Polarized discussions on what math students should be taught and how, often referred to as the “math wars,” have been ongoing in the nation for decades.
An April report by the Center on Reinventing Public Education (CRPE), Navigating the math wars: A practical guide to the divides and debates influencing math instruction, provides background on the issue and presents strategies that could help end the longstanding dispute.
As the report points out, influential education reformer John Dewey observed two “opposing camps” forming in 1900 and advised that math education not be treated as an either/or choice. However, that has happened — with dedicated organizations, curricula and spokespeople for the respective perspectives.
The traditional approach to math instruction is centered on procedural fluency and proponents believe math has “a structure and a sequential skill hierarchy that demand mastery of the basics” before conceptual understanding, according to the report. They argue that mastering arithmetic facts and algorithms frees up working memory for complex problem-solving and point to evidence that suggests fast and accurate recall of arithmetic facts can be achieved independently of conceptual knowledge.”
Related instructional priorities for this model are that it’s teacher-led, pushes mastery of established subject matter and systematic and sequential coverage. Other priorities include explicit instruction, acceleration and earlier introduction of algebra, and using standardized testing as an accountability measure.
Conversely, proponents of the reform approach advocate for conceptual understanding before procedural fluency so that students can “grasp underlying mathematical ideas (e.g., place value, number magnitude) before learning formal procedures,” the report states. “They worry that rote execution of algorithms without understanding leads to “fragile knowledge,” meaning that students may produce correct answers but cannot explain why or apply their knowledge flexibly.”
This method — known for being student-centered and built on their interests while teachers act as facilitators — prioritizes inquiry-based instruction, integration into real-world scenarios and flexible pacing and untimed testing.
Common Core State Standards, introduced in 2010, intended to create a shared framework for K-12 that addressed divides, but it instead reignited tensions, the report recalls. Common Core is no longer in the forefront of the situation, but some math curricula have faced scrutiny and the Science of Math movement as emerged “arguing that instructional decisions should be grounded in cognitive science and empirical research, a goal shared by many on both the traditional and reform sides of the Math Wars,” CRPE explained.
Although media coverage often frames conflict as an and/or choice, contention is primarily about timing, sequence and emphasis.
“Most advocates today agree that conceptual understanding and procedural fluency are both essential and reinforce each other. The real debate is about sequencing and emphasis — which comes first, and for which students. That’s a narrower disagreement than the media framing suggests, but it still shapes real decisions about curriculum, instruction, and who gets access to advanced math.”
The report delves into research on what practices take place in classrooms and how teachers are often stuck in the middle of the discord.
California’s revised math framework is highlighted as are developments in other states to showcase the policy landscape’s variety. Widely seen as “more reform-oriented,” with more emphasis on discovery learning, group work and sociocultural responsiveness and less on memorization and direct instruction, it “drew sharp criticism from STEM professionals and parents who argued that it downplayed traditional content mastery,” the report states.
Finding peace
CRPE asserts that a new national panel on mathematics should be convened as the last advisory panel’s report was released in 2008 and updates are needed.
Steps that can be taken by state and district leaders to improve instruction without resolving all disagreements are detailed in the report. They include:
- Understanding the instructional realities
- Clarifying practice priorities
- Developing a district math playbook
- Embedding data cycles and job coaching
- Prioritizing coaching that sticks
- Bringing high-leverage supports to core instruction
- Supporting active participation and mathematical talk for students
An accompanying document answering frequently asked questions on the subject is also available.
