Making Sense of Mathematics for Teaching to Inform Instructional Quality. Juli K. Dixon

EPILOGUE

       Next Steps

       APPENDIX A

       The IQA Toolkit

       IQA Potential of the Task Rubric

       IQA Implementation of the Task Rubric

       IQA Teacher’s Questions Rubric

       IQA Teacher’s Linking Rubric

       IQA Teacher’s Press Rubric

       IQA Students’ Linking Rubric

       IQA Students’ Providing Rubric

       IQA Implementation Observation Tool

       Framework for Different Types of Questions

       APPENDIX B

       Suggested Answers for Activity 1.4

       APPENDIX C

       Suggested Answers for Activity 3.2

       APPENDIX D

       Additional Support for Rating Tasks

       Level 1

       Level 2

       Level 3

       Level 4

       APPENDIX E

       List of Figures and Videos

       References and Resources

       Index

       About the Authors

      Melissa D. Boston, EdD, is a professor of mathematics education at Duquesne University. She teaches mathematics methods courses for elementary, middle, and high school teachers, and previously taught similar courses at Slippery Rock University and the University of Pittsburgh. Earlier, she taught middle school and high school mathematics. Dr. Boston provides professional development and conducts research across the United States. She has obtained and directed grants for professional development projects from the Heinz Foundation, National Science Foundation, and Spencer Foundation, and she has served as external evaluator for three Mathematics–Science Partnership grants. In her research, Dr. Boston examines mathematics teaching and learning through classroom observations and collections of students’ work using the Instructional Quality Assessment (IQA) in Mathematics Toolkit, for which she is lead developer.

      Dr. Boston is a member of the National Council of Teachers of Mathematics (NCTM), Association of Mathematics Teacher Educators (AMTE), and Pennsylvania Association of Mathematics Teacher Educators (PAMTE). She has served on NCTM’s Student Explorations in Mathematics committee, as associate editor of Mathematics Teacher Educator (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