Some want streaming to be abolished, saying this will remove the stigma of the Normal stream.
Another call is for the Primary School Leaving Examination (PSLE) to be done away with, so as to remove stress and unfairness as those from better-off families get more help to ace their exams.
Yet others think that universal welfare can be a solution to Singapore's inequality problems.
Yesterday, Education Minister Ong Ye Kung advised caution in undertaking such moves.
He noted that President Halimah Yacob's call in her address on May 7 for "bold changes" has received a lot of attention.
But, "while we should be bold, we should not be reckless, for this would undo what had worked and undermine the fundamentals in our system", he said. "All these have served our students well over the years."
"We must be bold and we must be wise," he added. "To do this, we need to put our ears close to the ground, and listen to the voices of all segments of Singaporeans. And if we listen close enough, we will also realise that the 'voice of the people' does not deliver a singular message - rather, it offers a diversity of views, conflicting and complex, even as they remain compelling."
So, for example, not all students want to be in the Express stream.
"They will tell you they prefer to be a big fish in a smaller pond, rather than a small fish in a bigger pond," he said.
Many students in the Normal (Technical) course also feel that the hands-on curriculum plays to their strength, he added.
"Remember, stigma is not an education policy, but the result of our own attitudes and biases."
As for the PSLE, many parents actually support it as it teaches children the value of hard work, and allows them to showcase what they have learnt, he said.
The PSLE, he added, is seen as an objective and transparent way to decide which secondary schools children go to and also enables children of humble backgrounds to make it to a school of their choice.
"The alternative, which is to go by residential location, is even more unfair," he said.
When the PSLE T-score system is replaced with Achievement Levels from 2021, he said, pupils will not be differentiated so finely during the Secondary 1 posting. For those with similar scores, citizenship, choice and ballot will be used to break the tie.
Said Mr Ong: "I am confident that this will reduce the stress of students and help them enjoy learning more."
In his speech, the minister also noted calls for universal welfare to be introduced to ease inequality. Proponents argue that providing assistance to not just the low-income, but also the middle-income will remove the stigma linked to social assistance, and preserve the dignity of the low-income.
But Mr Ong warned that having universal welfare would mean that tax rates would have to be raised.
Half of Singapore's population do not pay personal income taxes, and the goods and services tax "is still a single digit", he noted.
"If we want universal welfare, taxes on ordinary folks, including the middle-income, will have to be much higher," he said.