Careers to Classrooms Act of 2001 - Amends the Elementary and Secondary Education Act of 1965 to establish a Careers to Classrooms program. Authorizes the Secretary of Education to award competitive grants to States for: (1) teacher recruitment, education, training, referral, placement, and retention activities to place eligible individuals as certified teachers in public schools through State-approved alternative certification programs; (2) stipends for eligible individuals enrolled in programs who agree to seek certification through teacher certification programs in that State and teach in a high-need school in that State, with preference for those individuals needing such assistance; (3) grants to high-need elementary or secondary schools to offset the teacher mentoring, alternative certification, and other direct costs associated with accepting eligible individuals under this Act; (4) grants to accredited institutions of higher education to develop alternative certification programs, with preference given to programs tailored to eligible individuals; and (5) other activities determined by the State to be reasonably necessary to carry out the purposes of this Act. Requires preference for such grants to be given to States that have developed, or are developing, alternative certification programs that: (1) rapidly place quality certified teachers into the classroom; (2) emphasize subject matter content; and (3) lead to the certification and placement of a large number of teachers in relation to the number of public elementary school and secondary school teachers in the State.