Jan 30, 2021

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Background to the story:

This is a story about a math teacher who creates an incredibly motivating classroom environment and sees the results show up in standard test scores. The concepts that are applied in this story can be applied to any subject across the grades. The primary storyline is that students become problem designers and the teacher becomes a model pupil. There are two core principles at work. One is to provide students with skills to “learn how to learn” and to tap their creativity and natural curiosity. The second highly related principle is to provide teachers with deeper insights into student thinking.

 

The Story:

A friend of mine, Jessica, loves teaching Geometry in a suburb of Dallas. Like many of us, Jessica began to shoot photos from her daily life when smart phones put a camera in her pocket. Often, her photos had something obvious to do with the subject she taught – triangles, circles, squares. At other times you had to use your imagination to dig for the geometry buried in the photo, such as the center point between various objects. Every photo had at least one geometry challenge if not infinite.

 

A few years ago, Jessica began to share some of these photos with her students to support their thinking about geometry in daily life. Within days of sending out her first photo, responses from her students made her realize that she had unleashed a sense of creativity and excitement within her students to take up their own hunt for the daily application of geometry. The process also had an impact on the social-emotional intelligence of many of her students; especially those who did not see themselves as successful students.

 

What I believe is one of the most important aspects of Jessica’s work is how she evolved from expecting all of her students to solve the same problem in the same way ( similar to taking a test) to empowering students to design their own problems. This is an aspect of one of the most important questions we should be asking during this time of unheralded change in the tools and information sources available to support learning, What is the balance of control between a teacher managing learning and students taking responsibility for managing aspects of their own learning? Further, where are there opportunities for students to inspire one another? In Jessica’s classroom that balance is being recalibrated toward student ownership and more student collaboration with some amazing results.

baseball field

The first photo Jessica shared with her class was a shot of the infield while she was at a Texas Ranger’s baseball game with her husband. She challenged her students to put a mark in the photo of the location of a perfect bunt. Solving that problem requires you to imagine the circumcenter of the triangle formed by the pitcher, third baseman, and catcher.

 

Her challenge required all students to get the same answer and demonstrate the same content knowledge. This kind of challenge fits the traditional model of assessment. Give the same problem to every student and measure if they can solve it. Since she told her students that this assignment was for fun and would not count toward their grade, she was stunned when the majority of her class chose to solve it. That motivated her to send out another photo. But she made a fundamental change in the complexity of the assignment.

cup and math equation

With the second photo of a paper-cup, Jessica added what appears to be a very simple change to replace the word SOLVE with INVOLVE. For example, compare these two challenges: 1. Solve for the volume of this cup. (every student gets the same answer) 2. Involve the volume of this cup in a problem of your own design. (No two students have the same design.)

 

The second “involve” challenge would require students to use their imagination to come up with their own problem rather than look for an answer to a problem presented by the teacher. To Jessica’s surprise, the first student to respond submitted a very complex problem. He added 3 measured ice cubes to the side of the cup photo. He also added dimensions for the vertical and radius of the cup. His problem, “If I add these three ice cubes to the cup with an inch left at the top will the cup overflow?”

 

This problem involved the displacement of ice. That concept is covered much later in the Geometry curriculum. When a teacher is desperately trying to cover the curriculum in order for all students to finish the year and do well on a standardized test, it can be disruptive to jump around the curriculum or add in content from other subjects such as physics. Potentially, multiply this one disruption by 20 – 30 students for every problem associated with a simple photograph and you can see how “covering the curriculum” can spin out of control.

 

However, time management can be managed. First of all, Jessica does not grade the problem designs.  Research quoted by Dan Pink in his video, “The Surprising Truth About What Motivates Us” points out that “When a task gets more complicated, and it requires some conceptual, creative thinking external rewards do not work.” In other words, taking the time to grade can be counterproductive. Furthermore, students do not even have to solve the problems.   The goal is to inspire students to see geometry in their daily lives and to spark discussion about the application of the subject.  

 

This challenge actually leads to Jessica saving time instead of adding something else to a packed curriculum.   She enjoys listening to the class conversation about applying geometry sparked by the student-authored problems.  Jessica has also learned from years of experience with this process, that students often design problems that fit into the curriculum, and she can use some of their examples to design future homework and tests.  

 

Every once in a while, Jessica chooses to model how she would solve a student-designed problem. An argument can be made that teaching students how a teacher learns can be more powerful than sharing what she already knows. If the teacher struggles along the way and makes mistakes – all the better. Watching a teacher cope with failure can be an enormous relief for many students who lack confidence in their own skills.

 

Compare the two different approaches of solve vs. involve. When the class is guided to arrive at the same answer for the “baseball game “solve” photo”, the teacher learns about specific content knowledge. There are two possible drawbacks to this approach. The simple one is that some students might copy from their friends. The more complicated one is that it is possible for a student to memorize how to solve a problem without actually understanding how to apply the knowledge beyond the structured support of the teacher. However, when the directions shift to “paper cup “involve” in photo 2”, the teacher gains an extra insight into the creativity of the student to design a problem.  Now the teacher has a deeper understanding of a student’s comprehension.

 

Jessica comments on students as problem designers, “I really get to know my students better. What is sad, is that so many of my students come to class thinking they are not good at math. All my students seem to have doubts. It kills me because they are good. They just do not know it. I can see the stress of worrying about failure melt away when they start designing and writing their own problems. It also helps them become better test-takers because they learn to understand the structure of different kinds of problems as authors. The other day, one of my students, Andrew, pulled the concept of collinear into an example of a photo of a line of defenders in his soccer match. It was a spot-on application. Now I know he really understands that concept. I will probably use that photo in the future because all of the soccer players in the class said “that makes perfect sense.”” Inevitably, I have students ask me when will they ever use quadrilaterals in their life. I am honest with them and tell them “probably never.” But then I explain that they will be faced with having to struggle with learning something they really will need. I promise them that they will learn how to learn. Many students value that.

 

Jessica adds yet another level of excitement and challenge by sharing her students’ designs in an online community. Many students have this natural curiosity about wanting to know what their classmates are

thinking. (This can also be a source of stress when they do not know how they fit in with classmates.) Since there is no concept of cheating embedded in this process, it makes huge sense to create a shared online space for students. This community sharing can inspire students to push their own thinking as problem designers and potentially to be more creative.

 

By the way, within days of posting her first photo, students in her class were shooting and sharing their own photos of geometry in their daily life. This is another source of learning more about her students’ interests. Jessica encourages discussion between her students to ask each other questions and make comments. This online commentary can also provide students with a classmate’s image or explanation that provides an extra scaffolding for learning.  Sometimes, the extra question of a first-time learner can help another student even more than a teacher’s careful lesson.  

 

Remarkably, some of her students continue to send in photos and design problems after they have left the class.  To her delight yet consternation, in her second year, she had to send a firm message to the previous year’s class to hold back from contributing online to allow the new class to fully participate!  How many teachers have to caution past students to control their enthusiasm for learning to allow participation for the new class?

 

Conclusion:

The messiness of the “Involve” approach of using a photograph (or a quote, graph, short video, painting, video game screenshot, or a tweet quoting Shakespeare) to challenge students to design their own problems can be a powerful approach to deepening students’ thinking and creativity. It can also provide teachers with greater insights into how students think and see the world. Add in continuous sharing in an online community and you have created an ongoing engine for student motivation to think and share thoughts as problem designers. Furthermore, there is a built-in aspect of social-emotional intelligence to help students manage stress and the dread of failure.

 

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