Flexible classrooms are successful because they go hand in hand with a change in pedagogy.
The impact of flexible spaces though can be almost incidental at times, as is with the case of Maths:
Flexible, welcoming spaces had a startlingly large effect on learning in math—73 percent of the students’ progress that was attributed to classroom design was traced back to flexibility and student ownership. The reasons are a mystery, but Barrett and his team hazarded a guess: Academic subjects that provoke anxiety—in math, that’s a known issue—are better addressed in classrooms that feel comfortable and familiar to students.
This speaks of agency as much as it does of the chairs in the classroom.