The marches are the latest in a spate of at times violent anti-government unrest that erupted in February and has claimed at least 41 lives.
By the end of the day, some 23 people, including eight minors, had been detained by police for putting up roadblocks in eastern and southeastern Caracas, Interior Minister Miguel Rodriguez Torres told state television.
Authorities also used tear gas to disperse the demonstrators.
The Education Ministry recently started consultations to reform the country's basic school curriculum in a move opponents say is aimed at "indoctrinating" students with socialist rhetoric promoted by late longtime leader Hugo Chavez and his political heir and successor, current President Nicolas Maduro.
An estimated 3,000 mostly young marchers turned out in the capital Caracas, initially gathering near a university.
Some demonstrators carried signs that read "education is not indoctrination" and "fight for education that teaches us to think and not obey."
Others slammed recent restrictions on protests with banners such as "protesting is my right."
On Thursday, the Supreme Court issued a ruling requiring demonstrations be approved ahead of time by authorities or risk being dispersed, in order "to guarantee the right to free movement."
Opponents say the ruling goes against democratic principles.
Similar protests took place in other cities around the country, including Valencia and Maracaibo.
More than 700 people have been injured in the months of anti-government unrest as angry students and others denounce rampant crime, inflation, widespread shortages of basic goods and other economic woes.
The demonstrations have died down recently but continued sporadically in pockets of eastern Caracas, which tends to be well off and anti-Maduro.
Maduro was narrowly elected to succeed Chavez last year after the populist firebrand died of cancer.
