, economic, financial, behavioural, or even literature. For this reason history becomes an all-important and favourite in any time of life like mathematics and science. Though it is an art to study history, and it is a subject of liberal studies, it is after all a social science. Reading history gives you vast knowledge and sharpens your foresight. As I have mentioned about how you can win your heart to love history, I am sure you have decided to give it your best shot this time and in your future exams. I say – ‘The past is a past and it will always chase you’. Take a challenge as you know how history learning will help you now.

Go, Go, Go for History!

Ranjani Sastry has done her graduation in Psychology and diploma in Counseling and skills. Currently, Ranjani is pursuing her Masters in Public administration. She is a co-founder and an active member of ’Satori-let’s not yawn’*, a multilingual literary club based in Ahmedabad. She expresses her passion and compassion through reading, writing and involving herself in areas where she can contribute to personal growth. Her friends describe her as ‘if you meet her you will find someone who thinks out of the box and ideas galore’. Presently she is reading ‘I have a Dream’ by Ranshmi Bansal.

Learnhive is a leading provider of technology based learning solutions for K12 students, parents, and tutors. Our goal is to make curriculum based learning more effective and fun. We specialize in providing after school learning solutions for students and parents. Our flagship product, Personal Concept Tutor™ gives students the flexibility to learn concepts at their own pace using a wide variety of materials and resources suited for their individual needs. Our technology is compatible with multiple device formats such as desktops, laptops, tablets and smart phones to make learning more fun, interactive and available to students anywhere and at anytime. Signup for free to access the learning materials (lessons and exercises).

# How to beat the fear of Algebra?

By Arindam Nag.

Elementary Algebra is generalized form of arithmetic. It provides a language to represent problems and functions. Algebraic thinking is also one of the first forms of abstract thinking that students develop in mathematics. It is most critical to understand what mental model your child has established and then look to mould and correct that model giving different examples. Lets look at some of the common gotchas of algebraic learning.

# Fear of the unknown x

In Algebra, we use a mixture of numerical digits (constants) and alphabets (variables). For many children, after having done arithmetic, they get pretty confused with the introduction of alphabets in mathematical expressions. Also, with x being the favorite letter for a variable, it is even more confusing since it is the symbol used for multiplication. In computer programming parlance, x is overloaded.

The easiest way to introduce alphabets in arithmetic is to use them as placeholders while solving word problems. Consider the following problem: 5 bananas cost 20 rupees. What is the cost of each banana? Such type of problem is introduced quite early, as soon as children learn multiplication and division. You can start with using a sketch of a banana to represent cost of one banana. You can show that instead of writing 5 x Cost of one banana = 20,

they can draw a picture of a banana. Then they can replace that picture with an alphabet, say b to represent the banana. So, now they have a language to represent the problem to say

5 x b = 20

This is the beginning of Algebra. Algebraic thinking can be introduced by asking them what happens if the cost of 5 banans increases to 30 rupees and then 40 rupees.

# Algebraic expressions to represent functions

In the above example, the letter b really represented one value. The essence of Algebra is that an alphabet is used to represent a variable quantity which can take on different values and thus represent a function. Using Age related problems is a great way to explain this concept. Start by asking your child to express the following statement as an algebraic expression : Father is 30 years older than the son. How would you write this?

Age of son : x

Age of father : x + 30

Then proceed by asking what happens to the father’s age as the son’s age increases. This will build a mental model of a function. Then one can easily introduce the concept of an equation. When the father is 50 years old what is the age of son?

x + 30 = 50

Solve for x.

Another common mistake that almost all children make is dealing with expressions like this.

What is 5x – x ?

Most children will answer that as 5, especially when the problem is asked verbally. This is because of two reasons. First reason is that they forget x is really a shorthand for 1x. The other reason is that children have a mental model of the above expression as:

5(x – x)

rather than

(5 – 1)x

This can also be explained with an interesting age problem. The father’s age is 5 times the son’s age. The difference in their current ages is 20. What are their ages?

5x – x = 20

Solve for x.

# Conclusion

Remember that Algebra is beginning of abstract thinking in mathematics. Hence it is very important that we understand what is the model they have in their mind and then help shape that model. Most important is to remove the fear of use of alphabets in mathematical expressions. Make it fun by using puzzles and then inculcate the understanding of function representation. Then, definitions around like terms, coefficients and others will naturally follow.

# References:

1. Making Meaning in Algebra Examining Students’ Understandings and Misconceptions — David Foster http://library.msri.org/books/Book53/files/12foster.pdf

2. On the learning of Algebra — H. Wu. http://math.berkeley.edu/~wu/algebra1.pdf

Arindam Nag is a  Founder and Director at Learnhive; he has over 15 years experience in information technology. He worked for over 13 years at one of the world’s leading investment banks, Goldman Sachs in various engineering and technology leadership roles. He has a Masters in Computer Engineering from the University of Texas at Austin. He is a recipient of National Talent Search Scholarship. He is a staunch believer in using technology to bridge the gap in the educational divide that exists not just in India but the world over.

Learnhive is a leading provider of technology based learning solutions for K12 students, parents, and tutors. Our goal is to make curriculum based learning more effective and fun. We specialize in providing after school learning solutions for students and parents. Our flagship product, Personal Concept Tutor™ gives students the flexibility to learn concepts at their own pace using a wide variety of materials and resources suited for their individual needs. Our technology is compatible with multiple device formats such as desktops, laptops, tablets and smart phones to make learning more fun, interactive and available to students anywhere and at anytime. Signup for free to access the learning materials (lessons and exercises).

# How involved are you in your kid’s education?

By Tajinder Singh

Do you know which subjects your kid is taking at school? Do you know which of them your kid loves the most? Do you know the name of your kid’s best friend in school?

Photo Credit: http://www.sxc.hu/photo/495427

School going kids spend 60-70% of their waking hours, including the weekends and holidays, outside of their school. Time and again it has been seen, the more the parents gets involved with their kid’s education and school, the better their school results have been. The parent’s active involvement helps in emphasizing in the kid’s mind, that the home and school are inter-connected.

There are several ways you can get involved. As my wife and I go about parenting our 2 kids, who are in the 10th and 7th class, here are few tips (that we got from others) that are working for us.

Show consistent interest in what they are doing in school. We continue to learn a thing or two from our kids or sometimes have a good laugh, when they come home excited to tell what happened in school today. This conveys to them that you value what is happening in school.

Get passionate and learn up about any sport, activity, hobby that your kid is crazy about, and participate whole heartedly in it. Yes, it can be an online/video game too! The enthusiasm and camaraderie that you will build here will help you have better conversations around their learning and education.

Sometimes, have conversations with them on what they don’t like about their school education or what worries them. It will identify issues that you might be in a position to help and fix. However, be mindful that there will be some lame excuses here!

And of course, visit their school regularly, especially when they are participating in any school activity or sport. That goes a long way in boosting their confidence.

So how are you involved? Do share your thoughts, and we would love to learn from your tips.

Tajinder Singh Sidhu is a Founder and Director at Learnhive. He has over 20 years of experience in various leadership roles designing and managing complex technology solutions. Prior to Learnhive, he worked for over 14 years at Goldman Sachs in New York. He holds a BTech degree in Computer Science & Engg from IIT, Delhi, and a Master’s in Computer Science from College of William & Mary, Virginia. He has taught students as part of the NSS scheme in India, and currently is a volunteer teacher with the Literacy Volunteers of America.

Learnhive is a leading provider of technology based learning solutions for K12 students, parents, and tutors. Our goal is to make curriculum based learning more effective and fun. We specialize in providing after school learning solutions for students and parents. Our flagship product, Personal Concept Tutor™ gives students the flexibility to learn concepts at their own pace using a wide variety of materials and resources suited for their individual needs. Our technology is compatible with multiple device formats such as desktops, laptops, tablets and smart phones to make learning more fun, interactive and available to students anywhere and at anytime. Signup for free to access the learning materials (lessons and exercises).

# Having fun with simple interest

By Arindam Nag, Founder, Learnhive

One of the best ways to make learning fun is for parents to engage children in activities
from our day-to-day lives, tying the activities to concepts that they learn in school.

Photo credit: http://www.sxc.hu/photo/815274

Take for example the concept of simple interest that is usually introduced around the 5th  grade in Indian schools. I have twins, a boy and a girl, who are currently in 6th grade. My son was probably a financier or accountant in his previous life. He has kept a keen interest in money matters from a young age. He seems to remember all of his (pocket) money earnings and promises of monetary benefits made by us. However, my daughter on the other hand is more than happy to let her brother handle her accounting and easily parts with her share. So naturally when they were being taught simple interest, one showed more interest than the other.

My wife and I decided to use this opportunity to give them some real world experience of managing money and explain how banks function. We opened up accounts for both of them and asked them to put a portion of their pocket monies in their respective accounts. We explained that the money in the bank would earn them interest as they had learnt in school. Once they had sufficient money, they could even opt for a fixed deposit that would earn them higher interest. This was followed by some quick calculations to show how many additional scoobi strings / novels and other goodies they could buy by keeping the money in the bank rather than at home. This led to further conversation on how banks could afford to give interest. Both of them then got into finding their perfect signature. This entire episode seems to not only have piqued more interest in my son to read financial news articles (he now regularly looks at the currency rates in the morning newspaper), but seems to have also kindled more awareness on money matters for my daughter. They will be learning compound interest in school later this year, which they are looking forward to.

Masterchef Australia is also one of their favorite TV programs. The twins have started using terms like “adding acidity to the sauce” when they help their mom in the kitchen. Examples for chapter on Acids and Bases…here we come…

What were your experiences in explaining concepts to your children? What examples did you use?