Staff at the Learning and Skills Council are on strike for the day over plans to cut some 1,100 jobs across its 48 offices in England.
The strike, by members of the Public and Commercial Services Union, is to be followed by a work to rule.
The union said workers were facing day-long IQ and assessment tests to decide who would keep their jobs.
The council, which wants to redirect £40m to learners, says it wants to keep as many as it can in its new structure.
The LSC funds all post-16 education and training outside universities, though students are not affected directly by the industrial action.
Union general secretary Mark Serwotka said it was "embarrassing" that the body charged with spending billions of pounds to improve the skills of young people and adults was using assessment tests on its staff.
He said: "Even women on maternity leave have been told they are required to sit the test, which we believe is discriminatory.
"One woman whose test was due two days after she gave birth was told she would be given childcare so she could sit the test, which is quite extraordinary.
"Here, we have the quango with the biggest budget on a crusade to downsize and get rid of people they don't think fit the bill."
He said the LSC was "effectively forcing people to reapply for their jobs rather than seeking to re-skill and retrain staff".
But the LSC's human resources director, Sally Stewart, denied everyone was being tested.
Where someone's job remained after the reorganisation, they would stay in the post, she said.
The union said the aim was to cut a third of the posts in the LSC but Ms Stewart said the final number of staff who would leave would depend "to a significant degree" on individual circumstances.
"We are looking for every opportunity to redeploy staff to other suitable positions.
"We have expressed our commitment to maximise the appointments of existing employees and we expect and want to minimise compulsory redundancies," she said.
Staff were being offered funding for learning and development courses and access to in-house training to support them "during this difficult process".