Kindergarteners pointing fingers for good (math) or bad (gunning for teacher)
Posted by mark in Uncategorized on May 2, 2010
On the one hand, I see this report of a kindergartner suspended for making a gun with his pointer-finger. That’s discouraging. But on the other hand, I come across this news from New York Times writer Benedict Carey of a program called “Building Blocks,” developed by the School of Education at the University of Buffalo, that teaches preschoolers fundamental math skills, so when they point a finger, it’s a one, not a gun. 😉
My wife teaches preschool. She tells me that her kids learn how to count to 100, recognize numbers up to 20, and enumerate physical objects. In his article on “Building Blocks” Carey refers to this as the “numeric trinity” – crucial to “fuse” kindergarteners for learning math.
Previously educators viewed training on math as being developmentally inappropriate for young children. This created an inertia that many kids could never overcome.
“ ‘I’m not a math person,’ they say – and pretty soon the school agrees.”
– Doug Clements, Distinguished Professor of Learning and Instruction at State University of New York (SUNY) at Buffalo
But now “research has demonstrated that virtually all young children have the capability to learn and become competent in mathematics.”* One can only hope that in future kids coming into kindergarten will be pre-charged for math and school in general, so there will be less finger-pointing (gunning) at teachers.
*Source: Description for Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity a report published in July, 2009 by the National Academies Press, which calls for a national initiative to improve mathematics education for preschoolers. See this press release leading to the full report.
Over-reacting to month-to-month economic statistics
Posted by mark in politics, Uncategorized on April 18, 2010
In his column this weekend the Numbers Guy at Wall Street Journal, Carl Bialik, notes* how uncertain the monthly statistics for unemployment and the like can be. For example, the Census Bureau reported that sales of new single-family homes fell to record low last month. However, if anyone (other than Bialik) read the fine print, they’d see that the upper end of 90 percent confidence interval estimates an increase in sales!
“Most of the month-to-month changes are not only nonsignificant in a statistical way, but they are often straddling zero, so you can’t even infer the direction of the change has been accurately represented.”
– Patrick O’Keefe, economic researcher
The uncertainty stems for the use of sampling as a cost-saving measure for government agencies and ultimately us taxpayers. For example, field representatives covering 19,000 geographical units throughout the U.S. only sample 1 out of 50 houses to see whether they’ve been sold.
The trouble with all this uncertainty in statistics is that it ruins all the drama of simply reporting the point estimate. ; )
*(See “It Is 90% Certain That Unemployment Rose. Or Fell.” and a related blog on “What We Don’t Know About the Economy” )
A wonderful pairing: Baseball and statistics
I managed to procure a seat to the opener yesterday for the new Minnesota Twins baseball stadium (Target Field) in Minneapolis. Although many questioned the wisdom of leaving it open to the elements, dire predictions of early games being snowed out did not materialize, at least this year. In fact, we enjoyed an unseasonable warm day while watching the hometown club defeat the Boston Red Sox to rousing cheers of the nearly 40,000 fans in attendance (39,715 to be precise). Many of the statistics for the landmark game are captured in this ESPN boxscore. Oh, oh, here I see an anomaly – the attendance reported at only 38,145 (96.6% full). My hunch is that the other 1,030 fans might be found at hometown hero Hrbek’s Bar – a spacious gathering spot in the stands of the Target Field.
Although the pre-game festivities and competition provided great entertainment, I eagerly awaited the breaks between half-innings to peruse the details in the Minnesota Twins 2010 Record and Information Book – a 396 page tome filled with 6 point type. Nearly every page features a statistic biased in favor of the team or a particular player. This is done by focusing on one specific attribute and then choosing the time frame which puts it in the most flattering light. For example, we learn on page 122 that “Anthony Swarzak became the first starting pitcher in club history to pitch 7.0 scoreless innings in his Major League debut.” I like the way they put the carry the statistic to the tenth’s decimal. : )
Creativity defeats sensibility for paper helicopter fly-off
Posted by mark in design of experiments on April 9, 2010
Twice a year I teach a day on design of experiments (DOE) at Ohio State University’s Fisher College of Business. The students are top-flight executives seeking six sigma black belt certification. To demonstrate their proficiency for doing DOE, I ask them to break into teams of three or four and, within a two hour period, complete a two-level factorial on paper helicopters.*
It’s always interesting to see how intensely these teams from industry compete to develop the ‘copter that flies longest while landing most accurately. However, this year one group stood out as being less competitive than the others. Therefore, I was very surprised that they handily won our final fly-off. It turns out that one of their factors was dropping the helicopter either wings-up or wings-down – the latter configuration being completely non-intuitive. It turns out that going upside down makes it easier to drop, the flight time suffers only slightly and the flight becomes far more accurate – a premium in my overall scoring.
“The chief enemy of creativity is ‘good’ sense.”
– Pablo Picasso
Ironically, another team who benefited from having an expert in aeronautical engineering and a very impressive work ethic all around – they did more runs by far than anyone else – never thought of flying the ‘copters upside down. In fact, their team leader objected very vigorously that this orientation must not be allowed, it being clearly unfair. Fortunately, other executives in this black-belt class hooted this down.
I thought this provided a good lesson for process and product improvement – never assume that something cannot work when it can be easily tested. That’s the beauty of DOE – it enables one to screen unknown (and summarily dismissed) factors to uncover a vital few that often prove to be the key for beating the competition.
*I also do this experiment for a class on DOE that I teach every Spring at South Dakota School of Mines and Technology. In fact, I am writing this blog from their campus in Rapid City where I’ll be teaching class tonight. For details, pictures and results of prior experiments here and at OSU, see this 2004 Stat-Teaser article on “Playing with Paper Helicopters”.
Misuse of statistics calls into question the credibility of science
Posted by mark in science, Uncategorized on March 28, 2010
The current issue of Science News features an indictment of statistics by writer Tom Siegfried. He pulls no punches with statements like this:
“…a mutant form of math has deflected science’s heart..”
“Science was seduced by statistics…”
“…widespread misuse of statistical methods makes science more like a crapshoot.”
“It’s science’s dirtiest secret: …testing hypotheses by statistical analysis stands on a flimsy foundation.”
“Even when performed correctly, statistical tests are widely misunderstood and frequently misinterpreted. As a result, countless conclusions in the scientific literature are erroneous…”
Draw your own conclusions on whether science fails to face the shortcomings of statistics by reading Siegried’s article Odds Are, It’s Wrong.
My take on all this is that the misleading results boil down to several primary mistakes:
- Confusing correlation with causation
- Extrapolating from the region of experimentation to unstudied areas
- Touting statistically significant results that have no practical importance
- Reporting insignificant results from studies that lack power to see differences that could be very important as a practical matter.
I do not think statistics itself should be blamed. A poor workman blames his tools.
Test and evaluation of the Great Panjandrum – a spectacular failure for weaponry
Posted by mark in history, science, Uncategorized on March 23, 2010
When time becomes available – mainly while I do cardio-exercise on my home elliptical, I’ve been watching a classic 26-episode BBC series on The World at War that my oldest son gave me. It’s extremely compelling – rated 9.7 out of 10 by over two thousand voters at the Internet Movie Database (IMDb).
This morning I watched the chronicle of D-Day. Being that I just returned from the Annual National Test & Evaluation Conference by the National Defense Industry Association (NDIA), it was interesting to see what the boffins of Britain invented to defeat the defenses put up along the Normandy beaches. Perhaps the most amazing device was the Great Panjandrum, a rocket-propelled cart, which according to this write-up for Wikipedia was developed by the Admiralty’s Directorate of Miscellaneous Weapons Development. (One wonders about the “miscellaneous” bit.) The clip I viewed on the spectacular failure of the Great Panjandrum can be seen (along with other incredibly-inept military devices for D-Day) in a video on British Secret Wartime Follies posted in this article by UK’s Daily Mail. Check it out!
PS. The Brits continue to come up with the most audacious inventions, such as this flame-throwing moped developed as a deterrent against derelict drivers competing for motorway lanes.
Evolutionary operation
Posted by mark in design of experiments, Uncategorized on March 7, 2010
Last December, after an outing by the Florida sea, I put out an alert about monster lobsters. This reminded me of an illustration by statistical gurus Box and Draper* of a manufacturing improvement method called evolutionary operation (EVOP), which calls for an ongoing series of two-level factorial designs that illuminate a path to more desirable conditions.
With the aid of Design-Expert® software, I reproduced in color the contour plot in Figure 1.3 from the book on EVOP by Box and Draper (see figure at the right). To illustrate the basic principle of evolution, Box and Draper supposed that a series of mutations induced variation in length of lobster claws as well as the pressure the creatures could apply. The contours display the percentage of lobsters at any given combination of length and pressure who survive long enough to reproduce. Naturally this species then evolves toward the optimum of these two attributes as I’ve shown in the middle graph (black and white contours with lobsters crawling all over them).
In this way, Box and Draper present the two key components of natural selection:
- Variation
- An environment that favors select variants.
The strategy of EVOP mimics this process for improvement, but in a controlled fashion. As illustrated here in the left-most plot, a two-level factorial,** with ranges restricted so as not to upset manufacturing, is run repeatedly – often enough to detect a significant improvement. In this case, three cycles suffices to power up the signal-to-noise ratio. This case illustrates a big manufacturing-yield improvement over the course of an EVOP. However, any number of system attributes can be accounted for via multiple-response optimization tools provided by Design-Expert or the like. This ensures that an EVOP will produce more desirable operating conditions overall for process efficiency and product quality.
It pays to pay attention to nature!
*Box, G. E. P. and N. R. Draper, Evolutionary Operation, Wiley New York, 1969. (Wiley Classics Library, paperback edition, 1998.)
**(We show designs with center points as a check for curvature.)
Beware of bugs bearing backpacks
Posted by mark in science, Uncategorized on March 3, 2010
I am attending a conference sponsored by the National Defense Industry Association (NDIA). They provided all of us participants a copy of the latest issue (March) of their publication National Defense. While wiling away the time listening to some long-winded higher-ups I paged through the magazine and admired the weaponry developed to keep our war-fighters supported to the max. However, on page 17 a very odd picture caught my eye – a cockroach carrying a radiation sensor on its back! A researcher at Texas A&M reports that these bugs are ideal for sweeping potentially contaminated areas, ideally in teams of twenty. They can be operated remotely via devices that stimulate their leg muscles.
There is one problem though: Cockroaches cannot crawl backward. One had better hope that none of the bad guys wear pointy-toed cowboy boots, because they will be ideal for killing the sensor-bearing bugs that become stuck in the corners.
Simplifying the witches brew in Shakespeare’s MacBeth
Posted by mark in Uncategorized on February 14, 2010
Last week I enjoyed an innovative performance of Shakespeare’s MacBeth at the Guthrie Theater in Minneapolis. The director, Joe Dowling, takes some liberties with the original production, such as dropping the warrior MacBeth on stage down a ninja rope and equipping him with a machine gun. However, mostly the gruesome killings that riddle this dark play are accomplished with old-fashioned daggers and swords.
Being a chemical engineer who abhors overly complicated recipes, it bothers me that the three weird sisters in Macbeth put so many ingredients into their witches brew. It would be very hard to scale up their potent product from bench-level kettle to massive manufacturing. By the way, thanks to this heads-up by Nigel Beale I cracked this coven’s confidential code on components; for example, eye of newt, which cannot be easily sourced, is really readily-available mustard seed. Nevertheless, I’ll bet that a good mixture screening experiment, followed-up by an in-depth formulation design, such as this one on a cell-culture medium, would reveal that only a few key ingredients might do the job for enabling clairvoyance or whatever a witch might be up to.
Keep it simple, I say. Or as Shakespeare advises more eloquently, “Brevity is the soul of wit.”
Skepticism versus cynicism about science experiments
Eric Felten’s latest “De Gustibus” column in Wall Street Journal reports New Episodes of Scientists Behaving Badly. It details various scandals, for example the retraction of a landmark publication linking autism to childhood vaccines. This creates a great deal of cynicism such as that expressed by this parent of a kid she helped on a science project:
“The experiments never turned out the way they were supposed to, and so we were always having to fudge the results so that the projects wouldn’t be screwy. I always felt guilty about that dishonesty, but now I feel like we were doing real science.”
Ouch!
Coincidentally, Stat-Ease received an email from someone who goes by the pen-name “The Pyrrhonist.” (I see a trend here: I need to work on a scholarly-sounding moniker.) While researching pyrrhonism, I came across this skeptical quote by a Greek named Carneades who set the stage for his countryman Pyrrho:
“Nothing can be known, not even this.”
That’s tough to get around!
I truly believe that some degree of skepticism is healthy, such as judicious use of the null hypothesis for assessing the outcome of experiments. However, it’s not good for experimenters to abandon all standards by succumbing to an attitude of scornful or jaded negativity, especially a general distrust of the integrity or professed motives of others – the definition of cynicism (according to the Free Dictionary).
So, be skeptical, but not cynical.