Preparing to design a task
The final project for this course is to design your own task and then to participate in critiquing others' tasks. Optionally, if you have access to a classroom or to a group of students (or adults) to test your task on, you may wish to field test your task.
Elizabeth Cohen (1994) writes about the difference between routine objectives and conceptual objectives. Routine objectives in a mathematics class involve practicing a teacher-taught skill, completing exercises that are similar to an example that's already been covered, or reviewing for a test. By contrast, a conceptual objective involves working with a problem that has multiple perspectives or solution paths and requires higher-order thinking skills and inventing your own solution strategies.
In this course we are going to be focusing on primarily on the second type of task, those with conceptual objectives. Cohen says that these tasks require equal exchange, in which no one person can do the task alone and thus have to rely on exchanging ideas to complete the task.
To begin creating your task, start by thinking both about the standards for mathematical practice as well as the broader content standards that you're hoping students will achieve. Now, look at things in a broader sense; what is the overall topic or conceptual understanding you hope students will achieve.
For some ideas about problems that might form a basis for your task, you might take a look at the nrich collection of problems: http://nrich.maths.org/public/leg.php
Keep in mind that these problems on the nrich site are only a starting point; even if you begin with one of those tasks, you still have to flesh it out below.
Also keep in mind that all work that you submit here on this site is licensed under a creative commons license, meaning that other teachers can borrow from them to create their own tasks and are free to use them without your permission. You still should give credit when borrowing someone else's ideas, however!
Write some of your ideas for tasks below, providing references if you borrow from other sources. Include any standards for mathematical practice and content standards that you are utilizing in your design.