New Zealand schoolkids' performance on international maths tests leaves a bit to be desired. Both the Programme for International Student Assessment test (PISA) and the Trends in International Mathematics and Science Study (TIMSS), the two main global benchmarks, show declining scores.

Among 15-year-olds, the drop in PISA scores is across-the-board – students at the top, middle, and bottom of the class all dropped by about 20 points from 2003 to 2012.

The New Zealand Initiative's report by Rose Patterson, released this month, puts some of the blame on an experiment in maths teaching rolled out in the 2000s. Experiments are often worth trying – just look at the government's recent initiatives with social impact bonds. But they also require later evaluation so we can tell what has worked and what hasn't.

The Numeracy Project, as it was called, had some really great elements. Rather than simply rote learning facts, students would also build their understanding of why six by nine is 54 and alternative strategies for figuring it out. Those alternative strategies can really help when trying to multiply larger figures beyond the twelve-by-twelve that those my age had to memorise.

But something went wrong in the implementation – or at least in some schools. There is a lot of school-by-school variation in New Zealand – and this is a good thing. But some schools took the Numeracy Project a bit too literally. Rather than complementing the times tables with the additional strategies, they threw out the rote learning part.

Patterson's report suggests this too great a lean against rote learning lies behind some of New Zealand's recent poor maths scores. Kids who have to spend time working out six by nine use up mental capacity that then is not available to take the next steps. Those who memorised it can move quickly to the next step in applying their answer.

Far from a call to abandon modern teaching practices in favour of rote learning, Patterson's report argued simply that the pendulum has swung too far. We need both rote learning and understanding. The report also recommended measures to help parents ensure that their kids' teachers are ready to really apply the more modern mathematics teaching methods which require greater teacher numeracy than teaching simple rote memorisation.

While the Initiative's Twitter stream filled with the usual attempts to pigeon-hole our recommendations into the Kiwi Twitteratti's ideological view of the world, our email inbox filled up with supportive messages from teachers, university lecturers, and maths tutors who agree that New Zealand kids really deserve better.

Auckland University research fellow in data analytics Dr Matthew Courtney told us, "Before working at The University of Auckland, I taught junior mathematics at secondary school level. I found that a great many students, even in the top streams, lacked the basics. Because of this, very few could move onto more sophisticated maths. Without heavy remedial work, many of these students were destined for failure. Your work represents a move in the right direction."

Massey University chemist and distinguished professor Peter Schwerdtfeger won last year's Rutherford Medal – New Zealand's highest honour in the sciences. He told us, "We are destroying a whole generation of students with these new sociologically inspired methods. The level of maths competence has been in decline for years, and we are having to fix these problems at university."

Remedial maths tutor Dorinda Duthie, who has to help clean up the mess, added: "The teaching methods used in the Early Numeracy Project are fundamentally flawed. They simply do not work for most children. The top 10 to 20 per cent are fine, but they would do well regardless of the way in which they are being taught. The horizontal layout for addition and subtraction is confusing and ignores the basic concept of moving to the next column when a total is above 10."

Lower Hutt high school maths teacher Jon Nash told us: "I feel I spend ages undoing poor teaching from earlier years. I am also a huge advocate of rote learned basic facts."

Those who have read our report know that we are not calling for any simplistic return to rote-learning on its own. We think students need to memorise basic facts so that they can go on to use the more interesting approaches more successfully. Rote learning is a necessary complement to greater mathematical understanding. It is the base on which approaches like those added during the Numeracy Project trial could really build. But we do need that basic foundation.

And so we wonder a bit about the literacy skills of some of our report's critics, like those suggesting we want a bizarre return to the 1950s. The times tables are neither bizarre nor a relic of the 1950s. They're a necessary part of a broader and better curriculum. Check that your kids are learning theirs.