On jumping to conclusions and historical data.

In discussions that refer to data about historical topics, the non-math folk often fall for the correlation - causation error, as well as misinterpreting their evidence.

It is generally accepted that height actually declined somewhat in late period and early modern times (see, for example, preserved sites like Williamsburg or Jamestown, where door frames and hallways are significantly smaller than nowadays), the reason having to do with more widespread malnutrition and chronic health problems emerging in the 14th century and continuing on until the 18th century. (from a mailing list focusing on medieval history.)

Average is a really tough thing to deal with here and there are a bunch of problems with this statement.

Let's deal with averages first. It's pretty easy to find the average height of modern people. They're alive and measurable. You call together twenty folks at the mall and ask them their height. Convenience sample leads to selection bias, so you retry with a cluster sampling. That's better, but did you happen upon the community of immigrants who are shorter? SO you expand your search and try a more systematic approach. In the end, you have a sense of the average height.

Now try that for the 14th century. Your sources are whichever bones you've been able to find and measure and a few written claims. Not much for numbers there.

Second issue is that pre-19th century doors, hallways and buildings weren't built for standard-sized people. They were built for the occupants and those occupants had different needs. Stating that door frames and hallways are smaller than currently because of a lesser average height is a conclusion that doesn't necessarily follow.

Your average tells you about the group but not much about individuals, so your building codes are set for the 99.8% who are shorter than +3 standard deviations from the mean so that no one is inconvenienced. But what is the average height? That's easier to tell now, but not so much for earlier demographics.

Room size does not correlate to occupant height either. My classroom ceiling, for instance, is nearly twelve feet high. Can we really conclude anything from that? On the other hand, all of the occupants for the last twenty years have been shorter than 6'5" and half of them were averaging 5'4" (the girls). All classrooms built in the last twenty years have 8' or 9' ceilings, becuse of changes in the building code, not because people kept hitting their heads.

The windows are huge, nearly 3' by 8', but that speaks to the need for free light and air rather than a race of giants.  Need and purpose are better indicators of door size in pre-code days.


The typical pre-1850 house has low ceilings and doors I want to crouch for (but that are still taller than I am), for a couple of reasons.

A room with a low ceiling is easier to heat, less difficult to build, and uses less wood in the building process. A 7' ceiling is not a problem for anyone who was going to use it - the builders were making houses for themselves and they didn't feel the need to give themselves 2' of headroom.

Sure, it's shorter than today, but only relatively. We notice because the standards have changed and it FEELS lower, not because we need to duck.

The same is true for the door. It's shorter. It was custom-made and of varying heights. Often it wasn't "square" but rather built to fit the space rather than the other way around. It might have a corner cut off to fit under the eaves or clear a stair. In any case, the door was built for the prospective occupants, not the rare fraction who needed a 6'8" door. Andre the Giant could bloody well duck.

Likewise hallways. What's the need for a wide hallway? It's just wasted space. Your big furniture was on the main floor or was carried up in pieces and assembled in place. There were no ADA-type requirements. Again, we feel constricted, but the person of that time would consider our modern requirements to be ostentatious displays of wealth. The typical house of the 15th century was maybe half the square footage of 20th century houses, and that is being dwarfed by 21st century ones. This correlation is with wealth, not height.

Other factors chime in: the cost or taxes assessed on road (or canal in this case) frontage might dictate your building style. For an extreme example of this, check out houses in Amsterdam: narrow, almost useless staircases and a hoist mechanism outside for lifting pianos and furniture to the second or third floor.


The takeaway for math teachers is to stress that we need more than correlations to justify cause. I might state the original paragraph and have the kids try to punch holes in it. Critical thinking and all that. I'd be looking for points like those above and:

• If the claim is that people were taller before the Templars' suppression at the hands of Philip the Fair, became shorter during the 14-17th centuries and then started getting taller again in the 18th, then your doors should show the same trends for the same time periods, in the same types of houses and at the same socio-economic levels. If the doors to churches showed the same decrease and increases, that would be a good sign.
• How could the builder know the average height of 15th century mankind? Communications were difficult and slow, the size of the foot varied by region among other factors. Besides, even if he did know, why would he care? He's building for the man in front of him, not some mythical beast. Is there evidence that builders knew the average?
• Is the rural house different from that in the city?  See the Amsterdam note above.
• What are other reasons for the differences do you see? 

• War.  Make your attackers duck as they enter. Some Indian adobes have four foot doors for this reason. This picture is from Doune castle.
• Security. A smaller door is easier to bolt closed.
• Religion. Make your visitors bow in humility as they enter.
• Practical. They wanted to reach the ceiling beams for storage hooks.
• Sexism.  Only women used this door so who cared about it being more than 6'? 
• This was where the children slept.  There was plenty of room under the eaves.
• Mathematical considerations:
• Can the average height be measured?  Is that number meaningful here? Should the anthropologist use median or mode instead?  What was the builder using?
• What kind of sampling would work best for ascertaining that measure?
• Historical considerations:
• How do we know that people did get shorter? Did they or is this a myth?
• If they were, was it due to nutritional deficiencies? Were chronic health problems all that widespread in just those four centuries or merely the Black Death taking all the headlines? Was the 9th century healthier?  How about NYCity in the 1800s tenements?  London's Soho at the time of cholera epidemics?
• Were the doors shorter during the time period in question? What was he looking at when he measured?
• What would the students do as step two to confirm or deny these theories? Why haven't they started?

I love math.

Merry Christmas

That'll improve the school

Think they'll pass muster?

Forget about replacing the teachers ... replace the students. Bring in the superstars, the superheroes and the supernerds.Then our scores are sure to go up.  New Trier High School, Fairfax High School -- we're looking at you. Let's trade yours for ours!

Never mind.

Funny idea, though.

Science shouldn't be politicized.

It's a vital part of teaching ... helping students develop a healthy skepticism about what they see and hear. I show them videos, ads, other things and we dissect and analyze them in class. It's probably what I'll do tomorrow during the last day of school before break. I pick on the quacks, mostly: iRenew bracelets, QRay bracelet, Kinoki Footpads, Dr Marks Ion Cleanse Detoxifying foot baths, etc. Of course, during this process there is the inevitable question of global warming. It's with this in mind that I ran across the following article and thought I'd share.

From the Albany Times Union, Science shouldn't be clouded by politics
By Randy Simon

Is there solid evidence that the earth's average temperature is getting warmer, mostly as a result of human activity? What do you think?

Before answering, consider these scientific questions:

• Has coronary CT angiography made coronary catheterization obsolete?
• Are the hotspots in the earth's crust explained by phenomena in the upper mantle rather than in the earth's core?
• Can molecules exhibit intrinsic electronic functionality?
• Is lactose intolerance a genetic inherited trait? 

(to which I'd add "Will the Large Hadron Collider destroy the Earth when turned on?" and "Why won't value-added measures work to instantly maximize our schools' performances?" "Vaccines cause autism and backwards walking in cheerleaders.")

You probably are thinking: "How am I supposed to know?" That is, unless you are a cardiologist, geologist, condensed matter physicist or geneticist, or at least someone highly informed about these disciplines. These questions are in fact quite controversial in their respective fields, meaning that there is considerable disagreement among the experts.

Yet, you were probably all set to offer your opinion on global warming although you are not a climate scientist and are undoubtedly not well-versed in that discipline either. Furthermore, the question posed is not even controversial among experts in the field; there is overwhelming agreement that the answer is "yes."

So what gives here?

The answer is that you can't get opinions about most scientific questions from pundits and politicians but you can't avoid getting opinions on global warming from them.

Would you make decisions on how to treat a heart arrhythmia based on what a talk radio host believes? Would you have a senatorial candidate evaluate an aircraft design instead of an aeronautical engineer? Of course not. They aren't experts.

Clearly, we have come to believe -- or at least to act as if we believe -- that there are two kinds of scientists in the world.

There are those who work on a myriad of topics that have managed not to become political issues. They are obviously highly intelligent and accomplished individuals who have brought us brain surgery, iPads and the Space Shuttle.

Then there are those who work in areas that have become the subject of political and/or religious attention -- such as climate change and evolution -- and they are apparently dishonest, confused and deficient in their knowledge.

We are not becoming a society of Luddites; we surely want the fruits of modern science in our lives. Instead, we divide science into "good science" and "bad science" and allow partisan politics to make the distinction. It would be humorous if it were not alarming.

The political debate about global warming is fueled in part by scientists who take the position that the phenomenon does not exist, or at least that it isn't a result of human activity, or that it cannot be remediated by human intervention. This is no more compelling than the arguments in the 1960s and 1970s by a few medical doctors claiming that cigarette smoking was harmless. Indeed, there are always scientists with differing opinions on any topic.

When the overwhelming majority of scientists observe the same phenomena and draw the same conclusions, there are abundant reasons to take them seriously. The fact that we don't like the results (or even worse, political dogma doesn't like them) should not matter.

Could the majority opinion be wrong? Absolutely. But ignoring that opinion because you don't like it is foolishness.

Every day we trust our lives to the fruits of modern science. Medical technology, aircraft design, structural engineering and many other disciplines impact our safety and our very survival and, by and large, we feel that we can count on them.

Yet, when thousands of climate experts around the world draw serious conclusions from a wealth of data, we reject those conclusions because of our politics. It is nothing less than astonishing.

Perhaps you are not surprised by this at all. Some may see this discussion as an analysis of current attitudes toward science but others, I suppose, will cast it aside as "left-wing propaganda." And that, I suppose, is the problem in a nutshell.

One of the comments on this article was "We all have daily experience with weather, and through experience, with climate. To have some understanding of climate and none about the other issues is not surprising."

Really?

So I visit the doctor a couple times - does that make me qualified to judge his work?
I teach high school math and physics but I can't do a simple probability analysis. Should I be commenting on the LHC?

Watch it all or forward to Walter Wagner at about the 2:15 mark.

I used to run daily. Did that make me a physical therapist?
I eat food every day. Does that mean I know the nutritional value and positives / negatives of an Activia-fueled diet?
I go to the mall and I walk. Is iRenew a good product?

I went to school. Does that make me an education expert?

There is a huge difference between "I have experience with these" and "I have studied these in a scientific fashion." One is a guess. There other is not.

Dozens of TV shows and thousands of people believed that cheerleader who claimed the Flu shot made her walk backwards. Quantity is not a proof. Science is not a debate.

Another commenter:

So, where are the counter examples where scientists/experts got it wrong? This whole article is built on a fallacy--trust the experts. If it were to be the least bit helpful, it would have explained what we know, what we don't know and the strengths and weaknesses in our methods of knowing about the climate. But, of course, newspapers would rather make stupid arguments than educate the public so they can make better decisions.

Which I find somewhat amazing. Scientists get lots of things wrong. Then they fix the model and try again. Just because someone was wrong doesn't mean they can't fix it and get it right.

Rush Limbaugh is not a counter-argument.

And why the complete distrust of the "experts"? Do we refuse to drive a car because an expert mechanic worked on it? Does the expert computer technician bring us calm hope that our problem will be resolved or do we scream invectives and demand that the other politician really knows what's going on?

If you find that you can't trust those who spend their lives working on a problem in favor of someone with a monetary axe to grind, you'll simply wind up with "More doctors smoke Camels than any other cigarette."

Converting from metric is always tough.

In this piece from the Lancashire Evening Post, there seems to be a bit of a problem with conversions:

A Medieval silver broach dating back 600 years which was discovered using a metal detector in a Lancashire field has been declared treasure. An inquest at Preston Coroner’s Court heard that the 35mm silver dress closure was discovered by a pair of a metal detecting enthusiasts in a farmer’s field in Croston, near Chorley, in October.  The piece is half-an-inch in diameter, with groove decorations around it and a hook believed to have been used to fasten clothes.

35mm or half-an-inch?

Arrgh. One more day.

Who scheduled school to the 23rd? Bah! Humbug, indeed.

from interfacelift.com

Classy

Just saw the Christmas Card.

Is it just me, or are Bruce Jenner and Lamar Odom the only one with class and style in this photograph?

What's it worth if it isn't scored accurately?

SCores are being held consant.

The next time your principal complains about how the scores aren't going up, think about this.

From the Loneliness of the Long Distance Test Scorer: For some mysterious reason, unbeknownst to test scorers, the scores we are giving are supposed to closely match those given in previous years. So if 40 percent of papers received 3s the previous year (on a scale of 1 to 6), then a similar percentage should receive 3s this year. Lest you think this is an isolated experience, Farley cites similar stories from his fourteen-year test-scoring career in his book, reporting instances where project managers announced that scoring would have to be changed because “our numbers don’t match up with what the psychometricians [the stats people] predicted.”

Let's hear it for testing!

The whole article is interesting, but that line caught my eye.

It's cold. No Global Warming Again.

According to Andrew Watts, Cancun COP16 attendees fall for the old “dihydrogen monoxide” petition as well as signing up to cripple the U.S. Economy

Oh dear, some of these folks aren’t the brightest CFL’s in the room. Readers may remember this famous Penn and Teller video from 2006 where they get well meaning (but non thinking) people to sign up to ban “dihydrogen monoxide” (DHMO), which is an “evil” chemical found in our lakes, rivers, oceans, and even our food!

Ha, ha. Since some people at the conference fell for the old joke, global warming is therefore totally false. As is everything else they said, believed, wrote or thought. And since there's cold weather in Cancun, Global Warming is further debunked.

Jesus, people. Grow a brain.

Looking for the Education

We're below average on test scores.

U.S. students are below average in math skills, according to PISA, while Asian countries excel.

So somebody decided to look at why. Family attitude seems to be the key: working your butt off and getting extra help seems to be the key to doing better on the test.

source: Just as the latest international testing data once again highlight the relatively poor performance of U.S. students in math, a new report has come out to further explore why the United States may be struggling, with a focus on the math attitudes, beliefs, and behaviors of parents, and their children's out-of-school activities. Among the key findings: Parents in Singapore are far more likely than those in the United States and England to engage a math tutor to help their child, they're more likely to get assistance from teachers and others in how to help their child, and their children more often take part in math competitions and math/science camps.

I'm okay with that.  If you want to do better on something, you practice it. If you want to test better, you need to practice on the test.

Just don't call it an education.

Call it "Education Hero."

Just as Guitar Hero ruins the ability to play an actual guitar, Education Hero shouldn't be used on actual students.

Critical Thinking is not for Everyone.

The latest act in the worldwide WikiLeaks comedy: on Friday, the White House told federal employees and contractors that they're not allowed to read classified federal documents posted to WikiLeaks unless they have the proper security clearance.

It's posted for all the world to see, but if I work in Gov't, then I must adhere to the security limitations so the only people who won't read it are in Gov't.

Stunning.

Update from the drive home:

And then I thought about it a bit. Those with clearance randomly undergo security screenings and occasionally polygraph testing.  One question usually deals with "Have you seen, read or otherwise had knowledge of classified documents for which you did not have the proper security clearances?"  If I had seen something on Wikileaks, the honest answer would have to be "Yes."  That would lead to a whole lot of unpleasantness.

This advice might just save a few jobs.

What happened to "Education"?

Joanne Jacobs has a piece on evaluation programs that are looking to videotape teachers as they give lessons and then "Go Look at Tape." The issue seems to be that

More than 99 percent of teachers are rated satisfactory by their principals, reports a study on “the widget effect” by the New Teacher Project.

and this is somehow "bad," hence the need for overhaul. While I would argue that you need to improve the system so that middle-managers (Admin) can appropriately rate, measure and evaluate their assembly-line workers (teachers), I'm not sure that going to videotape is much of an improvement. If the Principal can't see the "errors" while sitting in the class, how is he supposed to make anything out of the 17th such review, even if he did have the time. Well, they have an answer for that ... Gates figures we'll pay outside evaluators who will somehow be able to see what the highly paid admin can't or won't.

The Gates Foundation is developing a new model, with the help of social scientists and teachers, reports the New York Times. Outside evaluators analyze videotapes to determine whether teachers are teaching well.

We've got money for outside evaluators? Pretty cool. I'll sign up. What gives you the idea that I'll be any more or biased/petty/superficial than the current system? The fact that I'll be able to rewind the tape? More likely I'll fast forward through it. The fact that I don't know the teacher so I'll be more honest? More likely, I'll make a snap judgment and move on.

You know we'll pay for training out of our RTTT money or something, hire bunches of consultants to teach teachers to evaluate other teachers who are trying to teach students. Pretty amazing, ain't it?

Hundreds of teachers will be trained to review 64,000 hours of classroom video. They will look “for possible correlations between certain teaching practices and high student achievement, measured by value-added scores.”

Let's say it's 800 teachers - that's 80 hours of tape to watch, per person. Asking a lot? I can't even spend that much time watching TV or movies in a month while sitting mindless and half-comatose. I'd need to be unemployed to look at 80 hours of tape multiple times and evaluate someone.

But here's the crux of my complaint ... those correlations. I've had students who completely and utterly bombed in class but did well on testing. I've also had plenty who did well in my class, well in the next couple of classes, had a great high school career, and then a great college career, and are now cranking out 6 figure salaries ... but didn't do well on testing. How do I know they did well? They told me.

Since when did value-added scores on NEAP mean an education? Since when could anyone figure out what I do that "works" by watching 10, 20 hours of videotape? Really? Do they know me? Since when did someone watching a few hours of video actually have a clue as to what went on and who and how the students were effected? Ten hours of video? That's two days. Does anyone here think that I couldn't fake it for two days and mess around the rest of the year if I was of a mind to?

I didn't think so.

Awards for all?

Joanne Jacobs has a piece about a parent complaining that only some kids were recognized for their performance on state testing. I actually agree with the parent on this one.

This, he said, was unfair to students who traditionally score lower on standardized tests and might not reach proficiency no matter how hard they try — mainstreamed special education students, for example.

Some kids will never reach proficiency. It's just a fact of life. If you make your standards low enough for all, then the achievement is meaningless and all of the kids know it and blow you off.The better response, for me, is to simply thank everyone publicly, en masse, and announce the barbeque for all. Then, reward or thank the good students separately.

Really, the "Always Praise in Public" rule isn't always your best course of action. I am against, for example, the tactic of an academic assembly during the first two periods of the day for which every class trudges down to the gym and sits by class.

"Everyone is sure to be a winner
with these fun 4" trophies."

What happens next is the whole point and is also the most excruciating part: the Guidance counselor, feeling all very important because she gets to "honor" the "good" students and bask in the reflected glory, reads the names of the high honor roll (20 kids), honor roll (140 kids), and merit (15 kids). She asks them to stand while this endless list is being read. Do you know how long it takes to read 175 names?

A little subtraction shows that there's maybe 30 kids in that grade who couldn't manage to get anything ... administration is proud that they didn't publicly shame any of them by saying their names. Except that they are still sitting down while everyone around them is standing up. Is it any wonder that they feel like shit? Most memorable student quote about the assembly (in informal geometry afterward): "Here are all the smart people in the school and none of them are YOU."

Back to the fun. Guidance has them sit ... and does the 11th grade. And repeats for the 10th. And the 9th. Can't have anyone left out, can we? An hour and something later, you've managed to humiliate as many people as possible, so you send the school back to class. "Don't make any comments to the Dweeb in the hallway, now."


Maybe the proper response is to not require everyone to recognize them. Give them their own awards night and invite them and their parents to come or not, as they choose.  You know, like the sports awards night, where the non-athletic can avoid having to sit through endless coaches' attempts at public speaking.

God knows there is nothing worse than a coach with limited vocabulary and no experience speaking to a crowd who's attempting to appear smart, clever, witty and interesting ... for each of his 54 football players, naming and praising the "spectacular work ethic" of every member of the 1-6 team, including the kids who lost eligibility for drinking and fighting.


It was also interesting that the rest of the fall teams had much better seasons, one winning a state championship, but the football team spent the most time congratulating itself.  But I digress ...

Maybe the takeaway from all this is simple:  The people who attend an awards night should be the ones who were there to watch the achievement itself.  Anyone else is excused. Those who wish to attend can do so.  I'd much rather have an awards night with the rest of my team and the spectators who were at the games. Everyone else feels like "Johnny come lately" hangers-on.  The same is true for academic awards:

If you weren't there when we did it, why would you want to be there to celebrate it?

If you can answer that question, then you can come to the ceremony and we'll all have a blast. If you can't, then you shouldn't be required to be there and we probably would feel uncomfortable if you did show up.