Little more than half of pupils met the government’s tougher new standards in literacy, writing and mathematics at the end of primary school, according to national test results.

The new tests for year six primary school pupils in England – used for the first time this year – had been criticised by teachers, academics and unions for being poorly constructed, while the Department for Education was blamed for a series of mistakes involved in their introduction.

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The national figures, published on Tuesday, show that just 53% of pupils reached the government’s “expected standard” in all four topics – reading, maths, spelling, grammar and punctuation, and writing – with just two in three making the grade in reading.

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Than a rule of thumb, the expected standard equates to the previous 4B level. Last year, 69% of pupils aged 11 and 12 reached level 4B in the subjects that were tested.

Despite the results, a DfE source said: “These results show that our children and teachers are capable of achieving the higher standards we expect of them and vindicate the reforms introduced by Michael Gove and continued by Nicky Morgan.

“While previous governments were happy to celebrate ever higher results at the expense of declining standards, these bold secretaries of state have taken the important decision to prioritise our children’s future ahead of short-term political wins.”

Morgan had earlier warned parents that the new tests could not be compared with previous year’s results, which were based on a different curriculum and measure of attainment.

“Neither schools nor parents should try to compare this year’s results with previous years. The tests are new and are based on a new, more rigorous national curriculum,” Morgan said before the results were announced.

The biggest differences appear to have come in maths and reading. In 2015, about 80% of pupils reached 4B in reading, compared with 66% who reached the expected standard this year.

In maths, where 77% reached level 4B last year, this year just 70% met the DfE’s definition of expected standard.

In other areas, 72% of pupils met the new standard in grammar, punctuation and spelling, which could be an improvement on previous years given the more demanding curriculum. In writing, 74% of pupils met the expected standard, which could also be an improvement.

Tuesday’s results only give the national picture, with school level results to be published later in the year. The DfE has already said that because of the uncertainty around the results of the new testing regime, only the lowest performing 6% of schools will be classed as below the government’s targets.

Russell Hobby, general secretary of school leaders’ union NAHT, said the results give a misleading picture of school performance.

“The government is proud to say this new curriculum is harder than in previous years, but seemingly happy to put these children at an automatic disadvantage” compared with children in previous years, Hobby said.

“Added to this, the government has made serious mistakes in the planning and implementation of tests this year, with delays and confusion in the guidance materials.”

Lucy Powell, Labour’s former shadow education secretary, called the new tests a “total shambles”.

Nicky Morgan should spend less time sucking up to Tory leadership candidates and more time trying to sort out the mess she has created,” said Powell, who resigned from Labour’s frontbench last week. “There’s no dressing these results up – there has been a big drop in results and standards have fallen due to the chaos and confusion in assessment created by Tory ministers past and present.”

Tim Farron, the Lib Dem leader, joined the attack, saying that the Conservatives were “treating students like a lab rats in their big ideological experiment”.

He added: “These results show starkly that they are gambling the futures of these young people on Michael Gove’s misty-eyed world view where every school is a prep or grammar school, students are robotic and teachers skip around teaching past participles and antonyms by rote to seven-year-olds.