Are charters really doing a better job educating the city’s public school students than the traditional public schools? That was the question of the week, after state test scores came out on Tuesday showing not only far greater proficiency in English and math by third through eighth graders who attend the city’s charters, but also far more improvement this year.

Mayor Michael R. Bloomberg left no doubt about his answer to the question. Speaking on “The John Gambling Show” on WOR Radio on Friday, he said the results of the state tests proved that charters were making a difference — just as he had said they would.

“There’s a reason people want to send their children to charter schools,” he said. You can hear his full remarks about schools here:

The state test results showed that, over all, city scores rose three points in both math and English Language Arts in 2012, with improvements in all grades and groups except for English Language Learners.

Still, as Al Baker reported on SchoolBook on Tuesday, that left fewer than half the students at proficiency levels in reading:

The scores posted by about 440,000 students in third through eighth grade, who took the tests in April, showed that 60 percent passed the statewide math tests, compared with 57 percent last year.

But fewer students showed proficiency on the English exams, though the results improved from last year: 47 percent of students achieved proficiency compared with 44 percent last year, according to the state Education Department.

At the same time, there was a large leap in proficiency levels for charters, which were already well above those of district schools. As Yasmeen Khan reported for SchoolBook:

For the third year, the city’s charter schools outperformed traditional public schools in math and English, and the spread in results between the two groups has increased.

In math, 72 percent of charter school students passed the state tests this year, compared with 60 percent of traditional public school students. In English, 51.5 percent of charter school students passed this year’s tests compared with 46.9 percent of traditional public school students. (About 30,000 charter school students took the tests; 400,000 students took the tests in traditional public schools.)

According to Gotham Schools on Friday:

Bloomberg blamed the teachers union contract for the districts schools’ inability to duplicate the success of privately managed charter schools, which have longer days and greater flexibility in hiring decisions.

But instead of making points about issues such as teacher tenure or seniority-based layoff laws, Bloomberg invoked more salacious news items.

“The union keeps protecting people that shouldn’t be in the classroom that touch, have sex, whatever it may be,” he said. “It embarrasses other teachers.”

To which the teachers’ union president, Michael Mulgrew, responded, according to Gotham Schools:

“He just can’t get over the fact that he has been wrong on so many issues — from closing schools to test scores — in what was supposed to be his administration’s legacy,” Mulgrew said in an e-mail.

Earlier this week, the charter schools also crowed about the test results, as SchoolBook reported.

“What we’re seeing, and what we’ve seen all along,” said James Merriman, chief executive officer of the New York City Charter School Center, “is that the longer school day and longer school year that characterizes charter schools, as well as simply a focus on instruction and the sense of having a schoolwide culture that everyone buys into, results in these kinds of achievement scores.”

And the editorial boards of some of the city’s newspapers are onboard the charter school bus. The Daily News’s concluded:

Thanks to ingrained habits and a United Federation of Teachers mind-set that holds sacrosanct a member’s right to let kids down, traditional public schools have few of those ingredients of success. Instead, the UFT defends contract rights while blaming bosses and a supposed lack of money.

Cash is not the answer, as documented by a new study from Harvard’s Program on Education Policy and Governance and the journal Education Next. New York led the nation in raising school spending from 1990 to 2009 while racking up subpar test score gains compared with other states.

Mayor Bloomberg, former Schools Chancellor Joel Klein and current Chancellor Dennis Walcott have fought to accomplish school reform over steadfast opposition. That they’ve gotten this far is testament to a sustained drive, while the latest scores document that gains are real.

But some say the test results are a simplistic and perhaps unfair way of judging success, as commenters to various school sites have been pointing out this week.

Wrote Arthur Reynolds:

Say you’re the guardian of a good student in a low-income neighborhood with chronically underfunded, or simply badly-run schools. A charter comes in. Who is more motivated to get their kids into the new school? Does the fact that the new school then outperforms the old ones mean anything?

And Pam Pruyn wrote:

Unfortunately, charter schools cherry pick their students even when they have lotteries that appear to select randomly. Why do I say that? Because we have charter schools near our traditional public school and when the children are not doing well or have more needs than they can handle, instead of MEETING the needs, they send the parents to look at our school and help them TRANSFER OUT. If the parents complain to the charter school, the students somehow magically disappear into the “public” school system. So much for better teaching!

Still, with city students’ improvements in reading and math at best “incremental” — the word used in the news release from the State Education Department on the scores — the charter school results appeared to be a bright spot. And Mayor Bloomberg was clearly looking for that light.

As Beth Fertig reported this week on SchoolBook:

… while Mr. Bloomberg continues to say that his stewardship of the schools has led to improvements in student achievement, the latest results of state proficiency tests are further indication that the change he has been hoping for has largely been incremental, rather than transformational.

Still, she went on to say, Mr. Bloomberg saw the latest results “as ‘very positive’ progress”:

“Virtually every single grade, three through eight, virtually every single ethnicity or special group, showed improvements this year,” he said at a news conference at the Tweed Courthouse, the Education Department’s headquarters. “If this doesn’t put a smile on everybody’s face, I don’t know what on earth you can do. This is the future of our children and of our state and our city and country.”

But surely, after the student and teacher upheavals and legal battles and constant changes in city schools of the last few years, some folks at Tweed and at City Hall may be hearing an old song in their heads this week: “Is That All There Is?”

The week ended with continued uncertainty about the fate of the 24 schools that the city wants to shut down, to reshuffle staff and administrators, then reopen in the fall with new names, though the same students.

City officials finally reached out to the affected teachers — some 3,000, who were either facing the need to find jobs in other schools or were expected to start work at the reconstituted schools in the fall — and provided instructions that would seem to indicate the city expects the schools to stay as they are in the new school year.

As Beth Fertig reported on SchoolBook:

The Education Department sent out two letters on Wednesday. One was sent to 150 teachers who are known to have applied to transfer to another school, according to education officials. It asks them to inform the city whether they still intend to transfer by completing an online survey, due July 27. Decisions to transfer are binding.

An Education Department spokeswoman, Erin Hughes, said the city sent a second letter to 2,700 teachers who were assigned to the 24 schools in 2011-12, saying they did not have to take any action to reclaim their jobs. It asks them to state whether they have changed their plans, though whatever they say is not binding.

They can seek other jobs in the city schools through Aug. 7, Ms. Hughes said.

Still, on Friday Mr. Bloomberg was clinging — perhaps unrealistically, as lawyers and others have concluded — to the hope that a judge would overturn an arbitrator’s decision that forbids the city from carryout out its staff shake-ups. He told John Gambling on WOR that he was optimistic the city would prevail.

The parties are due back in court on Tuesday, before Justice Joan B. Lobis of State Supreme Court.

Other news of the past week that might have slipped by you:

Gov. Andrew M. Cuomo signed a bill making kindergarten mandatory for all 5-year-olds. The bill was initiated at the efforts of the City Council’s speaker, Christine C. Quinn.

PBS’s “Frontline” ran a report on the work of a Johns Hopkins University researcher, Dr. Robert Balfanz, who has identified indicators that he says can predict how likely a student is to drop out of high school. The report shows how the research is being used at Middle School 244 New School for Leadership and Journalism in the Bronx.

The Local East Village posted a video interview with a former gang member who has returned to the East Village after 18 years in prison, and is now speaking to local students at Public School/Middle School 34 Franklin D. Roosevelt about the perils of gang life.

And The Queens Chronicle reported that a building that used to be part of a detox center on Parsons Boulevard in Flushing would become a Muslim charter school in the fall.

Here’s what’s coming up in the week ahead.

Saturday is the Harlem Book Fair. It will include a teen forum, facilitated by the author Ellis Cose, at the Schomburg Center that will try to answer the question, Does race still matter to teenagers? You can find out more about the book fair at The Root Web site.

This weekend look for the responses to this letter, denouncing the amount of testing in schools, in The New York Times’s Sunday Review section.

Finally, SchoolBook invites school officials, parents, teachers and community organizations to use our pages — one for every public, private, parochial and public charter school in the city — to post news about accomplishments, programs and events from the end of the school year or this summer.

Apparently there are a lot of things for schools to brag about, based on the e-mails to SchoolBook@nytimes.com with announcements and requests for coverage. But there are too many of them to properly cover with our summer staff, so feel free to use our conversation tool and post them on your individual school pages.

And while you are there, students and parents have been posting queries about entry requirements and back-to-school information, among other things, about individual schools. Help them out, please, and provide some answers.