PATERSON, NJ – Six weeks into the academic year, one of the academies at Eastside High still has at least seven vacant teaching positions, including a math class that’s supposed to help students pass a mandatory state test for high school graduation, according to a guidance counselor at the school.

Speaking at Wednesday night’s Board of Education meeting, the guidance counselor, Betsy Antonoff, said some students at the School of Culinary Arts, Hospitality and Tourism have substitute teachers for three of their classes because of the vacancies.

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“We are not sending the right message to our students that we care about them,’’ said Antonoff. “There’s chaos in the streets. There should be order in the schools.’’

“Are the substitutes teaching? No,’’ she added. “Are the children learning? They’re not learning what we want them to learn.’’

District officials did not dispute the accuracy of Antonoff’s comments on the vacancies at the culinary academy. Spokeswoman Terry Corallo said, “The placements at Culinary are now approved and the onboarding will occur quickly. They had been posted and candidates were identified. The principal has been advised of the status.’’

The district is already more than halfway into its first marking period. Students in danger of failing were supposed to get their progress reports on October 9. The marking period ends November 15.

Some school board members were upset when they learned of the vacancies, especially because the information had come from a school-level staff member and not from district administrators.

“I don’t get it,’’ said Commissioner Errol Kerr. “People are crawling over each other to get jobs. This should not be. Certainly, there’s a problems when we have a situation like this.’’

“I’m deeply troubled with having substitute teachers for extended periods of time,’’ said Commissioner Jonathan Hodges.

“We share your concern,’’ said state-appointed superintendent Donnie Evans, during Wednesday’s meeting.

Under state rules, substitute teachers are allowed to teach a class for a maximum of 19 days, board members said. But the president of the teachers’ union, Peter Tirri, said Paterson simply has shifted other substitutes into the vacancies to get around that rule.

Tirri said the problem at the culinary academy is happening at other schools in Paterson. “There are still vacancies all over the place,’’ said Tirri.

In fact, at Wednesday’s meeting, a parent with two children attending one of the academies at the Kennedy High complex said they have had substitute teachers in some classes for much the year so far. “I don’t understand how we want to hold students accountable, but we don’t have teachers in the classroom,’’ the parent said.

When asked about the number of teaching vacancies throughout the district, Corallo said, “You can see the number of open teaching positions on our job postings website.  I think I see 8 positions.” Those eight positions did not include the ones at the culinary academy, apparently because those already are being filled.

Tirri said the problem with the vacancies stems from the district taking a last-minute approach to picking people for teaching positions that should have been filled at the start of the summer. Tirri said more than 120 teachers have been hired since August 20 and 280 others have been transferred among different city schools since August 1.

“We’re a state-operated district, we’re supposed to do these things the right way,’’ Tirri said.

Some school officials have said that the implementation of the district’s “transformation” plan, including the reconfiguration of some schools, caused last-minute shuffling of teaching assignments.

District officials have acknowledged their system for recruiting and hiring teachers needed work. At a meeting earlier this month, officials discussed their plan for making improvements in those areas.