I have been sent this paper (on problematising mathematics) and am confused. Am I missing something…?

The paper argues (argued, in 1996) that maths reform is best achieved through problematising maths:

In-practice, this focuses on students doing their own reasoning, problem-solving rather than practising; learning but not being taught.

It seeks to go beyond what it describes as a historic split between acquiring knowledge (in school) and applying it (out of school):

The paper advocates ‘understanding’ maths (Is this separate from ‘knowing’ or ‘being able to do’ maths? This seems unlikely to me, but I’m not a mathematician)? (I know maths gets broken down into sub-domains, but this is _only_ advocating understanding).

The teacher’s role is to create a community – although they should not be constrained from sharing some information with students…

The most important result of this approach – residue – is strategic skills.

So a good task is one which students can problematise and which leaves a residue (H10) and such problems can come from anywhere.

My questions:

- Is this contrary to what we know from cognitive load theory?
- Do ‘strategic skills’ = ‘weak methods’?
- Will a carefully-tailored task leave a better residue than a student-generated one?
- Does this rely on procedural knowledge, but build it inefficiently

I can see how students problematising an idea might make it more engaging (the authors say that’s not what they seek), and that this is a good approach to take. But it seems to me that this must rely on a bedrock of knowledge and skills.

Is there an argument I’m missing here, or a subtlety to the function of problematising that I’m missing?

Hiebert, J., Carpenter, T., Fennema, E., Fuson, K., Human, P., Murray, H., Olivier, A. and Wearne, D. (1996). Problem Solving as a Basis for Reform in Curriculum and Instruction: The Case of Mathematics. Educational Researcher, 25(4), pp.12-21.