Kindergarten math is crucial
In my new story at The Hechinger Report, I find that classrooms don't pay enough attention to it
In Sumner County, TN, kindergarteners are learning flexibility with numbers, like all the different numbers that make up 5.
Back in January, I spoke with education researcher Amanda VanDerHeyden, wondering aloud whether schools are missing opportunities to build better foundational skills in math.
“Kindergarten is a crucial year for math learning,” she told me. “It’s when gaps are the smallest between kids, and easiest to close.”
There has recently been increased awareness around the idea that learning to read has foundational skills, like phonemic awareness and vocabulary building, that are crucial to being a proficient reader. But can the same be said for foundational math skills? What do they look like?
Being able to count is certainly important, and so is understanding that numbers represent quantities—and there are some students who come to kindergarten who need a lot of work in that area. But an equally important foundational skill is a kind of flexibility with numbers, sometimes called “number sense”—being able to fill in missing numbers; to “count on,” or be able to keep on counting up or down when presented with a random number like 17 or 31; and to understand how numbers fit together, and how they fit inside other numbers. Like the number 5, featured in the photo above: 0, 1, 2, 3, and 4 are all numbers that can fit inside 5, and can be bonded together in different ways to add up to 5. When 2 is added to 3, or 1 added to 4, all make 5.
This number flexibility—knowing your way around numbers, and how they are linked together—is key to getting to the next steps of addition/subtraction, and later multiplication/division. It’s the foundation upon which the house of math is built, so to speak. But many kinder students just don’t learn that number flexibility, and it ends up hurting them later on when they need it. Math is “relentlessly hierarchical,” VanDerHeyden and many other experts have told me. Those first few steps up the math ladder really matter.
But what I found in new reporting for a story at The Hechinger Report, “Kindergarten math is often too basic. Here’s why that’s a problem,” is that kindergarten math often misses the opportunity to build those foundational skills, and it ends up hampering kids’ ability to do more complex math later on. This happens for a variety of reasons, some of them familiar by now: lack of a decent curriculum that aligns kinder with first grade expectations; low teacher confidence in both their own math skills and in teaching math (most kinder teachers get into the gig because they love kids and love reading, experts and researchers told me, and so they might end up downplaying math, or spending less time on it); and good teacher training on how to teach these vital foundational skills.
Running through these challenges like a river is an underlying assumption—or maybe a directive from leadership—that literacy matters most (which is understandable, but not sufficient).
A lot of kindergarten math is about learning numbers and how to count—and teachers told me that there are definitely students who come to kinder needing those important skills. But what Mimi Engel, a researcher at University of Colorado, Boulder, found is that much of kindergarten math is getting stuck on the basics—often that looks like a lot of counting (anybody dress their kindergarteners up like senior citizens for “Count to 100” day? I sure did!)—and never moves on to teach kids that number flexibility.
What’s fascinating is how important kindergarten’s math foundation is to the rest of students’ learning. Studies show that kids’ math ability in kindergarten is highly predictive of future overall academic success—and, perhaps not surprisingly, kids who get exposure to those advanced concepts in kinder, learn more math later on.
“In a 2013 study, researcher and University of Colorado Boulder associate professor Mimi Engel found that students who spent more time on the advanced concepts in kindergarten learned more math. Engel hypothesizes that exposure to more advanced content in kindergarten may help students in later grades when content grows more complex.”
In the story, I provide two examples of curricula that appear to be expanding kindergarteners’ math learning. Both are evidence-based, and both closely monitor kids’ growing skills. Both are (crucially) well-aligned to future skills in first and second grade, ensuring that the foundation is being built for what they actually learn later.
The first is SpringMath, VanDerHeyden’s intervention, which I have reported on before—because it’s unique. It’s an intervention built for the entire class, not just the strugglers, meant to bolster foundational skills needed to be successful at core math instruction. It’s VanDerHeyden’s researched understanding that even students who are doing all right in math benefit from solidifying foundations—and they’re often missing or weak in key skills that teachers may not notice if they’re not doing close monitoring. SpringMath is meant to be extra math (schools say it requires anywhere from 15-30 extra minutes a day), but the skills are highly tracked and sequenced, so teachers are always monitoring at the student level which skills need more work and which have been mastered.
It’s also unique because kids are not practicing on screens—they’re using manipulatives, paper and pencil, and games to develop number flexibility. Here’s a little of what it looks like:
“On a recent morning, the children used plastic red and yellow dots for a counting exercise: One student tossed the coin-sized dots onto a cookie sheet while another hid her eyes. The second student then opened her eyes, counted up the dots and picked the corresponding number from a stack of cards.
“The dots showed up again a few minutes later in a more complex task. Murphy set a two-minute timer, and students counted as many dot arrays as they could, adding or taking away dots to match a corresponding written number. Four dots next to a printed number 6, for example, meant that students had to draw in two extra dots — an important precursor to learning addition.”
The other is Eureka Math. I went and had a look at how it’s being used in Sumner County, Tennessee, about half an hour from my home. Sumner’s superintendent, Scott Langford, is obsessed with getting high-quality instructional materials into teachers’ hands, and schools are already seeing how the kindergarten math curricula is building that flexibility with numbers.
In Hailey Lang’s class, I saw how the students were looking at pictures of a quantity of items like penguins, and then figuring out how to manipulate that quantity of penguins in different ways:
“Kindergarteners in Hailey Lang’s classroom at Dr. William Burrus Elementary School in Hendersonville, Tennessee, were recently counting penguins — a digital whiteboard showed a photo of a mother penguin with seven fuzzy babies in tow.
“‘Can we make a math drawing about this picture? No details, you can just use little circles,’ Lang said. Students drew one big circle and seven smaller circles on their papers to represent the penguins. Then they translated the circles into a number sentence: 1 (big circle) + 7 (small circles) = 8.”
And perhaps most important of all: kindergarten students, experts told me, are capable of doing a lot more math than we give them credit for. Learning flexibility with numbers is complex, but it doesn’t have to be dull and excruciating—a misunderstanding about math learning that seems to compound itself throughout our schools. In fact, some students may learn number sense at home, playing board games and card games with their families and friends.
Young kids’ math champion seems to be John Mighton—a Canadian mathematician who has created the JUMP math curriculum as almost a revolt to how Americans think about school math. When I interviewed him, Mighton got very animated talking about how kids love solving puzzles, they love “small iterations on a theme,”—he has a way of talking about it that makes math sound downright…fun.
Mighton said:
“Getting students working together, successfully tackling a series of challenges that build on each other, can create a kind of collective effervescence — a feeling of mutual energy and harmony that occurs when people work toward a common goal.”
Like the last several stories I’ve done about math learning—on curricula, practice, research on how students learn math—I hope to be building for the public a better understanding of all the places where math learning is going off the rails, and how we can effectively get it back. The foundational skills of kindergarten math seems to be a big one.
Read the kindergarten math story here. Let me know what you think in the comments.