The first of these heuristics is reinvention through progressive mathematization. According to thehttp://files.eric.ed.gov/fulltext/ED472048.pdf, the students should be given the opportunity to experience a process similar to the process by which the mathematics was invented
That’s the general approach I use to breaking down new concepts. For a topic like linear algebra, I’ll start getting a list of formal concepts (from Wikipedia, i.e. matrix, determinant, eigenvector) then start searching forums (reddit, math overflow) for analogies. I try to come up with intuitive ways to describe the technical term and create diagrams/examples that help.
For example, I came up with an analogy of a matrix being like a “spreadsheet” (which most of us are familiar with), then we find ways to update the spreadsheet with new info. It’s not official, but it helps me grok what’s happening. You can see that article here: