Tensions between City Hall and Connecticut Coalition for Achievement Now escalated last week as two independent companies released contradictory reports on the quality of New Haven’s education system.

New Haven Board of Education officials said they stand by one study, a quality review report completed by Cambridge Education, a private international education consulting firm, that praised the school system for making “big strides” in student performance and other areas, such as leadership and vision.

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But they criticized another, a report card produced by ConnCAN, a private education outreach and research organization. The report card said New Haven schools made negligible or below-state-average performance gains in standardized test scores over the last year and ranked among the worst 10 cities in the state for percentage of students who met the target range for standardized test scores set by the Connecticut Department of Education.

“Clearly, we have work to do, but we also have made movement,” New Haven Public Schools Director of Communications Catherine Sullivan-DeCarlo wrote in an e-mail Saturday.

BOE members interviewed were quick to trumpet the findings of the Cambridge study, which featured interviews with administrators and teachers from across the city.

New Haven Public Schools Superintendent Reginald Mayo said he respects the criticisms included in the report.

“We are pleased with the overall findings, especially considering how thorough the review was,” Mayo said in a statement released on February 21.

Sullivan-DeCarlo, meanwhile, criticized the ConnCAN report card, which she said only considered test scores, not other aspects of the public education system, such as its leadership. She suggested that ConnCAN often makes “significantly flawed” assertions about public schools in its studies in order to promote a charter-school agenda.

“The fact is that ConnCAN uses data to drive support and public dollars toward charter schools,” Sullivan-DeCarlo wrote in the e-mail.

But she declined to comment on whether the conclusions drawn in the recent report card were flawed, saying she had not yet read it.

In response, Director of Communication and Research for ConnCAN Marc Porter Magee said the organization had a transparent and clear methodology behind creating the report card.

“Anyone can go to the state and replicate it,” he said. “Our methodology is straightforward, and I don’t know how you can imagine in any order that the results are skewed toward any school.”

He added, “Cambridge is focusing on the process and input — what we’re focused on is outcome.”

This is not the first time ConnCAN has butted heads with City Hall.

Last year, after ConnCAN Executive Director Alex Johnston criticized the wide achievement gap among various ethnic and socioeconomic classes in the New Haven public-school system, Mayo, BOE President Brian Perkins and Mayor John DeStefano Jr. signed a letter in September striking back at the group.

The letter accused ConnCAN of “abuse and denigration of public schools and relentless promotion of charter schools.” Johnston wrote a letter in response that said the three had “misconceptions” of the group’s overall mission.

According to the ConnCAN report card, charter schools usually fare better than public schools in state rankings of students who attain the average score in standardized tests for students for all grade levels.

The Cambridge study makes no mention of charter schools or their effects on the education system, but it does suggest that the New Haven school system needs a formula-based plan to be more transparent in the distribution of budget funds.

Connecticut State Senator Toni Harp, among others, has criticized City Hall for its resistance to working with charter schools in the area.

In the quality report, Cambridge evaluators found that third graders, seventh graders and high-school students have improved sufficiently in standardized test scores. The report also praises New Haven for its commitment to raising student performance levels in the schools.

But that commitment is not enough, according to ConnCAN.

Among fifth graders, the report concluded, New Haven schools made 2-percent gains in student performance in standardized tests over one year, half the state average of 4 percent. And for eighth graders, New Haven schools made no gains in student performance, while the state average was an improvement of 3 percent, according to the report card.

The report does not include any data for high-school students’ performance, which Magee attributed to the lack of data for high school students.

And across the three schooling levels, New Haven ranked in the bottom 10 in the state for percentages of students who made the state-determined minimum test score for grade level, ConnCAN reported in the study.

According to its Web site, ConnCAN used test score data from the state Strategic School Profiles database — a statewide registry of school expenditures and student standardized test scores — and results from the Connecticut Mastery Test and Connecticut Academic Performance Test, two standardized tests administered to Connecticut students in public elementary and middle schools.

ConnCAN did not consult with NHPS when creating the report card, Sullivan-DeCarlo wrote in the e-mail. NHPS was “very involved” in the Cambridge study through discussions with those conducting the report, she added.

A representative of Cambridge Education relayed comment to the Department of Education. Members of DOE staff could not be reached for comment over the weekend.

It remains unclear how the studies will affect city legislation, but Sullivan-DeCarlo said NHPS will focus on the improvements Cambridge suggested — including the creation of a support plan for students with behavioral problems, an idea long advocated by some residents and members of the Board of Aldermen.

Andrea Jackson-Brooks, chair of the Board’s education committee, who said she had not seen the two studies, declined to comment. Other members of the committee did not return messages left on their answering machines on Sunday. City Hall Spokeswoman Jessica Mayorga did not return multiple requests for comment over the weekend.

Drawing from the Cambridge suggestions for improvement, the BOE plans to draw a district-wide behavioral support plan to support students with emotional troubles.