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  A-Squared E-Newsletter
© Copyright 2007 Lanny Buettner All rights reserved.

First Things First

My plans to publish a monthly newsletter had to be put off until summer. In January, I began teaching a single middle school math class at St. Benedict School and in early March, I got the opportunity to increase the number of classes to four. Stepping in to teach mid-stream is very time consuming, since one is building up lesson plans from scratch, trying to get to know fifty new faces, names, and special talents and needs, and, of course, grading papers. I have continued to tutor, as well, so there has not been much time for this. Now that school is out, however, I’m happy to kick things off with this first newsletter of the summer.

Summer Learning Opportunities from A-Squared Tutoring

Studying in the summer!? Well, not all day long, but summer is a great time to improve your skills in a difficult subject or prepare for a tough course you plan on taking in the fall. A-Squared Tutoring is offering a number of series of sessions designed to help students learn important core concepts in various subjects, including algebra, geometry, Trigonometry, Calculus, Physics, and Chemistry. Go to ASquaredTutoring.com for more information. Tutoring for SAT and other standardized tests is also available.

Learning Strategy
Do the Math: Study Habits Essential for Learning Mathematics

Studying is studying, right? Not right. Different subjects must be studied in different ways. Learning mathematics requires special methods, different from studying literature, history, social studies, or science.

First, whenever possible, experience the concepts under study first hand. This is how children learn to count and add and subtract. Yet at higher levels, teachers and textbooks tend to rely more on the printed word/number. This can work for some students, but even they benefit when they can experience the concept.

For example, factoring polynomials: This asks a student to determine how a polynomial may be produced by multiplying simpler polynomials. For example, x2 + 2x – 8 is the product of (x + 4) and (x – 2). Usually this is taught by showing how we can try different binomials (things like x +4 and x –2) so that when we do the math, it results in the given polynomial. But all things in math are based on the real world. Polynomials are no different.

One way to see how multiplying polynomials works uses something called algebra tiles. These can be made with cardboard, purchased from educational supply stores, or (best of all) simulated on the Internet (example 1, example 2).

The tiles help the student see there is a geometrical connection between the polynomial and the products that produce it. The example at the right shows
x² + 5xy + 6y².   Each block’s area is determined by the lengths of each side.
In this case, the longer side is x and the shorter side is y. But the large block made up of the smaller blocks has one side of length x + 3y and the other side x + 2y. So this demonstrates that (x + 3y)*(x + 2y) = x² + 5xy + 6y².

The next step is to study examples of factoring polynomials found in the textbook, provided by the teacher in class, and found on the Internet. Look at each step and don’t look at the next step until you understand what was done and why.

Finally, do the math! Work on problems for which the answers are provided. Most textbooks have the answers to odd numbered problems at the back of the book and many Internet sites provide the answer when you click on a link. Don’t look at the answer before you try to get it yourself. Review the examples and try to do the same steps. Work it out with algebra tiles. Once you have an answer, check to see if you are correct. If not, go back to the previous step. If correct, try another.

Most teachers assign homework so that students must practice problems at least a certain number of times. But the practice is only valuable when you are doing the problem correctly. Learn how to do the problems before attempting the homework.

When homework is assigned, always do the homework in advance of the due date. This way, if you have trouble doing the problems, then you can ask for help from your teacher. If you put off the homework until the night before it is due, it is too late to get this kind of help.

You don’t need to wait for a homework assignment, however, to go through the steps listed to learn how to do the problems. Do this as soon as you know that the material is to be covered by your teacher. It is helpful to attempt to learn the material on one’s own before seeing a teacher explain it. Studies have shown students remember material better when they do this.

Finally, always have a way to check your answer (other than looking at the back of the book). This way, you don’t have to wait for the teacher to grade the homework to see if you got the problems correct. If you make a habit of this and do it on all homework, quizzes and tests, you can catch mistakes and improve your grades! It also boosts your self-esteem to know you are correct, without waiting for someone else to confirm it.

News from the Worlds of Math and Science

Journey to the Center of the Earth                                    

When we think of frontiers, we usually think of outer space, yet we know less about the inside of the earth than we do about our solar system. The attempt to understand this hidden foundation of our world demonstrates the creativity and enterprise needed to do first rate science. Students interested in science may wish to go into earth science to contribute to this important area of study.

Science cannot understand what it cannot measure. We cannot (at present) get any kind of direct measure of the inside of the earth, except what the earth provides for us in volcanic eruptions. While this tells us much, it still only scratches the surface, so to speak, of the dark depths of the earth. Most of what we know comes from measuring the vibrations of the earth caused by earthquakes, which criss-cross the inside of the earth and are deflected and refracted by the solid and liquid portions.

Science fiction has long speculated what we might find if we could send some kind of craft into the earth. While it is very unlikely we can create a craft capable of keeping people alive in the inhospitable temperatures and pressures of the earth’s inside, we may one day send some kind of scientific instruments into the earth to relay more direct measurements. Read more about one scientist’s idea for how to do this in the following article in Discover:

Journey to the Center of the Earth

For more information on what scientists currently think is true about the inside of our planet, see the following links:

Pittsburgh Supercomputing Projects (www.psc.edu/science/)

Nevada Seismo Labs

Ask Geoman (Mike Strickler: http://jersey.uoregon.edu/~mstrick/)

Robert Lang: Physicist, Origamicist

There have been a number of recent articles on a physicist, Robert J. Lang, who quit his job at a fiber-optics company to work full time on designing origami models of insects and other complex things.

If this seems odd, think again. Both physics and origami, the art of folding paper into artistic figures, have strong connections to mathematics. Physics, of course, uses very complex mathematics to try to understand the universe, sometimes inventing new fields of mathematics just to solve a problem. Origami demonstrates many mathematical principles related to geometry in ways that are hard to match with a straight edge and a compass.

Lang pioneered the use of computer software to help design origami figures. Until this innovation, origami figures tended to be rather simple, with at most about thirty steps. It was not so hard to make a rather abstract looking cat or bird or butterfly, but making a spider or beetle with wings was not possible. The steps needed to reach such models are so complex that it is ideally suited to a computer program to work out. This work has suggested ways to understand things in the real world, such as how strands of DNA fold up to fit compactly in the nucleus.

Read the following articles for more on Lang, Origami, and Math.

Into the Fold (Smithsonian Magazine)

Gallery of Lang Models in Symmetry Magazine

The Origami Lab (New Yorker Magazine)

Robert Lang and the Global Reach of Origami

(reprint of The Origami Lab, but with photos of Lang Models)

Sites relating Math and Origami

Richmond Education Calendar
A listing of events in the Richmond Area with educational value.

Coral Reef Adventure
Now through July 12, 2007

Science Museum of Virginia IMAX Theater

Take a trip with underwater filmmakers to the coral reefs of the South Pacific in this amazing IMAX film.

Dinosaurs Alive
Now through July 12, 2007

Science Museum of Virginia IMAX Theater
Take a journey that stretches from the Gobi Desert in Mongolia to sandstone buttes in New Mexico, as you witness dinosaurs come to life on the IMAX screen through computer-generated animation!

Savage Ancient Seas
Now through September 03, 2007

Science Museum of Virginia
Enjoy a look back at our world's "Savage Ancient Seas," featuring more than 50 prehistoric marine skeletons, giant fossils and more. Included with museum exhibit admission. Science Museum of Virginia

Summer Vacation Preparation
Thursday, June 14, 2007, 7:00 PM
North Park branch, Henrico Public Library
Get ready for your vacation with travel tales, map hunts, and a chance to design your own postcards and travelogs. For Elementary (5-11 yrs), Preschool (3-5 yrs).

LiveSky (planetarium show)
June 15, 2007, 6:00 PM
Science Museum of Virginia

If you are fascinated by the ever-changing night sky, this interactive planetarium show is for you.

Sky Watch
June 15, 2007, 9:00 PM

Science Museum of Virginia
Join members of the Richmond Astronomical Society on the front lawn as they share their telescopes for a look at the night sky (weather permitting). Free.

Science Saturdays Adventures in Physics Day.
June 16, 2007

Science Museum of Virginia
The Science Museum is the place to be on Saturday afternoons. You can have a blast with hands-on activities, science demos, interactive exhibits and more.

Environmental Book Discussion Group
Monday, June 18, 2007, 7:00 PM
Tuckahoe branch, Henrico Public Library

The general discussion will focus on urban planning and growth management. The featured book will be Ecocities: Rebuilding Cities in Balance with Nature by Richard Register. For Adults, High School (14-18 yrs)

Scooper Bowl XV
June 23, 2007 10:00 AM —4:00 PM

Science Museum of Virginia
Celebrate summer with a huge party and all the ice cream you can eat. Celebrate summer with a huge party. Get wet in a water maze. Fly down a water slide. Find out about brain freeze. Test your aim with a medieval siege machine. Learn how to ride a Segway® Human Transporter. Cheer on your favorite rat basketball player. See Kung Fu demonstrations from the Shaolin Dragon School. Peruse massive skeletons of the creatures who ruled the ocean while dinosaurs roamed the land. And eat ice cream - plenty of ice cream. $12.