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Abstract
In regarding mathematical thinking as proceeding via operations involving a small number of ‘items’ at any one time, an important feature is the phenomenon in which a section of mathematical structure may be mentally held as a single unit, possessing an inferiority that can be subsequently expanded without loss of detail and trigger connections with other parts of cognitive structure. This article discusses the role of this phenomenon of ‘compression’ and ‘expansion’ in the manipulation of statements involved in certain types of mathematical proof. Implications for teaching linked to an awareness of these aspects is also discussed.
The title is taken from a phrase used by Professor Hyman Bass in the opening plenary session of the BCME-5 conference.
The title is taken from a phrase used by Professor Hyman Bass in the opening plenary session of the BCME-5 conference.
Notes
The title is taken from a phrase used by Professor Hyman Bass in the opening plenary session of the BCME-5 conference.