Conceptual and Brain Processing of Unit Fraction Comparisons: A Cogneuro-Mathed Study

This mixed-method, qualitative/quantitative study examined (a) how a constructivist-based intervention (CBI) effected adults' learning of unit fractions and performance on whole-number (WN) or unit fraction (FR) comparisons and (b) brain circuitry implicated (fMRI) when processing these comparisons. The CBI used unit-iteration based activities to foster a shift in participants' understanding of FR, from the prevalent, limiting "one-out-of-so-many-equal-parts" idea to a multiplicative relation conception and thus inverse magnitude relation among FR (1/n>1/m though m>n). Pre- and two post-intervention tests indicated CBI impact on decreased reaction time in comparing not just FR but also WN and differentiated brain regions implicated for each. Implications for theory testing and CBI impact on WN-FR links are discussed. [For the complete proceedings, see ED597799.]