About Arindam Nag

Arindam Nag is a Founder and Director at Learnhive. He is a staunch believer in use of technology to bridge the gap in the educational divide that exists not just in India but the world over.

Keep your concepts warm this summer with Learnhive!

By Arindam Nag,

Summer vacation is that time of the year when extra-curricular activities are in full swing. We at Learnhive encourage all to use this time to focus on hobbies and sports that may have taken a back seat, especially over the last couple of months of academic rigour. Take that art class or music lesson or enrol in your favourite sport camp.

 

But summer is also the time when we tend to forget some of the important concepts we may have learnt in Math and Science. This is where Learnhive can help you with the basic nourishment you need to keep your Math and Science brains sharp and be ready for the new academic year.

Each week we will send you a topic each in Math and Science that you need to revise and/or get introduced to a new topic for your upcoming year. All you have to do is 3 simple steps:

Step 1: You log in to Learnhive with your account

Step 2: View the video related to the topic, and play some games that are listed

Step 3: Take some fun practice exercises on the topic you just read or watched video on.

All it will take is an hour of your time per week. And you can do it at any time, anywhere on your PC or phone or even if you’re on a vacation, as per your convenience. And best of all it costs nothing! Also, you will earn points each time you view a video or take an exercise. These points will add towards the Learnhive Summer Contest.

You will need a Learnhive account to access this program. If you do not have one, sign up here for your account. We will send you a calendar listing the various topics being covered this summer to your email address. This program is presently targeted for students moving to Grades 5 – 10 in the coming academic year.

About the Author:

Arindam Nag is a  Founder and Director at Learnhive; he has over 17 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.

About Learnhive: 

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 any time. 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,

5 x Cost of banana = 20they 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

 

Father and son

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.

 

 

Misconception about subtracting variables

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.

Algebraic terminology

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

About the Author:

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.

About Learnhive: 

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).

The secret to understanding fractions

By Arindam Nag, Founder, Learnhive

So your child can easily share half his cake or a third of his chocolate, but when confronted with adding 1/2 + 1/3, comes up with 2/5 ? Welcome to one of the most common mistakes that children (and perhaps even grown ups) tend to do while dealing with fractions.

Why are fractions so important?

World’s resources are limited and they have to be shared. We use fractions to do that. Fractions is the basis for mathematical concepts such as rational numbers, percentages, ratios, and proportions. Understanding of fractions and decimals is crucial for calculating simple and compound interest problems. Solving algebraic expressions requires knowldege of fractions. In Geometry, calculation of area and volume for any shape other than a square or rectangle requires knowledge of fractions. Fractions are an integral part of our day to day lives.

When do children learn about fractions?

In most curricula, the concept of fractions is introduced as early as Grade 2. It is repeated with increasing complexity every year until about Grade 7. The notation to represent fractions and categorization into different types of fractions is taught in Grade 4. Operations on fractions is done in Grades 5 and 6. Decimal notation of fractions is introduced around Grade 5.

What are the common mistakes with use of proper fractions?

The concept is usually introduced to children by showing them how to share a cake or pizza or chapati (Indian bread) which is pretty well comprehended by children. In this form, fraction is represented as part of a whole, a proper fraction.

Difficulty usually creeps in when the number notation is introduced. Is 1/3 more or less than 1/4? Children may divide something  like a sheet of paper into 3 parts and another one into 4 parts and count these parts and incorrectly say that 1/4 is greater than 1/3. What is important to explain is that they need to compare the resultant (as in size) and see which one is bigger or smaller.

When you compare natural numbers, you are comparing how many (count).

How many?

When you compare fractions, you compare how much (size or amount).

How much?

A similar complication arises while adding proper fractions. The most common mistake done by children is to add the numerators and the denominators separately treating them similar to natural numbers. Once the how many versus how much is well explained, they can then easily grasp why it is necessary to convert the various fractions being added to like fractions (denominator is same) . Multiplication throws up another interesting challenge. When you multiply natural numbers, the result is larger. Multiplying proper fractions gives you a smaller result.

How to explain improper and mixed fractions?

Improper (3/2) and mixed (1 1/2) fractions are explained best by giving another definition of fraction: as part of a collection. You have 3 slices of cake. How would you divide that amongst 2 siblings? Intuitively they know that can share one slice each and the third slice needs to be divided equally amongst them.

So, sound understanding of fractions is absolutely essential for children since not only does it form a pivotal basis for many of the other math topics, it is something they will use in their everyday lives.

What are other misconceptions have you seen children having with fractions?

About the Author:

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.

About Learnhive: 

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.

save money

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?

About the Author:

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.

 About Learnhive: 

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).