Indian Math Online - Blog

From the editorial pages of USA Today

Here is an interesting column from an English teacher about Math...read it in full - it is worth it. As someone that grew up in an educational system where knowing the "basics" was an expectation (for example: I was required to memorize the first 15 multiplication tables and perfect square roots!), I can relate well to this column. The only piece of "help" we could take to our exam was the "Clarke's tables"...thank goodness Scientific Calculators weren't populuar!

----

Math meltdown

Summertime means school for an increasing number of high school students who have struggled in their math courses. But the system could be contributing to the kids’ poor performances.

By Patrick Welsh

Sam Cooke once cooed: "It's summertime, and the living is easy."

Tell that to the increasing number of middle and high school students who will be sweating out summer school this year because of their meltdown in math.

(Illustration by Web Bryant, USA TODAY)

How bad are things?

• Recently, the Georgia Department of Education said about 40% of eighth-graders failed the state's math test. Students have been urged to attend summer school. Other states have reported high failure rates on similar eighth-grade math tests, which measure how well students have learned a state's content standards.

• A new study by the Center on Education Policy found that state test scores in mathematics have increased since 2002. Even so, the study noted a familiar, and troublesome, trend: Math proficiency declines as students move from elementary school through high school.

• In March, the National Mathematics Advisory Panel, a 24-member group appointed by President Bush, released its report. Among other things, it noted that U.S. students lack a deep understanding of basic skills, including a grasp of whole numbers and fractions.

The panel wants to streamline the K-8 curriculum and increase the number of seventh-graders taking algebra I and high schoolers taking algebra II. The importance of algebra is significant. The panel noted: "Students who complete algebra II are more than twice as likely to graduate from college compared (with) students with less mathematical preparation."

Members of this panel could have spent more time with students. At T.C. Williams High School in Alexandria, Va., where I teach English, we have been graduating hundreds of kids who need a calculator to figure out that nine times five is 45. At the same time, many of the brightest students have had so much math thrown at them — courses such as discrete math, statistics and calculus — that they never want to take a math course again.

I could only laugh when I looked at Virginia's Standards of Learning — 64 pages detailing what math gurus in Richmond think kids should absorb at every step in their 13 years in school.

The result of these grand plans, says T.C. math teacher Gary Thomas, is that "we are ending up with kids in upper-level math courses who do not know how to add, subtract or divide unless they use a calculator and who are lost when it comes to fractions." As a consequence, when he gets kids in algebra II and trigonometry, says Thomas, he is constantly having to backtrack to teach skills students should have learned years ago.

One reason for the teacher frustration is that the state's math gurus have de-emphasized memorization in favor of "conceptual thinking." The same philosophy has crept into English classes, where "creativity" has been elevated over knowledge of grammar, and into history classes, where knowing historical trends — "the big picture" — has replaced knowing dates of important events. The result is seniors who are not just incapable of multiplication, but also unable to identify the verb in a sentence or come within 100 years of placing the Civil War.

Kids also are taught the wrong material at the wrong time. This fact is most obvious in the push to get as many as possible to take algebra in middle school. "There's a myth that if they are not in algebra by seventh grade, they won't get into a good college," says math specialist Kristen Race. "For a small number of middle school kids, algebra may be fine, but it's not for 90% of the kids; developmentally, most of them are at a stage where they can't think abstractly."

Taylor Pearson, who enters the University of Virginia this fall and was put into algebra in seventh grade, agrees. "Looking back, I realize I was too young to grasp the concepts. … You learn everything quickly so you can spit it out on a test, and then pass on to the next thing without really grasping the concepts."

The same misguided "acceleration" plays out in high school, with guidance counselors pushing kids to take calculus because they think it will help them get into college. In fact, frustrated college math teachers are telling their high school counterparts to slow down. It might sound presumptuous for an English teacher to suggest how to improve math instruction, but after talking to students and to math teachers, I come to one main conclusion: In math, as in so many subjects we try to teach, less is more. Virginia's math learning standards, like those in most states, are a mile wide and an inch deep. There has to be more emphasis on memorizing to get kids to have the ability to instantly recall basic addition, subtraction, multiplication and division.

There also has to be a conviction that all kids can "get" the basics of math. Those who do not "get it" have to be given more time to do so through additional classes, tutoring or summer school.

Students are not the only ones who must "get" math. Many elementary school teachers are notoriously weak here. It might take paying math majors bonuses to teach in elementary and middle schools, but that's a price worth paying if it leads to more students such as Sam Alexander, a T.C. graduate heading to Case Western Reserve University in Cleveland to study engineering.

Alexander says he doubts he would love math if Kristen Race had not been his elementary school math teacher. To him, math is like a language. "You can break it down in a grammatical sense so it is not just numbers. There is something beautiful about all those signs."

Patrick Welsh is an English teacher at T.C. Williams High School in Alexandria, Va., and a member of USA TODAY's board of contributors.

How bad are things?

• Recently, the Georgia Department of Education said about 40% of eighth-graders failed the state's math test. Students have been urged to attend summer school. Other states have reported high failure rates on similar eighth-grade math tests, which measure how well students have learned a state's content standards.

• A new study by the Center on Education Policy found that state test scores in mathematics have increased since 2002. Even so, the study noted a familiar, and troublesome, trend: Math proficiency declines as students move from elementary school through high school.

• In March, the National Mathematics Advisory Panel, a 24-member group appointed by President Bush, released its report. Among other things, it noted that U.S. students lack a deep understanding of basic skills, including a grasp of whole numbers and fractions.

The panel wants to streamline the K-8 curriculum and increase the number of seventh-graders taking algebra I and high schoolers taking algebra II. The importance of algebra is significant. The panel noted: "Students who complete algebra II are more than twice as likely to graduate from college compared (with) students with less mathematical preparation."

Members of this panel could have spent more time with students. At T.C. Williams High School in Alexandria, Va., where I teach English, we have been graduating hundreds of kids who need a calculator to figure out that nine times five is 45. At the same time, many of the brightest students have had so much math thrown at them — courses such as discrete math, statistics and calculus — that they never want to take a math course again.

I could only laugh when I looked at Virginia's Standards of Learning — 64 pages detailing what math gurus in Richmond think kids should absorb at every step in their 13 years in school.

The result of these grand plans, says T.C. math teacher Gary Thomas, is that "we are ending up with kids in upper-level math courses who do not know how to add, subtract or divide unless they use a calculator and who are lost when it comes to fractions." As a consequence, when he gets kids in algebra II and trigonometry, says Thomas, he is constantly having to backtrack to teach skills students should have learned years ago.

One reason for the teacher frustration is that the state's math gurus have de-emphasized memorization in favor of "conceptual thinking." The same philosophy has crept into English classes, where "creativity" has been elevated over knowledge of grammar, and into history classes, where knowing historical trends — "the big picture" — has replaced knowing dates of important events. The result is seniors who are not just incapable of multiplication, but also unable to identify the verb in a sentence or come within 100 years of placing the Civil War.

Kids also are taught the wrong material at the wrong time. This fact is most obvious in the push to get as many as possible to take algebra in middle school. "There's a myth that if they are not in algebra by seventh grade, they won't get into a good college," says math specialist Kristen Race. "For a small number of middle school kids, algebra may be fine, but it's not for 90% of the kids; developmentally, most of them are at a stage where they can't think abstractly."

Taylor Pearson, who enters the University of Virginia this fall and was put into algebra in seventh grade, agrees. "Looking back, I realize I was too young to grasp the concepts. … You learn everything quickly so you can spit it out on a test, and then pass on to the next thing without really grasping the concepts."

The same misguided "acceleration" plays out in high school, with guidance counselors pushing kids to take calculus because they think it will help them get into college. In fact, frustrated college math teachers are telling their high school counterparts to slow down. It might sound presumptuous for an English teacher to suggest how to improve math instruction, but after talking to students and to math teachers, I come to one main conclusion: In math, as in so many subjects we try to teach, less is more. Virginia's math learning standards, like those in most states, are a mile wide and an inch deep. There has to be more emphasis on memorizing to get kids to have the ability to instantly recall basic addition, subtraction, multiplication and division.

There also has to be a conviction that all kids can "get" the basics of math. Those who do not "get it" have to be given more time to do so through additional classes, tutoring or summer school.

Students are not the only ones who must "get" math. Many elementary school teachers are notoriously weak here. It might take paying math majors bonuses to teach in elementary and middle schools, but that's a price worth paying if it leads to more students such as Sam Alexander, a T.C. graduate heading to Case Western Reserve University in Cleveland to study engineering.

Alexander says he doubts he would love math if Kristen Race had not been his elementary school math teacher. To him, math is like a language. "You can break it down in a grammatical sense so it is not just numbers. There is something beautiful about all those signs."

Patrick Welsh is an English teacher at T.C. Williams High School in Alexandria, Va., and a member of USA TODAY's board of contributors.

How do I manually determine the square root of 2795?

Indian Math Online recently received a request for help on this math question:

 

How do I manually determine the square root of 2795?

 

There are a number of ways of solving this problem….without using a calculator! First you have to understand what exactly a “square root of a number” is. A square root of a number is a special number that when multiplied by its self (or squared as we say), the result is the original number. Take the number 9 for example. The number 3 multiplied by itself gives a result of 9 (3 x 3 = 9). Another way of saying this is 3 squared is 9 (3² = 9). Therefore, 3 is the square root of 9 (3 = √9).

 

On a multiple choice test where 4 possible answers are given, you could easily just square the 4 answers to see which one is the correct answer. However, that is not very challenging and it takes away all the fun.  So if you are not given 4 possible answers to choose, and you don’t have a calculator, it is time to learn how to manually calculate square roots.

 

GUESSING

The first real method would be to make educated guesses! Most students learn what are called “perfect squares” when they are in middle school. Perfect squares are integers that have integers as a square root. The number 9 is a good example of this because its square root is 3. The number 10 is not a perfect square because its square root is 3.1623.  Students memorize these perfect squares, usually as high as 625 which has a square root of 25. So to apply the guessing method to finding the square root of 155, knowing that the two closest perfect squares are 144 (which has square root of 12) and 169 (which has a square root of 13), it is safe to say that the square root of 155 is somewhere between 12 and 13. That is as far as guessing can take you.

 

PRIME FACTORIZATION

The prime factorization method only works when trying to find the square root of a number which happens to be a perfect square. So unless the question specifies “Find the square root of the perfect square 784”, this method may be a waste of your time trying to use it properly. To find the square root of 784 which is in fact a perfect square, you need to break it down into its smallest factors. The number 784 can be factored into 2 x 2 x 2 x 2 x 7 x 7 (because 2 x 2 x 2 x 2 x 7 x 7 = 784). The next step would be to group these smallest factors into pairs: 2 x 2 is a pair, 2 x 2 is a pair, and 7 x 7 is a pair.  If you multiply one of each pair together, you get 2 x 2 x 7 = 28.  The square root of 784 is 28.

 

LONG DIVISION

Finding square roots by long division can be the most difficult method to understand at first, but it will always work for any number, even decimals! To solve the question asked by our student, “what is the square root of 2795”, we must first group 2795 into pairs of 2 digits (27 and 95) and write it like a long division problem:

   ______

  | 27 95      NOTE: If the number were 12549, it would be grouped as 1, 25, and 49

 

STEP 1: Find the largest number whose square is equal to or less than the first pair. In this case, that number would be 5 because its square is 25 which is less than 27. The number 6 is too big because its square is 36 which is greater than 27, so 5 is the largest number. We now write the 5 in three spots, and its square of 25 in one spot:

 

 

       5      

5  |27 95

5    25

 

STEP 2: Then on the left side you add the numbers, and on the right side you subtract them:

 

          5    

  5 | 27 95

+ 5  -25

  10    2

 

STEP 3: Next you want to carry down the next pair of numbers, 95, and put an x after the number 10.

 

          5      

  5 |  27 95

+ 5   -25

10x     295         NOTE:  10x represents a 3-digit number, and the remainder here is 295

 

STEP 4: You now want to determine the largest number x such that the number 10x times x is equal to or less than the remainder. In this case, that largest number x is 2 because 102 times 2 = 204 which is equal to or less than 295. The number 3 gives 103 times 3 = 309 which is greater than 295, so 2 is correct. Now write the 2 in three spots, and the 204 from earlier in one spot:

 

           5 2   

  5 |  27 95

+ 5   -25

102     295

   2     204

 

STEP 5: Then on the left side you add the numbers, and on the right side you subtract them:

 

          5 2   

  5 |  27 95

+ 5   -25

102     295

+ 2     -204

104       91

 

STEP 6: You have run out of numbers to bring down, so bring down two zeros (00) which are after the decimal points. Also put an x after the number 104.

 

          5 2 .    

  5 |  27 95.00

+ 5   -25

102     295

+ 2     -204

104x      9100

 

At this point you would continue repeating steps 4, 5, and 6 until you have a remainder of zero (0), or you have gotten as many numbers after the decimal as required. The square root of 2795 is 52.86775955…. and keeps going, so usually when you are asked to find the square root manually of a number such as 2795, the question will say to only go as far as 2 or 3 decimal places.

 

Indian Math Online (IMO) has materials that explain these methods in further detail and with more examples. You can see IMO’s “Solution Explanation” on how to perform all of these methods by going here.

 

Or you can watch one of IMO’s learning assignments on this topic here.

My daughter (Meera) does do IMO!

Back in November 2006, Bob had posted a picture of his daughters and mine (here is a link to that post) - the four girls had gotten together for Thanksgiving. Meera was 5 at the time.

She just graduated from Kindergarten (yes, she is an October birthday and regardless of how 'qualified' or 'ready' she was, she could not begin grade K until Aug 2007. BTW, Kindergarten is OPTIONAL in the State of Indiana!). Her teacher told us she did VERY WELL.

Knowing that her global counterparts are already mastering multiplication and division, I made a deal with her - for every IMO assignment she completed successfully she would get a $$ incentive, provided she got at least 30 questions right in an assignment containing 35 questions (see picture of her actually working on the IMO assignments)

Yes, she does like to eat and do math. And her sister keeps her company when she does math!

The 'deal' seems to be working so far - in a given week, she devotes time to do a minimum of 4 assignments. When she needs that extra dollar, she comes to me asking for more...{and my wife is responsible for making sure Meera spends her money wisely!}

I know there are several parents who have young children that are around my daughter's age. I also realize getting them to dedicate time for math work (or reading/writing) is a difficult task. My experience so far is this - with a proper incentive and making it easy for her to gain success in small increments seem to work well. Sometimes, Meera would say - "Daddy, this is hard and taking too long". My response is - "break it up into two installments and get it done by end of the day". That seem to do the trick with her.

I tried getting her to do the assignments online - after the first 10 or so questions, she gets distracted by the 'glamor' of the computer and she wants to do Gmail. So, I print out the worksheets (hint: product improvements are on the way!) and she completes the assignments. Then either she inputs the answers or I input the answers.

I have compiled the relevant 'dashboards' to illustrate a point - click here to see the results.

What I have discovered is that she needs help in "Subtraction" and "Money" and we are diligently focusing on those topics. With Indian Math Online it is very easy to focus the Practices on just those two topics and we are doing just that.

My wife and I have also discovered that her reading has improved significantly - most of the math problems in Indian Math Online require her to read well and comprehend the sentences.

Both mom and dad are proud of Meera!... best news of all, Meera likes Math!

{Posted with approval from Mom and Meera!}

Co-Founder, Bob Compton in his own words

Some of you may be wondering why Bob (Compton) and I started Indian Math Online and where did the inspiration for IMO came from. Many of you have emailed me in the past with that curiosity as well.

You can now view and listen to Bob describe his inspirations for starting Indian Math Online.

Here are links to samples of Assessments, Learning Assignments, Practices that Bob refers to in his video.

Sample Assessment (click on the image below)

Sample Practice (click on the image below)

Sample Learning / Reading materials (click on the images below)

 

 

Here is a sample of the 'dashboard' a parent sees after the child has completed an assignment (click on the image below)

Differences in American and Indian education systems, process and culture

For many Americans, it is difficult to understand the education system, process of education and the culture of education in countries such as India (and China).

While Indian Math Online is based on the principles of mathematics as practiced in the Indian education system, we still have a large contingency of subscribers from within the United States. It is my gut feeling that some of you have limited knowledge on the differences between the American system of education and the Indian system of education.

First, let us acknowledge some of the similarities – both systems have –

· Structured curriculum / syllabus

· Reasonably qualified teachers

· Good labs, facilities and decent infrastructures

· Concept of “private”, “for-profit” and “public schools”

· A willingness on the part of children and parents to get the proper education

While there are some broad similarities, there are significant differences between the two systems (Indian and American). While it would be difficult to write in detail on all the differences, I wanted to highlight a few key differences that would make you think and apply these differences to your particular context.

1. Numerous Standards – In the US system of education, there are different standards throughout the country; each state determines the curriculum and the standardized testing. So practically, we could have 50+ versions of curriculum and standardized testing. Of course, it will be argued as ‘freedom of choice’.

However, imagine the difficulty this must pose to parents and children who have to move from one state to another (for job reasons, for family reasons) – it must be a heavy burden for the parents, children the extended family to keep up with the differences in requirements and expectations among the different states!

What about the situation where a child is performing superbly in the chosen curriculum – does that child have a choice to accelerate his or her learning beyond the AP courses?

Conversely, in India, there are two standards at the national level and typically one standard at the individual state level. These national and state standards are governed (typically) by ‘boards’ of education and follow a consistent pattern of building the curriculum upon prior years of knowledge. Students, parents and teachers know what is expected of them, and strive everyday to meet those goals.

2. Role of the Family, Teachers/Tutors and Society - As explained on the Indian Math Online’s page “Principles Guiding IMO”, Indian families take education very seriously and believe that a solid education is the key to success in life. While many American families certainly share the same sentiments, it has often been discussed that the American education system is designed according to maintaining students’ high self-esteem. Therefore, nearly everyone in the class will pass so long as ‘feelings’ aren’t hurt and the teacher is not looked upon as doing an inefficient job in his/her classroom; regardless of what the actual students’ proficiency levels are in that subject area. Instead of pushing the students harder to achieve beyond their current potential, teachers often “dumb down” the subject material to ensure that students’ grades remain high.

On the other hand, most Indian children fear failure in the classroom and push themselves to work harder and longer, thus maximizing their fullest potential by being self-motivated. This is also true of their parents and teachers, as school administrators pride themselves on being able to recruit new batches of students based on the academic achievements of outgoing classes.

Sumit Gupta, a former post-doctoral researcher in computer science at the University of California, Irvine, who is now a senior product manager at NVIDIA, a world leader in visual computing technologies, supports this line of thought. His findings show that at the end of many American’s first year of college, they are just at the equivalent level to high school graduates in India in terms of math study. He says that the Indian emphasis on math and engineering programs in high schools is why India produces so many good software engineers. Gupta has studied in both India and the U.S. and you can read more of his impressions of the Indian versus American education system in this article.

3. Trained/Certified teachers - In India, experts feel that for someone to become a good teacher, face-to-face guidance from experts is essential. With this, the Parliament of India set up a resolution in 1995 with the National Council for Teacher Education (NCTE) and gave it statutory powers for framing regulations and norms for maintaining standards of teacher education in the country. Since the NCTE has been given a broad mandate with legal powers for improving the quality of teacher education and preventing commercialization, its functions have had direct bearing on teacher certification.

As mentioned in a previous blog post, in India it is very common for teachers at all level (primary through high school) to have obtained advanced degrees and to have spent 6-10 additional years acquiring more education after receiving their undergraduate degree. In addition, teachers needed to be specifically trained in a particular subject area so that they are “experts” in that subject when teaching to others.

In the United States, according to the No Child Left Behind Act (NCLB) which went into effect during 2002-03, teachers who teach core academic subjects are required to be “highly qualified.” The law defines a highly qualified teacher as an individual who:

· Has obtained full state certification;

· Holds a license to teach in the state;

· Has not had certification or licensure requirements waived on an emergency, temporary or provisional basis.

· In addition, there are requirements for demonstrating subject-matter knowledge that vary depending on what grade level an individual is teaching, and whether he/she is new to teaching or is a veteran teacher.

The "highly qualified" teacher requirements do not apply to all individuals, such as supplemental service providers and charter school teachers, who teach public school students.  It is common that para-professionals are not being provided with the range of options necessary to demonstrate that they are qualified, nor the financial support necessary to meet the requirements. Often in private school settings, teachers are exempt from needing to be fully licensed or are given a few years leeway to obtain their license. Therefore there is a vast difference in being “highly qualified” in India, than in the United States.

4. Curriculum builds on each year – As part of the 2 Million Minutes (a documentary film on the state of Global Education produced by co-founder Bob Compton) project we have done an extensive deep dive into the Indian education curriculum and compared it to a typical curriculum in US. For example, the curriculum for grade 9, in India, builds on the things a student learned in grade 8. Our analyses indicate that this is not necessarily true in the US curriculum.

5. Extra-curricular activities – In America, parents and school systems place a strong emphasis on extra-curricular activities and pour vast amounts of funding and resources into giving their children and students the best experiences in athletics, fine arts and social clubs. While these extra-curricular activities are necessary, however, in India, the focus remains on academics, as Indian parents, teachers and administrators realize that it is by getting good grades and high scores on tests, that children will go on to becoming successful adults. Instead of investing in private athletic coaches or additional gym time, Indian parents place the priority on investing in tutors to accelerate their child’s learning. Tutors are used to help their children excel in a subject area, not just for remedial work.

Can't open a Practice or Assessment?

Are you just starting to use Indian Math Online and experiencing issues with Practices or Assignments? If so, make sure that the child is logged into IMO, not the parent.  From there the child should click the "Start" button next to the assignment they want to take.  Then click "Begin Assessment/Practice" and the assignment should open immediately.  If your computer asks you to save/open a ".do" file, it means you need to install the Math Player.  Download and install it from here:

http://members1.indianmathonline.com/MathPlayerSetup.exe

Still having problems? You may also need the MathML Fonts support file.  Download and install it from here:

http://web.mit.edu/atticus/www/mathml/mit-mathml-fonts-1.0-fc1.msi

Once you have these installed, try opening a Practice or an Assessment lesson again, and this time it should open the assignment automatically. You will not be asked to open or save any ".do" file at all. When your child is finished with the assignment, be sure to click "Save and Exit" at the bottom, and your results will be available shortly.

Ask the Expert - A question from one of our subscribers

An IMO subscriber recently asked for help on this question:

Mrs. Margaret weighs 85 lb and her daughter weighs 42 lb less than her. What is the difference of their weights?

85 - 42 = 43 pounds  (easy right?!)

WRONG!

Look again; if you read the question carefully, you will notice that the daughter is not 42 pounds, but that she weighs 42 pounds less than her mother who weighs 85 pounds.  So the daughter actually weighs 43 pounds, and 42 pounds is their difference in weight. In fact, you don't even have to subtract here at all.

Got you confused? A similar question would be: A book used to cost one dollar but it now costs 10 cents less. What is the difference in the two prices?  10 cents!

This question was submitted via the "ASK THE EXPERT" link which is found on the left side of the Indian Math Online home page. Anyone is welcome to use submit a question there, and we do our best to respond in a timely manner. If the question came from an IMO practice or assessment, please reference the question number which is found at the lower right corner of each question.

Teach math, science? You're hired!

A friend of mine forwarded this article to me yesterday.

At a recent job fair, a 22-year-old aspiring teacher wore a name tag that said she majored in math. Immediately, Anastasia Batsios became one of the most popular recruits in the room.

School officials from across the nation, including a few from the Houston area, had descended on her Michigan campus, Grand Valley State University, during March.

"They saw 'math' and said, 'Hey, come here. We'll give you a job,' " recalled Batsios, a Michigan native who ended up accepting an offer from the Galena Park school district. "It was overwhelming but encouraging. At least I picked a good major."

You can read the full story here.

As the title says, there is an urgent need for qualified teachers in the American school systems. Good for recent graduates like Anastasia - I am sure it makes them proud to graduate in Math and Science and feel wanted in the work force.

When I read this article, it reminded me of my school days in India. As many of you can guess from my name (Suresh), I was born and raised in India. I am a proud product of the Indian Education system. When I reflect back on my teachers' names and their salutations, it was not uncommon to see the names of "degrees" they had obtained as part of their education. For example, my primary school math teacher (yes, specialization at the primary school level) Bhavani (I will spare the last name for privacy reasons!) had three degrees listed next to her name - "B.Sc, B.Ed, M.Ed".

A little explanation - B.Sc - is for Bachelor of Sciences (3-year program) - typically in Math or Sciences; B.Ed (3 year program) - Bachelor of Education; M.Ed (2 year program) - Masters in Education.

B.Ed and M.Ed are mostly required qualification if a person intends to pursue a teaching profession in primary or high school. Some teachers will go on to do Masters in the chosen Sciences field as well.

At the time I was going through primary-middle-high school, it was an accepted norm that the teacher that was teaching a specific subject (math, physics, chemistry, etc) was specifically trained in that subject. If a school were to hire less qualified teachers, there would be mass exodus by the parents and students.

So, as I read the Houston Chronicle article, I am thrilled to see that being specifically educated and trained in subjects like math and science is REALLY wanted by the school systems here in the US. This is only going to benefit our children!

 

Investing in your Child’s Future

I first met Bob Compton, one of the co-founders of Indian Math Online, and Executive Producer of the documentary film - Two Million Minutes, at a screening in early April 2008. He was on a panel of various high school administrators and students at a private school. He asked one of the students what grade he received in his math class. The student, who was among the top in his class, proudly responded “A’s”.

Bob then asked if he had a tutor for his math classes. Confused by the question, the student responded that he didn’t, and then Bob went on to question the entire audience at-large about why was it that Americans will spend hundreds of thousands of dollars to make their above-average students excel even more in athletics and fine arts, but won’t put forth the additional dollars to help their children shine academically by investing in tutors or academic programs.

Everyone in this country is aware that only a small percentage of students go on to receive athletic scholarships for colleges; and an even more minuscule number become professional athletes later on in their career. However, academic scholarships are abundant, and the brightest students often wind up with the highest-paying jobs down the line.

So rather than investing in athletics and fine arts as much, shouldn’t we be investing in academics?
That is the reason Americans are falling behind developing countries such as India and China, because in those countries, their focus is on academics and the ability to compete in global economy. Meanwhile, American students’ focus is often on the social aspects of life, and most often students wait until college graduation to find out that their global competitors are often acquiring all of the jobs that they sought after.

Investing in Indian Math Online is helping your child prepare for these global competitors by giving him/her the resources necessary to become proficient in mathematics – a subject area where Americans are consistently falling behind. Indian Math Online is designed to help your child challenge him/herself academically, where some school curriculum will not.

Speaking of investing in IMO, there currently is a promotion to save $20 when you sign up for the IMO Summer Program. See below for details -

 

To Learn more about Indian Math Online click here -

 

Why Should I Learn Math?

Whether you are a doctor, a nurse or an airline pilot, you use Math every day. Even professionals such as Artists use Math in their daily life.

We believe Mathematics is the language of the 21st century. We have compiled a presentation titled "Why Math?" which will provide you insights into where Math is being used daily and the careers that involve Math.

Click here to download and read.

How can we apply the Gauss Elimination method to solve m question?

Recently a user to the Indian Math Online web site submitted a question for one of our math experts. The user who we will refer to only by first name - Amresh - submitted this question and picked "Grade 1" as the grade. We do not believe this is a question from a 1st Grader. This is a question for higher grades, perhaps even taught in early years of Engineering programs.

Here we go - the question first;

"How can we apply the Gauss Elemination method to solve m equation? For example z1 = ax^n + bx^(n-1) + ... + m (mod p) z2 = ax^n + bx^(n-1) + ... + m (mod p) ..................................... ..................................... ..................................... zm = ax^n + bx^(n-1) + ... + m (mod p) I want the mod p vale of a,b,c... "

Our answer follows - if after reading the answer, you have more questions or need further clarifications, please click here. A pdf version of the answer can be downloaded here.

Gaussian elimination method:

This is an elementary elimination method & it reduces the system of equations to an equivalent upper triangular system which can then be solved by back substitution.

Although quite general, we shall describe the method by considering the below mentioned system of equations for the sake of clarity & simplicity.

Let the system of equations be

axⁿ+bx^(n-1)+………………….+m(mod p)= z1

axⁿ+bx^(n-1)+………………….+m(mod p) = z2

axⁿ+bx^(n-1)+………………….+m(mod p)= zm

We first form the augmented matrix

a b m(modp) z1

a b m(modp) z2

a b m(modp) zm

    

To eliminate xⁿ from the second equation, we multiply the first equation by –a/a & then add it to the second equation. Similarly, to eliminate xⁿ from the third equation, we multiply the first equation by –a/a & then add it to the third equation. This procedure can be shown thus:

 

   a b m(modp) z1

-a/a   a b m(modp) z2

-a/a   a b m(modp) z3

    a b m(modp) zm

where –a/a & -a/a are called multipliers for the first stage of elimination. In this stage, it is assumed that the first element in the first equation a≠ 0. The first equation is called the pivotal equation & the first element a is called first pivot. At the end of the first stage, the augmented matrix becomes:

    a b m(modp) z1

  0 b’ m(modp)’ z2’

  0 b’ m(modp)’ z3’

 
-a/a   0 b’ m(modp) ‘ zm’

where b’,(modp)’……….. are all changed elements. The first b’ of the second equation is the new pivot & the multiplier is –b’/b’.

After completing all stages, we should have the upper triangular system:

 

   a b m(modp) z1

  0 b’ m(modp)’ z2’

  0 0 m(modp)’ z3’

   0 0    0  zm’

 

from which the values of xⁿ,x^n-1 can be obtained by back substitution.

Those values will be substituted in the original system to get a system of equations

which can be solved to get the values of a,b, c etc

It is clear that this method will fail if one of the pivots vanishes. In such a case , the method can be modified by rearranging the rows so that the pivot is non-zero. This procedure is called partial pivoting & can be implemented on a computer.

If this is not possible, then the matrix is singular & the equations have no solution.

In particular, the number of non zero diagonal elements in the final augmented matrix will represent the rank of the original matrix.

Don't Let Your Child Forget Math This Summer!

We realize school is out for the Summer. Don't let your child forget the math they learned in school this past year.

Indian Math Online has created a Summer Program that you can sign up and save $20. It is an ideal complement to your child's summer activities.

Sign up any time between June 01, 2008 and August 01, 2008 and SAVE $20.

• For three (3) months from the date you sign up, you will receive the IMO Professional Plan for just $40! - That’s a savings of $20!
• Just enter in the promotional code - SUMMER08 - when you sign up! 

The IMO Summer Program is available for students in Grades 1-6 and the program includes:

• Unlimited Assessments
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To learn more visit www.indianmathonline.com

Indian Students from the documentary film visit US

As I had written in an earlier post, Bob (Compton) and I have been very busy with the promotion of the documentary film - Two Million Minutes. The two Indian students - Apoorva and Rohit - joined us for over 10 days as part of the film tour in April 2008.

The trip was fun and hectic. Neil and Brittany - the two students from Carmel High School joined us as well.

A couple of interesting posts -

Apporva's view after visiting America

Comparison of High Schools in India, China and US 

Simple Interest - is there a simple explanation?

An IMO User sent us this question on Feb 25, 2008 -

I was wondering If you could tell me a simple way to find out Simple Interest. I don't get it at all. If you don't know what I mean then I will give you a sample problem: S. Find the interest earned on a $490 deposited in a savings account at an 8 1/2% per year for 6 months? Thank you for your time!

----------------------------Explanation-------------------

To understand the concept of Simple Interest, we first need to understand the different components that are involved in the calculation of Simple Interest.

There are five important components of Simple Interest. They are

• Principal
• Term or Period.
• Rate of interest
• Interest
• Amount    
      

The money deposited by a depositor in a Bank or the money loaned by a Bank to a borrower is called the ‘PRINCIPAL’

The duration for which the money is kept with the Bank or the duration for which money is taken on loan from the bank is called ‘PERIOD or TERM’

Banks charge a fee on the principal loaned and this is called the Interest. Bank’s major income comes from interest charged on loans.  Banks also pay interest to depositors for any money deposited with them.  Thus, in order for Banks to be profitable, they charge more interest on loans when compared to the interest paid on deposits

The interest one gets from the bank or the interest charged by a Bank on a loan is normally expressed as a percentage for a year. This is called the ‘RATE of INTEREST’.

Interest is the extra amount payable to the bank or by the bank for the money deposited or loaned

Amount is the sum total of Principal and Interest payable at the end of the term or period.

 

To calculate Simple Interest:

Simple Interest is calculated on the principal, (or on that portion of the principal which remains unpaid), for the term or period and at the Rate of interest.

When money is borrowed, interest is charged for the use of that money for a certain period of time. When the money is paid back, the principal (amount of money that was borrowed) and the interest is paid back together.

If

P = Principal amount (The sum borrowed or the sum loaned)

T = Period or Term of Deposit or loan in years

R = Rate of Interest (The interest amount on every $100 for one year)

I = Interest paid by borrower to the money lender or to the bank for use of money (P) borrowed

A =the amount paid or payable at the end of period, then (A = P+I)

For simple Interest calculation we use the formula:

Simple Interest I= PxTxR/100

Let us analyze following statement -

Find the interest earned on a $490 deposited in a savings account at an 8 1/2% per year for 6 months?

Here,

Principal P= $490

Time T = 6 months = 6/12 years = ½ year

Rate of interest R = 8 ½ % = 17/2 %

Interest =?

Now, we use the formula to find the Simple Interest

Simple Interest I= PxTxR/100

Substituting the values of P,T & R in the above formula, we have

I = (490 x ½ x 17/2) / 100

 

  =  (490 x 17) / (100 x 2 x 2)

By simplification, we have

I = 20.825

Therefore, the interest earned on a $490 deposited in a savings account at an 8 1/2% per year for 6 months is $20.825

 

Unitary method for finding simple interest

What does 8 ½ % interest mean? (The bank agrees to pay $8 1/2 for every $100 every year)

It is given that for $100, the interest is $ 8 1/2 per year (8 1/2% interest)

For $490, the interest is 8 ½ x (490/100) = (17/2) x (49/10) = $41.65 per year

Since the deposit is $ 490, the interest earned is $41.65 every year

For 6 months (1/2 years), the interest earned is 41.65 x1/2 = $20.825

Thus, the interest earned on a $490 deposited in a savings account at an 8 1/2% per year for 6 months is $20.825

In banking terms this method of arriving at interest is called ‘Simple Interest’

-----------------------------Brought to you by Indian Math Online

 

 

 

 

Compelling documentary on Global Education

As founders of Indian Math Online, we (Bob and Suresh) have been keenly interested on the topic of global education standards and how that impacts the global economy. During the trips we made in late 2005 and early 2006, we became convinced that India and China take education very seriously and that is reflecting in the number of qualified engineers these two countries are producing.

We wanted to highlight this phenomenon in a documentary style film and elevate the discourse on Global Education Standards and its impact on the global economy.

The result - Two Million Minutes - a documentary film comparing the education process in US, India and China.

You can view the trailer here and read more at www.2Mminutes.com