Summertime is fun time, when kids can make and sell lemonade, read for fun, catch and release fireflies at twilight, and daydream. These last few weeks of the best time of the year can provide your child with rich opportunities to grow their brains while enjoying the traditional pastimes of the season.

While the emphasis on testing in public schools might compel you to drill your child with work sheets all summer, “this type of learning should not replace original problem-solving,” says Jane Healy, author of “Your Child’s Growing Brain.” Save the work sheets for rainy days or short practice time over the summer months, and allow your child the opportunity to develop original thoughts and deepen understanding through active learning.

Float Like a Butterfly

Active play builds language skills. In fact, when children are asked to name tools, the same region of the brain is triggered as when they physically use those tools. That’s important to keep in mind as you fret over the reading tests you know your child will begin to take again in the fall. Feeling the tickle of a caterpillar in his hand may just do more for your child than a flashcard with the word caterpillar printed on it. Healy says, “If you want to help your child build a keen brain for vocabulary, make sure plenty of physical play is on the program.”

Movement may also improve math scores. Science, too. Children develop greater abilities with spatial relationships when they explore more actively. (Think hunting for the caterpillar rather than passively sitting with that stack of flashcards). And, Healy says, “greater ability with spatial relationships is one of the best predictors of math, physics, and engineering aptitude.”

So order a butterfly growing kit online. Let your child observe metamorphosis in preparation for biology class. Render the life cycle through art. Sequence the stages of development from egg to caterpillar to chrysalis to butterfly and prep for math. Then, on a shining August day, release the butterflies in Rock Creek Park, lay back in the grass with your child, and let him daydream about the miracle of the life he helped grow.

One article published in a journal of the Association for Psychological Science advocates incorporation of more daydreaming, or “mindful introspection,” in the classroom. “While outward attention is essential for carrying out tasks and learning from classroom lessons, for example, the reflection and consolidation that may accompany mind wandering is equally important, fostering healthy development and learning in the longer term,” it says.

Twist and Shout

When silent meditation in the grass explodes with a giggly roll downhill, just laugh along. According to Healy, movements like rocking and rolling stimulate the cerebellum, the part of the brain that “interacts with higher, frontal levels in the brain for cognitive skills.”

Healy says that the cerebellum goes through a significant period of growth from birth to age 2 and continues to grow and change through adolescence. “The fact that most kids love to spin and hang by their knees — and most adults don’t — is one more evidence that the brain tends to seek out the activities that it needs at different periods of development.”

Encourage free-range roaming as much as possible. Healy says experimental rats raised in enriched cages have bigger and heavier cortical tissue than rats raised with little stimulation. But rats that live in the natural environment, and which therefore face the natural challenges of life in the woods, have the biggest brains of them all.

Resist the urge to speed along with a stroller. Unlock those straps, slow down and let your baby enjoy toddling to what interests her. Your little one will be marching toward a future of higher math and reading comprehension scores as she navigates the world around her.

Big kids and teens also require free play to stimulate the brain. Make sure they go digging for clams, chasing fireflies, running back and forth with the waves in Ocean City. According to a January 2012 article published in the Journal of the American Medical Association, in pediatrics “there is a strong belief that regular participation in physical activity is linked to enhancement of brain function and cognition, thereby positively influencing academic performance.”

Relax and Read

Chasing bubbles by day and fireflies at dusk is enough to exhaust anyone. When your kids (and you!) need quiet time this summer, resist the temptation to spend money on baby genius apps or school-age educational DVDs. Some media products marketed as learning tools can actually reduce a toddler’s vocabulary, according to John Medina, author of “Brain Rules for Baby,” and big kids with TVs in their bedrooms scored an average of eight points lower on language arts and math tests than kids with no TV where they sleep.

The American Academy of Pediatrics suggests absolutely no screen time up to age 2 — that includes phones, tablets, and laptops, as well as good old-fashioned TV. Experts such as Healy encourage parents of preschoolers over age 2 to “limit TV, movies, and video and computer games to one to two hours a day (or less, or even none) of educational, nonviolent content.” Your young one will become a better thinker if you keep media away from her growing mind.

Instead, read books to your baby every day. Some of the best award-winning picture books are written and illustrated by African Americans and feature beautiful brown faces to delight your own perfect angel child. Look for authors including Virginia Hamilton, Nina Crews, Tom Feelings, Varnette P. Honeywood, Jabari Asim and Walter Dean Meyers to start building your child’s library. As your child grows, his library should grow, too.

A paper published by the Britain-based National Union of Teachers calls reading “one of the most effective ways to engage social change.” According to the union, “poor reading skills correlate heavily with unemployment, lower wages and fewer opportunities for advancement.” Encouraging reading can change all that. Students whose parents had a lower occupational status but read more for pleasure scored higher on reading tests than students with parents of middle or higher occupational status who read less.

Books can change the game for your child.

Lemonade Stand

So can entrepreneurship. Help your kids squeeze and mix a few pitchers of lemonade, then send them outside to sell it. Count the lemons, measure the sugar, gaze at the pulp as it twirls with each swish of the wooden spoon, then let them manage the money they’ve earned selling Dixie cups of homemade sweetness to your neighbors and friends. Their math and science teachers say thank you.

Fly a Kite (but Build it First)

For more homegrown joy, bond while you build with your child. Look online at Aviation for Kids (www.aviation-for-kids.com/kites.html) for instructions on how to make a kite. Manipulating the materials needed to construct a kite increases fine motor skills, measuring the materials before assembling them improves math skills. According to the Web site, building a kite with your child can also help her learn about lift, drag, tension, center of gravity, center of pressure and torque, so she can really make sense of the fundamental laws of physics. NASA will be calling her in no time.

We’ll talk more physics in the last part of this series as we examine the new science, technology, engineering and mathematics initiative in American schools.

Eisa Ulen has a master’s degree from Teachers College, Columbia University and more than 20 years of experience in education.