Principles of Design
These principles guide the design and facilitation of all our work.
Get the ‘grain size’ right – when planning for instruction and/or identifying learning outcomes, a ‘unit of study’ rather than a lesson is the appropriate grain size.
Surface ‘soft spots’ in learners’ understanding early and often, and push on those ‘soft spots’ throughout the unit.
Build a classroom culture that helps learners express their ideas clearly. All learners have mathematical ideas worth listening to.
Meet a range of learner needs through the use of choice and ‘expandable tasks’ allowing access to all and yet challenging every learner.
Mathematical discourse and convincing mathematical arguments are essential. Teachers are not the answer book. The soundness of the mathematics should be the arbiter of whether or not an idea is reasonable.
Through questioning and listening carefully to what they have to say, continually seek to understand others’ thinking.
Embrace mistakes as sites for new learning; they provide opportunities to look more deeply or consider ideas that might not otherwise be encountered.
Recognize confusion or cognitive dissonance as a necessary, and even desirable part of the process of learning; a natural step on the pathway to constructing new understanding.
Learner sense-making always matters. Recognize that whether or not any given strategy is efficient lies in the thinking and understanding of the individual learner. Value and encourage diverse ways of solving any given problem.
Create a learning environment where all learners feel safe sharing their mathematical ideas.
Recognize that understandings develop over time through confronting ideas in multiple contexts. The ‘big ideas’ are never fully mastered; they deepen in complexity over time.