As soon as he had the floor during Tuesday’s joint legislative hearing, Assemblyman Dean Murray of Long Island zeroed in on an issue that he said has been bothering him.

“It seems we’re basing graduation — in many people’s opinion, including myself — too much on test scores,” Murray said.

Murray is one of several legislators who latched onto an issue the State Education Department is currently tackling: How to find new, legitimate ways for students to graduate if they struggle to pass required Regents exams. The Board of Regents, New York’s education policymaking body, opened up several new options last year, but support from legislators is key if the state wants to make more options broadly available.

“The opportunities to look at different approaches to graduation are important,” State Education Commissioner MaryEllen Elia said during testimony. “That, of course, takes funding.”

The state is interested in piloting “project-based assessments,” which would evaluate students on a series of tasks, or tests that assess foreign language skills. But developing those alternatives requires money. (The Board of Regents sets education policy, but state lawmakers control the budget.)

Though some lawmakers expressed support for new graduation options at Tuesday’s hearing, securing funding is likely to be a battle. The Regents asked for $13 million to explore these pathways, but Cuomo’s proposal did not include that funding.

The Regents’ interest in expanding graduation options stems from concerns that deserving students are falling short of the state’s requirements.

A 2012 state decision required students to pass five Regents exams with a score of 65, instead of the previously required 55, to receive a traditional diploma. In 2014, the Regents provided a buffer of sorts by deciding students could substitute a fifth required Regents exam for an alternative route in an area like the arts or career and technical education.

Last year, they went even further. In March, they decided students could swap out a final Regents exam for a skills certificate and in June, state officials made sweeping changes to graduation requirements for students with disabilities. Under the new rules, some students with disabilities could earn a “local” diploma by passing only the math and English Regents exams.

But without more widely accessible exams, those students may find there are only limited options at their schools.

Elia gave some clues during her testimony about the direction the state education department is headed. She said she is “very interested” in piloting portfolio-based tests and suggested the state is also looking into creating new science assessments.

Any mention of additional options is music to the ears of Senator Todd Kaminsky, who has been a leading legislator calling for more ways to help students graduate. Kaminsky hosted a panel recently in Long Island attended by Regents Chancellor Betty Rosa, and urged state officials to continue down their current path.

“When you talk about 400-plus lives being improved by your measures that’s great,” Kaminsky said, referring to the number of students with disabilities who graduated under the new provisions passed in June. “I just want to let you know that people are now hoping for a next step, or a follow-up step this year, as a way to recognize the potential of all students.”