Tuesday, April 10, 2018

Circles + Squares

I've been experimenting with Question Formulation Technique (QFT) in my math classes this year. I used QFT for the fourth time today. And I had a big ah-ha after the lesson.

The purpose of QFT is to shift the intellectual authority from the teacher to the students (or maybe from the teacher to the students AND the teacher...since I'm still part of it).  The result is student-centered, student driven lessons that appeals to students' curiosity while also meeting content standards. Easy, right?? Not really.

My first attempt was ok. I used QFT as a launch for a Project Based Learning Statistics unit.  As I look back, I think the QFT was great. My follow through was lacking (more on that in a minute).

My second attempt exceeded my expectations. But that was a perfect storm of a lesson. I also spent way too much time planning that lesson. And my follow through was on point.

My third attempt was ok.  We used QFT to launch the exponentials usit. Actually, after some reflection and a quick conversation with the amazing people from The Right Question Institute, I think the third attempt was decent. But my follow through was non-existent. And I think the achilles heel of QFT is the follow through.

I am not an expert in QFT, but my process for QFT tends to look like: 
  1. Have students participate in some event. Watch a video clip, or a lab demonstration, or read a provocative quote, see a startling statistic, etc. But the event needs to evoke the curiosity of students. 
  2. Give students the "QFT Rules". Again...I'm not an expert. Here are my rules. Mostly stolen ideas from others. 
  3. Let students ask as many questions as they can. (you def need to encourage them to keep questioning. 
  4. Go through some filtering. Have groups change close-ended questions to open-ended and have groups select their top 3 questions.
  5. Have a class share out. The goal is to make sure each groups top questions are represented. 
  6. Then...do something with the questions. This is the follow through. And, in my experience, the follow through is the tough part. 
As a participation structure, QFT is genius. One reason I like QFT is that it gives students an opportunity to show different ways to be smart in my class. Since I teach math, students with strong procedural fluency are sometimes assigned status by peers and labeled as smart. QFT helps address that. 

QFT also pushes students to be curious. Sometimes learning can feel prescriptive or rigid. While the structure of QFT is somewhat prescriptive, the process creates a safe, encouraging space that supports students in the process of taking intellectual risks and asking really good questions. 

Today, I used QFT to introduce the quadratics unit. I showed students a bingo chip and showed them a 23x23 inch square I had measured on the board. I asked them how many bingo chips fit into the big square. (This is borrowed from the Penny Circle task...the algebra 2 teachers at my school build most of the quadratics unit around the Penny Circle task and they kindly asked that I modify so that it isn't immediately recognizable to students. Hence, Circles + Squares Task.) The task is linked below...nothing special though. 

Then I gave each group a few squares and a lot of bingo chips. I had squares of side length 1, 2, 3, 4, 5, 6, 7 and 8 inches. Each group got 2 or 3 squares. Students collected the data. We put the data into a class data table (averaging the number of bingo chips for a given side length as needed). I then asked students to tell me what type of function would best model the data in the table. I gave them like 3 minutes to discuss this. The goal WAS NOT that they have a definitive answer. The goal was to get them to explore the data in the table or graph (some groups also graphed the data). 

Then, I stopped them and we started the QFT process. They had really good questions. I teach two classes of algebra 1. These are the QFT results from both classes. 

The QFT was great. But the follow through...sigh. The follow through. Here is what I realized today:

QFT is awesome, but QFT isn't really the goal. The goal is to make my classroom student-centered and to make learning student-driven. QFT doesn't do that. What I DO with the questions students come up with is where QFT really becomes a tool to make my classroom more student-centered. 

In my first attempt at QFT, the QFT went great. But we never really used the questions to drive the project or the learning. 

In my second attempt at QFT, the questions the students generated BECAME the students' projects. The questions drove the learning and the focus of our work. And that was powerful, student-centered and student driven. 

In my third attempt, the QFT was great, the questions were solid, but I got buried in other work and never really referenced back to their questions as we moved through the unit. 

Thus, the goal with quadratics is to explicitly connect our learning back to the questions generated for the QFT. This is my opening slide for the next lesson (there are two different slides because 2nd and 3rd block had different questions):

2nd block
3rd block

I also plan to revisit these slides at the end of that lesson as a debrief. 

Basically, I took the lesson I had planned, looked through their questions and then found the questions that matched the existing learning objectives (or learning goals...or standards...not sure on the right term).

I think it will be powerful to show them this tomorrow. I also am amazed that they came up with the questions that, more or less, align with the standards I have to teach. 

Each time I do QFT I learn a little more. Which is the motivation to keep doing QFT. 

But, as I am finding, the QFT can be phenomenal, but if I want to effect change in how I teach and how students learn, the crux of the work happens in the follow through. That is, what I do with the questions the students generated is essential to the process. 

My goal now it to keep referencing back to the students questions as we move through the quadratics unit. I'll let you know how it goes! 



  1. Hi Rick~
    Thank you for your post. I am just learning about QFT and thinking of how I can implement it in my 8th grade pre-Algebra class. I am having a difficult time coming up with the "Question Focus". If I am reading your post correctly...it sounds like you have the students do some exploring or an activity and then have them follow up with QFT. Am I correct? I think this might be a better approach for me instead of trying to develop a "Question Focus". If you have any advice or thoughts about the best way to approach QFT as math teacher. I would really appreciate your advice. (I did a practice round today on something "non-math". We had an assembly this afternoon. College athletes came as part of our health day fair. The 'Question Focus" I gave was "Being a Division 1 College athlete". I used the QFT template and was really impressed with my students questions. (at least most of them :-). I think this can be very powerful as I prepare these students for high school. We (teachers, parents) encourage students to "ask questions", but I am realizing so many of my students don't even know how or where to begin to ask questions. Sorry for the long response.
    Thank you for any advice you can give me!

  2. Hi Dianne,

    Thanks for the comment!

    You are correct: I have found that the best question focus is a hands on task (could be a digital exploration on Desmos.com). As I experiment and learn more, I think a modeling task is a great question focus. This is what I did with the Circles + Squares task. I think this works well with high school algebra for most units I teach. For middle school, I could see starting with a pattern task and then doing QFT. Or looking at number patterns, asking students to make a prediction, and then QFT.

    One thing I've learned is that students don't need to answer the question I ask to stimulate their thinking during the question focus. For example, we never answered how many chips fit into the big square. So, when I designing a question focus and QFT, I might ask students a question that I don't fully expect them to answer. The goal of my question is to focus, direct and stimulate their thinking.

    My advice: be patient with yourself and with the students! This has been a big shift for me and for the students...so each time I try QFT I learn something new about what I do and what I want them to do. Also, I really think the power of this is in the follow through. So as you design a question focus and QFT keep in mind how to design something that is sustainable for you throughout the unit. It is really cool for the students to see their questions become part of the unit and the learning!

    Let me know how it goes for you! There is so much for me to learn about QFT in math...I love talking with other teachers about their experiences.




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