On-Your-Feet Guide: Modifying Mathematical Tasks: Eight Strategies to Engage Students in Thinking and Reasoning (On-Your-Feet-Guides)

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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

Margaret (Peg) Smith is a Professor Emerita at University of Pittsburgh. Over the past three decades she has been developing research-based materials for use in the professional development of mathematics teachers. She has coauthored several books including Five Practices for Orchestrating Productive Discussions (with Mary Kay Stein), the middle and high school versions of the Taking Action series (with Melissa Boston, Fredrick Dillon, Stephen Miller, and Lynn Raith), and The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussion in Your Classroom series (with Victoria Bill, Miriam Gameron Sherin, and Michael Steele). In 2006 she received the Chancellor’s Distinguished Teaching Award given annually to honor outstanding faculty at the University of Pittsburgh. In 2009 she received the award for Excellence in Teaching in Mathematics Teacher Education from AMTE. In April 2019 she received the Lifetime Achievement Award from NCTM.

Victoria Bill is a former elementary and middle school mathematics teacher. She is currently a Fellow and lead of the mathematics team with the Institute for Learning at the Learning Research and Development Center, University of Pittsburgh.  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. Bill was the Co-Pi on a collaborative research project between researchers from the LRDC, the IFL, and the Tennessee Department of Education in which an instructional Mathematics Coaching Model was developed. Bill regularly speaks at the National Council of Teachers of Mathematics, National Supervisors of Mathematics, and National Council of Teachers of Mathematics Research Conferences. She is co-author of the NCTM best seller Taking Action: Implementing Effective Mathematics Teaching Practices Grades k-5.  

Michael D. Steele is a Professor and Chairperson of the Department of Educational Studies in Teachers College at Ball State University. He is a Past President of the Association of Mathematics Teacher Educators, current director-at-large of the National Council of Teachers of Mathematics, and editor of the journal Mathematics Teacher Educator. A former middle and high school mathematics and science teacher, Dr. Steele has worked with preservice secondary mathematics teachers, practicing teachers, administrators, and doctoral students across the country. He has published several books and research articles focused on supporting mathematics teachers in enacting research-based effective mathematics teaching practices.

Dr. Steele’s work focuses on supporting secondary math teachers in developing mathematical knowledge for teaching, integrating content and pedagogy, through teacher preparation and professional development. He is the co-author of NCTM’s Taking Action: Implementing Effective Mathematics Teaching Practice in Grades 6-8. He is a co-author of several research-based professional development volumes, including The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your High School Classroom,

Mathematics Discourse in Secondary Classrooms, and We Reason and Prove for All Mathematics. He directed the NSF-funded Milwaukee Mathematics Teacher Partnership, an initiative focused on microcredential-based teacher professional development and leadership. His research focuses on teacher learning through case-based professional development, and he has been an investigator on several National Science Foundation-funded projects focused on teacher learning and development. He also studies the influence of curriculum and policy in high school mathematics, with a focus on Algebra I policy and practice, and is the author of A Quiet Revolution: One District’s Story of Radical Curricular Change in Mathematics, a resource focused on reforming high school mathematics teaching and learning. He works regularly with districts across the country to design and deploy teacher professional development to strengthen effective secondary teaching practice.

Dr. Steele was awarded the inaugural Best Reviewer award for Mathematics Teacher Educator and was author of the 2016 Best Article in Journal of Research in Leadership Education. He is an active member of and regular presenter for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematics, and the Association of Mathematics Teacher Educators. He reviews regularly for major mathematics education and teacher education journals.