Thanks for your comment — it got me thinking!

I should have been more explicit in saying it is unreasonable to ask students to sketch graphs from a given form (y=mx+c in this case) when arriving at that form depends on a prior skill that has not yet been mastered. I have amended the comment.

Your plotting method was not known to Inny as it was to come in a later lesson. We could have taken that as our basis but the homework was set in the expectation that students would first get the expression in the form y=mx+c. While maths is absolute in its truth, the way it is encountered by students depends on the context of curriculum and instruction.

I absolutely agree that the sequence of learning objectives need not be unique. There are usually multiple pathways to understanding, as your own example highlights. But the main premise of my article is that, when a sequence is forced on a student (in this case, rearrange equations and then sketch linear functions from the standard algebraic form), it is critical that they master each learning objective in turn. Building multiple representations of knowledge should be a parallel goal.

I don’t think anyone sane would advocate going back to New Math —the mastery of core knowledge need not be abstract or long-winded!