Students are asked a tremendous amount of questions daily, and yet they rarely spend time crafting their own questions or answering questions posed by their peers. This is true in my own math classroom, where most math problems encountered by students come from textbooks, digital curricula, blogs and suggestions from colleagues at school and on Twitter. But lately, I have been asking students to pose their own mathematical problems, with much success.
What exactly is problem posing? There is no exact definition, but problem posing occurs when students generate their own questions about classroom material that could be further explored by themselves or others. “Problems” don’t have to be reserved for math classes. Students could generate their own writing prompts in humanities classes or their own questions about historical events or scientific phenomena. The point is to shift traditional sources of inquiry from authority figures to the students themselves. Research has shown that asking students to generate their own problems in math class leads to positive outcomes on students’ knowledge, problem solving skills, problem posing abilities, creativity, and disposition toward mathematics. It would not surprise me to see the same positive outcomes in other classes. Students exert much effort in service of other people’s questions. Problem posing gives students an opportunity to experience ownership over their learning, to ask a question about the world and set about answering it. In “The Having of Wonderful Ideas”, Eleanor Duckworth writes:
“First, the right question at the right time can move children to peaks in their thinking that result in significant steps forward and real intellectual excitement; and, second, although it is almost impossible for an adult to know exactly the right time to ask a specific question of a specific child—especially for a teacher who is concerned with 30 or more children—children can raise the right question for themselves if the setting is right.”
Despite its many benefits, teacher ought to think carefully about how they implement problem posing in their classrooms. It takes a good deal of domain-specific content knowledge to generate good questions. If students are asked to create their own questions too early in a topic, a problem-posing activity may lead to frustration for everyone. Even if students possess the right amount of content knowledge, they’re probably unaccustomed to crafting their own questions. Teachers can take steps to position students to pose rich, meaningful problems. I’ll conclude with some brief advice based on my own problem posing experiences in the classroom.
Take a Breath
Take a breath and pause before asking your own questions. If you have shown students a graph of a parabola, a map of Europe, or several lines of poetry, invite students to generate their own questions instead of jumping straight to asking your own. If done frequently enough, students will learn to anticipate the possibilities of questions that could be asked about a given type of problem or image.
Highlight and Challenge Assumptions
Highlight the assumptions that underlie the topics your students are learning and let them know that it is okay to challenge those assumptions if doing so raises interesting questions. If they are learning how to add fractions, have them consider what you end up with when you “incorrectly” add numerators together and denominators together. If they are exploring a map of Europe, have students consider how economic, political, and social interactions would differ if the geography of Europe was different. Often, students gain a better understanding of an idea when they see what it is not.
In my experience, peer feedback has a positive impact on students’ problem posing activities. Problem posing inherently contains elements of creativity, an area where students sometimes feel insecure. Creating your own problems means creating something personal and exposing yourself to criticism. I have found that students are extremely encouraging in their feedback toward others, particularly when it deals with student generated questions. The fact there is no single, definitive answer leads students to be kind rather than judgmental. Such encouragement has created a positive feedback loop in my classroom, where kind words have given students more confidence and more willingness to take risks with their problem posing activities.
There’s no substitute to giving it a try. Good luck!
Melvin is a middle school math teacher interested in encouraging students to seek out answers to their own questions about math, science, and society. He is currently a Math for America Fellow and alumnus of the Park City Mathematics Institute. He is an avid cyclist and maker of graphs. Follow him on Twitter @m3lvinp3ralta