For example, P(|) is relatively high,but P(|) would be very low.

In 2008, 52 Ohio schools were forced to restructure because of persistent failure. Even after several years of significant attention, fewer than one in three had been able to reach established academic goals, and less than half showed any student performance gains. The Columbus Dispatch concluded, “Few of them have improved significantly even after years of effort and millions in tax dollars.”

The four parts of the program are:

Type in a search like  and Googleinstantly comes back with Showing results for:.

That gives us:Now it is time to evaluate how well this program does.

For a word of length , there willbe deletions, -1 transpositions, 26alterations, and 26(+1) insertions, for a total of54+25 (of which a few are typically duplicates).

From that I extracted twotest sets of corrections.

For example,However, if we restrict ourselves to words that are —that is, in the dictionary— then the set is much smaller:We'll also consider corrections that require simple edits.

For example, occurrences of "the" make up about 7% of English text, sowe should have P() = 0.07.

Our program enumerates all corrections withinedit distance 2.

A small number of progressive leaders of major urban school systems are using school closure and replacement to transform their long-broken districts: Under Chancellor Joel Klein, New York City has closed nearly 100 traditional public schools and opened more than 300 new schools. In 2004, Chicago announced the Renaissance 2010 project, which is built around closing chronically failing schools and opening 100 new public schools by the end of the decade.

So far, only looks at one word at a time.

These principles can be translated easily into urban public education via tools already at our fingertips thanks to chartering: start-ups, replications, and expansions. Chartering has enabled new school starts for nearly 20 years and school replications and expansions for a decade. Chartering has demonstrated clearly that the ingredients of healthy, orderly churn can be brought to bear on public education.

But we'll leave that for another day...

The churn caused by closures isn’t something to be feared; on the contrary, it’s a familiar prerequisite for industry health. Richard Foster and Sarah Kaplan’s brilliant 2001 book Creative Destruction catalogued the ubiquity of turnover in thriving industries, including the eventual loss of once-dominant players. Churn generates new ideas, ensures responsiveness, facilitates needed change, and empowers the best to do more.

Consider the misspelled word ="thew" and the two candidate corrections ="the" and ="thaw".

We can distinguish two sourcesof error in the language model.

Without data I couldn't build a good spelling error model, so Itook a shortcut: I defined a trivial, flawed error model that says all known wordsof edit distance 1 are infinitely more probable than known words ofedit distance 2, and infinitely less probable than a known word ofedit distance 0.

Well, "thaw" seems good because the only change is "a" to "e", which is a small change.

in the Sumerian city-state of Lagash.

Class lessons that engage students’ visual, auditory, and tactile/kinesthetic learning modes contribute to effective learning. But what about homework?

So we can make  produce the first non-empty list of candidates in order of priority:

Clearly we could use a better model of the cost of edits.

A generation ago, few would have believed that such a fundamental overhaul of urban districts was on the horizon, much less that perennial underperformers New York City, Chicago, and Baltimore would be at the front of the pack with much of the education establishment and reform community in tow. But, consciously or not, these cities have begun internalizing the lessons of healthy industries and the chartering mechanism, which, if vigorously applied to urban schooling, have extraordinary potential. Best of all, these districts and outstanding charter leaders like KIPP Houston (with 15 schools already and dozens more planned) and Green Dot (which opened 5 new schools surrounding one of Los Angeles’s worst high schools) are showing that the formula boils down to four simple but eminently sensible steps: close failing schools, open new schools, replicate great schools, repeat.