Circling Around the Subject

March 26, 2018

Small group learning appeals to progressive educators, who cite socialization and collaboration as vital 21st century learning skills.  For these pedagogs, stations are a welcomed alternative to traditional teaching.  Although well intentioned, this mode of instruction is damaging to mathematical learning.  Stations fail to match the subject’s nature, provide an atmosphere unfavorable to learning math, and misdirect teacher energy.

Mathematics is learned best through concrete, pictorial, abstract progressions.  It is also a linear subject in which foundations are essential to learning harder topics (see table below). After students master one concept, they’re ready to move on to a more challenging one.  Through informal assessments, teachers play a vital role in guiding instruction, because they must constantly advance or remediate problems based on their students’ foundational knowledge.

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Rotating stations creates circular learning.  Students enter and exit this carousel at different points, sometimes beginning with harder, abstract tasks and moving to simpler, concrete or pictorial ones.  Because mathematics is a sequential subject, the station learning system is antithetical to its design.  It also defocuses students.

Succeeding in math requires deep thinking and unfettered concentration, both of which are challenging in distractible environments.  Therefore, the setting in which the subject is taught has an enormous impact on learning outcomes.  Uncooperative behavior aside, station configurations are not conducive to heightened concentration.  Teacher presence often generates student focus, but when the latter feels disconnected from the former, their attention tends to wane.  Mature, driven children might stay centered when they’re unsupervised, but the majority of students become lax.  This, paired with teachers equally distributing their attention, leads to inefficient instructional time.

All elementary school math classes possess a range of student skill and conceptual levels.  The strongest students can usually work independently for extended periods, and often self-educate when they realize they’ve made mistakes.  Feeling successful, they’re often motivated to persevere when they confront a new challenge.  When they do need teacher help, it occupies very little of the instructor’s time.

Lacking both skill and confidence, weaker students need extra scaffolds to access harder content, and it’s difficult for them to progress without teacher assistance.  Because of this reality, it’s illogical for teachers to equally distribute their instructional time.  Instead, students should begin lessons in a whole-class learning structure, and gradually transition into small groups.

The best math lessons begin with low floor, high ceiling problems that captivate all students.  As the concept develops, however, better skilled and/or faster processors need new challenges, while less skilled and/or slower processors require more instruction and reinforcement.  Exemplary math teachers recognize this and transition the former into learning clusters while continuing to work with the majority of the class.  As the lesson progresses, more children advance to harder problems, while the teacher directly supports fewer and fewer students.  By the end of class, a learning pod archipelago forms.

Stations can be a valuable learning vehicle in some elementary subjects, but have little to no utility for mathematics.  This is because the instructional mode contradicts the subject’s intrinsic design, in the process creating distracting learning environments and shifting teacher attention away from students who need them most.

The best math teachers understand that whole-group instruction and collaborative learning are not mutually exclusive, and that dynamic lessons aren’t predicated on classroom seating configurations.  They also recognize that thinking and reasoning skills are more valuable today than ever before, and use appropriate instructional methods to ensure their acquisition.