Mathematical Task Framework

Mathematical Task Framework Overview

The Mathematical Task Framework outlines the three phases that tasks pass through. Tasks pass through these stages before they make it to the student in order for the student to learn. First, tasks will appear in the curriculum and/or instructional materials, like in a textbook or on ancillary materials. Next, the tasks are set up by the teacher and announced and presented to the students in class. The way the teacher presents the task to the students has a lot to do with the success of the next and final stage. Finally, the tasks are implemented and completed by the students themselves, meaning how the students actually go about working on the task at hand. Each of these phases that the tasks pass through are crucial to student learning. Each task must go through each phase before the student learns! Although each phase is important, the final phase, the implementation phase (student’s actually work on the task) is very influential on what the students actually learn. Below is an illustration of this framework and the phases each task must pass through (Smith & Stein).

Tasks Changes throughout Phases:

The nature of the task can actually change as the task passes through each of the phases. This can happen due to uncontrollable variables within each of the different phases. The most changes will normally occur between the second phase (task set up and presented to students by the teacher) and the implementation phase (when students work on the task at hand). Changes occur most during this transition because the task at hand can and will often be altered based upon different human factors involved. For example, as the teacher gives instructions for the task, there may be students that ask multiple questions- causing the teacher to give the students a "step-by-step" explanation of how to work on and complete the task. If the teacher does this, it makes the implementation stage almost useless- the students aren't having to think critically and dig deeper in order to complete the task, which in turn takes away the learning.

Levels and Complexity of Tasks:

There are also different levels/complexity of tasks. There are High-level demand tasks and also Low-level demand tasks (these different tasks will be further explained in detail on a different tab on this blog). Sometimes a teacher can set up a task to be a high-level task (require meaningful and complex thinking in order to solve/work on the task), but by the time the task reaches the implementation phase, it has evolved into a low-level demand task. If the teacher limits student thinking or has to guide students through the implementation phase, the high-level demand quality transitions to low-level demand quality. Also, sometimes students can be intimidated by high-level demand tasks because they are used to working on tasks that are low-level and don’t require much meaningful thought. Students can fear these tasks if they aren’t exposed to them and given the opportunity to work on tasks such as these on their own.

Mathematical Task Framework Used as a Tool for Reflection:

Not only is the delivery and implementation of these tasks are important, but also the chance of reflection for the teacher holds much importance. Following this Mathematical Framework can give teachers more to reflect on. Using this framework as a lens for reflecting on instruction and also as a language for discussing instruction with your fellow-teachers/colleagues. Considering tasks go through many stages in order to achieve student learning, it can be easy to “pin-point” where the lesson/task at hand went “wrong” or what you (as the teacher) could do in order to make sure the task stays at a high-level demand task. Using this framework can ensure each task is more organized and easier to fix once flaws are noted. Teachers that use this framework can easily alter instruction/tasks based upon the phases the task pass through. If you set up a task to be high-level but it evolves into a low-level task during the second phase (set up and presented to students by the teacher) because you have to explain how to complete the task step-by-step due to an overflow of student questions- then the teacher can automatically pin-point what went wrong, and how to fix the problem for future instruction.

Endless Benefits

The utilization of this Mathematical Framework can be super beneficial for students and also for the teacher. Not only does this framework clearly describe the phases each task should go through, what the tasks should accomplish, when to transition from each phase, and what each phase entails, but it also gives the teacher a very useful tool for reflecting on their own teaching and instruction- which can improve teaching and student learning!

Reference:

Stein, M. K., & Smith, M. S. (n.d.). Mathematical Task Framework as a Tool for Reflection: From Research to Practice. In Mathematics Teaching in Middle School: (4th ed., Vol. 3, January 1998, pp. 268-275). National Council of Teachers of Mathematics.