The vast majority of students won鈥檛 take algebra until middle or high school.
But teachers can start laying the groundwork for this pivotal class a lot sooner, some researchers say鈥攁nd instilling these algebraic thinking skills when children are young could improve their math ability overall.
That鈥檚 the theory behind Project LEAP, an early algebra program developed by researchers at TERC, a math and science education research nonprofit, and several colleges and universities.
Studies have shown that the intervention improves measures of algebra content knowledge and thinking skills for students in grades 3-5鈥攇ains that persist into 6th grade. Now, ongoing research funded by the National Science Foundation asks whether these lessons can benefit students in K-2 as well.
The research connects to larger debates about how much conceptual knowledge young students need as they learn early math. Surveys have shown that K-12 糖心动漫vlog tend to place more importance on math fact fluency, while the post-secondary instructors who train them are more likely to emphasize problem-solving and mathematical thinking.
But research suggests that many of these skills actually develop in , with procedural knowledge supporting deeper conceptual understanding, and vice versa.
Building algebraic skills in elementary school follows the same logic. 鈥淭he kinds of things we鈥檙e doing, operations on numbers, are deeply synergistic with the arithmetic they鈥檙e doing,鈥� said Maria Blanton, a senior scientist at TERC and a principal investigator on the project.
Traditionally, early grades math focuses on arithmetic: foundational skills like adding, subtracting, multiplying, and dividing. Students ideally get comfortable manipulating numbers. But then, 鈥渢hey鈥檙e dropped into a class where, all of the sudden, the numbers become letters,鈥� said Blanton.
Project LEAP aims to smooth that transition, preparing students to speak 鈥渢he language of algebra,鈥� said Angela Gardiner, a senior researcher at TERC and a co-principal investigator on the study.
The elementary schoolers aren鈥檛 working with Algebra 1 content鈥攖hey鈥檙e not solving equations or simplifying radical expressions, Blanton said. Instead, the lessons introduce 鈥渉abits of mind鈥� that are core to the subject, such as generalizing, representing, and reasoning.
鈥淥ur focus is not on the [equations] you do, but the ways you think,鈥� she said.
Lessons focus on conceptual understandings
In the current study, 41 schools were assigned to either implement Project LEAP lessons in K-2 or continue with their usual math instruction. Teachers started using the materials this September, and the study will track outcomes through May 2027.
The lessons focus on teaching core concepts that underpin success in algebra鈥攍ike understanding the meaning of the equals sign.
The equals sign represents a relationship: The quantities on one side are equal to the quantities on the other. Other has shown that understanding the relational nature of the equals sign supports students鈥� ability to solve equations in algebra.
But young children can have the misconception that the equals sign is an operational symbol that means 鈥渢he answer comes next,鈥� the .
鈥淚 assumed that this was a very elementary concept, and they would have that going into it. I assumed that those early lessons would be a review, but it wasn鈥檛,鈥� said Robin Hiatt, an elementary math teaching and learning specialist in Johnston County schools in North Carolina, who participated in the Project LEAP 3-5 study as a 3rd grade teacher.
Hiatt remembers students not understanding expressions that didn鈥檛 include an operation鈥攖hey were confused by the idea that 8=8, for example. 鈥淲e had to take it back to a real hands-on, conceptual level,鈥� Hiatt said.
The lessons don鈥檛 take the place of arithmetic instruction, but rather extend it, said Blanton. In early grades, for example, students learn which numbers are even and odd, and why, she said. The early algebra lessons teach students about the characteristics of these numbers, allowing them to make generalizations about how odd and even numbers operate.
That might sound complicated and abstract, but the lessons aim to make these ideas concrete. For example, they represent numbers with cubes. Every even number is made up of pairs of cubes, but odd numbers have an extra singleton.
This aspect of odd numbers explains why two odd numbers added together always make an even number鈥攂ecause their singletons join together to make a pair. 鈥淭hat type of representation-based argument is general,鈥� Blanton said.
In the previous study in grades 3-5, students using Project LEAP got better at making these kinds of representational arguments, which are core to algebra, compared to their peers in the control group. But their overall ability was still low, Blanton said.
Hopefully, she said, giving students even earlier practice with this skill could boost scores further.
