What are low-floor, high-ceiling tasks?
Low-floor, high-ceiling tasks are activities that provide access for all students, but also challenge students with extension to high levels of problem solving. Essentially, every student can get started and every student can get stuck which allows students to work at their own pace within their own level of challenge. The purpose of these activities is especially important within mathematics as it shows students what they can do and does not focus on what they cannot do yet.
First, a low-floor provides every students with a starting point. This helps students feel capable as they are able to understand the activity and then get started easily. On the other hand, if the floor is too high, students cannot get started and then feel frustrated and incapable. This does not mean that low-foor, high-ceiling tasks are easy. Instead, it means that students have the prior knowledge necessary to begin and have strategies in mind for problem solving. Second, a high-ceiling means that students have potential to grow and be challenged. This provides students with plenty of room for exploration and opportunities to get stuck. Students can hit challenges within problem solving where they may not immediately know what to do next. This is also important within mathematics as students are able to not only build resilience, but strengthen their mindset and develop strategies to overcome being stuck. It is inevitable that students will hit points of challenge, but because students have built confidence in their problem solving skills they are able to see challenges as mere obstacles instead of stopping points.
These activities provide differentiation for the majority of learners as the tasks allow students to build confidence in their math abilities and extend to more challenging concepts through exploration. Students feel capable as they begin which lessens anxiety towards thoughts of failure and incompetence. Students are able to practice their math skills while also finding opportunities to strengthen their resilience. Additionally, the whole classroom is able to work on the same task while students work at their own level of engagement and challenge. Therefore, there is no separation among students predetermined skill set, instead students are able to achieve within their own abilities.