Problem-posing by students makes them reason about topics of their own choice. It can be used at all levels.
Problem-posing is ideal for assessment because it demonstrates a student's:
- ability to solve a problem
- sense of what a problem is
- interest in developing and managing appropriate solution processes
- individual ability to explain the solution and procedures used.
This is the work of mathematicians!
Very young students can construct quite complex reasoning. In the article on the AAMT website Autumn Leaves, a year 1 teacher bases her teaching on reasoning and problem-posing.
There are many topics on which older students could focus. For example:
- historical events using data (e.g. the First Fleet convicts, dates for societal development, population growth in Australia or the world)
- saving for a car
- the skate ramp
- environmental issues
- hobbies, such as ballet movements, football percentages and ladders, how to strategise in particular games.
While it is not desirable to base whole mathematics programs on problem-posing, it allows assessment of students’ mathematical reasoning and how it relates to everyday life.