The action will affect two councils a day until 6 February, starting with Glasgow and East Lothian.
On Friday Education Secretary Shirley-Anne Somerville said she remained committed to a "fair and sustainable pay deal".
Members of the EIS, Scotland's largest teaching union, the NASUWT, Scottish Secondary Teachers' Association and the Association of Headteachers and Deputes unions were involved. Ms Bradley told the programme the offer that was made in November was "practically the same" as the previous one in August.
"What we would say is that with the resource that the Scottish government has they should be able to attend to the needs of both sets of workers."EIS members have already taken three days of national strike action - one in November and two in January.It will include two days of national strike action in all schools on 28 February and 1 March, followed by a rolling programme of strikes for 20 days between 13 March and 21 April.
Their next meeting is not due until the end of next week although a special meeting could be arranged sooner.
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