britishsummer I have not taught A'level, but have spoken to enough other maths teachers and looked at text books and exam papers to know that HL is more advanced than A'level.
But that wasn't your question.
There are some that I have spoken to who think that HL is equivalent to FM, and others who say it is somewhere in between.
A'level does give a student to study mechanics, which is not part of the HL syllabus. But then (in my opinion) HL does require a student to demonstrate mathematical nouse and problem solving skills with unfamiliar situations in a way I have not seen necessary in A'level.
TOK is where it all comes together! I will not be able to fully explain why I love it. It challenges a student to question why they think they 'KNOW' something, rather than just 'BELIEVE' something.
It does this by looking at some of the different ways in which we 'know' something and challenges how reliable or essential they are (Language, Reason, Emotion, Sensory)
It encourages students to listen to people they do not agree with and to respond without falling into many of the fallacies that feature in so many day to day arguments.
In previous classrooms I have had Christian, Bhuddhist, Muslim, Atheist, Hindu, Agnostic students all discussing stuff in a way you would rarely see a group of adults.
I love to help them grapple with the different types of reasoning, with how our senses can be fooled, with how language is so important to interpretation...
And loads of other stuff. It's just amazing to see young minds exploring ideas.
It does have it's woolly bits