"Exemplary" or "Expert" level work in my math classrooms were awarded for students who could solve a complex performance task using two distinct strategies. Students also needed to show how the two strategies were connected and discuss this connection. The philosophy is that to solve a complex task, arrive at a valid answer and to prove …
"Exemplary" or "Expert" level work in my math classrooms were awarded for students who could solve a complex performance task using two distinct strategies. Students also needed to show how the two strategies were connected and discuss this connection. The philosophy is that to solve a complex task, arrive at a valid answer and to prove your approach using calculations and representations should be celebrated. But, if a student could then explore a separate strategy, maybe one that was more efficient, or simply distinct from the first, we are now allowing the scoring to inspire deeper thinking about the mathematical concept we are asking a student to explore. When students can solve the same problem multiple ways, they are building a flexible and creative mastery of mathematics. To me, this pushes students towards becoming a mathematical expert. Do this regularly, and the mathematician you have inspired will be truly, "Exemplary".
This makes a lot of sense for classes where it would apply. In my upper-level electives, it's not always feasible or even possible to find a meaningfully different method. I do think that individualized challenges fill a similar role, and also the option -- when it makes sense -- for me to insist that students need to find a different approach that's simpler, more concise, etc.
"Exemplary" or "Expert" level work in my math classrooms were awarded for students who could solve a complex performance task using two distinct strategies. Students also needed to show how the two strategies were connected and discuss this connection. The philosophy is that to solve a complex task, arrive at a valid answer and to prove your approach using calculations and representations should be celebrated. But, if a student could then explore a separate strategy, maybe one that was more efficient, or simply distinct from the first, we are now allowing the scoring to inspire deeper thinking about the mathematical concept we are asking a student to explore. When students can solve the same problem multiple ways, they are building a flexible and creative mastery of mathematics. To me, this pushes students towards becoming a mathematical expert. Do this regularly, and the mathematician you have inspired will be truly, "Exemplary".
This makes a lot of sense for classes where it would apply. In my upper-level electives, it's not always feasible or even possible to find a meaningfully different method. I do think that individualized challenges fill a similar role, and also the option -- when it makes sense -- for me to insist that students need to find a different approach that's simpler, more concise, etc.