An on-line teaching, learning and assessing system provides a teacher rapid feedback while teaching a classroom lesson on STEM principles by measuring student progress in learning the principles wherein student progress is measured by students' correct answers to assessment questions. The system includes at least one teacher computer and a plurality of student computers linked to the at least one teacher computer by a communications network. Each computer includes an input device and a touch sensitive screen for receiving handwritten input. The teacher inputs the teacher computer with at least one assessment question and at least one corresponding correct answer to the question, both inputs being handwritten using math expressions and STEM sketches. The student inputs the student computer with at least one student answer corresponding to the assessment question, the answer being handwritten using math expressions and STEM sketches.