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.
See the 17 Comments below.
16 Dec 2008 at 5:51 pm [Comment permalink]
An additional method of gaining focus is to use the technology of sound/light machines.
I use the NeuroProgrammer2, which is rather cheap considering programs, and most effective when inducing brain states conducive for focus, memory, creativity, etc. I've shared it with a few of my college professors (I/O psych), and they agree it is a great program. They also supply references to all of their research.
I have a form of ADD which greatly affects my ability to concentrate, and I refuse to use the drugs available to control it. This program works just fine without drugs.
16 Dec 2008 at 7:06 pm [Comment permalink]
Thank you very much for those helpful tips to remain in focus! I knew about most of them but you just provided a wider concept.
And as always, a very interesting letter! 🙂
16 Dec 2008 at 8:03 pm [Comment permalink]
Mick: Thanks for the information. I had a look at the NeuroProgrammer2 site and it looks interesting. I couldn't see any reference to neurofeedback - does it involve that as well?
Hassan: Thanks for your kind comment and I'm glad that you find the Newsletters interesting.
16 Dec 2008 at 8:40 pm [Comment permalink]
Hassan and Zac, glad I could be of service.
The program does not entail neurofeedback, for which you will need some biofeedback hardware, but only brainwave entrainment. You can purchase additional hardware for this NP2 program in the form of light goggles, but I find the screen flashing function works fine, and usually I only use the sound through headphones. The program itself has a user guide under the help button, and contains a wealth of information including references to scientific papers which support the theory behind the program. The only feedback I get is the increased ability to focus in on a task, or the effects that different programs produce, such as imagery, etc.
I have considered biofeedback machines which involve neurofeedback, but at this time, I really don't think they are necessary for my personal growth.
I hope this helps.
Best wishes,
Mick
16 Dec 2008 at 10:32 pm [Comment permalink]
Dear Murray, --- In order to support my studies in ontology, the study of the nature of being, existence and realities, I am back again to calculus and surounding math. I have a very effective course:" Change and Motion: Calculus made clear" by professor Michael Starbird of the University of Texas at Austin. These lessons come from : The Teaching Company.
Other books are " Quick Calculus ( a self teaching guide) by Daniel Kleppner and Norman Ramsey. Also; The mathimatical Tourist by Ivan Peterson. Very interesting. And just een Algebra 1 tekstbook that I borrowed for infinite time from the Highschool here in Bayborough.
It is not easy for those ancient brains of mine, but challenging and, at the end, victory. I thank you again for your letters.
I wish you and your loved ones a merry christmas and a truly happy and properous New Year. Alhamdulillah. Johan de Nijs.
17 Dec 2008 at 4:46 pm [Comment permalink]
Thanks for your greetings Johan and the same to you.
I have The Mathematical Tourist and find it an enjoyable read.
You may be interested in Godel, Escher and Bach by Hofstadter and The Infinite in the Finite by Wilson.
All the best to you.
17 Dec 2008 at 6:57 pm [Comment permalink]
amazing
17 Dec 2008 at 10:10 pm [Comment permalink]
thankyou for your comment.but here is one que i would like to ask you i want study math in deep naw i am going to be math but i am not confident i wanna study in deep pleace send me an adivise. at last i wish you a happy christmas
18 Dec 2008 at 4:44 am [Comment permalink]
I love those tips for how to focus!
19 Dec 2008 at 12:00 am [Comment permalink]
I tutor students in 8th grade math. I recently had a student with ADHD so bad that sometimes he would just sit and bang his head against the table. I started sending him to the gym for 15 min. of extremely vigorous activity, running, etc. "Don't come back till you're sweaty". It worked wonders in getting him to focus. Bill Rosquist
19 Dec 2008 at 7:57 am [Comment permalink]
Thanks for the great story, Bill.
We tend to diminish the connection between mind and body too much. Generally, if the body isn't happy, the mind will also have problems. Your solution was a good one.
26 Dec 2008 at 4:31 am [Comment permalink]
The CO2 story is sobering, and fortunately I think it is finally getting told, simplistically, in the mass media. Bloggers were no doubt onto it long before the other mass media.
I wonder what the highest level of CO2 was in the atmosphere since multi-cellular organisms arose. Couldn't find it with a quick search...
Note that organisms which depend on calcium carbonate (shells, for example) may be challenged by higher CO2 levels. Dr. Richard Mitterer (Univ. Texas at Dallas) pointed out that CO2 dissolved in water (which occurs naturally all the time) in turn makes water a solvent of calcium carbonate.
28 Dec 2008 at 2:39 am [Comment permalink]
I could not participate in your survey because I do not have any math anxiety, rather, I have a great passion for it. I do math problems the same way others do crossword puzzles. Nothing makes me happier than a good math problem! I haven't used any calculus for many years but I still use algebra and trig on a regular basis just figuring out things that life presents. Your newsletter is great for people like me! Thankyou!!
1 Jan 2009 at 10:47 pm [Comment permalink]
Thanks for the GeoGebra reference. I've been enjoying learning and and using it.
11 Jan 2009 at 1:41 pm [Comment permalink]
hi..thank you for helping me in my assignment in advance algebra.. I've been enjoying learning and using your website.. thanks a lot.. may god bless you and your family .. take care..
22 Jan 2009 at 5:11 am [Comment permalink]
i am getting ready to do my G.E.D on Feb,10th please send me some math problems that pertain to the g.e.d thank you for being supportive i've been working on my math for 4 months now and feel confedent that i'll pass.
Lorraine medina
22 Jan 2009 at 9:08 am [Comment permalink]
Hello Lorraine
After checking your IP address, I worked out that you are talking about the GED in California, correct?
[For those who don't know what a GED is, it stands for "General Education Development" and is seen as an alternative to a high school diploma (although there is great debate about its equivalency.]
Here’s some tips on how to study the GED math portion.
Hope that helps.