Teaching with Rich Math Tasks

SFUSD units are designed around four tasks. These tasks offer all students opportunities to engage in meaningful and rigorous mathematics that allow for the development of the Standards for Mathematical Practice. They give information about how students are learning the core concepts and skills of the unit.

All tasks are used for formative assessment—gathering information about what students know and are able to do—but they are not tests. The Entry, Apprentice, and Expert Tasks allow for student collaboration and individual accountability without being used to grade students individually. The Milestone Task can be used as an assessment for grading students individually (see section on using rubrics for letter grades in this Math Teaching Toolkit).

Why are group tasks important?

Tasks support productive struggle.
Tasks 

• are relevant and engaging
• have multiple entry points that allow for initial success
• have high cognitive demand 
• allow for divergent ways of thinking
• are not scaffolded in ways that reduce cognitive demand
• are not timed; students should not be rushed 

Tasks build conceptual understanding.
Tasks 

• allow students to make connections to prior learning
• allow students to answer with multiple representations
• embed multiple Standards for Mathematical Practice
• can provide a preview into the next level of learning

Tasks allow students to show what they know and are able to do.
Tasks

• cover multiple standards that are central to the unit
• contain a balance of skills, concepts, and problem solving
• generate student work that a teacher can analyze to measure understanding and to inform instruction in the next lesson series    

Group tasks provide a perfect environment for students to implement the Mathematical Practices outlined in the CCSS-M.  Group work and collaborative learning are effective in academically and linguistically heterogeneous classrooms, and the evidence for the academic and social benefits of these instructional strategies is substantial.

Group-worthy tasks require students to share their experiences and justify their beliefs and opinions. In such activities, students analyze, synthesize, and evaluate; they discuss cause and effect, explore controversial issues, build consensus, and draw conclusions. Group-worthy learning assignments rely on using materials that incorporate multiple representations of the academic content, thereby supporting various ways of learning, the development of multiple literacies, and deeper and more sophisticated understandings. They create and support interdependence among members of a group, which is the essence of collaboration.

Group-worthy tasks have academic and social benefits; they foster students' critical thinking skills and contribute to friendlier classrooms. 

• Problem-Centered Mathematics Teaching, by Sarah Lubienski from Mathematics Teaching in the Middle School. 
• Read more on Misconceptions about Multiple Methods in a blog post by Bill McCallum, one of the authors of the Common Core State Standards for Mathematics.