Inquiry-based learning in STEM classrooms, long a contentious topic, has been making news since the introduction of the controversial California Math Framework. This student-led approach aims to foster engagement by sparking curiosity and critical thinking. Rather than passively receiving knowledge from an instructor, students take an active role in their learning by searching for evidence, constructing arguments, and collaborating with peers.
So does it work? The short answer is yes, but only when done well and at the correct skill level.
Much of the recent criticism of inquiry-based learning (or at least the version of inquiry-based learning embraced by California) stems from its discouragement of rote memorization. That, in turn, could hinder students’ development of “math fact fluency,” or the ability to recall addition, subtraction, multiplication, and division facts flexibly and efficiently. My colleague Daniel Buck has pointed to seemingly problematic examples of students suggesting multiple ways to solve a multiplication problem. For example, to multiply 12 by 7 in an inquiry-based classroom, some students might add 12 seven times, while others take the sum of 10x7 and 2x7—whereas a student who has memorized their math facts can quickly and confidently recall “84!” without needing to engage in higher-order thinking.
So what’s more valuable: students creatively constructing a well-rounded picture of their math facts or the ability to recall facts quickly when needed?
Both my experience as a middle-school math interventionist and common sense suggest that this is a “both/and” situation. A student who has achieved true number sense should be able to recall the answer to 12x7 without hesitation and to deconstruct the problem in multiple ways.
But don’t just take my word for it. Study after study suggests a combination of automatic recall and critical thinking skills is necessary for developing a robust understanding of mathematics.
Still, grade level and other contextual factors matter when it comes to striking the right balance—and here, the California Framework goes astray. Plenty of research shows that early learners, especially those who are low-achieving, benefit from explicit instruction that is intended to build math fluency. To put it simply, students should absolutely memorize their math facts. Rote memorization and direct instruction are essential during the foundational stages of learning mathematics.
But once students have achieved math fact fluency, inquiry-based learning, done right, offers a pathway to much greater depth of understanding in math and science classrooms. In fact, a growing body of evidence suggests that students learn better with this approach, particularly in the later grades. For example, a 2008 study based in the Detroit Public Schools Community District showed that a new inquiry-based science curriculum in select seventh and eighth grade cohorts was associated with higher standardized achievement test gains on the Michigan Educational Assessment Program (MEAP) exams compared with the rest of the district.
Critics of inquiry-based learning often misunderstand the role of the teacher. Yes, students drive the discussion, but that does not mean they choose where the car is headed. For example, one effective technique is to use “back-pocket questions”—a series of scaffolded questions designed to match individual skill levels and promote productive struggle. During the lesson, the teacher circulates the room, assessing how close students are to finding the correct answer. For groups that are struggling, the teacher poses increasingly leading questions, thus allowing students to think independently while still getting to the right answer.
As this example suggests, inquiry-based instruction is an art rather than a science, and in practice, it requires immense preparation and skill on the part of the instructor. Thus, schools and districts adopting this approach should provide substantial professional development and coaching for teachers. Poor implementation can be detrimental, leaving students to struggle without adequate support.
When executed correctly, inquiry-based learning can significantly boost achievement, especially in later grades. But completely dismissing memorization and direct teaching in the early grades is misguided and risks stunting mathematical development in young learners. A “both/and” approach that considers when direct versus inquiry-based teaching is appropriate will build the strongest number sense. And especially in middle and high school, well-planned inquiry-based lessons could transform STEM classes for the better.
