An attempt to find out how many children in England are being educated at home suggests the number might range between 7,400 and 34,400.
Home-educated children do not have to follow the national curriculum
But the study, commissioned by the Department for Education and Skills, concludes there is no accurate picture of the extent of home educating.
And it says the rules governing home education are "too vague".
Parents cited bullying and inadequate local schools as among the reasons for teaching their children themselves.
Home education, where parents choose to educate their children outside school, remains a legal option for families - as long as they provide a suitable full-time alternative.
But this study's attempt to find out how many children are being taught this way was inconclusive - not least because there is no obligation on families to tell their local authorities that they are home educating.
Estimates between 7,400 and 50,000 children in England
Education is compulsory, attending school is not
Home educated children do not have to follow the national curriculum or take tests
Each child must have "efficient, full-time education suitable to their age, ability and aptitude"
No obligation to register or inspect home-educated children
The sample study of nine local authorities found between 0.09% and 0.42% of school populations being taught at home - but this would not include any children who were not registered as home-educated.
If these figures were applied nationally, this would mean between 7,400 and 34,400 children were being taught at home - most of them in the secondary age group.
But the study concludes that even a full national survey would not be likely to deliver a reliable figure, because many home-educated children would remain unknown to local authorities and home-education organisations.
Common reasons for home educating, the study found, were fears about bullying and unhappiness with the quality or style of education available in local schools.
But the study points to the lack of a clear picture of the scale or motivation of home educators - and questions how the learning of these children could be assessed.
And it also says that there is too much vagueness surrounding what is the "suitable" education that has to provided for children learning at home.
These latest figures for the number of children being taught at home are considerably lower than an often-quoted figure of 150,000 home-educated children.
But Ann Newstead, a spokesperson for home education group Education Otherwise said there never had been any clear evidence for the 150,000 figure - and that research from home educators suggested a total in the region of 40,000 to 50,000 children.
She echoed the findings of the research, that bullying and fears about the suitability of school for their children's individual needs were among the main reasons that parents opted out of the school system.
In her own children's case, she said schools were unable to provide the type of education needed for their particular special needs.
And she rejected the idea that children taught at home would miss out on the social aspect of school.
Based in Kent, she says she belongs to a support group of 70 families that meets regularly, giving children a chance to socialise and play together.
"For some children, the social side of school can be the worst.
"The playground can be an absolute nightmare for children who, for whatever reason, don't have anyone to play with."
In terms of the trends among home educators, Ms Ashtead said an increasing number of parents of very young children were now entirely opting out of the school system, teaching at home from infant-school age.
For those who do attend school, a survey suggests that in England and Wales they are doing so increasingly from the age of four, not five as the law requires.
Of 66 councils asked by the Times Educational Supplement, more than half began the year in September and four more were planning to do so from 2008, which would take the total to 68%.
Fewer than one in 10 had an April start, compared with a quarter in 1997.
A third had two starts, September and January, up from a quarter in 1997.
Traditionally children have begun reception classes, as "rising fives", at the start of each of the three terms during the year.