Elementary Mathematics-Science SMILE Meeting
20 February 2001
Notes Prepared by Porter Johnson

Announcements:

• Roy Coleman announced that a CD-ROM containing all material on the SMILE website http://www.iit.edu/~smile/ is available for \$10.  Also, an updated version may be obtained for \$5 plus the old CD.
• Monica Seelman (Williams-St James) recommended the book Zero: The Biography of a Dangerous Idea by Charles Seife [Penguin 2000]  ISBN: 0-1402-96476, a very readable history of the number zero, up to the development of Einstein's Theory of Relativity.

Section A: [K-5]

Barbara Lorde (Attucks School) Exploring Triangles, Rectangles, Circles, and Squares
She has been teaching for a long time, and has a third grader to type up her lessons for her.  Her purpose was to introduce shapes and make designs. She cut down on some of the activity by cutting out the shapes herself.  We formed groups to arrange patterns on paper.  One group made a rectangle, measured its length and width with a ruler, and computed its area using the relation (third grade activity on Math Skills)

Area = Length ´ Width

• For kindergarten level you would count the squares and use the word "area" to plant the seeds of understanding for when they are exposed later.
• Students can use a tape measure or ruler to measure the perimeter.  They should estimate the perimeter and area before finding them, and their estimates needn't be too accurate.
• You can use the various shapes to make bar graphs, to display measurements of perimeters and areas.
• Triangles can be used to re-enforce addition and subtraction facts.  Squares can be folded to make triangles.
• One can estimate how many little cubes fit inside a big cube, and then put them in to determine the answer.
•  The groups got together to form creative patterns with the shapes, and they showed their patterns to the whole group, who guessed what it was.

Leticia Rodriguez (Peck School, First Grade)
provided a variety of activities relating to volcanoes, including a video of Magic Sound Bus Blows Its Top.  She showed a Volcano Kit, which makes a correspondence between volcano parts [lava, magma, ring of fire] with parts of a boiled egg [yolk, egg white, shell].  This was a very rich presentation of information and visualization on the environment, which introduced big words and made them easy to understand.  She gave us instructions on making a volcano from scratch, and presented it as a scientific experiment with hypothesis, data, and conclusions to employ the scientific method.

She showed us the invisible Ring of Fire on the Globe.  See the websites

She also discussed illustrating the concept of potential energy at the first grade level with a slingshot and a rubber band eraser.

Jean Essig (Woods School, Kindergarten) Air Science Tricks
made a Hot Air Snake, and caused it to spin and spin and spin.  She invited us to make our own snakes from colored paper. More than ten of us were soon showing how our snakes moved up and down like spiral springs.  She also suggested several extensions:

• measure the length of the snake
• measure the spring of the snake at its longest and shortest
• decorate the snake
• attach a string to the snake
• what is the longest / shortest snake you can make?
• how do you make it short or long?

Mamie Hill (Woods School)
used dried peas and toothpicks that had been soaked overnight to make all kinds of figures, including three dimensional figures.  Soaking provides flexibility and softness that greatly simplifies the construction of figures. When the peas dry overnight the figures become stable.

Beverly Merchant (Soujourne of Truth School)
made colorful and sparkling shapes out of pipe cleaners using an Epsom Salt [Magnesium Sulfate] solution. She put a shaped pipe cleaner into the saturated solution, and the salt crystallized out along the pipe cleaner. People were given their cups of solution and pretty colored pipe cleaners, for making their own shapes and showing them next time.

Notes taken by Earl Zwicker and Bob Foote

Section B: [4-8]

Roy Coleman, Lee Slick, and Kerri Kerfin (Morgan Park HS)  How to React to An Experiment
led a measurement of reaction time (to check to see if you are still alive).

The idea is for one person to drop a meter stick held vertically, with its bottom at the top of the fingers of (partially opened) hand of another person, which is resting on a table top. The first person drops the meter stick, and the second catches it as quickly as possible.  The meter stick typically falls a distance s of 20 - 30 cm, corresponding to a total reaction time (t) determined from the formula s = 1/2 g t2 ;  or s [cm] = 490  t[sec]

 s (cm) t (sec) 11.0 0.15 19.6 0.20 30.6 0.25 44.1 0.30
This reaction time is the sum of three separate times:
Reaction Time = Brain Processing Time + Nerve Transmission Time + Finger Closing Time

They estimated the first time by setting up two funnels attached with rubber tubing and held from behind at the ears of a participant.  When the tubing was tapped, the participant was able to hear which ear heard the sound first and louder, unless it was tapped within s = 5 - 10 cm of the middle of the tubing.  Thus, the Brain Processing Time is given as s / Vsound = 0.0003 sec.   The finger closing time is estimated by seeing how quickly the fingers can be opened and closed [about 30 times in 10 seconds, corresponding to a closing time of 0.167 sec.] They then conclude that most of the time is associated with the Finger Closing Time, and that the Nerve Transmission Speed is comparable to the velocity of sound, or about 300 meters/sec.

Comments by Porter Johnson:  The nerve transmission speed is certainly not larger than the speed of sound, and most estimates indicate that it is considerably smaller.  Check these references:

• How Fast Do Your Nerves Carry Signals?  See http://www.accessexcellence.org/AE/AEPC/WWC/1991/axon.html for one type of experiment on this subject.  Their results: 6-9 meters/sec].
• Carpal Tunnel Syndrome [http://www.ninds.nih.gov/disorders/carpal_tunnel/detail_carpal_tunnel.htm excerpt] These cases call for a special diagnosis, called a nerve conduction study. By implanting electrodes across the carpal tunnel and at another location farther up the arm, this diagnostic procedure records the speed at which the nerve signals travel. The norm is about several metres per second, or about the same speed we travel in a car on an urban street.
• Actually, speeds within neurons are much greater than speeds across neurons, and the speed varies with the size of the neuron:  See http://people.eku.edu/ritchisong/301notes2.htm.
• Excerpt from the (no longer active) website:  http://www2.rz.hu-berlin.de/linguistik/institut/syntax/mind/psychology.htm
A further foundational issue concerns the speed of human thought. In the 19th century, many believed that thought was either instantaneous or else so fast that it could never be measured. However, Hermann von HELMHOLTZ, a physicist and physiologist, succeeded in measuring the speed at which signals are conducted through the nervous system. He first experimented on frogs by applying an electric current to the top of a frog's leg and measuring the time it took the muscle at the end to twitch in response. Later he used a similar technique with humans, touching various parts of a person's body and measuring the time taken to press a button in response. The response time increased with the distance of the stimulus (i.e., the point of the touch) from the finger that pressed the button, in proportion to the length of the neural path over which the signal had to travel. Helmholtz' estimate of the speed of nerve signals was close to modern estimates -- roughly 100 meters/second for large nerve fibers. This transmission rate is surprisingly slow -- vastly slower than the speed of electricity through a wire. Because our brains are composed of neurons, our thoughts cannot be generated any faster than the speed at which neurons communicate with each other. It follows that the speed of thought is neither instantaneous nor immeasurable.

Beth Womack (Gunsaulus School) Bridge Design (Project-Based Learning)
provided the groups with a supply of the following materials:  Clay, Craft Sticks, Tape, and Newspaper, and presented us with the following questions:

1. Getting Started
• Can your group build a bridge on one desk?
• Can your group build a bridge from one desk to another desk?
2. Design Description
• What did your group use for the base of your bridge?
• How high is your bridge and what instrument did your group use to find out?
• How long is your bridge and what instrument did your group use to find out?
• How strong is your bridge and what did your group use to find out?
3. Conclusion
• How does your group's bridge compare with those of the other groups?
• What other materials can be used to build a classroom bridge?
We constructed several types of bridges in the various groups.  Three made tower bridges out of sticks and clay, one made a tube bridge out of newspaper and clay, one made a popsicle-clay span, and one made a pontoon bridge.

Barbara Pawela (retired) Seeing the Invisible

• She took a coffee can with the top removed , with a plastic bag held tautly over the top with a rubber band.  She sprinkled grains of sugar on the top , and hit the side of the can.  The grains moved around on top---vibratory motion.
• We suspended Aluminum foil by a thread, and tapped the glass with the foil held close.  The foil moved, since sound was transmitted  through the air from the glass to the foil.
• Barbara opened a perfume bottle in the front of the class.  Its odor gradually diffused throughout the room.
• Roy Coleman demonstrated a corrugated flexible plastic tube, which he whirled over his head, cowboy style.  A sound was produced, which increased in pitch as the tube moved more quickly.
• We filled an empty plastic bag with air by swinging it over our shoulders.
• Barbara took a pop can containing hot water, and dunked it snout first into a container with ice-cold water.  The can crinkled but did not collapse, because we ran out of time and could not get the can hot enough.

Notes taken by Porter Johnson