Pre-school children can be given a flying start in language and maths if their parents interact with them correctly, research suggests.
Studies show a strong link between gestures, pointing at objects and the ability of very young children to pick up vocabulary, say scientists.
Relating numbers to the real world - such as counting chicken nuggets on a plate - is said to be vital for promoting understanding of maths.
Psychologists attending a major scientific meeting at Boston in the US spelled out what parents have to do to provide the springboard to help their children grow up with good language and maths skills.
For language, the critical time was around the age of one, before a child had even learned to speak.
Dr Meredith Rowe, from Harvard University, said there was a major gap in language achievement between children from poorer and better off backgrounds.
And the reason more advantaged children did better could be traced to gestures. When parents backed up their use of words with gestures, it helped their children link words to objects.
Dr Rowe said: "There's this window of opportunity when children are just getting into their productive communication, 10 months to about 18 months.
"I'm talking about the kind of gestures you see parents using when interacting with their children, like pointing at things.
"You might point and say look at the doggy. But what that does, it gets the child engaged and interacting that way.
"The parents who are gesturing to more things have children who are gesturing to more things, and that predicts their language ability very strongly later.
"We found that even if you look back as young as age one there is a socio-economic gap in children's use of gesture that predicts their use of vocabulary in kindergarten."
A wide range of factors could explain why low income parents were less likely to use gestures, including lack of confidence, stress and depression, she said.
Colleague Dr Liz Gunderson, from Temple University, found that pre-school interaction had a similar impact on maths ability.
The key here was to help a child refer numbers to objects they could see and touch, either around them or in a book.
"If you're talking about the three chicken nuggets on your plate you can actually see the three chicken nuggets," said Dr Gunderson.
Her team conducted an experiment involving number books and children aged two and a half to three.
Dr Gunderson said: "What we found from parents is that reading these books about four times a week for a month really substantially boosted children's number knowledge.
"We saw gains that would be similar to what you would see in three to four months with natural amounts of interaction.
"This really shows that something as simple as reading number books with your child can really boost their knowledge."