Bass (2008, January) has considered habits of mind as practices—things that mathematicians
do. Such practices include asking „natural‟ questions, seeking patterns or structure, consulting
the literature and experts, making connections, using mathematical language with care and
precision, seeking and analyzing proofs, generalizing, and exercising aesthetic sensibility and
taste. Bass claims that children can, and should, cultivate these practices from their early school
years on. By capitalizing on children‟s curiosity their inquisitive minds can be harnessed.
Goldenberg (2009, January) offered some strategies that capitalize on children‟s phenomenal
language-learning ability and abstracting-from-experience ability to develop certain algebraic
ideas such as breaking [apart] numbers and rearranging parts (commutative property,
associative property), and breaking arrays and describing constituent parts (distributive
property). Goldenberg provided evidence to show that children can indeed use “algebra” as a
language to describe a process or a pattern and to express what they already know.
For Leikin (2007), “employing habits of mind means inclination and ability to choose
effective patterns of intellectual behavior” (p. 2333). With respect to the mental habit of solving
problems in different ways, Leikin considers a problem-solving strategy as a habit of mind when
it is within one‟s “personal solution spaces of many problems from different parts of [the]
mathematical curriculum” (p. 2336). One goal of mathematical instruction is then to move
solutions from students‟ potential solution spaces (containing solutions that are produced with
the help of others; i.e., solutions that are within one‟s zone of proximal development) into their
personal solution spaces.