Blending algebra and geometry: An approach to high school math slowly gains favor

The Great Math Divide: Integrated Learning Challenges Traditional High School Pathways

In a quiet rural Kansas classroom, sophomores at Chapman High School are grappling with a complex problem: finding the precise intersection of two lines. This isn't just another algebra exercise; it's a glimpse into a fundamental shift in how high school math is taught across the nation, a move away from rigid, year-long silos of algebra and geometry towards a more interwoven approach.

A New Equation for Learning

For years, the standard high school math progression has been a predictable sequence: Algebra I, followed by Geometry, and then Algebra II. This traditional model, often referred to as AGA, has been the bedrock of secondary math education. However, a growing number of districts and even entire states are beginning to question its efficacy, opting instead for "integrated math."

Integrated math, as implemented in places like Chapman Unified School District, breaks down these traditional barriers. It weaves concepts from algebra, geometry, and even trigonometry into a cohesive, multi-year learning experience. This means students might transition from a geometry lesson on angles to an algebraic exploration of equations within the same academic year, keeping concepts fresh and interconnected.

James Bell, a math educator at Chapman High School and a contributor to the district's integrated math curriculum, has witnessed the impact firsthand. "You're going to have the opportunity to change course and change direction and see different things," Bell explains. "Students even do a little trig—which is a scary word for kids, but when it's integrated into every year of math, it doesn't sound as scary." He believes this approach offers "the best of both worlds" for students.

The Data Behind the Shift

The move towards integrated math isn't merely an educational experiment; it's often driven by a desire to improve student performance on state assessments. In Chapman, the introduction of integrated math in 2015 coincided with a dramatic leap in student proficiency on the state math test, climbing from 11 percent to 41 percent in the first year. By 2025, this figure had reached an impressive 67 percent.

Kate Thornton, principal of Chapman High, points to the state's 10th-grade math test as a key catalyst for their district's decision. The test frequently incorporated concepts from both Algebra I and II. Under the traditional model, students who took geometry as sophomores often experienced a "whole year with no algebraic involvement," leaving them unprepared. Integrated math ensures continuous exposure to a broader range of math skills.

Nationwide, integrated math is still a minority approach, with a 2023 report indicating that approximately 16 percent of districts offer it, either exclusively or as an option alongside AGA. However, growth is evident, particularly in Western states like California. Lora Kaiser, executive director of the Center for Education Market Dynamics, notes a trend where districts are increasingly moving away from offering a choice between AGA and integrated models, opting for integrated math as the sole offering.

Modernizing Math for a Modern World

Beyond test scores, a significant driver for the integrated math movement is the urgent need to align high school mathematics with the demands of higher education and the contemporary workforce. Initiatives like the Launch Years Initiative, supported by the Charles A. Dana Center at the University of Texas at Austin, are actively assisting 27 states in reimagining their secondary math pathways.

The goal is to offer students a wider array of mathematical options beyond the traditional calculus track. This includes courses in data science and statistics, subjects increasingly relevant to everyday life and a variety of professional fields. Integrated math can free up valuable space in students' schedules to explore these crucial areas.

Lya Snell, director of building capacity for innovation at the Dana Center, emphasizes the necessity of adapting to a rapidly evolving technological landscape. "Where we are right now with tech and innovation is a lot different than where we've been before," Snell states. "We have to look at how we are preparing students for life today and in the future, and it requires us to create a more relevant experience."

Statewide Adoption and Evolving Curricula

Maryland is one state making a bold move, mandating a two-year integrated algebra and geometry course for all students beginning in the fall of 2027. State leaders are optimistic that this will bolster student achievement, as only 30 percent of high schoolers currently score proficient in math on state exams.

Lyndsey Brightful, director of mathematics in Maryland's division of instructional programs, explains that the state's previous math progression was misaligned with its educational goals. "If we wanted students to be ready for an entry-level college math course by grade 11, then we needed students to be finished with their foundational math skills by the end of 10th grade," Brightful notes. The traditional AGA sequence often fell short of this objective for on-grade-level students.

Following their two-year integrated math sequence, Maryland students will have access to a diverse range of advanced math pathways, including calculus, college algebra, data science, and statistics. This expansion reflects a growing recognition that rigorous, college-level math encompasses more than just calculus, acknowledging the importance of statistics and data science for students pursuing various fields, including humanities, nursing, and business.

The state is actively working to align university admission requirements with these new pathways, aiming for the two-year integrated math course to be accepted in place of the traditional three years of AGA. This represents a significant shift in how foundational math proficiency is defined and assessed.

Mixed Results and Lingering Questions

Despite promising outcomes in some regions, the effectiveness of integrated math remains a subject of ongoing debate and research. The varied implementation across states and districts, with some offering two years of integrated math and others three or four, makes direct comparisons challenging.

Utah, for instance, points to its decade-long adoption of a three-year integrated math sequence as a contributing factor to its students' consistently strong performance on national assessments like the NAEP and ACT. Mike Spencer, secondary math specialist at the Utah State Board of Education, highlights the benefit of continuous exposure to concepts: "Some of the value in integrated math is you see things come up each year, versus having gaps in some of that content knowledge."

California, however, presents a different picture. Despite widespread adoption of integrated math over a decade, only 37 percent of California students are proficient in math, a figure that lags behind many other states. Research on the impact of integrated math in the U.S. context is still developing.

Elizabeth Huffaker, an education policy researcher at the University of Florida, conducted a study comparing integrated math students with those in traditional pathways in California. Her findings indicated a "small and positive" effect on 11th-grade test scores, but she cautions that these gains were observed concurrently with the implementation of Common Core math standards, making it difficult to isolate the impact of integrated math alone. "I would not make this change expecting giant, transformative, high-impact-tutoring-type impacts," Huffaker advises.

Concerns for STEM Pathways

While integrated math may offer benefits for a broad range of students, concerns persist regarding its preparation of students for STEM-intensive fields. Some university professors express apprehension that students arriving without a solid foundation in traditional high school calculus and trigonometry may struggle in demanding college-level STEM courses.

David Merryman, a professor of biomedical engineering, notes that students who lack high school calculus often find themselves "completely lost" in their first-year university math courses. He questions whether integrated math, even when it incorporates trigonometry, adequately prepares students for the rigor of engineering programs. "The kids who come to my class and are weak in trig, they struggle," Merryman states. "For the non-STEM students, integrated math is probably great... I don’t think it serves kids who’re going into STEM."

This tension is leading some states and districts to re-evaluate their integrated math mandates. Ben Kitchl, a university student, recounted a personal experience where his prior eighth-grade Algebra I credit didn't transfer to a high school that only offered integrated math, forcing him to repeat material and fall behind his desired academic trajectory.

The Road Ahead: Balancing Innovation and Tradition

The evolving landscape of high school math education is characterized by a dynamic interplay between the promise of integrated learning and the established strengths of traditional pathways. As states and districts navigate this transition, the focus remains on creating a math curriculum that is both rigorous and relevant, preparing all students for success in college, career, and life.

In North Carolina, the state board of education is exploring a two-year integrated math model, similar to Maryland's, to create more space for statistics and data science. Emily Hare, director of pre-K-12 math for the state board, believes attitudes are shifting away from a singular focus on calculus. "I think that we have proven that the integrated pathway can work," Hare says. "It’s just teaching it in a different order."

The conversation around integrated math is far from over. As more data emerges and educators share their experiences, the nation will continue to refine its approach to equipping the next generation with the mathematical skills they need to thrive in an increasingly complex world.