Learners Posing Their Own Problems
"Only a problem the student sees as his or her own problem can focus the student's attention and energy on a genuine search for a solution". (Mason and Johnston-Wilder, Fundamental Constructs, p 94).
There is strong evidence to suggest that when pupils generate their own questions (and then swap with a neighbour to solve each others) they are more motivated and think more deeply about the mathematics they are doing.
Main Section
Do you have any anecdotes from your own classroom which illustrate the issue raised above?
What, for your children, are intuitive ways of calculating using addition, subtraction, multiplication and division?
What sorts of problems give rise to children using their own intuitive methods?
You could bring some examples of children's own intuitive approaches to calculating to your next meeting together and share and discuss them.
What are the main differences between these and other approaches that you, as their teacher, might want them to use?
What implications do these discussions have for your own practice?
Probes and Prompts
Do people have any anecdotes from their own classroom which illustrate the issue raised in the paragraphs above?
You could use the Standards Unit materials, “Improving learning in mathematics” to provide some rich examples of this “problem posing / problem solving” teaching strategy.
You and your colleagues may like to work on the examples provided on page 25 of the “Challenges and Strategies” booklet and generate some more mathematical topics where this strategy could be applied.
Case Studies
Taking Action
You might invite individual learners to describe to everyone else what they can see in a visual image (such as the 3-way great dodecahedron poster). Probably, as learners struggle to communicate what they see, and others try to understand what is being communicated, discussion will be generated which prompts learners to ask questions about aspects of the image.
Research Sources
See Also
Categories
Pedagogy