This self-guided professional learning series was design by Grace Kelemanik and Amy Lucenta,  authors of the books Routines for Reasoning: Fostering the Mathematical Practices in All Students and Teaching for Thinking: Fostering Mathematical Teaching Practices Through Reasoning Routines in collaboration with the math team at Port Richmond High School in Staten Island, NY. This series will engage mathematics teachers and instructional coaches in the work of developing students’ capacities to construct viable arguments and critique the reasoning of others. 

Notice & Wonder is a quick routine designed to engage learners with vastly different perspectives and prior knowledge by providing entry points, creating positive mathematics culture, by getting their mathematical juices flowing. In this routine students observe a graph, video, image, expression, or other representation and respond to the questions: What do you notice? What do you wonder?

Debbie Olson, CEO of the Mathematics Education Collaborative (MEC), a non-profit organization co-founded by Ruth Parker, one of the creators of Number Talks, designed this self-guided professional learning series to support teachers through every step of developing and implementing the powerful mathematics routine: Number Talks. This routine provides students with increased opportunities to develop meaningful number sense, the development of positive and empowered mathematical dispositions, and engages them in authentic student-to-student discourse. 

Stronger and Clearer Each Time is designed to provide a structured and interactive opportunity for students to revise and refine both their ideas and their verbal and written output (Zwiers, 2014). This routine provides a purpose for student conversation through the use of a discussion-worthy and iteration-worthy prompt. The main idea is to have students think and write individually about a question, use a structured pairing strategy to have multiple opportunities to refine and clarify their response through conversation, and then finally revise their original written response.

Tell A Story is a routine that invites students to invent and tell a story about an image. This approach provides a window into the world of each student’s community, culture, and lived experiences, while simultaneously expanding access to and engagement with the mathematical ideas within a task or representation.

Which One Doesn’t Belong is an instructional routine designed to support all students in doing mathematics, particularly the art of argumentation and justification. In this routine, students are presented with four figures, numbers, diagrams, graphs or expressions and must decide which does not belong with the rest. This requires them to define the set – creating one category in which three of the items fit, and one does not – and describe relationships among the items. Engaging students in Which One Doesn’t Belong, creates space for students at different levels of understanding to make meaningful contributions in a low stakes environment.