In my PreCalculus class this semester, I was excited to create opportunities for my kids to be mathematicians and pose their own questions, making their own conjectures and discoveries, and also be creatively frustrated. I speak about my problem of practice in greater depth in my first blog post here.
I wanted to provide opportunities for my kids to be mathematicians about their end of term PBAT (project based assessment task) for our course with focused on earthquake magnitudes and logarithmic scales and functions. During previous semesters, all students answered the same question: Why do we use logarithmic scales to measure magnitudes of earthquakes? This semester, with immense support from my amazing department, I very explicitly embedded opportunities for students to ask, tweak, refine, even toss out questions throughout the course of the project. My solution included a project journal booklet template created by my colleague Daniel (thanks, Daniel!) that students used to record the evolution (this is the key!) of the topic question of their project as they worked on completing their project
“First I asked how the year of the earthquake impacted the number of fatalities for that earthquake. Then I learned from my collected data set that it didn’t really. So then I wondered how the richter magnitude impacted the number of deaths.”
The above reflection was written by BB, one of my PreCalc students with a learning disability. With the help of some sentence starters, she was able to clearly communicate her curiosity through the questions she was asking based on her own observations from her data set.
Students used this tool to assist them in writing their essays for the project. Linked is student JM’s PBAT essay*, in which she beautifully communicates the evolution of how her wonderings and noticings in conjunction with her data helped her develop one topic question to focus on.
*If interested, here’s a link to their essay outline template and their project packet.
Some things that I believe helped the successes above include:
1. Having a separate place for students to track the evolution of their question(s) helped organize their thoughts as well as physically make explicit the process of writing and revising their question.
2. Students felt it was a powerful experience to be able to vet the questions posed by their classmates as a way of helping others understand and process together what a “good” question sounds like.
3. At the suggestion of my department members, I included icons in the project packet to signal to students when there was an opportunity to record their responses (particularly leaning in to any emotional responses they were having) to new data, as well as an icon that reminded them to go back to their topic question which is a draft of a curious thought that may change over the course of the project. The bottom half of page 5 of their project packet is pictured below.
Some challenging questions/situations that came up include:
– What happens when students pose questions that are too far removed from the main content ideas?
– Or the opposite where students “can’t think of anything to ask”.
– How can I support all students without taking away any of the creative freedom of being a mathematician?
Something I want to try next semester is making small adjustments in my teaching around allowing students to ask their own questions as we go, not only during more higher stakes project time. If you’ve got ideas, feedback, suggestions, love – comment away!
Having students ask their own questions is such an important part of teaching a rigorous and engaging class. I love that you want your students to be “creatively frustrated”. It’s such a succinct way to express what so many of us are searching for in our projects, seminars and daily classwork. I believe by helping your students to see themselves as mathematicians, you are facilitating the work of helping them form meaningful questions. I really believe that if I’d been treated more like a mathematician in high school and my questions, interests and views had been more valued, I might have a completely different feeling about math today. Thank you for sharing this!
I know we’ve talked about this a bunch in person, but reading your beautiful blog post has my gears turning about physical demonstrations of questions we have as a class (a starting question, if you will), and revising that question over and over as we have more information. So at the least, students see ONE or TWO consistent examples of questions that have edits physically made to them over time…
Now if only I knew where to house these questions….
Ahhh so inclusive! I love the brain and heart icons. It’s amazing to me how much energy and attention goes into formatting scaffolds to help students develop and track their ideas. You had a goal and you created every step in the ladder to help students reach that goal. Very cool!
I honestly get so excited when my students ask real, meaningful questions… their curiosity has been sparked, their brains are processing and sorting, they have a desire to know more… and this is when authentic learning takes place. It’s so important to model strong questions and provide our students with opportunities to practice asking questions…so I love that you’re doing this! I think it’s particularly cool to see both the thought and revision process of your student, BB. I bet that she learned a lot more about the Richter Scale through her self-lead trial and error/question revision process than she would have had you just provided students with a question for the project. And of course I really love the visuals you included in the project packet!!! (I <3 visuals). I wonder if, for the students who "can't think of anything to ask", you could incorporate some additional visuals to facilitate brainstorming. For this particular project, maybe pictures of the damage from various earthquakes, maps showing areas where earthquakes commonly occur, charts with earthquake statistics?