Prevent Summer Learning Loss ~ Tip #2 ~ Math Skills

Tweet One of the ways to keep your math skills up during the summer is to make a recipe. However, you need to change it up a bit.

Find a recipe that serves four. Then increase each ingredient in order to turn it into a recipe for six. This means you'll need to multiply each ingredient by one-and-a-half.

There are several ways to do this, depending on the original value you're increasing. For instance, if the original amount is 3 tablespoons, it's probably easier to just multiply 3 times 1.5. But if the recipe calls for 2 teaspoons, it might be easier to just use one (2 teaspoons) and a half (1 teaspoon) and then add them together to get 3 teaspoons. Find a method that works best for you and your recipe.

Now enjoy what you've made. Next time, make it a little harder by increasing the recipe so it serves 5 people.

Mathematics Suffers Again

Tweet Russian mathematician Dr. Grigori Perelman may turn down a one million dollar prize for solving the Poincare Conjecture. He turned down a similar prize several years ago, and may also turn down this one offered by the U.S. Clay Mathematics Institute. The 46-year old reclusive genius does not seek fame or fortune.

In one way, I applaud him for his love of mathematics and his total devotion to it, not wanting the awards. I also appreciate his integrity.

In another way, it bothers me that once again we have a genius mathematician who does not fit into society, nor wants to. It gives the "normal" members of society another reason to think that anyone who devotes their life to mathematics is "weird." The study of mathematics is already held in disdain by many. We really don't need to give them any more reasons to think this.

Khan Academy

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When I first visited the Khan Academy, I was so impressed with the videos Sal Khan has placed on YouTube, I emailed the website link to the teachers I used to work with. Most of the videos are the same thing students see in class, but since they're online, the students can go back over them as many times as needed; something not possible in the classroom. The following video gives background information about Khan Academy. I know that if I were teaching now, every one of my students would have the link to his website and his YouTube videos.

http://www.youtube.com/watch?v=HycjWQcAymQ

Ten Reasons I Love Pi

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Pi is such an excellent number. Pi Day is just around the corner. Here are the reasons I love it

1. Pi has its own day. March 14th is Pi Day. You get it ... 3/14 (3.14). Cool, huh?

2. Pi has its own song:

http://www.youtube.com/watch?v=hJJJmQojcLM

3. If you memorize more than two decimal places of pi, people will think you're a mathematical genius. Here are a few: 3.1415926535897

4. There are jokes about pi. What do you get when you cut a jack o'lantern through it's diameter? Pumpkin Pi

5. Pi has it's own movie. Here is the trailer:

http://www.youtube.com/watch?v=oQ1sZSCz47w

6. Without pi, we couldn't have anything round (like cherry pie or pizza pie).

7. Without pi, we wouldn't have trigonometry. That means no waves...no microwaves, no radio waves, no sound waves, no light waves, no x-rays, no surf. Okay, we might have them, but we would have to use degrees instead of radians.

8. Computer calculations of pi allow us to increase our computing power.

9. Pi is totally irrational. That means it cannot be represented exactly as a fraction where the numerator and denominator are integers. It also means that its decimal form never ends and never repeats.

10. There are pi limericks:

There once was a number Pi

Very special like e and phi

Circumference to d

Is the ratio for me

And it's not a multiple of i

Now go and celebrate pi and Pi Day.

The Human Calculator

Tweet Every once in a while you run across something that is just amazing. It's been a while since I've seen this man on television. He is a bit older, but still impressive. His name is Scott Flansburg and he's called The Human Calculator. I believe the following video says it all much better than I can. I don't know about his mathematical abilities, but his calculation skills are incredible.

http://www.youtube.com/watch?v=1LyoeWLmclU

Chisenbop

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Today I was thinking about a method of adding and subtraction using your fingers. I saw a classroom of children do this on television years ago. They were so fast, much faster than the adults sitting there with calculators. The method is called Chisenbop. The following videos explain it well, but don't really show the speed that one can attain.

The first video is of a teacher explaining Chisenbop. The second video is of a five-year-old boy using it to add. It really is pretty amazing.

http://www.youtube.com/watch?v=FJx7GSLhOro

http://www.youtube.com/watch?v=prT6o40CBWg

Not Just a Stupid Education Fad of the Day

Tweet Michelle Malkin describes herself as "a mother, wife, blogger, conservative syndicated columnist, author, and Fox News Channel contributor." Yesterday, on her blog, she evidently decided to give the liberals in government a break while she criticized mathematics education. It's obvious why "math teacher" is not included in her bio.

It seems a group of students at Mesa School in Somis, California is studying "Mayan Math." Ms. Malkin is concerned about the "social justice-tainted effort by educrats to corrupt and undermine rigorous math education in this country" and calls the topic the "stupid education fad of the day."

In my experience as an actual math teacher, I was always concerned that students know the subject matter. I always tried to teach the basics and then extend that learning into rigorous mathematics. In all my years of teaching, I never met a math teacher who wasn't concerned about this.

But there are different paths that lead to the same result. One teacher might make the students take timed tests to learn their basic multiplication facts. By taking these tests over and over, the students eventually learn those facts. Another teacher might have students work with each other using flash cards. A third teacher might have the students practice those multiplication facts using a teaching program on a computer. Is one method any better than the other? The methods all lead to the same result, but different students respond favorably to different methods. Some will learn better with the drills, others with the flash cards, and others with the computer. But if they all learn their multiplication facts, then the methods are all successful.

Who's to say that Mayan Math won't help a student learn? Teachers are always trying different strategies to reach as many students as possible. If Mayan Math causes a few students to become interested in mathematics and want to learn more about it, then it's worth it.

My fifth grade teacher taught us several different bases in math. I remember learning base 2, base 3, base 4, base 8, and base 16. The work reinforced and strengthened my learning of the base 10 system we use everyday. Learning base 2 and base 16 was also valuable in my computer programming classes, since these are the languages on which computers are founded.

Mayan Math uses base 20. It's quite possible that a student learning base 20 will be a better math student for it. They may understand base 10 better. And if they're planning to do any computer programming, learning different bases is a necessity, not just a "stupid education fad of the day."

I am all for rigorous math programs, but until you are in the classroom day after day, working 24/7 to keep 150 students achieving at proficient levels, you really shouldn't be judging. I know that some modern math initiatives are worthless, but taking 3 or 4 days during the school year to learn something interesting or fun or different or cultural does not take away from a rigorous mathematics curriculum. It may actually enhance it. But I'm sure Michelle Malkin would just think that was "Perfect dogma in the Age of Obama: Feeling over facts. Cultural connection over competence. Diversity uber alles." I just disagree with her.

Source:

http://michellemalkin.com/2010/01/25/stupid-education-fad-of-the-day-mayan-math/

Four Websites for Improving Math Skills

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When there is something I need to know or review, I find one of the following websites usually has the answers.

Khan Academy

http://www.khanacademy.org

The Khan Academy has an amazing collection of over 1000 videos on YouTube. Topics cover everything from basic arithmetic to physics, calculus, and finance. It is a not-for-profit organization whose mission is to provide high quality education for everyone.

Wolfram|Alpha

http://www.wolframalpha.com

Wolfram|Alpha allows you to input words or equations and get solutions. They explain it this way "We aim to collect and curate all objective data; implement every known model, method, and algorithm; and make it possible to compute whatever can be computed about anything." It's a little like a search engine, a little like a calculator, and full of information.

MIT OpenCourseware

http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

MIT OpenCourseWare contains almost all MIT course content. It is open and available to everyone and contains free lecture notes, exams, and videos from MIT.

Brightstorm

http://www.brightstorm.com/d/math

Brightstorm has videos on math topics ranging from Algebra to Calculus. Over 2000 free online videos are presented by some of the best educators. There are also lessons for SAT and ACT Prep, but after a free 7-day trial, there is a charge for this.

Lattice Multiplication

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To any student having trouble with multiplication, the first thing you should do is memorize your basic multiplication facts. All math from 2nd or 3rd grade on is based on these facts. You don't want to have be looking them up on a table or putting them into a calculator each time you need them. Just imagine doing a complicated Calculus problem and having to put 8 x 7 into a calculator because you never learned those basic facts.

When you start multiplying larger numbers, lattice multiplication may help you understand your work a little better. Lattice multiplication is also fun.

Below are two videos. The first will demonstrate lattice multiplication. The second will explain why it works.

LATTICE MULTIPLICATION

http://www.youtube.com/watch?v=gS6TfWUv97I

WHY LATTICE MULTIPLICATION WORKS

http://www.youtube.com/watch?v=S3z4XqC_YSc