But he has made clear that the controversial primary one tests are here to stay. There have been 400,000 Scottish National Standardised Assessments undertaken since being introduced last year. But critics say the 40-minute tests in literacy and numeracy are happening to early for youngsters, particularly in deprived areas.
“I'm very sensitive to the argument about P1 assessment and I acknowledge the debate going on about this point," Mr Swinney told Holyrood's education committee today.
"So I'm taking a very careful and close interest in it and I'm listening to what people are saying to me about this."
Liberal Democrat MSP Tavish Scott said there were concerns from pupils in deprived areas about the value in testing literacy and numeracy of children at such a young age.
"Particularly for young children, it's just a challenge to have them in a class never mind dealing with a test," he said.
"I would be grateful if the cabinet secretary could reflect on that because I think there are some real issues there."
Mr Swinney accepted that concerns had been raised among teachers over the tests, but insisted they have a key role to play in tackling the attainment gap between schools in poorer and more affluent areas of Scotland.
"It's not presented in exam circumstances like the Scottish Qualifications Authority specialise in. It should be done in a very relaxed environment within the classroom. It shouldn't take any longer than 40 minutes. That's once a year.
"I don't say that in any way trivialise the issues because I'm very alert to these concerns. One of the reasons why we want to do this is to help to inform teacher judgement about where young peoples' educational development needs the greatest amount of educational support . So it's to inform the professional judgement of teachers about how they can then deploy their professional skills.
"It will help us with how we assess how much progress we are making year by year in closing the poverty-linked attainment gap.
Mr Swinney said ministers want to identify the needs of children as early as possible so these can be addressed at a young age.
"I'm very happy to acknowledge that I'm sensitive to the issues that have been raised about the P1 assessments and I'll listen carefully to the feedback that get.