Activity aim: To engage students in higher-order thinking; to deepen and consolidate learning of abstract concepts; to gauge student understanding
Materials needed: Varies
Critical pedagogue, Paolo Freire, saw problem-posing in education as a way to renegotiate the student / professor binary that assumes that professors ultimately possess all knowledge and students are passive recipients of it. Instead, Freire (and others) sought to make the classroom a space of negotiation in which teachers and students co-construct knowledge.
Studies show that problem-posing is an effective way to engage students in critical thinking, to help them to become more active participants in their own learning, and to increase motivation and engagement. Integrating activities with a slightly lower barrier to entry (such as a problem-posing journal) can be a useful way to get started with active methods | methodology.
In a math / computer science classroom:
In a math / computer science classroom, problem-posing can take many shapes. It can refer to the reformulation or the generation of a problem (Silver, 1989). It could help students to challenge the way that a problem has been formulated and invite them to reconstruct it (Song, Yim, Shin and Lee 2007). In this section, we’ll look at examples of both of these approaches.
1. The rewrite / extend chart:
Students choose 5 problems from a homework assignment. Instead of solving these, they should put them in a journal as follows:
|Original word problem||In my own words…||How should I solve this?||Extend the equation|
|“Maria is planning to buy breakfast and lunch for campers at a summer camp, and she’s trying to decide how much she can spend. There are 50 campers, and her budget is $5,730 per week. If breakfast costs $7 per person, how much can she spend per person on lunch?”||Maria needs to buy breakfast and lunch for a summer camp. She needs to figure out how much she can spend on each camper’s individual lunch. We know how much breakfast costs and how many campers there are, but we need to figure out how much lunch will cost for each person.||We know that breakfast costs $7. First, I can multiply this by 50 campers. That’s $350 per day (50x$7) or $2,450 per week ($350×7 days). That would mean that Maria has $3,280 left ($5,730-$2,450).
So, we need to divide that amount by 7 (the amount of days in a week). That’ll mean she’ll have $468.57 per day. If we divide that by the number of campers (50), that means she can spend $9.37 on each lunch.
|Maria got a discount! Breakfast now costs $5.50 per camper, and they won’t have lunch on Sunday because the parents are coming to pick everyone up. How much can she spend on lunch now?|
Note: Instead of checking each one of these problems individually, you could check a few at random, or designate a student (at random) who could share their entry in class.
In class, after checking a problem, you could ask students to solve each other’s extensions in pairs or choose an extension for everyone to solve individually and then check.
In writing-intensive classrooms:
Asao Inoue’s excellent open-access book on antiracist writing ecologies (web link) includes some important models for more holistically integrating problem-posing pedagogical strategies and assessment models into writing-intensive classroom. In his problem-posing reflection letter (web link), he asks students to reflect on the problems of assessing a colleague’s writing after a peer review in order to discuss and bring awareness to the role of power and identity in the assessment of writing.
Do you use problem-posing in your classroom? Write to us and let us know how! We’ll feature (and credit) you in this entry.