The unit said parents should abandon their "fixed mindset" of their child's abilities and instead push them to stretch themselves.
It also advised teachers to give pupils two marks - an actual grade and a "possible" grade, to give pupils the confidence to improve.
The idea - which the document admits has no evidence behind it - is based on Energy Performance Certificates prepared for homebuyers, which show energy ratings and what the score could be if improvements were made.
Last night Margaret Morrissey, of pressure group Parents Outloud, branded the report "crazy".
She said: "The response of parents throughout the country will be: I am responsible for my child and I will bring them up how I want.
"There may be a right way to do things in the eyes of government, but it's up to parents.
"There are too many ways these people seek to make us feel guilty. The Government should get on with running the country and we'll get on with bringing up our children."
The BIT is jointly owned by the Government and charity Nesta.
Government departments spend tens of thousands of pounds commissioning the unit to produce research into behavioural science.
The report on education was commissioned by Pearson Education.
It said too many parents have a "fixed mindset", meaning they think their child has only the talents they were born with and that improvement is difficult.
Instead, it says they should aim for a "growth mindset" - concentrating on prospects for improvement.
The document said: "Adapting responses to children's successes and failures could help to cultivate a growth mindset.
"Praising a child for effort acknowledges the challenge they took on and the hard work they put in to achieve their goal.
"It is easy to inadvertently promote a fixed mindset by praising only their talent e.g. 'you're just so smart' or 'you're a natural', instead of their effort e.g. 'well done - your hard work has really paid off'.
"Praising their talent can reinforce the idea that natural ability is all that matters."
The document even suggests "right" and "wrong" responses to a variety of situations their child finds themselves in.
The "mindset theory" was developed by psychologist Professor Carol Dweck, of Stanford University, who said parents could use it to "foster positive thinking patterns in their children".
She believes that, all too often, students give up when they struggle because they simply have not been born with the right talents to succeed.
The document added: "Family dinners may have benefits beyond learning. For example, teenagers from households where family dinner is a regular event are less likely to engage in high-risk behaviours such as substance abuse, sexual activity and binge eating.
"However, this is just a pattern found by researchers and doesn't mean that more family dinner necessarily guarantees good behaviour."
