(2012–2015), as series editor for NCTM’s 2017–2018 Annual Perspectives in Mathematics Education, on NCTM’s Principles to Actions Toolkit development team, and on research advisory boards. She was also awarded the Association of Teacher Educators’ 2008 Distinguished Dissertation Award.
Dr. Boston is lead author of NCTM’s Taking Action: Implementing Effective Mathematics Teaching Practices in Grades 9–12. She has published her work in scholarly journals (Elementary School Journal, Journal of Mathematics Teacher Education, Journal for Research in Mathematics Education, International Journal of Mathematics Teacher Education, Journal of Mathematics Education Leadership, and Urban Education) and book chapters. Dr. Boston received a bachelor of science degree in mathematics and secondary mathematics education from Grove City College and a master of arts degree in mathematics and a doctorate in mathematics education from the University of Pittsburgh. To learn more about Dr. Boston’s work, follow @MBostonMath on Twitter.
Amber G. Candela, PhD, is an assistant professor of mathematics education at the University of Missouri–St. Louis (UMSL). She currently teaches mathematics methods classes for prospective elementary, middle, and high school teachers in the teacher education program at UMSL. Previously, she taught middle school mathematics in both suburban and urban settings in Charlotte, North Carolina, and East Harlem, New York. Dr. Candela is focused on supporting teachers’ implementation of cognitively challenging tasks so each and every student has access to high-quality mathematics. In 2016 she was honored with the Gitner Excellence in Teaching Award at UMSL, and in 2018 she was honored with the Missouri Council of Teachers of Mathematics (MCTM) Outstanding Post-Secondary Educator Award.
Dr. Candela is an active member of the National Council of Teachers of Mathematics (NCTM) and TODOS Mathematics for All organizations. She has worked in schools providing professional development on selecting and implementing tasks and is dedicated to supporting each and every learner in the classroom and focusing on how tasks are implemented in inclusive settings.
Dr. Candela received a bachelor’s degree in mathematics and education from St. Bonaventure University, a master’s degree in mathematics education from Appalachian State University, and a doctorate in mathematics education from the University of Georgia. To learn more about Dr. Candela’s work, follow @AmCan36 on Twitter.
Juli K. Dixon, PhD, is a professor of mathematics education at the University of Central Florida (UCF) in Orlando. Prior to joining the faculty at UCF, Dr. Dixon was a secondary mathematics educator at the University of Nevada, Las Vegas and a public school mathematics teacher in urban school settings at the elementary, middle, and secondary levels. Dr. Dixon is focused on improving teachers’ mathematics knowledge for teaching so that they support their students to communicate and justify mathematical ideas.
She is a prolific writer who has authored and coauthored books, textbooks, chapters, and articles. She is also a lead author on the Making Sense of Mathematics for Teaching professional development book and video series as well as for the K–12 school mathematics textbooks GO Math!, AGA, Integrated Math, and Into Math with Houghton Mifflin Harcourt. Especially important to Dr. Dixon is the need to teach each and every student. She often shares her personal story of supporting her own children with special needs to learn mathematics in an inclusive setting. Dr. Dixon published A Stroke of Luck: A Girl’s Second Chance at Life with her daughter, Jessica Dixon. A sought-after speaker, Dr. Dixon has delivered keynotes and other presentations throughout North America.
Dr. Dixon received a bachelor’s degree in mathematics and education from the State University of New York at Potsdam, a master’s degree in mathematics education from Syracuse University, and a doctorate in curriculum and instruction with an emphasis in mathematics education from the University of Florida. Dr. Dixon is a leader in DNA Mathematics.
To learn more about Dr. Dixon’s work supporting children with special needs, visit www.astrokeofluck.net, or to learn more about Dr. Dixon’s work supporting teachers, follow @thestrokeofluck on Twitter.
To book Melissa D. Boston, Amber G. Candela, or Juli K. Dixon for professional development, contact [email protected].
Introduction
Effective teaching practice can be learned.
—National Research Council
Improving instructional quality is an important aspect of teaching mathematics effectively, as instructional quality in mathematics has been associated with student achievement (Darling-Hammond, 2000). Our vision of quality mathematics instruction aligns with the effective mathematics teaching practices described by the National Council of Teachers of Mathematics (NCTM, 2014) in Principles to Actions: Ensuring Mathematical Success for All. According to NCTM (2014), “Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies” (p. 17). In this book, we provide you with a process and toolkit for improving instructional quality that are specific to mathematics teaching and learning, that identify aspects of instruction that impact students’ learning, and that provide data to influence the planning and teaching of future lessons.
The Importance of Making Sense of Mathematics for Teaching
Previous books in the Making Sense of Mathematics for Teaching series have focused on developing a deep understanding of important mathematical content at different grade bands. They provide opportunities for mathematics teachers in grades K–2, 3–5, 6–8, and high school to engage deeply with the mathematics they teach. A central premise in each of these books is that you learn about the mathematics you teach by doing the mathematics you teach (Nolan, Dixon, Roy, & Andreasen, 2016).
In this book, we focus on the opportunities for thinking and reasoning embedded in mathematical tasks at all grade levels and present an instructional assessment framework to determine whether those opportunities are actualized during instruction. Just as the previous books in the Making Sense of Mathematics for Teaching series promote mathematical learning by asking readers to do mathematics, this book engages teachers in reflecting on mathematics instruction through the activities within each chapter. Throughout the book, we ask readers to solve mathematical tasks. In each of those instances, readers should take time to solve the tasks and discuss their solution strategies within their collaborative teams. This will provide greater insight when they later analyze the task or the lesson featuring the task.
About This Book
Making Sense of Mathematics for Teaching to Inform Instructional Quality provides teachers and teacher leaders with the opportunity to reflect on the quality of mathematics instruction at any grade level. As with previous books in the Making Sense of Mathematics for Teaching series, this book highlights the use of tasks, questions, and evidence (referred to as the TQE process; see figure Part 1 engages teachers in considering the quality of tasks and task implementation (connecting to the T in the TQE process). Part 2 supports teachers as they explore the quality and impact of their questions and other discourse actions (the Q in the TQE process). Part 3 guides educators to examine the evidence of their
