A Framework for the Geometric Habits of Mind
Mathematics habits of mind are productive ways of thinking that
support the learning and application of formal mathematics. The
learning of mathematics is about developing these mind habits. In
1998 in an article they wrote for Designing Learning Environments
for Developing Understanding of Geometry and Space,
Goldenberg, Cuoco, and Mark highlighted this notion of habits of
mind, equating it with mathematical power. People with
mathematical power perform thought experiments, invent things,
look for invariants or patterns, make reasonable conjectures,
describe things both casually and formally, think about methods,
strategies, and processes, visualize things, and seek to explain why
things are as they see them.
Mark Driscoll, in Fostering Geometric Thinking, provides a
framework of productive mental habits geared specifically toward
geometric thinking:
 Reasoning with relationships – actively looking for
relationships within and between geometric figures and
thinking about how the relationships can help your
understanding or problem solving
 Generalizing geometric ideas – wanting to understand and
describe the “always” and the “every” related to geometric
phenomena - Does this happen every time? Why would this
happen in every case?
 Investigating invariants – finding what about a situation
changes and what stays the same
 Balancing exploration and reflection – trying various ways
to approach a problem and regularly stepping back to take
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