I took a course in my Master's (URV.cat) where we had to do exactly this, implementing backpropagation (fwd and backward passes) from a paper explaining it, using just basic math operations in a language of our choice.
I told everyone this was the best single exercise of the whole year for me. It aligns with the kind of activity that I benefit immensely but won't do by myself, so this push was just perfect.
If you are teaching, please consider this kind of assignments.
P.S. Just checked now and it's still in the syllabus :)
I did this in highschool from some online textbook in plain Java. I recall implementing matrix multiplication myself being the hardest part.
I made a UI that showed how the weights and biases changed throughout the training iterations.
Is that paper publicly available?
The difference in understanding (for me and how my brain works) between reading the paper in what appears to be a future or past alien language & doing a minimal paper / code example is massive.