First Things First
This is the first issue of an electronic newsletter for parents and students, brought to you by A-Squared Tutoring. In each monthly issue you can expect study habits tips, links to websites with helpful tutorials and interactive learning activities, news from the world of science and math, and a calendar of educational events in the Richmond area. If you find this newsletter helpful, please show it to others who may be interested.
Learning Strategy: Triggers and Memory Pegs
We have all put in our time at the memorization salt mines. We make flash cards, get friends to quiz us, and cram just before an exam. But all too often we fail to use the memorized facts at the proper time. Or we memorize formulas but then do not choose the right one.
One way to help make memorization more effective is to memorize not just the fact or formula but also the context in which the fact must be used. The trigger and memory peg approach is designed to do just that.
A trigger is something that you learn to notice that reminds you there is something you have memorized related to this situation. When learning algebra, the presence of a letter among numerals and an equal sign triggers the thought that this is a variable in an equation. We then should remember the various strategies to solve equations, many of which have their own tell-tale triggers. In geometry, the image of a circle should trigger remembrance of the formulas for circumference and area of a circle.
For the trigonometry student, right triangles trigger one to remember a number of trigonometry functions which relate the various sides and angles. In proofreading, we should learn to let tricky spelling words, like their and there and they’re, trigger a check to see if we have used the right word for the context.
But the trigger does no good if we cannot then remember the fact or formula we need to know. We need ways to make the fact stick in memory. This is where the memory peg comes in. A peg is something on which to hang the fact to be memorized.
Having trouble with the area of a circle, which equals πr2? I remember a teacher once joked, “Pi R Squared is wrong. Pie are round. Cornbread are squared.” It’s silly, to be sure, but it is memorable and gives a way to remember the formula that goes beyond rote memorization of letters and numbers.
Another example is the rule for determining the right spelling order for the letters i and e: “I before E, except after C, and when it says ‘A’ as in neighbor and weigh.” Music students learned to remember the lines of the treble staff as Every Good Boy Does Fine, and the spaces of the bass staff as All Cows Eat Grass. Similar sayings exist for remembering the order of the planets from the sun, the colors of the rainbow, the color code for electronic resisters, and many more.
Jokes, rhymes, and phrases starting with certain letters are just three examples of memory pegs that help make the memories stick. You should make up your own when necessary. Especially tricky is the case where one has to pair up two facts with two situations. How to avoid confusing the two? In trigonometry, there are two formulas for relating the lengths of the sides of a right triangle to the angle (θ):
Cos θ = adjacent side to the angle / hypotenuse and
Sin θ = opposite side to the angle/ hypotenuse.
These are so similar that it would be easy to mix up cosine with sine or opposite or adjacent. My solution is to note that just as Cosine comes before Sine alphabetically, so adjacent comes before opposite.
But then one must remember that Tan θ = Sin θ / Cos θ. Now we have to put Sine over Cosine. How to keep that straight? How about noting that Sine is a shorter word than cosine, so cosine being heavier sinks to the bottom while Sine floats on top? There are probably many different ways to remember these facts. The important thing is to choose a peg you can remember!
The trigger and peg method of memorization provides a systematic way to focus memorization efforts so the facts you have crammed into your memory can be unpacked at the right time and place. Now if you can only remember to use them!
News from the Worlds of Math and Science
Finalists announced in the Intel Science Talent Search
For the past 66 years, Science Search, a non-profit organization to advance public understanding of science founded in 1921, has sponsored a competition for high school science students. With a top prize of a $100,000 scholarship and thousands of dollars for the top finishers, over 1500 students entered the competition last November. In January, the number of entrants was reduced to 300 and the final forty have now been announced. The students’ projects will be judged in March at the National Academy of Sciences in Washington D.C.
Among the semifinalists was Sohini Sircar, a student at Maggie L. Walker Governor’s School in Richmond. Sadly, she was not named for the finals. Ms. Sircar was the 2006 winner of the Richmond Metro Science Fair and has been recognized at other science competitions, including first place in the Genetics and Cellular Biology category of the 2006 Virginia Junior Academy of Science Awards, first at the Virginia State Science and Engineering fair, and fourth place at the Intel International Science and Engineering Fair.
The Richmond Metro Science Fair for 2007 will be held at Godwin High School on March 24. Be there and support the scientists of tomorrow. For more information:
http://mathsciencecenter.info/scifair/index.htm
http://www.mathsciencecenter.info/fnd/documents/SponsorBrochure2007.pdf
http://www.sciencenews.org/articles/20070203/fob7.asp
http://www.sciserv.org/Sts/
Popular Musician Infuses Math into Music
“It feels like poetry or painting, feeling around with abstract shapes and putting them together in different ways.” What is the person who said this talking about, do you think? Sculpture? Photography? Computer games? Actually he is talking about math.
Robert Schneider, the speaker of the quote, is the leader of the indie-rock band Apples in Stereo, whose new album, New Magnetic Wonder, incorporates alternative musical scales developed from logarithms of the frequencies of musical tones. Schneider took time out from his busy music schedule to study calculus and physics at a community college in Kentucky, and then incorporated his ideas into the music for the band’s next album. Schneider demonstrates that math may turn up in unexpected places and need not be confined to stuffy classrooms.
For more information:
http://www.topix.net/content/kri/0255016855060983606701518499003004956273
http://www.livedaily.com/news/11499.html?t=103
Listen to excerpts from New Magnetic Wonder at http://store.yeproc.com/album.php?id=11829
Richmond Education Calendar
A listing of events in the Richmond Area with educational value.
A Slave Ship Speaks: The Wreck of the Henrietta Marie
February 3 to May 18, 2007
Joel and Lila Harnett Museum of Art
University of Richmond Museums
The slave ship Henrietta Marie sank off the coast of Florida in 1700. It was discovered in 1972 and excavated in 1983. It is believed to be the world's largest source of tangible objects from the early years of the slave trade. http://museums.richmond.edu/hmaexhibitions/henrietta_marie.html
Also at the University of Richmond Museums:
New Colonies: Prints, Maps and Perceptions of the New World
January 23 to April 28, 2007
Joel and Lila Harnett Print Study Center
This exhibition brings together maps, prints, and books from 1590-1721 that reflect the early impressions of explorers and colonists in Virginia and the impact of these perceptions of the New World throughout Europe.
Native Plants of Virginia: Selections from the University of Richmond Herbarium
February 28 to June 24, 2007
Lora Robins Gallery of Design from Nature.
Saturdays in the Studio
Every Saturday 11 A.M. to 1:00 PM through April 28
Virginia Museum of Fine Arts
VMFA’s Teen Studio offers a variety of classes in drawing, fashion, digital art, painting, sculpture, zines, cartooning, collage, portfolio review, and more for students in grades 6 – 12. Advance registration required.
"Amazing Music Studio"
January 27, 2007 - May 06, 2007
Science Museum of Virginia
Learn about music as an art and as a science in this visiting exhibit. Free with museum admission.
Pocahontas: Her Life and Legend
February 10, 2007 - June 24, 2007
Virginia Historical Society
This exhibition explores the many myths and images of Pocahontas and compares them to the few documented facts about her life.
Science Saturdays
January 27, 2007 - December 31, 2007
Science Museum of Virginia
Enjoy interactive learning on Saturdays at the museum with science demos and hands-on activities.
Learning Links
Below are some links to web sites that offer help to students of various subjects. Take advantage of the many learning opportunities now on the Internet. For more links, visit ASquaredTutoring.com.
Physics
Physics Classroom
http://www.physicsclassroom.com/
This site is a very good general resource for high school physics students. It contains tutorials that explain important topics, a multimedia physics studio providing animated explanations and demonstrations, and extra help on selected tasks.
Chemistry
Science Help Online Chemistry
www.fordhamprep.org/gcurran/sho/sho/index.htm
This site provides a wide range of helpful material, including lessons, review quizzes, laboratory procedures, skills development, and worksheets. It also features a page with links to other sites that have chemistry information.
Astronomy
Planetary Mysteries
http://ology.amnh.org/earth/planetology/index.html
Created by the American Museum of Natural History, this colorful site provides lots of interesting facts about the planets but also mysteries that science has yet to explain. Lots to do for the curious mind!
Earth Science
Earth Science Enterprise
http://kids.earth.nasa.gov/
Produced by NASA, this site explores the earth and the science that studies it, with sections on people, land, water, air, and natural hazards, each with a spectrum of things to read, see, and do.
Biology
The Biology Place
http://www.phschool.com/science/biology_place/index.html
This has a lot of advanced biological science activities and information. It is divided into three sections: BioCoach, which has interactive visuals and practice of specific topics, LabBench, which has virtual lab experiments, and a Glossary.
Math
eNLVM interactive on-line math lessons
http://enlvm.usu.edu/ma/nav/bb_dlib.jsp
The opening menu provides a grid with areas of mathematics down the side and four grade levels across. Each link on the grid provides an impressive collection of Java interactive applications on a wide variety of mathematics concepts, from simple addition to fractal geometry.
Algebra
algebra.com
http://www.algebrahelp.com/
Comprehensive site with lessons, calculators, and worksheets, study tips, and other resources. There are some small ads along the edges of some pages.
Geometry
Euclidean
http://www.mccallie.org/myates/Proofs/default.htm
A very good site for step by step explanation of how to do proofs.
Trigonometry
Trigonometry Realm
http://id.mind.net/~zona/mmts/trigonometryRealms/trigonometryRealms.html
Step by step explanation of trigonometry, with some interactive graphics, as well as quiz/problems with answers provided.
Calculus
The Calculus Page
http://www.calculus.org/
Some good tutorials with practice problems and solutions, tips on how to do well in calculus, animated demonstrations, sample exams provide help on the most important concepts of calculus. Then there is a long list of links to other calculus sites.