This paper presents research activity on computer-based mathematics learning to study the effectiveness of open-source teaching computer platforms (Canvas) in computer-assisted instruction. We designed a set of multiple-choice online quizzes as a dynamical flow-chart of possible paths to follow while solving a difficult math problem on differential operators, Fourier series of partial differential equations of mathematical physics. At each step in the quiz the student is helped to resolve the partial question and then the dynamical flow-chart directs the student to either repeat the calculations or conclusions for that local answer, or go to a certain file library with content to read, or even directed solve an extra additional mini-quiz on the side, usually related to prerequisite knowledge, and then come back at the same point in the main quiz. This type of computer algebra assisted assignment allows the conversion of traditional paper and pencil math answers from analog form into digital form, so the assessments can be easily processed and graded as multiple-choice quizzes.