Shifting from the general to the specific and vice-versa is integral to working mathematically. It is what allows us to talk of infinity starting from simplicity. For example when talking of the commutativity of addition of the real numbers...I can specify an example:
1 + 2 = 2 + 1
but I can also speak generally and say that:
Task: Think about when you have worked mathematically, something which you couldn't do immediately, that posed a difficulty. What was your process at first? How did you attack the problem? How did you make it more manageable? How did you complexify? Did you extend? Think about how you can relate what you did to generalising and specifying.
Thinking about how we function in this case allows us to identify key moments and processes that if worked on can be used as tools for dealing with mathematical problems.
1 + 2 = 2 + 1
a + b = b + a
...for a,b ∈ R (member of the real numbers)
...for a,b ∈ R (member of the real numbers)
This demonstrates specifying an example and then conjecturing a generality to be tested based on that example.
Task: Think about when you have worked mathematically, something which you couldn't do immediately, that posed a difficulty. What was your process at first? How did you attack the problem? How did you make it more manageable? How did you complexify? Did you extend? Think about how you can relate what you did to generalising and specifying.
Thinking about how we function in this case allows us to identify key moments and processes that if worked on can be used as tools for dealing with mathematical problems.
