Parents, teachers and councillors have expressed confidence that they will succeed in "fitting a Jewish school into a hole designed for Catholics".

Three months after Tony Tankel quit as the head of Calderwood Lodge's parent council amid a dispute over whether the 50-year-old school was officially seen as denominational or not, the Glasgow Jewish Representative Council believe there is now "widespread agreement about the direction of travel".

The headteacher, East Renfrewshire Council and the new head of the Parent Council have all now accepted unequivocally that the primary is not "non-denominational… with a Jewish ethos", as Mr Tankel argued, but denominational, as the Rep Council always maintained.

The distinction is important because under Scottish law at denominational schools the appropriate religious body has the right to approve a specific supervisor of religious instruction and oversee religious staff appointments.

Although the school caters for non-Jewish children, up to two thirds are Jewish, from all branches of Judaism. Boys wear kippot, prayers are said daily and meals – ordered on a tablet computer - are kosher, while Friday assembly incorporates a kabbalat Shabbat service. Signs on the walls are written in Hebrew, while display boards inform that this month is Shevat. The school is regarded as "the jewel in the Glasgow community's crown"

For years the link between the school and the local Jewish community was seen to be indestructible, with Jewish education - Kodesh and Ivrit – coordinated by the private charity Calderwood Jewish Education. In 2010 the local authority assumed responsibility for this, including the £1,000 a year parents paid per child for it, with the proviso that there would be an independent advisory body to oversee it and maintain.

That body was disbanded last June "with no warning," said Paul Morron, vice-president of the Rep Council. "It's been a very unfortunate block that came from almost nowhere."

Without the advisory body, and with parents raising fears of slipping standards of Jewish education at the school, pressure grew for East Renfrewshire to clarify the school's status so that a religious supervisor could be chosen.

Now that this has been done, both the Rep Council and the Parent Council confirm progress is being made to appoint this person, whose role is not to meddle, said Mr Morron, but to "cover the cultural side of things, which is exactly what East Renfrewshire said when they first offered to take over".

The appointment is complicated because the legislation is designed for Catholic schools, where the denominational body is obvious. Calderwood is inclusive of all streams of Judaism and cannot be represented by one. The intention is for the Rep Council to take on the responsibility.

"I wouldn't say we are 100 per cent there," said Mr Morron. "But the atmosphere has changed. We're in agreement over the direction of travel - a considerable achievement – and really just working out the last elements."

The Parent Council has also taken steps to respond to concerns about Jewish education, including offering optional additional Hebrew classes after school for older pupils.

But they deny that standards have fallen since the takeover. "People don't like to see change, they always think there is a hidden agenda, but there wasn't, it was just to make the school better," said Parent Council member Adam Tomkins.

Parents are still invited to Jewish events such as kabbalat Shabbat, just along a revised schedule. While there are no longer designated Kodesh or Ivrit classrooms, Mr Tomkins said this is part of a national educational trend against there being "a school within a school", and falls more in line with Jewish schools in England. In addition to regular religious instruction, pupils might use their Ivrit in a maths lesson. "It cements their understanding of both at the same time," he said.

Calderwood's non-Jewish headmistress, Vanessa Thomson, admits it has been a learning curve since she arrived three years ago. But she came aware Calderwood was expressly a faith school, and insists this is obvious in terms of the children's experience. "The day is punctuated with moments of prayer. The school year is punctuated with festivals and the learning that precedes them," she said. "I work at embedding the Jewish ethos in the curriculum.

"We are now looking at additional things that underpin the whole curriculum as well as specific kodesh, for example the Jewish history project (created by LooktoLearn founder Nic Abery, that links torah and art)," said Ms Thomson. "We are encouraging them to make connections."

Richard Dover, a parent who raised concerns last year, said there are still questions over the balance between secular and Jewish education. "It's subtle, just the way things are presented. But parents are confident that things are going in right direction."

"There is the same commitment to Jewish education that there always was," added Rabbi Moshe Rubin, Calderwood chaplain. "The fact that the council took over the Jewish department is unusual and there have been teething issues but there is a strong desire to work with the council and for the council to work with us. It takes time to figure out how a new structure will work."

British-Jewry has changed dramatically in Calderwood's lifespan. "We can't expect things to stay the same," he said. "The community has really moved into modern times and Calderwood is part of it. It's healthy."

Today, there is praise for the current Parent Council. "It is now very open-minded. There is frank discussion which has been actively prevented for the last few years," said Mr Dover.

At the most recent Parent Council meeting, new chair Colin Cowan pledged transparency. "There is no subterfuge. If you've got concerns come and ask."

According to the Rep Council, there are now no issues of significance to be resolved. And the relationship appears to be thriving; Mr Cowan praised community groups for joining forces to ensure an annual school-trip to Amsterdam goes ahead.

All are aware that the school is a huge asset going forward for Glasgow's Jewish community, and urge more parents to take advantage of it. "We have got something that is amazingly attractive to people either looking to return to Glasgow or to relocate," he said.

The expectation on all sides is that a plan for the religious supervisor will be completed and handed to East Renfrewshire within a few weeks. "Now everybody is singing front the same psalm sheet, everybody wants the same thing, which is a close, harmonious, mutually supportive relationship between the school and the community," said Mr Tomkins. "Four months ago it looked like a big challenge. It doesn't now."