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My daughter—subjected to the vagaries of Everyday Mathematics (1), a math program her school had selected and put in effect when she was in the third grade—was having difficulty with key concepts and computations.  She was now in 6th grade, and with fractional division, percentages and decimals on the agenda, I wanted to make sure she mastered these things.
The Singapore math texts are part of the Primary Mathematics curriculum, developed in 1981 by Curriculum Planning & Development Institute of Singapore.
My daughter’s fifth grade teacher shared my disdain for EM and supplemented it heavily with photocopies of pages from an older textbook.  I told him once in an email that I was not happy with EM and asked him his opinion. Despite his knowledge and good teaching, there was still lack of a textbook and he was still consigned to the pacing and sequence of EM. Knowing that in 6th grade, they would learn fractional division, as well as decimals and percents, I feared a train wreck if I didn’t get to my daughter first. Fortunately, things progressed nicely with the two girls after that first lesson.  But I only had about four weeks before they hit fractional division—not a lot of time. Despite the victory with fractional division, the following week’s tutoring session left me slouched in my chair with my hand over my eyes. I’ve thought about why Laura could not understand the lesson at school, to the extent she could no longer recognize what a fraction was.
This does in fact make sense considering that for most people a particular concept or task starts to make more sense after they have moved on to the next level. In EM, however, students are exposed to topics repeatedly, but mastery does not necessarily occur. A casual glance at Everyday Math’s workbook pages does not reveal that there is anything amiss.  The problems seem reasonable, and in some cases they are exactly the same type given in Singapore Math. If the lack of proper sequencing, lack of direct instruction, lack of textbook and lack of mastery of foundational material prevents a student from making the necessary discoveries, he or she can be “pulled aside” and given material to read.  So teachers are left with a three ring circus of kids getting it, kids not getting it, and are expected to “adjust the activity” as needed. By the time EM gets to 6th grade, the workbooks are loaded with Math Boxes—the term for worksheet review sessions that come in the midst of a particular unit and consist of a mixture of problems from past years in the hope that the kids will finally master the material. I’ve told this story to many people since it happened—mostly people who have asked me what to do when their school has a problematic math program. There was no need for me to finish the conversation, because the conclusion is always the same: Poorly structured math programs are not fair to students, parents or teachers.
Through my experience teaching my daughter and her friend, I have come to believe that an essential requirement of textbooks is that they teach the teachers. When a Norfolk Southern train hauling chlorine through Graniteville, South Carolina, derailed in 2005, toxic gas poured into the town.
Seven hours later, a second Norfolk Southern freight train—two locomotives, 25 loaded cars, and 17 empties—approached Graniteville at 49 miles an hour. Trains carry 40 percent of America's freight as well as 650 million passengers a year, and in general, their safety record is good and getting better.
Although the railroad keeps our 21st-century economy running, it's essentially a 19th-century technology.Most worrisome are the 75,000 carloads of breathable poisons that trundle around the nation's tracks every year at speeds of up to 50 miles an hour. As bad as these accidents were, they could someday be remembered the way we recall the 1993 World Trade Center bombing—as a harbinger of worse to come. The chlorine released in the Graniteville crash killed nine people, sickened 72, and demonstrated the lethal potential of human error in the rail system. Forty years ago, the National Transportation Safety Board began urging railroads to design a way for a train to stop itself if the engineer "loses situational awareness"—that is, has a heart attack, falls asleep, gets distracted, or makes an all-too-human mistake. Railroaders call such technology—systems that slow or stop a train without human intervention when the engineer makes a dangerous mistake—positive train control (PTC).
In 1990, the NTSB put positive train control on its list of most-wanted transportation-safety improvements. In 2007, Congress finally got involved, passing a law mandating positive train control, but President George W. As a passenger-rail engineer, Robert Sanchez was, quite literally, a train wreck waiting to happen. Later texts suggest that Sanchez had indeed illegally let the teenager operate the train—two days before the accident—with passengers aboard. On the afternoon of September 12, in the last 69 minutes of his life, Sanchez exchanged 35 text messages with the teenager.
The collision drove Sanchez's locomotive 52 feet into the first passenger rail car, killing Sanchez and all 22 people in the car.
If I lose my iPhone, Apple's Find My iPhone feature will pinpoint its location anywhere in the world within a few feet.
Railroads have only a very rough idea, at any given moment, of where their 18,000-ton freight trains are and what they're doing.First, about half the nation's trackage is "dark territory," devoid of signals and invisible to controllers. Positive train control, as conceived today, is intended not to replace control rooms and signals but to supplement them.
At six o'clock one recent morning, Darrell Maxey, who's in charge of building Metrolink's PTC system, picked me up at my hotel at the far eastern end of the L.A.
We drove to Metrolink's maintenance yard, a sprawling, sun-blasted expanse of concrete where Maxey issued me a hard hat and reflective vest, hoisted himself aboard one of Metrolink's test trains' passenger cars, and ushered me up after him. Transforming railroads from a 19th- to a 21st-century mode of transportation means making the train itself responsible for its actions.
As I start down the track, the onboard computer is constantly comparing the train's progress to the downloaded programs.
The onboard electronics that make positive train control work on Metrolink's test train are stuffed into a tiny compartment down in the nose of the locomotive, where, were this a freight train, the engineer's toilet might be. For an industry that operates in much of the country as though it's in a western, this looked like a jump to Prometheus. On September 12, 2008, a Metrolink commuter train collided with a Union Pacific freight train in Chatsworth, California, killing 24 people and injuring 101. To disabuse me of that notion, Maxey drove us to a wayside signal being outfitted for positive train control. Metrolink used to be an organization of railroaders—men accustomed to mechanical challenges wrought in iron. The Class I's knew better than to object when Congress was passing the law mandating positive train control in the wake of the Chatsworth wreck. The Federal Railroad Administration says that building positive train control could end up costing $10 billion.
For that, the railroads will get a system that would have prevented the marquee Chatsworth, Red Oak, and Graniteville wrecks but would do nothing to prevent 98 percent of train accidents, including the types that cause the most deaths: knuckleheads walking on tracks or trying to zip across road crossings ahead of speeding trains. The disaster prompted the federal government to require railroads to install positive train control systems—which could have prevented the crash—on 70,000 miles of track nationwide. The industry is going to have to acquire 58,000 digital radios of a type never built before, and because trains travel on other railroads' tracks, each radio must be able to communicate with those of every other railroad.
In 1977, Mother Jones magazine broke the story that the Ford Motor Company had concluded, when its Pinto was blowing up with frightening regularity, that it was cheaper to pay the widows and orphans than it was to recall the cars and fix the problem.
In the case of positive train control, the Federal Railroad Administration needed to weigh the benefits of avoiding the tiny category of accidents that the system would prevent against the projected costs.
When the Federal Railroad Administration counted the average seven annual deaths and 22 injuries positive train control would prevent in a year and added the cost of the property damage and evacuations that positive train control would obviate, it concluded that positive train control would save the industry just $90 million a year. Every freight railroad to which I spoke, as well as the industry group the Association of American Railroads, inveighed against being forced to implement positive train control, especially by the end of 2015.
Of course, there also exists a very cheap way to help prevent train crashes: Let engineers sleep.
He and his union—the Brotherhood of Locomotive Engineers—have mixed feelings about positive train control, though, because they worry that it could make it easier for Class I freight lines to further reduce the size of a train's crew. Much as they revile the 2015 deadline for implementing positive train control, neither the individual railroads, the Association of American Railroads, nor the Federal Railroad Administration want to discuss adjusting working conditions as a means of improving safety.

In general, companies would much rather buy equipment than meddle with their employees' working conditions. The Association sidestepped the issue of unpredictable sleep schedules in a written response, saying only that positive train control "was never intended to solve the problem of a locomotive engineer falling asleep," an odd comment, as that is a big part of what it is intended to do.
The Federal Railroad Administration says it lacks the authority to order railroads to give engineers regular hours (the way things are done, say, in Britain).
Now that they've tried and failed to get Congress to push back the 2015 deadline, the railroads are grudgingly committing to it. Her teacher insisted they use the alternative algorithms offered by EM; she did not teach the standard algorithm for long division.
The technique is contained in the Teacher’s Manual, but that is something neither students nor parents have. I’ve asked other teachers this question and they usually chose not to answer—perhaps out of fear for their jobs. I believe these factors contributed to the lack of knowledge about fractions exhibited by my daughter and Laura. Given how little they knew about fractions during the first lesson, I felt that my fears were justified. Therefore, I decided to teach each chapter on fraction in the Singapore Math, from 4th grade to 6th grade textbooks in a concentrated burst. I believe it is because while Singapore situates decimals in the context of fractions, EM situates decimals in the context of the unfamiliar. Without knowing what the connection was between fractions and decimals, the fraction ceased being a fraction in her mind and was just a number on top and a number on the bottom with a line in between.  And somehow that strange looking number got transformed into a number with a point in it.
What the casual observer doesn’t know is what sequencing has preceded that particular lesson, nor how that lesson is conducted in class.
Students get ever increasing amounts of Math Boxes.  The expectation is that the nth time through the spiral is the charm.
It is unfair to students because they are essentially attending another class after a fully day in addition to finishing their homework for school. Children cannot make the connections the adults are making who already have the experience and knowledge of mathematics. This may happen to some degree with EM, but based on my experience with the program, not much gets transferred to the students.
That said, I will remain forever grateful to my daughter and Laura for having taught me so much about fractions.
At 6:10, a 12-car Norfolk Southern freight train pulled up to the Avondale Mills textile plant, and Jim Thornton, a conductor with 18 years' experience, climbed down from the locomotive to open a switch and let the train roll onto a siding.
The two most common are chlorine—the Graniteville chemical—and anhydrous ammonia, both of which can kill in particularly grisly ways if inhaled. Rail operators have known for decades that technological fixes could prevent rail disasters caused by the kind of human errors committed at Macdona and Graniteville, but they have been dragging their feet because those fixes are expensive and complicated. The modern version requires the train to be "aware" both of what it is doing and what is happening on the tracks ahead, using a combination of data radios, GPS, and cellular networks.
Clinically obese, with high blood pressure, enlarged heart valves, diabetes, and HIV, he may also have had sleep apnea, which can leave sufferers perpetually sleep-deprived.
As he drove his three-car train loaded with passengers west from Chatsworth, Sanchez was busy swapping text messages with a teenage train buff about the supercool world of locomotives—a huge violation of company policy. Focused on his smartphone, he missed a red signal that should have held him back from a single track shared by freight lines. It escaped nobody's attention that had positive train control been in place at Chatsworth, Sanchez never would have reached the freight track; the system would have stopped his train at the red signal. Railroads, though, have only a very rough idea, at any given moment, of where their 18,000-ton freight trains are and what they're doing. The railroad farthest along in post-Chatsworth implementation is, not surprisingly, Metrolink, which lost 24 passengers and an engineer on September 12, 2008. Slumped on every seat and scattered across the floor were hefty sandbags, simulating the weight of a full load of passengers. Were I this train's engineer, I'd start my day by downloading into the train's onboard computer a program about that day's run: the weight and length of the train, as well as everything the system needs to know about the upcoming length of track, such as speed restrictions, grade, curves, signals, switches, and stops.
I peered in at an incomprehensible tangle of wires surrounding a rank of plastic and aluminum boxes: a cellular modem, data radios that communicate with signals and the control room, a train management computer containing the downloads, and a big orange "black box" that the NTSB looks for after a crash.
We made our way back through the locomotive and stepped off, and Maxey pointed to the new adornments on the locomotive's roof. Until now, such signals were nothing but big traffic lights—red, yellow, green—on steel posts.
But with the move to positive train control, the railroad is acquiring a corps of IT types; they fill one of the biggest buildings I've ever seen. Maxey and his colleagues are convinced that positive train control will put an end to the kind of engineer-caused disasters that occurred at Graniteville and Chatsworth.
Even at a time when the Class I's are doing well—profit margins ran from 17 to 45 percent last year—$10 billion is a lot of money, roughly equal to everything the railroad industry spent on buildings and equipment in 2010.
Several railroads, particularly in big cities, are having trouble getting enough bandwidth in the crowded radio spectrum to launch the system. Totaling up the cost of wrecked equipment was fairly easy—and so, it turns out, was computing the value of the human lives that positive train control would save. That's just a tenth of the system's annual maintenance costs, and a wretched cost-benefit prospect—unless you or somebody you love is one of the seven people saved.
The 2 percent of accidents that PTC could prevent includes the most catastrophic possibilities—the black-swan big ones, like tankers of chlorine bursting open within a mile of the National Mall.
The Federal Railroad Administration sets limits on how many consecutive hours an engineer can work but nonetheless lets railroads treat freight engineers, in the words of one, "like plug-in flashlights." Engineers never know exactly when they're going to be called to work, so they never know when they should sleep.
Some of the teachers at her school offered tutoring services, so we hired one of them to teach her the standard algorithms.
There is a student’s reference manual, a hardbound book containing topics in alphabetical order and which can provide some guidance, but does not necessarily cover what was said in class.
SO OF COURSE THEY GIVE YOU SOMETHING THAT YOU CAN’T DO AND YOU’RE SUPPOSED TO FIGURE IT OUT? Although I really should have started all this back in 4th grade, doing it this way had an unexpected benefit: they saw almost immediately the connections between multiplication and division of fractions. It was a one page worksheet asking questions such as “How many ? inch segments are there in 3 inches?”  After four such questions, the text presented a formula in a box in the middle of the page, titled “Division of Fractions Algorithm”. It is unfair to parents who have to either teach their kids or hire tutors—and are held hostage to the school’s math program whether they like it or not.  And it is not fair to teachers who are expected to teach students based on an ineffective and ill-structured program.
With Singapore Math or any well structured and authentic mathematics program, both teachers and students greatly benefit.
It was getting close to the hour by which, according to law, the crew had to quit for the day and rest.
As early as the 1920s, the Santa Fe rail line between Kinsley and Dodge City, Kansas, used a rudimentary system to stop a train if it passed a red signal. If a discrepancy arises—a switch is open that shouldn't be or the locomotive is passing a red signal—and the engineer doesn't respond, the system takes control of the train, applying the air-brakes and shutting down the locomotive. Class I freight railroads—Burlington-Northern Santa Fe, CSX, Union Pacific, Norfolk Southern, and Kansas City Southern, all of which have annual operating revenues of hundreds of millions of dollars—simply ignored the agency. To make matters worse, his work schedule at Metrolink, the commuter rail service for the Los Angeles basin, seemed designed to leave a man exhausted. Congress hastily revived the 2007 mandate and folded it into the Rail Safety Improvement Act of 2008, which flew through Congress in just 34 days.

Although each railroad operates vast control rooms that look like they belong on the set of Dr. Conductors operate by written instructions and their watches, stopping their trains and climbing down to open and close switches by throwing big iron bars. In his mid-fifties, with a bristle-gray moustache and glasses, Maxey exudes a Midwestern-style bemusement at the breathtaking convolutions of his job. If I were using track owned by other railroads, I'd download a separate program for each, because every railroad has its own way of signaling and communicating.
If I fail to slow when I should or if the computer thinks I'm about to run a red signal, the system warns me. Up where a light and maybe a radio antenna used to sit, a forest of aerials sprouted: two 220MHz antennas for the data radios, two cellular antennas for redundancy, a GPS antenna, and the Wi-Fi antenna through which the train downloads its instructions prior to departure. It's an old General Dynamics cruise-missile factory a quarter-mile long that Metrolink slicked up with a big glass atrium, potted trees, and interior floor-to-ceiling windows. The major freight railroads, though, sound like 15-year-old boys being asked to mow the lawn. And the cellular backup will have to have a reliability rate of one failure in every hundred million tries. Ask a railroader to describe the technical challenges of implementing positive train control, and you can expect to listen for a while.
Yet for the past three decades, since President Ronald Reagan ordered cabinet departments and independent agencies to conduct cost-benefit analyses before issuing new regulations, such computations have been national policy. Call it the tyranny of technology in a litigious age: If a technological fix that may save lives is available, you're pretty well obliged to apply it. Start making concessions to employees, and it can go anywhere—and the company will be living with the changes forever. Thus, there is no textbook a student (or parent) can refer to go over a worked example of the type of problem being worked.
After the workers had shut down the train, Thornton called a taxi to take him, the engineer, and the brakeman to a nearby motel.
The disaster helped push the Avondale Mills plant, which had been making cloth in Graniteville for 161 years, out of business. Last June, two Union Pacific trains somehow ended up on the same Oklahoma track and collided head-on with such force that the locomotives almost fused. At Minot, the problem was poorly inspected rails and inadequate tank-car construction, but at Macdona, the cause was as simple as at Graniteville: The engineer failed to notice a slow-down signal and blew past.
Al Qaeda might do it, but it's more likely that a $55,000-a-year engineer, in the 10th hour of his shift, would simply nod off at the controls.
But the railroads could also cheaply and humanely achieve big safety leaps simply by improving the working conditions of engineers—something they're even less enthusiastic about doing.
In the mid-1980s, in the Minnesota iron range, Burlington Northern successfully operated the first GPS-based system to stop a train automatically if the engineer made a mistake; it dropped it within the decade, to save money. Only Amtrak responded, installing a type of positive train control on its Northeast Corridor trains in 2000 and a different version on some of its trains in the Midwest a year later. Sanchez started at six in the morning, drove trains until 9:30 in the morning, then started again at two in the afternoon and worked until nine at night—a 15-hour split shift. Strangelove—with enormous electronic schematics of their tracks displayed across the walls—the information that controllers receive is amazingly crude. While it's true that the vast majority of freight traffic and all passenger traffic travels on tracks with signals, even there, controllers can't see their trains the way I can "see" my lost iPhone.
He's an old railroader, a systems engineer by training, but installing positive train control at Metrolink is making him an IT guy as well. We threaded our way through the length of its interior, which felt like the engine room of a U-boat: hot, noisy, and diesel-pungent. Maxey took a key from his pocket and unlocked the steel door on a small, windowless concrete shed that stood beside the signal. As Maxey walked me through, he kept buttonholing people and asking them to describe their resumes. It just means we don't do a lot of other things." In other words, if a train rolls off a poorly maintained track, blame Congress for rushing the railroads to implement positive train control.
For its part, Congress would much rather order companies to buy stuff than to poke its nose into employee relations. It never occurred to him that, for the first time in his life, he'd failed to check the position of a switch that he'd opened. The Federal Railroad Administration, the railroads' regulator, had the power to make the Class I's fall in line behind Amtrak, but instead, the agency agreed with the Class I's: Positive train control was too expensive. The nation's railroads were given until 2015 to install positive train control on the 70,000 miles of track on which passengers or toxic-by-inhalation chemicals moved. They know only when a train has passed a given point—a switch or a signal that is wired into the grid. I could watch these downloads on an LCD screen mounted on the engine's dash; after that, I wouldn't have to look at the screen again, and, in fact, Metrolink is hoping I won't. It is designed never to let my locomotive pass a red signal, so it is constantly looking six miles—three signals—ahead.
Despite the shower of money, the bill to extend the deadline died without a vote, but that doesn't mean the railroads have given up the fight. Between the railroads' institutional resistance and the technical challenges they face, don't hold your breath. Three of the cars contained chlorine, a common industrial chemical; one of them sheared open. Three weeks later, 17 cars of a 98-car Norfolk Southern train went off the rails in Columbus, Ohio, busting open three cars of denatured alcohol and igniting a fire that forced the evacuation of about 100 people.
In the emotional aftermath of Chatsworth, neither the railroads nor the Federal Railroad Administration objected. Those points are anywhere from one and a half to three miles apart, creating "blocks" of track.
They'll tell anybody who will listen that positive train control will cost too much, isn't worth the money, places an undue burden on railroads and their customers, will make rail shipping less, instead of more, efficient, and is being forced upon them too quickly. A CSX coal train jumped the track in Ellicott City, Maryland, in August; six of its 21 cars tumbled into a parking lot, killing two young women bystanders. Controllers know when a train's locomotive has entered or left a block, but not how fast it's moving. A heavy train going downhill will get an earlier warning than a light train going uphill, but as a rule of thumb, it takes about a mile, or 90 seconds, to stop a three-car Metrolink train.
In November, a Union Pacific train plowed into a Veterans Day parade float in Midland, Texas, killing four.
They can talk to engineers by radio, but if they notice that a train has passed a red signal, all they can do is shout into the radio, and often they're too late even for that. Later that month, a CSX train derailed on a bridge near Philadelphia International Airport, tearing open a tanker filled with 25,000 gallons of vinyl chloride and sending 71 people to the hospital.

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