A report by the committee, published this week, also asks the Government to consider "golden handcuffs" whereby training debts are written off in return for each year spent in the classroom.
The report reveals that MPs were appalled both by the worsening shortage of would-be teachers and by the number of undergraduate primary teacher-trainees with poor A-level grades.
While the average A-level scores for all undergraduates is three Cs, the average for those on teaching courses is two Ds and and a C. They also point out that more than 18 per cent of postgraduate entrants had third-class degrees or lower (the figure for maths was 36 per cent).
The committee recommends that the Teacher Training Agency, together with the General Teaching Council, when established, set minimum standards of academic achievement for entrants.
Launching the report on Monday, MPs acknowledged that many teacher-training institutions are forced to accept poorer-quality candidates than they would like because their funding depends on numbers. They admitted that making it more difficult to get onto courses could mean that recruitment problems get worse before they get better. But, they argue, if teaching were to become more exclusive and thus more prestigious , the universities and colleges would have a bigger pool of hopeful candidates.
The report identifies factors that are putting potential recruits off: the poor public image of the profession; the prospect of unruly pupils, large classes, piles of paperwork and a depressing environment; the extra debts incurred by a fourth year of training; poor salary progression and the absence of fringe benefits compared to other professions.
To attract high-fliers, the committee suggests a "fast-stream" entrance grade for graduates with good honours degrees who pass "highly competitive" entrance exams, on the model of the Civil Service or the police. They would have the chance of accelerated promotion either to headship or the new grade of advanced skills teacher.
The MPs did not tackle the question of whether this would generate resentment among the rest of the profession. Sabbaticals - a refreshment year spent in industry or pursuing academic research - are another proposed enticement, but only for "excellent teachers".
The National Union of Teachers has already objected to this "invidious distinction between so-called excellent teachers and the rest of the profession".
The Government should consider writing off debts for newly qualified teachers provided they stay in the classroom, the report recommends.
Two schemes are proposed. First, a contribution towards the repayment of student loans for each year the qualified teacher teaches, with the amount of loan remission possibly varied to favour those in shortage subjects or those who teach particularly well. And second, spreading the first year's salary across the final year's training and the probationary year (an idea that would cost no more than the present system). The Government has already indicated that Pounds 10 million will be available next year to alleviate the cost of tuition fees for postgraduate teachers.
The committee also notes that many young people are reluctant to be locked into a career for life, and recommends the selling of teaching as a transferable skill. The Government is urged to review the local management of schools formula and teachers' pay scales to ensure that mature entrants are not debarred because they are too expensive for schools to employ.
The report is published against a background of depressing statistics on recruitment: an 11 per cent fall in undergraduates studying teaching, a third of all maths training places unfilled, and a wastage rate of one in four of all PGCE students.
Last week, Liberal Democrat education spokesman Don Foster, a member of the committee, released figures showing that 8,920 teachers took early retirement this September, compared with 7,880 in September 1996.
* A "golden handcuff" scheme whereby debts incurred during teacher training were paid off in return for each year spent in the classroom .
* A Civil-Service-style fast track for the brightest entrants to the profession.
* New rules to ensure nobody can train to be a teacher unless they had at least three C grade A-levels.
* Sabbaticals spent in industry or research to reward "excellent teachers".
* More use of non-teaching staff to lighten teachers' administrative load.
* Using enthusiastic teachers as ambassadors for the profession.
* Taster courses in teaching for undergraduates.
* Extending the advanced skills teacher idea by creating a new senior career path with a separate pay spine.
Platform, page 23