Diane Tinsely’s fourth-grade son dreams of becoming an astronaut. She worries that state tests in math and English might stifle his passion for math and science, rather than encourage him.

That’s why when his classmates sit for state assessments next month, her son will not. And asked recently whether she could be convinced to opt back into the tests, she was hard-pressed to think of changes that could change her mind.

“I don’t know what they could do with it besides do away with it,” she said.

Tinsley was inspired by leaders of New York’s test refusal movement, which convinced one in five parents across the state to boycott the state tests last year. (The share was much smaller in New York City.) The movement’s growth has forced Albany’s lawmakers to pay attention — and in the last year, leaders have rethought significant pieces of education policy, placing a moratorium on the use of test scores in teacher evaluations and starting reviews of the state’s learning standards and assessments.

But leaders of the testing boycott movement say they are not satisfied, and are using their influence to push for more changes. As students gear up to take the exams this year, that leaves a lingering question: What does the opt-out movement want to gain from boycotting tests again?

Leaders of the movement say bigger, more significant changes that get to the heart of the way state tests work. Opt-out leaders are asking for a larger reduction in testing time, closer to only one hour per subject, said Bianca Tanis, an elementary school special education teacher and co-founder of the New York State Allies for Public Education.

Leaders also want the tests to have no consequences for schools, teachers, or students, and no longer be the yardstick for the state’s receivership program — its turnaround program for low-performing schools.

These requests are tangled up in existing federal and state laws, and State Education Commissioner MaryEllen Elia has said any responsible revamp of standards and assessments will take time. Elia already announced a number of changes to the assessments this year, including allowing students unlimited time, shortening tests by one reading passage and several multiple choice questions, and promising to make more revisions in the future. But opt-out leaders have denounced these as minor adjustments.

“There are no changes this year that would even give me pause of opting my child back into the test,” Tanis said.

These statements leave some critics wondering whether the movement will be satisfied by any testing changes, or whether they will ultimately stand against standardized tests of any kind.

“Nothing goes as far as they want to go,” said Stephen Sigmund, the executive director of High Achievement New York, a coalition of groups that promote the standards. “There is no answer for them except for get rid of higher standards and any state tests.”

Last April, opt-out leaders outlined a list of six demands including the resignation of Regents Chancellor Merryl Tisch, an independent review of the state’s standards, and decoupling of test scores from teacher evaluations. These demands have largely been met, and others that Tanis mentioned, including making standards more age age-appropriate, are underway, Sigmund said.

Outside the opt-out leadership, parents are eager to see politicians respond to their concerns about testing. Some want to see the length and emphasis on tests wane. Others worry about how the tests will be used to judge their children, teachers, and schools.

At a testing forum at P.S. 133 in Brooklyn on Monday night, parents disagreed about whether any changes to the tests would encourage them to have their children take the tests.

Renee Burke said she is on the fence about whether her fourth-grader will take the tests.

“I’m not totally against testing,” she said. “I wish they would reform the testing. I don’t need it to be three days of craziness.” (Students currently take three days each of math and English exams.)

Others indicated they would be swayed by whether their choice would affect teacher evaluations. One mother asked whether her child’s teacher would be penalized because he is in a dual-language class and a quarter of the students are English language learners. (An education department representative at the meeting explained that the evaluation system is designed to compare student scores only to other students of similar backgrounds.)

As parents mull over whether their students will soon sit for the exams, the opt-out movement is trying to expand its influence. On Wednesday, the group will hold a press conference asking city Schools Chancellor Carmen Fariña to tell all parents about their opt-out rights.

The conference comes after Fariña said that it is OK for new immigrants or students with disabilities to refuse the test in an invite-only meeting last week, according to DNAinfo.

Fariña is not the only education leader softening her stance on opt-out. The Regents chancellor-elect said that she would opt her own child out of state tests, and state commissioner MaryEllen Elia sent an email to regional superintendents including a line that parents have the right to choose whether their children take the test.

Both Fariña and Elia have discouraged opt-out in the past. Fariña said she is “not a fan” of the movement and Elia has said encouraging it is “unethical.” City education department officials also said the data helps to inform better instruction and that participation is important to hold the system accountable for progress.

The change in tone has had an effect on at least one parent. Deb Waldman, the parent of two fourth-grade students at P.S. 133, one of whom receives special education services, was determined to have both her children take the test — that is, until she heard about Fariña’s comments.

“I was like, oh jeez. I was really feeling comfortable about my decision and then now I’m sort of starting to doubt myself,” Waldman said. “So I just thought, I should just come and learn more about it and really see like if I can come to a decision that I’m comfortable in for both of them.”