IntMath Newsletter - 12 Days, Calculus concepts, Why is math hard? and ADD
By Murray Bourne, 16 Dec 2008
16 December 2008
In this Newsletter:
1. The Twelve Days of Christmas - How Many Presents?
2. Best of 2008
3. Math tip - Calculus Concepts
4. Latest IntMath Poll - Why is math hard?
5. From the math blog
6. Final thought - We all suffer from attention deficit disorder
1. The Twelve Days of Christmas - How Many Presents?
One of the first math skills that we learn as children is to count. When we have large quantities of things, especially in probability, mathematicians need to come up with efficient ways of counting them.
This article takes a look at how to count the presents in the song, 12 Days of Christmas.
See: The Twelve Days of Christmas - How Many Presents?
2. Best of 2008
Here are the articles that created most interest and comment during 2008:
- Earth killer - composite trigonometry CO2 graph
- The Crazy Makers
- Greek Graffiti
- 21st century computer algebra literacies
- Algebra is the favorite math activity
3. Math tip - Calculus Concepts
A reader recently asked for some background to calculus.
Calculus is an incredibly powerful tool for solving a wide range of problems in science and engineering. It was developed by Isaac Newton and Gottfried Leibniz in the late 1600s.
Many people probably don't realize that the Greek mathematician Archimedes wrote about calculus concepts 2000 years before Newton was even born.
This article does not contain difficult math - it just involves finding the area of a triangle and putting dots on an x-y plane. The concepts are important ones in mathematics.
Go to: Archimedes and the area of a parabolic segment.
4. Latest IntMath Poll - Why is math hard?
Previous poll: A poll in Nov/Dec 2008 asked readers "Why do you have Math Anxiety?". The clear winner was that respondents felt "math is too hard".
37% Math is too hard
24% I don't believe in myself
22% Math teachers
11% Math is not relevant
7% Other people don't believe I can do math
Total votes: 1800
Latest poll: With such a large group of students responding that math is too hard, the latest IntMath poll asks readers what they find most difficult about math.
Please add your vote on any page in Interactive Mathematics. You'll see the poll in the right hand column.
5. From the math blog
1) The Twelve Days of Christmas - How Many Presents?
What is the math behind the "12 Days of Christmas" song?
2) Archimedes and the area of a parabolic segment
Archimedes had a good understanding of the way calculus works, almost 2000 years before Newton and Leibniz.
6. Final thought - We all suffer from attention deficit disorder
All of us have trouble focusing from time to time. Why do we focus on some things and not others?
Firstly, our brain is wired as a result of millions of years of evolution to focus on whatever may harm us. We are alert to the sight of traffic coming at us or the sound of someone walking behind us late at night. Bad smells get our attention immediately, since they usually mean something dangerous is nearby.
Your safety, hunger, thirst and oxygen needs are being monitored right now by your "primitive" (or reptilian) brain, the part down low, right in the middle of your head.
Limbic system (reptilian brain).
Assuming your basic physical needs are being met, then your brain is free to concentrate on whatever it finds most interesting.
Concentration occurs in the brain's pre-frontal cortex, the part just above your eyes. It's the area of your brain that is busy when you are thinking, reading, playing a computer game or solving a math problem.
Pre-frontal Cortex.
When something new, or exciting, or interesting holds our attention, our pre-frontal cortex
is bathed in a mix of hormones and neurotransmitters especially the "pleasure chemical" dopamine.
We actually become addicted to dopamine in the sense that we enjoy the feeling that it gives us, so we go back and do again and again the things that give us those good feelings.
Every day we are faced with a barrage of competing stimuli, all wanting our attention. Our parents, our children, advertising, our math teacher, our friends, our boyfriend/girlfriend, computer games, the Web and countless other things vie for our attention. We only have so much attention to give.
At night, when we are supposed to be doing math homework, our distractions include the Web, TV, phone, computer games, email, and noisy siblings.
And apart from all those distractions, the stresses of life are always at the edge of our "inner conversation", trying to take over our thoughts.
How to get focus?
Let's say you are trying to do your math homework, but just cannot get into it. Sounds familiar? Here are some simple ways to get focus:
a. Move! People used to walk 10 to 20 km per day before the chair was invented. Go for a short walk - it's amazing how you can see the solution to a problem when you walk away from it for a while.
b. Sleep. When's the last time you got 8 hours of rest? Sleep plays a very important part in learning - and the ability to focus.
c. Eat fruit, not junk food. Bananas are great brain fuel.
d. Think happy. This one might sound silly but works well. When my stress levels rise and I just can't concentrate on what I am supposed to be doing, I say to myself, "Think happy." It sounds goofy and I laugh at myself, which produces the desired result.
e. Turn everything off. Turn off your TV, the computer, the sound system - everything. Then plan to give yourself a media reward after (say) one hour of solid homework.
Good luck with your efforts to get focus.
Finally - Season's Greetings to all
December is a busy month for festivals.
Depending on your culture, I wish you...
- Happy Eid al-Adha (or "Eid Saeed!" - for the Feast of Sacrifice, on the 9th December - last week; called Hari raya Haji here in South East Asia),
- Happy Hanukkah (Festival of Lights, 21st December),
- Happy Christmas (birth of Christ, 25th December),
- Happy Kwanzaa (for African Americans, celebrating year-end harvest festivals, 26th December).
Forgive me if I left anything out.
And more than anything, I wish everyone the very best for 2009. I hope the economic crisis does not affect you too badly in your part of the world.
Until next time.
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