Administration - Identifying student readiness
I started my career believing that only the top 30% of students can cope with problem solving. 27 years later, I now have a different view. While it does seem that there are a few students who aren't "hard-wired" for mathematical thinking, it is my experience that the great majority of students can be challenged, and can gain success with problem solving. The difference between my thinking then and now is in the type of task I consider to be a meaningful problem.
In any of my classrooms I find there is a range of experiences with problem solving. There are those students with a high level of past exposure to and confidence with problem solving, and there are those who have had little exposure in the past with problem solving and therefore little confidence. I find that increasing the exposure of students to problem solving using well targeted and well graded problems can bring about increases in their level of confidence and subsequent success with problem solving. All students at my school are given meaningful problems to solve on a regular basis. They are given three problems ranging from simple through to complex. By having this range in complexity, I can ensure that all students can gain some success out of the exercise. Their responses are collected and analysed and the next lesson is used to model effective strategies and solutions both from the teacher and from other students.
So how do I identify students who can benefit from exposure to challenging Mathematics problems? I use two criteria only - I encourage those who are Interested and Able. I can tell if students are interested in "things Mathematical" by their contributions to classroom discussions, and whether they participate in out-of-class Mathematical activities . Although the term "Able" means many things to many people, I determine a students "ability" by classroom observation, and the students performance on the regular problem solving tasks that are given.
Sometimes the criteria are more like Interested or Able - because I never exclude or discourage students if they are interested in Problem solving. If a student doesn't display a lot of "ability" in the classroom, she/he is still welcome to try the problem solving enrichment program. Often this type of student displays a degree of lateral thinking and initiative which allows him/her to be quite a successful problem solver. Also, a well designed program (- like MATHGYM) focuses on the strategies and heuristic of problem solving as much as the knowledge of Mathematics. This is where MATHGYMis so very useful for my purposes, because students can access it from anywhere and at anytime, so there is no pressure on resources that might limit the number of students participating.