The Teacher Training Agency is also planning a network of "teacher advocates" to dispel the profession's gloomy image and promote teaching to youngsters.
The TTA is late joining the summer school bandwagon. Holiday learning schemes are already a key feature of Labour's drive to improve primary school literacy and numeracy.
Now the TTA wants to see fresh graduates volunteering for summer courses in becoming a teacher.
The camps would bring graduates up to speed with the new national curriculum for teacher training. They could also drum up interest in careers by offering a taster of professional life.
Anthea Millett, the agency's chief executive, told the annual meeting of the Mathematical Association that she would like an "extensive network" of schemes across a range of subjects.
The TTA is also exploring the idea of summer schools for freshly-qualified teachers as part of their induction training.
In a separate initiative, the agency is to set up a network of "teacher advocates", serving professionals willing to talk to the media, attend careers fairs and operate telephone hotlines.
"I would like to see teachers taking a proactive view," said Ms Millett. "Teachers are both the best advocates for teaching and the worst.
"When they sit looking depressed and rejected, and say 'Teaching has served me very well but I wouldn't recommend that you go into it', that just lowers morale and brings the profession into disrepute."
She urged teachers and lecturers to "come out fighting" and promote the profession, in the face of a slump in interest from graduates.
Writing in last week's TES, she criticised universities, local authorities and schools themselves for failing to do enough to encourage young people into teaching.
"We need more support from higher education subject departments," she told the conference.
"I also think our professional associations could do more than they do to help promote the value and worth of teaching."
The accumulated shortage of maths students coming forward has grown so severe that, in order to meet the total needed, half of all this year's pure maths graduates would have to become teachers.
Ms Millett told the conference there is room for "qualified optimism" over the recruitment shortage. The agency's advertising campaign, she said, appears to have produced a sharp increase in applications.