One problem with mathematical difficulty is its “invisibility”. We can’t see how other people are thinking, how they solve the problem, how they struggle. And sometimes, we cannot even explain our thinking! That’s why making thinking visible is so important! Because only then we can learn from the others, they can learn from us and we can see where it’s right and where is wrong.

One way to making thinking visible is to apply thinking routines, like: - what are given?

- what are the unknowns?

- what do we know?

- what do we need, how i can get there? (strategies)

- choose a strategy and explore it

- rethink the strategy and optimize it

- connect and reflex

Once we practice thinking routines, we will find it increasingly easier to explain our thinking and even be able to debug our work. If your class also applies thinking routines, it’ll get even easier for everyone to learn and understand each other.

I recommend the following books:

- Polya, How to Solve It

- Velleman, How to Prove It: A Structured Approach

- Ritchhart: Make Thinking Visible

Mathematical work is basically a series of equivalent transformations and logical reasonings, starting from the given informations to get where we want, thus once we knew the why, it should not be too difficult to explain our work because most are self-explanatory.

Hope it can help.