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What was said about what is important when doing maths

Nearly all teachers talked explicitly during maths lessons about what kinds of mental activity were important and relevant. They talked about, and praised:

Effort & study skills
Trying hard
Looking up earlier work
Working independently
Be organised
'Pushing ideas further'

Mathematical characteristics
Visualising without prompting
Being aware of difference and sameness
Volunteering conjectures
Creating examples to explore ideas
Asking good questions
Using efficient solutions
Asking why and why not
Talking about relationships
Taking time to understand mathematical ideas
Contrasting everyday observations with mathematical ones
Displaying the behaviour of a mathematician

Decisions and choices
Careful planning, e.g. when handling data, or when exploring variables
Choices about accuracy, e.g. using fractions and decimals as more accurate than remainders
Being aware some methods are more powerful than others
Not picking only easy questions to do
Deciding what to ask and what data to collect

Reasoning
Answers that voluntarily include reasons
Saying why and how
Proving to yourself
Having theories about your work
Justification

Descriptions of methods
Well verbalised methods and explanations
Showing methods
Checking answers another way

In a few lessons no statements about the nature of mathematics, or what it is important to do, or associated praise were heard at all.