A-Squared Blog
Summer Fun, Keeping Cool, and Learning a Lot
Well, it is summer and that means hot weather, vacation from school, and lots of time for kids to fill. As you are looking for ways to enjoy the summer here in Richmond and beyond, take advantage of the tremendous value museums offer, especially for families. Museums generally cost little to enter--a few dollars if you are not a member. They are air conditioned inside, with lots of room to explore. Young people can learn a lot without having to worry about taking a test about it later.
Here in Richmond, we have many fine museums. My favorite is the
Science Museum of Richmond, located at Broad Street and Robinson. The building is a fabulous attraction in itself. It was once a train station in the grand tradition of an earlier era. Inside you'll find a variety of exhibits--some are permanent; others change periodically. The current visiting exhibits include a look at the beach as a scientist sees it, a National Geographic exhibit on maps, and a photography exhibit of dramatic photos of Saturn. Check their website for special events that make learning about science fun.
For those who like the wonders of nature, don't miss the
Lewis Ginter Botanical Garden, just north of Richmond (get off I-95 at Lakeside exit). This garden is always changing, so you can visit it often and always find new plants to enjoy. They have a special area for children, with sandboxes and an area for frollicking in spraying water (bring a swim suit). They have many educational events and a great cafe and gift shop. The garden is open some evenings all summer, with family activities, concerts, and more.
The
Virginia Museum of Fine Arts just opened their newly remodeled and expanded facility on Boulevard in the Fan. I have yet to see it, but reports are that it is well worth a visit. Richmond also has a rich assortment of historic museums with exhibits on Virginia history, literary figures like Edgar Allen Poe, and more.
If you travel just a few hours, you can sample the national museums in Washington, D.C., and the Norfolk, Virginia area. If you are traveling further, be sure to check what museums are available where you are going.
Check out the Image Gallery for some photos of the flowers I took at the Lewis Ginter Botanical Garden (link is above on the left).
Don't be a victim of Physics!
Years ago, I cut out a cartoon that showed a middle-aged man on a riding mower making a sharp turn right next to a pond. He is in the process of falling off the mower into the water. The caption read, "Another victim of physics!" Of course, the real reason for the accident is ignorance of physics, in this case, Newton's first law of motion.
It is snowing again, with a chance of freezing rain. As I type, there are probably already vicitms of physics ignorance who have crashed their cars because they did not take into account some basic properties of friction and Newton's first and second laws. Before you drive in the rain or snow or on ice, make sure you understand the following laws of physics:
Newton's first law: Objects in motion, tend to stay in motion, moving in a straight line at constant speed, unless acted on by a force. This means in order to stop a moving vehicle, one must apply a force to the car in the opposite direction as the car is moving. Also if you want to turn, you must apply a force pushing the car in the direction of the turn.
Newton's second law: The amount of force needed to change the speed and/or direction of motion is proportional to the mass of the object and rate at which the velocity is changed. This means the faster you want to stop, the more force you will need.
When driving, the force needed to slow a car or to turn a car is provided by friction. But there is a limit to how much force friction can provide. This depends on the surfaces in contact and also on the amount of force pushing the two surfaces together. For a car or truck, the surfaces involved are the rubber of the tires and the road. The weight of the car determines how much force pushes the surfaces together.
Put all this together, and you have the physics of normal driving and braking. Under normal circumstances, the force provided by friction is enough to slow cars down when stopping or to round turns at reasonable speeds. But there is a limit to how fast one can stop and how fast one can round a turn. This limit is the maximum force the friction between the tire and road can provide. Exceed this limit and the car will skid.
Another fact of friction is that the force friction can provide is more when the surfaces are not shifting or sliding across one another. This is called static friction. When surfaces begin to slide, the amount of frictional force drops. This is why one does not want to lock the wheels when trying to stop quickly. The car will slide farther if it is skidding, plus turning the steering wheel will have no effect. Therefore, you do not want the car to skid!
But another fact of friction is that a wet surface generally can provide less frictional force than a dry one. An ice covered surface has even less friction. For rubber on asphalt, the maximum force friction can provide drops by 50% or more when the surface is wet. For rubber on concrete it drops 25% or more. That means it will take longer to stop on wet pavement; it also means the maximum safe speed for rounding turns drops on wet pavement.
The maximum stopping force of friction is even less for roads covered in snow or ice. The worst is wet ice, which reduces friction by 90% or more.
Conclusion: drive more slowly when the roads are wet and even more slowly when they are covered in ice or snow!
What if you are driving a heavy vehicle? Won't the frictional force be larger because the weight of the car pushes the surfaces together with more force? Yes, but remember that Newton's second law also states that the more mass a body has, the more force is required to get it to slow down or round a turn. So a Hummer or Escalade has to slow down just as much as a Mini-Cooper or VW!
Snowflakes: Nature's Geometry [1/30/10]
We just had a snowstorm in Richmond. As I write this, over a foot of fluffy white snow rests peacefully on the ground. I grew up in Indiana, so it does not seem like winter unless we get a few snows like this. Snowflakes are crystals of solid water. The crystals are not white, however; the surface of the crystal reflects all colors and the combination of all colors looks white.
But the true beauty of the snowflake can only be appreciated fully by looking at the snowflake under high magnification. The pioneer of snowflake magnification and photography was
Wilson Bentley, a Vermont farmer who, between 1865 and 1931, photographed thousands of flakes. At left is a small selection of his art. The almost infinite variety of snow crystals is an example of fractal geometry.
Fractal geometry was invented only about fifty years ago. This is not your father's geometry! It recognizes that nature's geometry is not the simple collection of circles, triangles, and squares of your typical 9th grade geometry class. This is the geometry of winding rivers, jagged coastlines, fluffy clouds, branching patterns such as in trees, blood vessels, and the brain. If you have a child taking geometry, encourage him or her to look at this side of geometry. It might help get through proofs of congruent triangles!
To see pictures of snowflakes and fractals, click on the newly added "Image Gallery" at the top of this page.
Perspective: Use it or Lose it! [1/20/10]
I checked out the Astronomy Picture of the Day and discovered a remarkable animation. It is called The Known Universe and was created by the American Museum of Natural History. It shows a view of the Himalayas from above and gradually changes to simulate moving away from earth at ever increasing speeds. Watch it and reflect on our place in the cosmos! Our ancient ancestors thought the universe consisted of the earth, flat like a plate, with a bowl over it (the sky) and beyond that a sphere containing the stars. Over time, scientific exploration of the heavens has revealed a universe that is larger and larger. Less than 100 years ago, we knew there were billions of stars, but thought our galaxy was the extent of the universe. Then better telescopes and clever use of information conveyed in the starlight showed that there are as many galaxies in the universe as stars in our galaxy. These same scientists found the universe is expanding, apparently from an explosion that literally created the universe about 14 billion years ago. By comparison, humans have been looking at the stars and wondering what they are for only a few million years.
Many people never realize how remarkable our universe is. They never look at what science has to show. Many never even look at the night sky from a location that shows the true glory of the heavens. Our city lights hide from us what every other human who lived more than a century ago could see every clear night. Some complain that if the universe is so big and old and we such a small portion of that space and time, it diminishes our significance. But we can gain more joy and awe in being a part of this inconceivably vast cosmos than we lose from climbing off the pedestal on which we thought we had been placed by God. Take a look and let your inner child wonder at this amazing universe. Then search the web for something fascinating about this universe that has been uncovered by scientists. Do this every day and you will feel very significant, very proud to be a part of this universe. [If you need suggestions on where to look, check out A-Squared Tutoring's Learning Links.]
For an older animation that attempts to show the same perspective, check out "Powers of Ten". This shows the same pan back from the surface of the earth, but then it zooms back in to reveal an ever more magnified view of the matter that makes up a human body, down to the sub-atomic scale. The universe contained in our own bodies is just as remarkable as that which surrounds us. Then consider that all the matter that makes up our bodies was once part of glorious stars; your feelings for this universe and your/our place in it will deepen profoundly.
I recommend one more mind-bending animation that shows another amazing dimension to our place in the cosmos. In the animation "Nothing but Zooms," we are taken into a mathematical marvel, the fractal complexity that scientists now know is found throughout the universe, from the very large to the very small. There are several other similar animations: http://vodpod.com/watch/1494074-fractal-tao-tao-as-the-watercourse-way
New Chemistry and Physics Links added to Learning Links Page
I have added some links to the Learning Links pages. One is called "Chemistry Interactive Review." It contains pages which allow a student to test his or her knowledge of Chemistry. Answers are provided so students can tell if they are getting the answers right. It does not give explanations of why certain answers are correct, however. It also has some advertising. This is part of a web site from ScienceGeek.net. There are links to chemistry tutorials, a list of freeware relating to chemistry (programs that can be downloaded free to use on a computer), 25 different versions of the periodic table of elements, and programs for the TI-83plus calculator. There are also links to similar sites for biology and AP chemistry, which I've also added to the Learning Links.
In the Physics section, I've added a link to HyperPhysics, a site designed by Georgia State University. It has links to all areas of physics in the form of a tree of topics linked to each other. Just click on the area of physics, say Heat and Thermodynamics, and then on the particular topic in this area. Explanations are detailed, with lots of cross linking of important terms and explanations. Many of the sections have calculators that demonstrate the principles; one enters specific data into fields and then the calculator calculates other values related to these through the relevant equations. A gold mine of helpful material!
Study Habits for Math Success [9/7/09]
Mathematics has one great advantage over all other courses. It is logical--extremely logical. So when a concept is presented, there is one and only one way to understand it. Once you understand it, it can be counted on to work whenever called upon. The circumference of a circle is the length of the diameter times pi (3.14159...). Even if you don't understand where the number for pi comes from, the relationship between the diameter and circumference is always the same. This quality of mathematics makes it important to study it in the right way. Here are some important habits to encourage anyone who studies math.
When learning a new concept, break it down and relate it to things you already understand. Everything in math builds on other things, and it all ulitmately goes back to simple concepts such as adding and subtracting. Where practical, make models, accurate drawings, conduct experiments, and generally throw yourself into the concept. For example, when studying geometry, get a compass or make circles using a soup can as a guide. Get a ruler and measure the diameter. Figure a way to measure the circumference. See how close to pi you get when you divide the circumference by the diameter. Double the diameter. Does the circumference double?
Follow examples. This may seem obvious but a lot of students seem to think that only wimps look at examples. In fact, the examples are your best friend. If you have to do a problem and you are not sure how to proceed, find an example of the same type of problem. Study each step of the example to understand what was done and why. Then apply this same process to your problem. In most cases, you can follow the steps straight on to the answer.
Write down examples provided by your teacher so you can study them later. If you don't understand what inspires each step, ask the teacher to explain.
Pay attention to terminology. In math, each term has a precise definition. While we may use the word "function" in many ways, in math, it has but one meaning. If a problem starts by defining a function, you can be sure that it has all the properties of a function. Highlight such terms in your text if you can. If you read something and hit a word you don't understand, find where the word is defined and study the definition.
Write down definitions your teacher may write on the board in class. This may duplicate what is in the text, but it may be in a form easier to understand.
Find ways to verify your results. There are usually several ways to find an answer. Also, answers ought to satisfy certain conditions given in the problem, so you may be able to test your answer to see if it does what it is supposed to do. Use calculators to good advantage. If simplifying an expression, you can test your result by plugging it into a calculator and getting a decimal answer. Test this by putting the original expression into the calculator to see if you get the same decimal result. Doing this can give you more confidence.
Solve problems in a step-by-step fashion. This not only forces you to think about the steps, it gives your teacher a way to judge your method of solving. If your answer is wrong, a good teacher will give you partial credit if you were applying the right method, but made a mistake in addition at some point.
* Start with what the problem gives you.
* Before going on, double check that you've copied the right problem and made no mistakes.
*
Write each step on a separate line below the previous step. Don't work sideways.
* Don't combine a lot of steps. Let each new line represent one change.
* When you get what you think is the answer, double check that you've given what the problem asked for.
* If the problem has an answer that comes from a word problem, make sure you've included any units (ft., hours, etc.)
* Reality check you answer where possible. Consider it if makes sense.
Keep your homework after it's been graded and study it when test time comes.
If you've followed step 7, you will have detailed solutions to study.
Summertime is the Time to Read! [6/26/09]
The summer break is a welcome change of pace for students and teachers alike. It is also a good time to do more reading. More reading!? It's vacation! Precisely. Reading is fun, especially when you choose the topic rather than having to read what a teacher requires. Read novels, articles on your favorite hobby, or read a religious or philosophical text. Read a self-help book or just read in depth about the news of the day. Read to a child. Or just go to a library or bookstore and browse until something catches your fancy.
The chief value of reading a lot, besides what you learn, is an improved vocabulary. For those who will be taking the SAT, vocabulary knowledge can boost your score considerably. The test designers know that a good vocabulary is generally a sign of a well read person, hence a person with more knowledge and a sharper mind. It is not easy to cram to improve vocabularly. It is much better to encounter words in their natural setting to and add them to your inventory of known words.
So take this summer reading tip: Keep a pencil, pen, or highlighter handy and whenever you encounter a word you don't recognize or know the exact meaning of, mark it. If possible, immediately check a dictionary for the definition. If you have access to the Internet, I recommend Dictionary.com. Once you know the definition, check out the synonyms and related words. Notice the origin of the word. Make this a habit and continue to do it whenever you read. When reading for a classroom assignment, this will insure that your reading sinks in and doesn't just float between your ears because you don't really know what the author is writing about.
Can't write in your book? Get some small sticky notes and use them as flags. You can write on them, and when you have to return the book, remove the notes.
If you are spending time on the Internet, make it a habit to check the Word of the Day at Dictionary.com.
Spelling tip [6/26/09]
Having trouble remembering how to spell a word? Try this exercise. Pretend you are writing the word in the air, like a sky-writer. Say each letter as you write it. Do this three times in a row. Then on a piece of paper, write the word three times, saying each letter as you do. Why does this help? Getting more senses involved helps the brain build a strong pattern of neurons to remember better. One teacher had her students stand and as they spelled a difficult word out loud, she had them stamp a foot for each letter. She saw marked improvements in spelling tests; many of the students were observed to be quietly tapping a foot as they wrote the words. Another example, in Akeelah and the Bee, a girl jumps rope while she practices words for her spelling bee competition. She gets a hard word in the final by jumping an imaginary rope as she spells the word. It works! Try it!
If you can read this, someone needs your help! [6/26/09]
A disturbing number of people reach adult age without being able to read or to read well enough to fill out a job application or understand written instructions. These people need help. One organization that provides that help is The READ Center. This organization has been teaching adults to read since the 1980s. With the economic troubles of this past year, more and more people are suffering because they cannot read well enough to get a job. The READ Center is a non-profit organization that does not charge the student for instruction. It is currently serving over a hunderd students with many more calling in each month. The center has a small staff of teachers (I am one of them), usually working with groups of up to 10 or 15 students. In order to give students the individual attention each needs, The READ Center relies on volunteers. If you have at least a high school diploma, are an adult, and are willing to commit just one hour a week for a year to help a student learn to read, please volunteer to be a tutor with The READ Center.
If you want to volunteer or find out more information about The READ Center, call 804-288-9930 between 8:30 AM and 5:00 PM, Monday through Thursdays. If you know an adult who has trouble reading, please have him or her call this number to find out about how they can start taking free reading classes. Thank you in advance!
Spring Break Practice, NY Regents Exams, and a Mal-ware Warning [3/21/09]
Spring is here and spring break, for most students, is fast approaching. While the point of a break is to do something different than a normal school week, it is a good opportunity to review concepts covered up to this point in the year. The key to doing well on comprehensive exams is to review early concepts at regular intervals throughout the semester, not just the night before the exam.
A word of warning, I did a search to locate this page today using the words "New York Board of Regents Exams" and clicked on a result that I thought was an official site, but it appeared to be a false site which tried to trick me into thinking the security program on my computer had activated because of a detected system failure. This initiated a scan of my hard drives (or so it appeared). I quickly activated my Task Manager (Cntl + Alt + Delete to get to this). I used the task manager to close the browser. This is best if you think you've stumbled onto a malicious site, as these sometimes do not work as expected, to keep you from closing the site.
This is a common mal-ware trick, to make it appear that your security or anti-virus software has detected a virus or some other problem and is initiating a scan or a fix. Or it may recommend downloading an alleged update. These are just covers for other activities, none of which is good for your computer. Shut them down at once. Besides the Windows Task Manager, another safe way to quickly shut down a site is to left click on the place at the edge of your Windows screen (usually at the bottom) where the open programs are listed. This should give you a Close option. It is better to close it this way than using anything built into the browser, as mal-ware sites can alter these functions to prevent you from quickly closing the site.
Have a great Spring Break!
Do You Sudoku? [1/25/09]
Sudoku is the name of a number puzzle. The rules are very simple. Solving the puzzle can be easy or hard, depending on the starting point. It is an excellent way to improve you logical thinking ability, which means it is also an excellent puzzle for young minds learning math and science. A sudoku puzzle is something like a crossword puzzle, but the boxes are filled with numbers, not letters. The numbers used are one through nine. The board is a nine by nine grid divided into nine boxes, each three by three. The goal is to fill the grid with the numbers so that every number appears exactly once in each row, each column, and each three by three box. Each puzzle starts with an assortment of numbers already filled in. There should be just one solution, one way to fill in the rest of the squares.
Sudoku requres logic to solve. The strategies used work by a process of elimination, to the point where there is only one position that can take a particular number or only one number that will go in a particular position. An easy puzzle can be solved in a matter of minutes, using very straight forward logic. For example, if one sees that a six is already positioned in the top row and the top left box, then no more sixes may be placed in the top row, the leftmost column or in the upper left box. If there is a six in the second box of the upper right box, then logic dictates that the six in the upper middle box must be on the third row from the top. If two of those positions are already filled, that leaves just one place for the six to go.
Harder puzzle require more complicated logic. It may be necessary to make note of which numbers are possible in the various open boxes and by the patterns of numbers possible, deduce which positions must take a particular number or which numbers are excluded from certain positions. Each number filled produces a new situation which should make it easier to solve.
I strongly encourage parents to introduce their children to Sudoku at an early age. There are simpler versions of the puzzle that just have six numbers and a smaller number of starting positions, making them easier. The process of solving puzzles should illuminate the power of logic and prepare them for other applications of logic in math, science, and debate. Sudoku puzzles are published in newspapers daily, in books available at newstands and bookstores, and on the Internet. Check it out. But be careful! Sudoku can become addicting!
Focus on Algebra [Added 7/27/08]
The US Department of Education sponsors the National Mathematics Advisory Panel. This group recently presented a report of findings about mathematics instruction in the US. One of the findings is that algebra is a critical step in the road to higher education and career success. Here is how the report summarizes it: The sharp falloff in mathematics achievement in the U.S. begins as students reach late middle school, where, for more and more students, algebra course work begins. Questions naturally arise about how students can be best prepared for entry into Algebra.
These are questions with consequences, for Algebra is a demonstrable gateway to later achievement. Students need it for any form of higher mathematics later in high school; moreover, research shows that completion of Algebra II correlates significantly with success in college and earnings from employment. In fact, students who complete Algebra II are more than twice as likely to graduate from college compared to students with less mathematical preparation. Among African-American and Hispanic students with mathematics preparation at least through Algebra II, the differences in college graduation rates versus the student population in general are half as large as the differences for students who do not complete Algebra II.
So if you have a child in grade school, make sure he or she gets a solid math education, with particular focus on skills that will be needed in algebra such as multiplication and division, addition and subtraction, fractions and decimals, and the concept of a variable.
If you have a child approaching algebra studies, usually a child in middle school, pay close attention to how your child is doing. If he or she is struggling, get help right away. This is a critical point in any child's educational career.
If your child has completed basic algebra, encourage her or him to take more algebra, algebra II or pre-calculus. Even if the child does not go on to study calculus or pursue a career requiring higher mathematics, the logic skills and familiarity with more complex mathematics concepts will pay off nonetheless.
Practice, Practice, Practice [Added 5/2/08]
There is an old joke about a guy in a car in New York City who is trying to find Carnegie Hall, a famous concert hall where many of the best musicians play. He pulls over, rolls down his window and asks a pedestrian, "How do I get to Carnegie Hall?" The man replied, "Practice, practice, practice!"
There is another joke, attributed to the great golfer Sam Snead. A reporter noticed Snead practicing putting after a round in a tournament after all the other golfers had long ago hit the clubhouse. Taking advantage of the opportunity, the reporter approached Snead and asked, "Mr. Snead, to what do you attribute your phenomenal success?" Snead considered a moment, made a practice putt, and said, "I'm just lucky, I guess." The reporter replied, "But you practice all the time, way more than the other golfers." Snead said, "Funny thing is, the more I practice, the luckier I become."
Scientists know that one of the keys to doing well at anything is repetition. Doing the same thing over and over, reinforces the brain's ability to perform a task in a precise way, like making wheel ruts along a road makes it easier to go down the road. Learning is no different, especially learning to do math and science problems. Most text books provide a supply of problems, half of which have the answers given at the back. But the Internet is rich with such help, mostly free.
A student of mine was recently studying for an exam that would consist of problems using various exponential functions, functions with the variable in the exponent. I went to Google and entered "Exponential Functions Practice Problems". Within the first two pages of responses, I found four sites with a variety of practice problems. Each problem had not only the answer available but a description of how the solution was obtained.
So use the power of the Internet to help use the power of practice. Check Learning Links on this site for some more sites, many of which have practice problems. Good luck on finals!
When Nature Gets Nasty [Added 3/15/08]
News reports today feature dramatic pictures of how destructive tornadoes can be. A tornado tore through downtown Atlanta last night (Mar. 14), collapsing buildings and injuring over two dozen people. As a child growing up in Indiana, I was acutely aware of the dangers of tornadoes. We were part of what is known as Tornado Alley because the landscape is ideal for the formation of these intense windstorms. On Palm Sunday 1965, I was ten when eleven tornadoes ripped through the state. These tornadoes were part of an outbreak of 78 tornadoes that struck from Iowa to Ohio and as far north as Wisconsin and Michigan. Twenty-one of these killed 271 people all told, 137 in my home state. One of the most deadly leveled a town less than 50 miles from my home and killed 25 people. This event fascinated me as a child. I still remember a sixth grade science project in which I created a diorama which demonstrated a tornado, complete with a silly-putty twister and a house whose roof blew off.
Tornadoes, like all destructive forces of nature, often fascinate children. This can make the topic a good way to get children interested in earth science and a great way to educate them about the natural world. The Internet offers a wide range of educational sites that explain how these forces develop and why they can be so destructive. Here is a list of some that focus on tornadoes. For more general earth science sites, see my Learning Links section.
Another Palm Sunday
tornado outbreak, this time in 1994 (large pdf file)
A Picture of the Universe a Day Keeps the Blahs Away! [Added 3/4/08]
There are lots of "picture of the day" sites. One that is especially appealing is the Astronomy Picture of the Day, from NASA. Today's picture is of the Cat's Paw Nebula, which I had never heard of before, and I've been looking at astronomy photos all my life. This is particularly beautiful, a swirl of reds and oranges resembling a pawprint of a cat. The site is not just a pretty picture frame, however, as each day there are links for more information about the subject of the day. In this case, you can link to articles on emission nebulae, the Cat's Paw Nebula, Scorpius (the constellation where the nebula is found), hydrogen, the sun, and the telescope that took the picture, as well as links on cats, paws, and Chile. Curious? Check it out. If you missed it on March 4th, you can still find it by clicking on the archive link.
Other interesting Picture of the Day sites:
Last night I watched a fascinating program on NPR about ways to improve your brain function at any age. The program is available on DVD, which includes computer based exercises which have been shown to stimulate important aspects of brain development. Much of the program is directed toward older people and how they (we :) can ward off the seemingly inevitable loss of mental faculties. But the information is equally important for people of any age, including children.
The following web site contains more information about this fascinating topic. Check it out and start exercising!
Geometry Using Straight Edge and Compass [Added 1/13/08]
I have tutored a number of geometry students and I notice that few of them are asked to make geometric figures using tools like a straight edge, protractor, and compass. These used to be part of the standard practice for teaching geometry, but I fear that computers and the Internet are replacing these age-old tools. That is unfortunate. A great deal can be learned by learning how to construct parallel lines, perpendicular lines, how to bisect a segment or an angle.
I strongly recommend all students of geometry obtain the following tools, available at any office supply store and also in most sections of stores with student supplies.
Straight Edge: This can be as simple as a book edge, but the best is a ruler. I would get one with centimeter and millimeter markings, and if available also inches divided into tenths. These usually come in six inch and twelve inch. Get the twelve inch for use at home, a six inch for taking to class.
Protractor: This is a semi-circular or circular piece of clear plastic with marks around the out
side for the degrees of an angle. Again, it would be best to buy a relatively large one for home use, and a smaller one for class. Compass: This is part of the A-Square Tutoring Logo and is used to draw circles and to mark off fixed lengths. One side has a sharp point and the other a pencil or pen. These may not be allowed in class, as the point tends to be an irresistible instrument of teasing, but they should be used at home.
Using these tools gives a student a first hand physical activity to make the concepts of geometry more concrete. Students usually learn better when they have such a way to physically "do" the work, rather than just think about it or express numbers and equations. This is called "kinetic" learning and it has been shown to be the most effective way to teach math.
For example, when a student is required to prove two triangles are congruent, given a particular figure with certain things specified, like certain segments or angles congruent, certain lines parallel, etc. If a student constructs a figure that satisfies the conditions given, it may be easier to see the relationships between different parts and to work toward the proof's conclusion.
Here are some links to web pages with instructions on compass and straight edge constructions:
Wolfram MathWorld: Geometric Construction
Inscribing a regular pentagon in a circle – and proving it
Compass and Straightedge Constructions