Even before mathematics scores dropped during the pandemic, students’ performance in the subject had largely stagnated for more than a decade. Elementary students have shown recent gains but not so secondary students. Findings from a recent University of California San Diego report show that many students entering college are not prepared for entry-level mathematics, with large numbers requiring remediation. The report has attracted national attention because it highlights concerns that extend beyond any single institution and raises broader questions about the state of mathematics preparation.
The reasons for these disturbing outcomes are likely complex and include not only the pandemic and its attendant increase in absenteeism but also the rise of smartphones and social media. Yet, the pattern has also prompted renewed examination of mathematics instruction itself. Increasingly, educators, researchers, and policymakers are asking whether current instructional approaches that stress exploration first are working. And in schools, teachers are pondering how to make the changes that might be required.
Most broadly, a growing “science of math” movement has begun to take shape, drawing on cognitive science to reexamine how students acquire mathematical knowledge. Its core premise is straightforward: Reasoning, problem-solving, and mathematical flexibility depend on knowledge that must first be explicitly and systematically developed.
In my work with school districts, I have seen educators recognize the need for more explicit instruction, only to find themselves working within systems that prioritize pacing guides, curriculum fidelity, common planning structures, and instructional routines built on the principle that exploration should come before structured teaching. Teachers are often expected to follow the same instructional sequence, pace, and teaching methods across classrooms. All of this limits their ability to modify instructional sequences when students need more support. These constraints are real, but they are not insurmountable.
Math classrooms shifted over time to the discovery model. Not suddenly, and not without good intentions. There was a deliberate move away from rote procedures toward reasoning, discussion, and problem-solving. The instructional system began to reflect a shared belief that students learn best by figuring things out on their own.
On the surface, this made sense. It emphasized thinking, engagement, and independence. Those are good goals, but the problem was the instructional sequence used to achieve them. Students were often expected to struggle with new ideas before they had been taught the underlying concepts. Instead of building understanding first and then applying it, students had to try to apply what they did not yet know.
The encouraging reality is that addressing this problem does not require new programs or a wholesale replacement of curriculum.
State frameworks shifted to emphasize inquiry-based and exploratory approaches. Curriculum developers designed materials to align with that vision in order for the materials to be widely adopted. As a result, many popular programs share common design features, including an early emphasis on exploration, structured discussion, and delayed explicit instruction. In practice, this can place responsibility on students to construct meaning before they have sufficient background knowledge.
Research in cognitive science has consistently shown that novice learners do not learn efficiently through minimally guided problem-solving. Instead, they benefit from explicit instruction and guided practice before independent application. When students are asked to solve problems before they understand the underlying concepts, they must rely on trial and error. That process places heavy demands on working memory and can limit the formation of accurate, usable knowledge structures.
The concept of “productive struggle” gained prominence alongside the shift toward inquiry-based instruction. In principle, struggle can support learning. Advocates argue that carefully designed challenges can be a meaningful part of the learning process. In practice, though, too much struggle can hamstring students. The research base for the effectiveness of the approach is still developing and often inconsistent, with many studies relying on qualitative designs and varied definitions rather than strong causal evidence.
Teachers and districts may recognize the need for change, but they cannot simply abandon the curriculum already in place. The encouraging reality is that addressing this problem does not require new programs or a wholesale replacement of curriculum. It requires a handful of practical changes to instructional sequencing and delivery.
1. Move instruction to the front. Before students are asked to explore, the teacher models the concept clearly and directly. This ensures that students begin with a foundation rather than confusion. Learning, by definition, requires alterations in long-term memory, and explicit explanation supports that process more effectively than unguided discovery.
2. Use worked examples. Incorporate worked examples. Instead of asking students to immediately solve unfamiliar problems, teachers present fully solved examples and walk through them step by step. Students then attempt similar problems with guidance still in place. This reduces unnecessary cognitive load and helps students focus on understanding the structure of the task.
3. Structure practice. Structured guidance for problems like the ones that have been given as fully solved examples helps students internalize procedures more efficiently. Open-ended prompts such as “figure out a strategy” can be replaced with clear, explicit steps that guide students through the process and help with accuracy.
4. Delay independent problem-solving. Independent problem-solving and real-world application remain important, but they should occur after students have developed initial understanding and fluency. Introducing them too early increases cognitive demand without improving learning outcomes. The National Mathematics Advisory Panel emphasized that students must develop foundational knowledge and procedural fluency to a level of automaticity before engaging in more complex mathematical tasks.
5. Limit the number of strategies during early instruction. Research on cognitive load consistently shows that reducing the number of elements learners must process at once improves learning, particularly for novices. Focusing on one clear method first allows students to build stable understanding. Later, teachers can introduce alternative strategies to build problem-solving capacity.
None of these recommendations requires new programs, abandoning curriculum, or large-scale reform. They require reordering what is already in place: Teach before explore, model before solve, guide before release, and apply after understanding. The materials already in classrooms can support that work but only if they are used in a way that aligns with how students actually learn.
Educators should not have to choose between adopted curriculum and applying what we know about learning. The two are not inherently incompatible. Students should absolutely reason, explain, and solve problems. But first, they need conceptual understanding to make that reasoning possible.
