Historicalexamplesofthesystematicuseofvariation.
Althoughthestudiesinthissectionarenottransferstudies,-knownapproachtoteachingmathematicscalledteachingwithvariation (Gu,Huang ＆ Marton,2005).Kangshen,Crossley,andLun (1999) (1991) ,forinstance,,,bypresentingalineperpendiculartoaradiusandintersectingthecircleintwopoints,thestudents' attentionisdrawntothefactthatatangentofthecirclehasonlyonepointincommonwiththecircle.
MasonandWatson (2005) .
AfinalexampleofthesystematicuseofvariationandinvariancecanbeseeninMariaMontessori',JeanMarcGaspardItard (1775-1838) andEduardSeguin (1812-1880).TheformerbecamefamousforhistreatmentoftheWildBoyfromAveyron,an11— (e.g.,learningtotellapartaroundfigurefromaflatfigurebytouch,redpaperfrombluepaperbyvision,andbitterfromsweetbytaste).Itardalsotriedtolinkthedistinctionsbetweensensoryimpressionstodistinctionsbetweencorrespondingwordsbymeansofsimultaneousvariationinsensoryimpressionsandwords (see,forexample,Itard,1801/1962;Lane,1977).IcancompareItard'sapproachwiththemorecommonapproachofintroducingoneconceptorwordatatimeandpointingtodifferentinstancesofthatconcept (e.g.,lookingataredroseandsaying “red”, followedbypointingtoaredappleandsaying “red”, andsoon).ThedifferencebetweenItard'sapproachandthemorecommonapproachisthedifferencebetweentheuseofcontrastsandgeneralization.
