Came across this excellent list on what it takes to be "Smart in Math" at Math Mama Writes.
'Smart in Math' Before students work in groups, it's important to help them understand that we typically have many misconceptions about what it means to be 'smart'. Typically, people think that someone who is 'smart in math' ...
- answers questions quickly
- always gets the right answer
But, really, people who are good at math ...
- doesn't have to work at it
- are persistent
- wonder about relationships between numbers, shapes, functions, ...
- check their answers for reasonableness
- make connections
- are willing to try things out, experiment, take risks
- are resilient
- want to know why
- contribute to group intelligence by asking good questions
- notice and learn from their mistakes
Students may also need to know how synapses (the connections between neurons that are created each time you learn something new) are strengthened by repeated use. A new connection isn't strong until it's been used:
- try to extend and generalize their results
- multiple times
- in multiple ways
- after a time away
Those first three bullets are not only way off the mark they are detrimental and harmful to the "smart math student". When those students who seem to always get the right answer come up against content that stops them in their tracks, they don't realize how much hard work is needed to keep the engine of their "smartness" running. Of course, this reminds me of Carol Dweck's work aroud the fixed and growth mindset. I also appreciate the sense of wonder and discovery that is embedded in the second list. When I come across the intricacies of math in nature it just boggles my mind - just don't ask me to come up with a proof using all the proper postulates. That task still gives me nightmares.