The National Council of Teachers of Mathematics (NCTM) has published a “Task Analysis Guide” which provides a rich set of guidelines around qualities of a task. Not all educators will agree on which category each task will fall into, but it is widely agreed that all activities in mathematics classrooms can be categorized into one of these four groups (Stein, Grover, and Henningsen 1996).
- Memorization Tasks
- Procedures Without Connections Tasks
- Procedures With Connections Tasks
- Doing Mathematics Tasks
These 4 categories guide the work of this site. Level 1 and 2 tasks are plentiful and can be found in most math textbooks from elementary school to collegiate texts. They do have a place in a mathematics classroom, to increase the fluency for students after the concepts are learned, however, more classrooms need more Level 3 and Level 4 mathematical tasks and teachers need access to those tasks.Task Analysis Guide
NCTM publishes many articles about the Task Analysis Guide and uses it in many of their papers and research articles including “Principle’s to Action” where they summarize the research. They elude to conclusions that students who engage in high cognitive demand tasks learn more than those rich in procedures alone and that Mathematical Tasks are challenging to implement and are often transformed into less cognitively demanding tasks during instruction.
Notice in the Lower Level demands students are reciting rules or reciting procedures without much attention for why the procedure works or engaging in multiple mathematical practices or habits of mind. The High-Level demand tasks require students to use models to make connections between representations in different ways and engage in thinking that requires justification or explaining a solution, skills students need even without mathematics.
Very quickly, teachers can change the types of conversations between students in class by providing them with the opportunities to engage in tasks that are higher cognitive demand and supporting those tasks well. There are many examples of tasks that can raise the level, there are some strategies to help with that, we hope to share those in future articles on this site.
However, simply providing students with Level 3 and 4 Tasks does not increase the outcomes alone, teachers are critical in switching their role in the classroom as well. Teachers must transition from being the “holders of knowledge” in the classroom to being the facilitator of knowledge.
Without proper execution, High Cognitive Demand Tasks lose their value in the classroom and can turn quickly into something they were not intended. That is why the teacher article section of this site is so critical in providing tools for teachers to implement well and find success along the way. After teachers select tasks, tools for asking great questions and facilitating are needed. Students often want to replace the burden of thinking back onto the teachers (because they know it’s easier for them), but teachers must resist this temptation of taking over the thinking for the student which can easily happen.
Implementing tasks in a classroom is challenging, however, it is very possible. Plus, the more teachers who implement tasks well in their classrooms, the more students understand the expectations for engaging in them and then more learning happens along the way. Task implementation is for everyone, it raises the bar for all involved regardless of background experience. Tasks can also be very frustrating for new learners (both students and teachers alike), but with patience practice and rehearsal, they become more simple to implement and students will learn more.
If you would like to learn more about this work and more, take a look at NCTM’s “Principle’s to Action” book. It is a very agreeable read and support for specific learning outcomes for teachers. Highly recommended.