Ball, Lewis & Thames (2008, էջ. 15) discuss this challenge for the elementary-grades teacher, who wants to give mathematical reasons for mathematical facts, but whose students neither use the same definition, nor would understand it if it were introduced. Ball, Deborah Loewenberg; Lewis, Jennifer; Thames, Mark Hoover (2008), «Making mathematics work in school»(PDF), Journal for Research in Mathematics Education, M14: 13–44 and 195–200, Վերցված է 2010 թ․ մարտի 4-ին
