Allan Gray, 65, abused seven girls aged between 12 and 16 at various locations across Lanarkshire.
Gray, of Carluke, South Lanarkshire, was a maths teacher for 35 years but took up tutoring after retiring.
On Friday, father-of-two Gray was found guilty of seven charges for incidents between September 2011 and May at Lanark Sheriff Court.
A father of a victim said: "He deserves to be punished for a long time for these disgusting crimes."
Recalling how Gray had touched her thigh, one victim said in court: "I was scared. I was in the house myself, but I wanted to pass maths."
Sentencing was deferred until next month.