For more than a year, Mayor Bill de Blasio’s campaign for free preschool has focused to a great extent on expanding enrollment at an unprecedented clip.

On Tuesday, his team will push a new agenda for 4-year-olds: Math.

Department of Education officials said they plan to spend $6 million in the coming fiscal year to roll out “Building Blocks,’’ a math curriculum that has had good results in Boston and other cities. It uses puzzles, games, art projects and songs to help children learn more about numbers, shapes and patterns.

Some studies suggest early math skills are a strong predictor of success in school and later in life. But researchers have found that beyond the most basic counting games, preschools across the country tend to ignore math.....

.....MDRC, a research group, is leading a randomized controlled trial of Building Blocks in the city’s 87 pilot classrooms to see how effective it is.

Gordon Berlin, president of MDRC, said in most cases the implementation was good or very good. He expects an analysis of its effectiveness to be finished next year.

“The city has undertaken an historic effort to increase the number of slots,” he said. “Now the right next step is to focus on quality.”

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