This morning there was a simply elegant explanation on the Teaching Channel for the hows and whys of open-ended questions here. In reflection, I decided to construct a checklist for what I think defines a perfect question. Maybe you can help by suggesting more filters.
- Clean on the teacher’s end – messy on the student’s end. A clean problem doesn’t involve glue, tape, or an hour to slice paper. Messy on the students’ end means they find themselves rapt in a scenario that is taking them to multiple engaging directions at once. Eventually, the problem smooths out toward a single productive path for the group (cleaned up for the teacher), but not necessarily the same path for all groups.
- Low floor and high ceiling. Every student can make a simple contribution; yet the question ultimately challenges all.
- Grappling with the problem reveals key benchmarks and gaps in understanding. I can hear and see evidence of learning or deficiencies as I walk around the room. The evidence directs me toward next instructional steps.
- Connects academic thought processes to those used in the workplace. Students are largely unaware of most of the interesting careers available that pay a living wage. Many in the workforce never make the connection between their thought processes and those that should be developed in high school. Analytical thought processes are the gateway to the vast majority of emerging careers. John Lipp, STEM coordinator for John Tyler Community College, put together a nice summary of the stats here. Most analytical thought processes can be tied to high school mathematical analysis. That bridge of understanding can help students to establish goals that make academics worth pursuing.
My perfect question this morning evolved from “The Joke” from http://mathforum.org/pows/
Do not forward email that is unrelated to our mission.
Okay, I know, that is not a question. As Gray (2016) points out, students will have no problem coming up with questions. Students will respond with emotion like:
Once their hormones stabilize, they will start trying to justify why they think that is a stupid rule. If we have taught them well, they will start thinking in terms of exponential growth and figure out some better rules with respect to chain-email. If they are not able to think about exponential growth, that reveals a deficiency that needs to be addressed. Students can then construct arguments for less restrictive rules (formulas) regarding forwarding email. Those rules (formulas) can be translated into mathematical symbols. A discussion may ensue as to the practicality of their formulas.
- Could the formulas be encoded such that the server would identify email that contradicts policy? (systems analysis, systems architecture, systems admin)
- How can the formulas be communicated to the users and those who determine corporate policy (infographics, animations, web news produced by technical artists, writers, communications specialists who can deal with math symbols without freaking out)
- Could such email affect productivity? (statistics within human resources and productivity analysis)
- How could this problem turn out to be productive within marketing strategies?
Most of the triggers I use for productive, engaging questions have been inspired by following reflective teacher-practitioners on Twitter. However, I think it would be most efficient if our administrators would bring in leaders from corporations supporting 21st Century Partnership (Partnership, 2015) who can enlighten us with their most intriguing questions. What amazing professional development would ensue as we worked together to connect industrial thought processes with those we are using with our students! Administrators, we need help coming up with those perfect questions; and you are in the perfect position to usher in that support.
Gray, Kristen (2016). Help kids understand math problems: take away the numbers and the question. The Teaching Channel, retrieved from https://www.teachingchannel.org/blog/2016/04/07/math-word-problems/?utm_source=newsletter20160409/
Lipp, John (n.d.). Retrieved from https://www.jtcc.edu/downloads/business/peer2014/Math-Science-Gateways-to-STEM-Degrees-Careers.pptx
Partnership for 21st Century Skills (2015). Retrieved March 4, 2015, from http://www.p21.org/our-work/p21-framework