Research by the security firm revealed 17 percent of parents of this group are unaware their child visits a social network.
Furthermore, 40 percent of eight to 12s believe all information they read on sites such as Facebook is true, while 27 percent of 12 to 15 year olds believe search engines only return URLs of sites that are genuine.
"There are times in children's development when a little up-front internet monitoring can be helpful to children as well as parents. One of those times is when children are heading into secondary school and engaging in social networking; another is when a child seems extra vulnerable," said Anne Collier, co-director of ConnectSafely.org.
"Then it's great when parents use tech tools for talking points in the kind of calm, ongoing family discussion that really protects children online and offline."
With this in mind, Trend Micro has launched parental control and internet monitoring software.
Trend Micro Online Guardian allows parents to view browsing history, wall postings, messages, photos and videos (shared and viewed), and chat logs to get an idea of what their children have been up to on the web, and initiate a discussion about safe web browsing. The software allows access to adult and inappropriate content to be blocked, time spent surfing the web limited and even block the sharing of personal information. The software also requires kids' permission to allow their parents to monitor them, so they are aware of what's happening.
"Keeping our kids safe online is critical, and parents often have to consider just how intrusive their monitoring of their kids' activities online should be," said Rik Ferguson, director of Security Research and Communications at Trend Micro.
"The key is to strike a balance between helping kids stay safe online yet allowing them to maintain a sense of independence. The idea behind Trend Micro Online Guardian is to provide the tools and information for parents to become aware of their kids' online activities, to create an opportunity to talk on a one-to-one level about internet safety and identify and prevent possible problems before they happen."
Trend Micro Online Guardian will be available from 21 March 2011 through retailers and the Trend Micro online store. It is priced at £29.95.