In the face of such different levels, I longed to find a way to differentiate the class. However, I did not want to fragment the class into different groups, for I value the community of the class. Furthermore, as a new teacher, I lacked the resources or experience to plan multiple lessons for different students.

 

In the face of this challenge, I turned to Low-Floor/High-Ceiling problems. Low-Floor/High-Ceiling problems—or LF/HC problems, as I will abbreviate onward—build in differentiation to discrete tasks. If properly designed, they allow all students to enter the Zone of Proximal Development. The challenge is neither too nuanced for lower students to find a foothold, nor is it too simple for a higher student to feel bored. Math blogger Dan Meyer humorously calls these “Roach Motel” problems, for all students can check in but struggle to check out.

 

While theoretically perfect for my class, I was curious to see how my students would take to LF/HC problems. Specifically, I wanted to know if my students would find LF/HC problems more engaging. Would they work harder and longer on LF/HC problems? Would students ultimately gain a deeper understanding of the topics tested by LF/HC problems? If so, I wanted to learn how to integrate more LF/HC into my curriculum. How could I create original LF/HC problems? How could I modify existing problems to become LF/HC? This Padlet documents an examination of these questions, synthesizing personal research and design with existing scholarship on the subject.

 

From this conclusion, I began to work on different approaches to designing original LF/HS problems and modifying existing problems to become LF/HS. While I continue to work on this process, and will only improve as I practice, I have laid out a framework for this process, which is linked below. I hope to engage with this template as I create more LF/HS problems in the school years to come.