I think the time and skill necessary to effectively utilise pictorial representations is often massively underestimated. As if it’s something pupils who don’t understand do to help them calculate and nothing more.

It’s likely we need to realign our focus so that we are able to provide pupils with the opportunity and freedom to represent what’s in their heads, rather than our own.

It is, of course, essential we model the use of pictorial representations and some, like the bar model, will be really effective in expressing structural properties of the mathematics at hand.

Ultimately though, the skill required of the teacher comes in the form of the ability to recognise these structural properties and relationship in models other than our own and continue accordingly.

As @Suchmo83 says, there’s nothing wrong with scaffolding children& #39;s use of different representations but this has to be a intermediate state, not the end goal.