Involvement in instructional games like these induces students to make sense of their ideas and the
interpretations of others. Discussion while playing facilitates the construction of mathematical knowledge
as each player’s thinking is articulated, allowing a conceptual framework to be constructed through a
process of reflection and social interaction. In turn, real mathematical issues arise out of the playing and
engender an exchange of ideas as students strive tomake sense of their actions and thoughts.
Mathematics can then be seen as a social process of sense-making and understanding, rather than a
set of rules handed down from some authority on high.
Coming to terms with numbers in this way also establishes many of the thinking patterns on which
mathematics relies. The equivalent forms used for numbers suggest that problems can be represented
in diverse ways; conceptions of place value and renaming coupled with a full knowledge of computation
concepts and basic facts is the key to fluent computation; and a sense of numbers coupled with
rounding is essential for estimation and approximation processes