Preschool 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.
Relating numbers to the real world, for instance by counting chicken nuggets on a plate, was said to be important for promoting understanding of maths.
Psychologists attending a scientific meeting in Boston in the US spelled out what parents have to do to provide the springboard that would help their children grow up with good language and maths skills.
For language, the critical time was about one, before a child had even learned to speak.
Dr Meredith Rowe, of Harvard University, said there was a major gap in language achievement between children from poorer and better-off backgrounds.
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.
"There's this window of opportunity when children are just getting into their productive communication, 10 months to about 18 months," Dr Rowe told the American Association for the Advancement of Science annual meeting.
"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 socioeconomic 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.
Dr Liz Gunderson, of Temple University in Philadelphia, found preschool interaction had a similar impact on maths ability.
The key 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," Dr Gunderson said.
"If you're playing hide and seek and counting to 10, that's not quite as useful."