Primary trainees will have to demonstrate similar confidence in the principles of mathematics, and for the first time, must develop at least one specialist subject to A-level equivalent standard.
Students must also prove they can do interactive whole-class teaching, keep control and stop lessons from becoming boring.
The leak will disrupt Mrs Shephard's election countdown. The launch of the curriculum, planned for next Tuesday, was meant to follow her A-levels reforms and her announcements on target-setting and appraisal this week.
The Teacher Training Agency curriculum, which controversially prescribes the content of what student teachers should learn, replaces government criteria on primary training and will come into effect in September, with a secondary-phase version following next year. Previous criteria merely described what a trained teacher should be able to do.
On Tuesday, Mrs Shephard, joined by the TTA chief Anthea Millett, will launch four documents, all of which The TES has seen: the curriculum for primary English and for maths, new rules for courses, and new standards that students must meet to gain qualified teacher status.
The tone of the announcement - whether or not to "get tough on the causes of bad teachers" - will depend on whether Mrs Shephard wants to use it to distance Tory and Labour education policy. The TTA see the curriculum as a way of re-professionalising the profession.
Labour has already accused Mrs Shephard of copying David Blunkett's intention to reform training. Colin Pickthall, the MP who drew up Labour's unpublished policy, says it will be less prescriptive.
The document says trainees must understand structure, derivations and meanings of words, the sound system underlying speech, and rules and aberrations in spelling.
Trainees must get pupils to identify and put together sounds that make up words and write letters that represent those sounds. They must be able to teach standard English. They must teach pupils to be "articulate and coherent", and introduce them to synonyms and antonyms, alliteration, and "imaginative ways of conveying meaning".
Students must learn effective ways to teach mental arithmetic, and learn examples of pupils' most common misconceptions. They must be able to teach how different areas are connected and use "questioning that elicits answers from which pupils' mathematical understanding can be judged". This echoes last summer's interest in interactive whole-class teaching as practised abroad.
Mrs Shephard ordered the "re-casting" of training last June after the Office for Standards in Education discovered poor standards of literacy in inner London, and blamed teacher training.
Course providers and schools have until May to comment on the curriculum. Universities and colleges are likely to react angrily. They see the move as an attack on academic freedom, and will question both the legality of the Government's attempt to stipulate the content of university courses and the need for a national curriculum at all.
They say that evidence from OFSTED does not suggest training is poor. Vice-chancellors have written to the Department of Education arguing that the 1994 Education Act prevents Mrs Shephard from using funding to influence course content.