On-Your-Feet Guide: Modifying Mathematical Tasks

  • Title:On-Your-Feet Guide: Modifying Mathematical Tasks
    Eight Strategies to Engage Students in Thinking and Reasoning
  • Author:Margaret (Peg) Smith
    Victoria Bill
    Michael D. Steele
  • Publication Date:March 2020
  • ISBN:9781071817674
  • Publisher:Corwin Press

Students learn what mathematics is and how one does it through their classroom instruction and the mathematical tasks they explore. Student learning is greatest when students have regular opportunities to engage with high-level or cognitively challenging tasks that engage students in thinking, reasoning, and problem solving and are essential to developing students’ conceptual understanding of mathematics.

How do you help students develop the capacity to think, reason, and problem solve, but your curricular resources don’t have many high-level, cognitively demanding tasks? Learn to modify existing tasks for higher-level thinking!

This On-Your-Feet-Guide provides:

  • 8 Key Strategies for modifying low-level procedural tasks and transforming them into high-level thinking tasks.
  • Examples across grades K-12
  • Opportunities to practice modifying tasks and reflect on how the modified versions better meet students’ learning needs
  • Helpful hints to set your tasks up for ultimate success.

On-Your-Feet Guides (OYFGs) provide you with the ultimate “cheat sheet” to implement effective change in your classroom while in the moment of teaching. Designed for accessibility, and providing step-by-step guidance, the OYFGs are written by experts who take research-based practices and make them doable for the busy teacher.

Each On-Your-Feet Guide is laminated, 8.5”x11” tri-fold (6 pages), and 3-hole punched.

Use On-Your-Feet Guides

  • When you know the “what” but need help with the “how”
  • As a quick reference to support a practice you learned in a PD workshop or book
  • To learn how to implement foundational practices
  • When you want to help your students learn a specific strategy, routine, or approach, but aren’t sure how to do it yourself


Author Bio

Margaret (Peg) Smith is a Professor Emerita at University of Pittsburgh. She has developed research-based materials for use in the professional development of mathematics teachers. She has authored or coauthored over 90 books, edited books or monographs, book chapters, and peer-reviewed articles.

Victoria Bill is a former elementary and middle school mathematics teacher. She has been designing and facilitating professional development with administrators, coaches and teachers in urban districts for more than 20 years. She also develops curriculum, intervention materials and performance-based assessments.

Michael D. Steele is a Professor of Mathematics Education and Chair of the Department of Curriculum and Instruction in the School of Education at the University of Wisconsin-Milwaukee. He has published several books and journal articles focused on supporting mathematics teachers in enacting research-based effective mathematics teaching practices.

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