But it's not clear - because Bloomberg can't back up everything he claims.
The mailer stacks four facts about Bloomberg's record as mayor against Thompson's time as president of the old Board of Education.
Not a surprise: Team Bloomberg has tried to make the phrase "Board of Education" a synonym for bad old New York, when crime was up, streets were dirty and kids didn't learn.
Except they can't support their most shocking claim about Thompson's tenure - "School Violence Soared."
A tiny footnote cites the Daily News of Sept. 18, 1995. A check of the archive reveals an editorial that claimed "Violence in the schools has soared" - but it doesn't cite statistics, and doesn't mention Thompson.
That's because Thompson didn't become board president until the following summer.
It's a funny error to make on a mailer emblazoned with the phrase, "Why is Bill Thompson distorting Mike Bloomberg's education record?"
The next item claims dropout rates rose four percentage points in Thompson's time, compared with falling 6.5 points under Bloomberg. It cites the same Department of Education report for both figures.
Yet a close reading of that report shows it also assumes Thompson was president when the class of 1996 graduated - which he wasn't. Ironically, if the report had cited his real tenure, the numbers would have been worse - a 4.5-point rise.
It's a strange lapse for the data-obsessed mayor, who relies on reams of statistics to judge how his administration is doing.
Perhaps the campaign is making him sloppy: When News reporter Erin Einhorn caught him this month inaccurately claiming to have equalized school funding for whites and minorities, a deputy mayor had to walk it back.
Statistics alone can be misleading, too: Dropout rates began rising during Thompson's time because the Board of Education began demanding higher performance.
When dropout rates were released in 2000, The News wrote: "Parents and advocates said the push for higher standards - from high-stakes tests to tougher promotion and graduation policies - is forcing struggling students out of the system without an adequate safety net in place."
Expect to be buried under an avalanche of education statistics for the next six weeks. Bloomberg will point to better performance, helped by money and control that Thompson never had.
Thompson will say the mayor has turned schools into testing mills that ignore arts and music - though in his first TV ad, he never mentions his time as board president.
Which argument wins the election?
When the Quinnipiac Poll asked New Yorkers in July, 56% said Bloomberg's school stewardship has been a success.
But it may end up less about numbers and more about impressions. Lots of New Yorkers are going to see Bloomberg's expensive mailers between now and Nov. 3 - and almost none of them are likely to check his footnotes.