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ASTON, Pa.鈥� In Jodie Murphy鈥檚 kindergarten class, math lessons go beyond the basics of counting and recognizing numbers.

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 鈥� an important precursor to learning addition.

Kindergarten may be math鈥檚 most important year 鈥� it lays the groundwork for understanding the relationship between number and quantity and helps develop 鈥渘umber sense,鈥� or how numbers relate to each other, experts and researchers say.

But too often teachers spend that crucial year reinforcing basic information students may already know.  that many kindergarteners learn early on how to count and recognize basic shapes 鈥� two areas that make up the majority of kindergarten math content. Though basic math content is crucial for students who begin school with little math knowledge, a growing body of research argues more comprehensive kindergarten math instruction that moves beyond counting could help more students become successful in math later on.

Because so many students nationally are  鈥� a longstanding challenge made worse by remote schooling during the pandemic 鈥� experts and educators say more emphasis needs to be put on foundational, early childhood math. But for a variety of reasons, kindergarten often misses the mark: Math takes a backseat to literacy, teachers are often unprepared to teach it, and appropriate curriculum, if it exists at all, can be scattershot, overly repetitive 鈥� or both.

Manipulating numbers in different ways, part of a supplemental math curriculum for Murphy鈥檚 whole class at Hilltop Elementary in this suburb of Philadelphia, is an attempt to address those problems. In an effort to improve math achievement district-wide, all elementary students in the Chichester School District get an extra 30-minute daily dose of math. In kindergarten, the extra time is spent on foundational skills like understanding numbers and quantity, but also the basics of addition and subtraction, said Diana Hanobeck, the district鈥檚 director of curriculum and instruction.

Chichester district leaders say implementing the intervention, called , along with other steps that include hiring a math specialist for each school, has brought urgent attention to students鈥� math achievement by bringing more students to mastery 鈥� and a lot of that has to do with how much students are learning in kindergarten. Student math achievement, which dropped to a low of 13.5 percent of students proficient or advanced during the pandemic,  across grades since the intervention began, although still below the state average. Last spring, 47 percent of the district鈥檚 fourth graders were proficient or advanced in math on the Pennsylvania System of School Assessment test.

鈥淭he intervention is very targeted by skill and gives teachers data for each student,鈥� said Hanobeck. 鈥淲e are seeing it close gaps for students, and they are more able to access elementary school math.鈥�

Murphy, the kindergarten teacher, said that while some students arrive at school able to do 鈥渞ote counting,鈥� others arrive with no prior knowledge or a very limited understanding of numbers and counting. The interventions have improved all students鈥� accuracy and fluency in more complex tasks, such as being able to count up or down from a number like 16 or 20, and adding and subtracting numbers up to 5.

鈥淚t used to take all year for some students to count on from different starting points, that鈥檚 actually really hard for kids to do,鈥� Murphy said. 鈥淪tudents are meeting their goals far faster now. We are moving on, but also moving deeper.鈥�

That deep thought is important, even in the earliest grades. Kindergarten math proficiency is especially predictive of future academic success in all subjects including reading, research has shown. In one study, students鈥�  in kindergarten 鈥� which includes the ability to understand number quantities, their relationships to each other, and the ability to join and separate sets of numbers, like 4 and 2 making 6 鈥� presaged mathematical achievement in third grade, with greater number competence leading to higher math achievement.

It鈥檚 also the time when learning gaps between students are at their smallest, and it鈥檚 easier to put all students on equal footing. 鈥淜indergarten is crucial,鈥� said University of Oregon math education researcher Ben Clarke. 鈥淚t鈥檚 well-documented in the research literature that gaps start early, grow over time and essentially become codified and very hard to remediate.鈥�

But the math content commonly found in kindergarten 鈥� such as counting the days on a calendar 鈥� is often embedded within a curriculum 鈥渋n which the teaching of mathematics is secondary to other learning goals,鈥�  from the National Academies of Science. 鈥淟earning experiences in which mathematics is a supplementary activity rather than the primary focus are less effective鈥� in building student math skills than if math is the main goal, researchers wrote.

The math students are taught in kindergarten often progresses no further than basic counting and shapes. In a , 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.

鈥淲e want some amount of repetition across grades in content,鈥� Engel said. 鈥淭here鈥檚 variation in kids鈥� skill sets when they start kindergarten, and, as a teacher, there are a number of reasons why you want to start with the basics, and scaffold instruction. But what I鈥檓 interested in is: when does repetition become redundancy?鈥�

According to researcher Amanda VanDerHeyden, founder of SpringMath, breaking numbers apart and putting them back together and understanding how numbers relate to each other does more to help develop kindergarteners鈥� mathematical thinking than counting alone. Students should move from using concrete objects to model problems, to using representations of those objects and then to numbers in the abstract 鈥� like understanding that the number 3 is a symbol for three objects.

To improve students鈥� math skills, some schools and districts have recently upgraded the math curriculum and materials teachers use, so they are able to build increasingly complex skills in an organized, orderly way.

Kindergarteners in Hailey Lang鈥檚 classroom at Dr. William Burrus Elementary School in Hendersonville, Tennessee, were recently counting penguins 鈥� a digital whiteboard showed a photo of a mother penguin with seven fuzzy babies in tow.

鈥淐an we make a math drawing about this picture? No details, you can just use little circles,鈥� 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.

The lesson is new to students this year since they adopted the Eureka Math curriculum. It鈥檚 what Sumner County Superintendent Scott Langford calls 鈥渉igh-quality鈥� instructional material, with lessons that move students beyond simply counting objects like penguins. Students look at penguins in a picture, translate them into representational circle drawings, then finally move on to their abstract number quantities.

Sumner County elementary coordinator Karen Medana said she appreciates the fact that the curriculum offers explicit guidance for teachers and builds on a sequence of skills.

One reason for redundancy in kindergarten math may be that classrooms lack cohesive materials that progress students through skills in an orderly way. A 2023 report from the Center for Education Market Dynamics showed that only  use high-quality instructional materials, as defined by EdReports, a nonprofit organization that evaluates curricula for rigor, coherence and usability. Eureka Math is one of several math programs that meet EdReports鈥� standards.

Often teachers are left to gather their own math materials outside the school鈥檚 curriculum. The  that large numbers of teachers use a district-approved curriculum as 鈥渙ne resource among many.鈥� Nearly all teachers say they gather resources from the internet and sites like Teachers Pay Teachers 鈥� meaning what students learn varies widely, not only from district to district, but from classroom to classroom.

What students learn might not even be aligned from one grade to another. In a new, unpublished paper still in revision, researcher Engel found 鈥渘otable inconsistencies鈥� between pre-K and kindergarten classroom math content and how it is taught in New York City schools. Engel said results suggest that in many classrooms, kindergarten math might be poorly aligned with both pre-K and elementary school.

When teachers have access to well-aligned materials, students may learn more. At Marcus Hook Elementary, a Title I elementary school in the Chichester District, kindergarten teacher Danielle Adler鈥檚 students were deep into first grade addition, using numbers up to 12. They had already completed all the SpringMath kindergarten math skills in March, so she let them keep going.

鈥淚n the past we did focus more on counting, recognizing numbers and counting numbers,鈥� Adler said, 鈥淏ut over the last three years I鈥檝e seen the kids鈥� skills grow tremendously. Not only what they鈥檙e expected to do, but what they鈥檙e capable of doing has grown.鈥�

What kindergarteners are expected to do at school has changed dramatically over the last 30 years, including more time spent on academic content. Adler and other kindergarten teachers agree that they hold higher expectations for today鈥檚 students, spend more time on teacher-directed instruction and substantially less time on 

Some worry that increasing time spent on academic subjects like math, and pushing kindergarten students beyond the basics of numbers and counting, will be viewed as unpleasant 鈥渨ork鈥� that takes away from play-based learning and is just not appropriate for 5- and 6-year-olds, some of whom are still learning how to hold a pencil.

Engel said kindergarteners can be taught more advanced content and are ready to learn it. But it should be taught using practices shown to work for young children, including small group work, hands-on work with objects such as blocks that illustrate math concepts, and learning through play.

Mathematician John Mighton, the founder of the curriculum JUMP Math, said it鈥檚 a mistake to believe that evidence-based instructional practices must be laborious and dull to be effective. He has  to think more like children to make more engaging math lessons.

鈥淐hildren love repetition, exploring small variations on a theme and incrementally harder challenges much more than adults do,鈥� he wrote 鈥� all practices supported by evidence to increase learning.

Simple lessons, when done well, can teach complex ideas and get children excited.

鈥淧eople say kids don鈥檛 have the attention,鈥� to learn more advanced concepts, he said, but he strongly believes that children have more math ability than adults give them credit for. Getting students working together, successfully tackling a series of challenges that build on each other, can create a kind of  鈥� a feeling of mutual energy and harmony that occurs when people work toward a common goal.

That energy overflowed in Adler鈥檚 classroom, for example, as students excitedly colored in graphs showing how many addition problems they got correct, and proudly showed off how the number correct had grown over time.

VanDerHeyden pointed out that, for young kids, much of a math intervention should look and feel like a game.

It鈥檚 often harder than it looks to advance kindergarten skills while keeping the fun 鈥� elementary teachers often say they have low confidence in their own abilities to do math or to teach it.  that teachers who are less confident in math might not pay enough attention to how students are learning, or even spend less time on math in class.

Teachers like Murphy have made some tweaks geared to engaging students. In class she calls SpringMath 鈥渕ath games,鈥� and refers to timed fluency tests as 鈥渕ath races.鈥� She even turned choosing a partner into a game, by spinning a wheel to see who students will get.

鈥淲e can do all these little things so they鈥檙e having fun while they鈥檙e learning,鈥� Murphy said.

This story was originally published on , a nonprofit, independent news organization focused on inequality and innovation in education

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