Given the complex social and environmental challenges facing our world, the generation of new knowledge is critical (Nahapiet & Ghoshal, 1998). New mathematical knowledge is of particular importance because it will underpin many of the technological and economic solutions necessary to meet these challenges. According to Wai, Lubinski, Benbow and Steiger (2010) reporting on the Study of Mathematically Gifted Youth [SMPY], career achievement in mathematics and related fields is correlated with the appropriateness of educational opportunities: “Rare accomplishments in STEM [science, technology, engineering, mathematics] appears to emanate from rich talent development opportunities experienced early in life” (p. 870). Hence, there is a need to understand how to educate exceptional students for knowledge generation in mathematics.
The generation of new knowledge has intellectual and social dimensions (Nahapiet & Ghoshal, 1998). There is considerable literature on the intellectual dimension of educating for mathematical eminence (e.g., Phillipson & Callingham, 2009). However, the focus of this paper is on the largely unexplored social dimension. The research question is: What is the role of social capital in education in the attainment of mathematical eminence? This investigation is informed by theories of (1) intellectual capital, social capital and knowledge generation, and (2) extraordinariness.
‘Intellectual capital’ refers “to the knowledge and knowing capability of a social collectivity, such as an organization, intellectual community, or professional practice (Nahapiet & Ghoshal, 1998, p. 245). New intellectual capital is created through the processes of combining and/or exchanging of existing knowledge (Nahapiet & Ghoshal, 1998):
"Knowledge creation involve(s) making new combinations-either incrementally or radically-either by combining elements previously unconnected or by developing novel ways of combining elements previously associated …
Where resources are held by different parties, exchange is a prerequisite for resource combination … Sometimes, this exchange involves the transfer of information within the scientific community or via the Internet. Often, new knowledge creation occurs through social interaction and coactivity". (p. 248)
Thus, there is an interrelationship between knowledge generation and social capital. ‘Social capital’ is “the sum of the actual and potential resources embedded within, available through and derived from the network of relationships possessed by an individual or social unit” (Nahapeit & Goshal, 1998, p. 243). New intellectual capital is created when one of three dimensions of social capital interact with one of four elements in the combination and exchange of intellectual capital (Nahapeit & Goshal, 1998). The social capital dimensions are structural (i.e., a network), cognitive and relational (e.g., trust). Combination and exchange of intellectual capital involve access, anticipation of the value of new knowledge, motivation and the capability of the combination. Thus, educating for mathematical eminence requires attention to developing social capital as well as intellectual capital.
Extraordinary individuals contribute to a field by assuming one of more of four roles, namely The Master, The Maker, The Introspector, and The Influencer (Gardner, 1997). The Master “is an individual who gains complete mastery over one or more domains of accomplishment; his or her innovation occurs within established practice” (Gardner, 1997, p. 11). The Maker “may have mastered existing domains, but he or she devotes energies to the creation of a new domain” (Gardner, 1997, p. 12). The Introspector undertakes “an exploration of his or her inner life: daily experiences, potent needs and fears, the operation of consciousness (both that of the particular individual and that of individuals more generally)” (Gardner, 1997, p. 12). The Influencer “has a primary goal the influencing of other individuals” (Gardner, 1997, p. 12). Hence, educating capable students with the potential to be knowledge generators in mathematics also needs to accommodate the diversity of roles that these extraordinary individuals might assume.
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