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We hear a lot about how American students lag behind their international peers academically, especially in subjects like math. In the most recent Program for International Student Assessment, commonly known as PISA, students in the United States ranked 26th out of 34 countries in mathematics. On the surface, it would seem that we’re a nation of math dullards; simply no good at the subject. But a spate of new research suggests that we may be underestimating our students, especially the youngest ones, in terms of their ability to think about numbers.

A study published in the April issue of the American Educational Research Journal, for example, finds that kindergarten students learn more when they are exposed to challenging content such as advanced number concepts and even addition and subtraction. In turn, elementary school students who were taught more sophisticated math as kindergarteners made bigger gains in mathematics, reported the study’s lead author, Amy Claessens of the University of Chicago.

Another study, published last year by Dr. Claessens with co-authors Mimi Engel and Maida Finch, concluded that as things stand, many children in kindergarten are being taught information they already know. The “vast majority” of kindergarteners have already mastered counting numbers and recognizing shapes before they set foot in the classroom, Dr. Claessens and her co-authors noted, yet kindergarten teachers report spending much of their math teaching time on these skills.

The students don’t gain anything from going over familiar ground: In the article published this month, Dr. Claessens and her colleagues report that pupils do not benefit from basic content coverage, but that all the kindergarteners in the study, regardless of economic background or initial skill level, did benefit from exposure to more advanced content.

Discussions about how to improve learning for young children usually focus on the length of the whole school day or the number of students in classes, but rarely on what is taught during the hours school is in session. Increasing the time kindergarten teachers spend on more advanced math concepts may be a simpler and more cost-effective way to boost learning.

What about the play and the social interaction that is so important for young kids? The researchers note that time for such activities could easily be preserved by replacing instruction on basic math concepts with the teaching of more sophisticated ones — especially in light of the finding that students aren’t benefiting from such basic coverage anyway. Kindergarteners could be tackling more challenging math ideas while still spending plenty of time in the blocks corner and the dress-up closet.

Young students are ready to learn more advanced math concepts, as long as they are presented in an engaging, developmentally appropriate way. The next time we lament the performance of older American students, we could think instead about how to improve the math instruction given to their younger brothers and sisters.

Read more on the latest in social science research about how we learn, like Designing Smarter Homework, on Annie Murphy Paul’s Brilliant blog. Annie Murphy Paul is the author of “Origins,” a book about the science of prenatal influences and “Brilliant: The New Science of Smart,” to be published by Crown in 2015.