Using subordination to teach and learn mathematics

The practice tasks we find in mathematics are often problematic, both for student motivation and for student learning. Often, nothing is learned because the student is involved in mechanistic repetition. Drawing on the idea that only awareness is educable, Dave Hewitt argues for an approach to practice that avoids thoughtless repetition by shifting the focus of the activity. His subordination tasks focus attention on a more engaging task, while still enabling practice. This action research study involves developing subordination tasks for principles of mathematics 10 students and investigates whether such tasks can be designed and implemented across the curriculum, and used in every class. Six tasks were created and implemented. An analysis of the results shows that in addition to the three characteristics of subordination defined by Hewitt, tasks need to consider the classroom milieu, be accessible, engaging, and relevant, practice an appropriate skill, and provide immediate feedback.