According to the official website of Columbia:

These recommendations must come from teachers who taught you in academic disciplines

For engineering applicants, one must come from a math or science teacher

We welcome an additional letter of recommendation if the writer has worked with you in a researcher or college course capacity. Any supplementary recommendations should not be completed on the Teacher Report forms, but instead submitted directly to our office. The Committee discourages the submission of additional recommendations, as admissions decisions will be based primarily on the required recommendations from your high school teachers and secondary school/guidance counselor.

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