Gum is an effective booster of mental performance, conferring all sorts of benefits without any side effects. … chewing gum is often a better test aid than caffeine. [However] gum chewers only showed an increase in performance during the first 20 minutes of testing.
Improves reaction time and improves mood (Smith, 2010).
On the other hand, while chewing might be good for most types of memory, one study found that chewing, and other rhythmic tasks reduces short-term recall of long lists (Kozlov et al., 2011).
Lehrer cites a 2004 review of the research on gum and memory, which describes chewing gum as, “a functional food with function but no food” (Scholey, 2004).
The takehome message for using gum while taking tests:
When taking a test, save the gum for the hardest part, or for those questions when you feel your focus flagging. The gum will help you concentrate, but the help won’t last long.
Diagram of the hydrogen sulfide system in a landfill.
Although it makes up less than 1% of the gases produced by landfills, hydrogen sulfide (H2S) is the major reason landfills smell as bad as they do. H2S is produced by decomposition in the landfill, and if it’s not captured it not only produces a terrible, rotten-egg smell, but also produces acid rain, and, in high enough concentrations, it can be harmful to your health (OSHA, 2005; Ohio Dept. Health, 2010).
Decomposition
A wall partially covered with drywall. Image via FEMA via Wikimedia Commons (Nauman, 2007).
Some hydrogen sulfide is produced when organic matter decays, but for big landfills like the one we visited, construction materials, especially gypsum wallboard (drywall), are probably the biggest source.
Gypsum is a calcium sulphate mineral, that’s made into sheets of drywall that are used cover the walls in most houses because it’s easy to work with and retards fire. The U.S. used 17 million tons of gypsum for drywall in 2010 according to the USGS’s Mineral Commodity Summary (USGS, 2011 (pdf)).
Gypsum:
CaSO4•2(H2O)
As you can see from the chemical formula, each gypsum molecule has two water molecules attached. In a fire, the heat required to evaporate the water keeps the temperature of the walls down to only 100 degrees Celcius until the water has evaporated out of the gypsum board.
A number of landfills have banned drywall because it produces so much hydrogen sulfide, but the one we visited still takes it. It’s big enough that they capture the landfill gasses, including the hydrogen sulfide, and then separate it from the other, more useful gasses, like methane, which can be burned to produce heat energy. H2S can also be burned, but they you end up contributing to acid rain.
H2S and Acid Rain
When hydrogen sulfide reacts with oxygen in the atmosphere it produces sulfur dioxide.
2 H2S (g) + 3 O2 (g) —-> 2 SO2 (g) + 2 H2O (g)
Sulfur dioxide, in turn, reacts with water droplets in clouds to create sulfuric acid.
SO2 (g) + H2O (g) —-> H2SO4 (aq)
Acid rain accelerates the dissolution of statues. (Image by Daniele Muscetta)
When those droplets eventually coalesce into raindrops, they will be what we call acid rain.
Acid rain damages ecosystems and dissolves statues. It used to be a major problem in the midwestern and eastern United States, but in 1995 the EPA started a cap and trade program for sulfur dioxide emissions (remember sulfur dioxide is produced by burning hydrogen sulfide) that has made a huge difference.
The head (top) of a well (vertical metal pipe) that captures the gas from inside the landfill.
Capturing H2S
Probably because of the EPA’s restrictions, the landfill company pipes all the gases it collects through scrubbers to extract the hydrogen sulfide. There are a few ways to capture H2S, they all involve running the gas through a tank of some sort of scavenging system that holds a chemical that will react with hydrogen sulfide and not the other landfill gases. At the landfill we visited the remaining landfill gas, which consisted of mostly methane, was used for its energy.
The Missouri Council of Teachers of Mathematics (MoCTM) has a Math & Art Contest that focuses on Geometry. It has fairly simple expectations, and it’s aimed at Middle School students and lower. The tie between the math and the art does not require much depth, but that’s probably appropriate for students who are still developing abstract thinking.
A tessellation. Image via Wikipedia.
I’m usually a bit cautious about the utility of contests. Their primary benefit is in the work that they motivate, not the reward (or hope of a reward) at the end; although, students do need to learn to win or lose with equanimity.
Spring has gone in the meadow
spring has gone in the flowers
spring has gone in the trees
and winter is coming
It is fall
with leaves to wrestle
and sticks to fall
for spring has gone
And there are many things to pick
to harvest the apple trees in the orchard
to harvest the paint berries
to harvest the vines
so there are many things that must come to pass
There are many things to end
many things to fall
winter lies ahead.
The future according to Orwell vs. Huxley. Image from world-shaker.tumblr.com.
World-shaker tries to draw the modern parallels to 1984 and Brave New World in graphic form.
Orwell’s (1948) distopian view of the future in 1984, warned against the government developing the ability to exert constant, repressive monitoring of everyone, controlling the means of communication and, perhaps more importantly, the use of language. Huxley’s (1932) Brave New World, on the other hand, saw a mass media using your apparent predilection for trivialities to distract you from the important things. These two books are staples of secondary school literature, and it’s easy to see modern parallels; “kinetic military action” is currently my favorite Orwellian term.
Unfortunately, drawing modern parallels to historic literature is fraught with difficulty because it’s so easy: the human brain is predisposed to seeing patterns. World-shaker’s attempt is interesting, but flawed. One of his commenter points out that he compares the entertainment website TMZ to Time.com’s news site, which only gets half as many visitors. However, the New York Times’ site gets three times as many visits as TMZ so perhaps he’s fudging the statistics a little to show the trend toward frivolous media.
There are other examples, but the graphic makes does provide a basis for an interesting conversation. The most interesting aspect is that it shows the U.S.A trending more toward Huxley, while repressive Middle-Eastern regimes seem to be trying to make Orwell’s vision more of a reality.
Animation showing the widening and shrinking of the parabola.
So I put together this interactive parabola program using VPython (code here) for students encountering these curves in Algebra.
Simple Excel program to graph a parabola.
It’s a more interactive version of the Excel parabola program in that you can move the curve by dragging on some control points, rather than just having to enter the coefficients of the equation. The program is still in development, but it is at a useful stage right now, so I thought I’d make it available for anyone who wanted to try it.
The program is fairly straightforward to use. You can move the curve (translate it) up and down, and expand or tighten the area within the parabola.
The program also displays the equation of the curve in standard form:
.
What the buttons do.
Next Steps
I’m also working making the standard equation editable by clicking on it and typing, and am considering showing the x-axis intercepts, which will give algebra students a nice, visual way to of checking their factoring.
