The measures used in the study were called adverse childhood experiences, or ACEs, and these included parents' drug-taking, violence, separation, incarceration and depression.
Before entering kindergarten, a total of 52.8 per cent of the children experienced at least one ACE.
After adjusting for other negative factors such as poverty, the researchers found that, for each additional ACE, children were 1.12 times more likely to be unable to count up from one to 10.
Study co-author Professor Rhema Vaithianathan said the results were in line with research overseas, as well as retrospective findings out of another New Zealand longitudinal programme, the Dunedin Study.
"We know that chronic stress is linked to reduced cognitive ability and affects the child's brain development," said Vaithianathan, co-director of AUT's Centre for Social Data Analytics.
But she said the other report offered some more positive findings.
"The most interesting part of the research was exploring more than 700 factors available in the data that could help us identify traits and characteristics that were typical of those children and parents who - despite having a number of challenges at birth that made them at risk of experiencing adversities - ended up not having any."
Key factors among these odds-beating kids were the quality of the relationship between the mother and their partner, and strengths like warmth and co-parenting support.
"What this tells us is that there is some cause for optimism, that despite challenges at birth, there are protective family-based strengths that can be identified and nurtured to help children get a better start in life," Vaithianathan said.
"We've been spending a lot of effort looking at the relationships between mother and child - but a lot of our programmes don't look at those between the mother and partner, who is there 24 hours a day," she said.
"So that should be part of the whole support system in the household – and maybe we are missing an opportunity to engage."
Insights MSD general manager Rob Hodgson said children taking part in the Growing Up in New Zealand Study were now turning 10.
"The value of the Growing Up in New Zealand study is realised through research providing insights that informs the design of policies and services that better support the diversity of families and children in New Zealand today.