The Math Tutor's Handbook

Steven Leinwand is a principal research analyst at AIR, the American Institutes for Research in Arlington, Virginia, and has more than 40 years of leadership positions in mathematics education. He currently serves as mathematics expert on a wide range of AIR projects that focus on high quality mathematics instruction, turning around underperforming schools, evaluating programs, developing assessments and providing technical assistance for school improvement. Leinwand co-authored "What the United States Can Learn from Singapores World-Class Mathematics System (and what Singapore can learn from the United States." He has spoken and written about effectively implementing the Common Core State Standards in Mathematics, differentiated learning and "What Every School Leader Needs to Know about Making Math Work for All Students." In addition, Leinwand has provided school and district-level support and technical assistance for the General Electric Foundations Ensuring Futures in Education project and the Microsoft Math Partnership. Before joining AIR in 2002, and after teaching high school math in Middletown, Connecticut, for eight years, Leinwand spent 22 years as Mathematics Consultant with the Connecticut Department of Education where he was responsible for the development and oversight of a broad statewide program of activities in K-12 mathematics education. Steve has also served on the NCTM Board of Directors, has been President of the National Council of Supervisors of Mathematics, and chaired the Writing Team for NCTMs Principles to Actions. Steve is an author of several mathematics textbooks and has written numerous articles. His books, Sensible Mathematics: A Guide for School Leaders in the Era of Common Core State Standards and Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement were published in 2012 and 2009 respectively. His most recent Invigorating High School Mathematics: Practical Guidance for Long-Overdue Transformation, co-authored with Eric Milou, was published in 2021. In addition, Leinwand was the awardee of the 2015 National Council of Supervisors of Mathematics Glenn Gilbert/Ross Taylor National Leadership Award for outstanding contributions to mathematics education and has been awarded the 2021 NCTM Lifetime Achievement Award. Caroline Welty is a senior at Cedar Ridge High School in Hillsborough, NC. She has tutored 4th-8th grade students in both math and English since 2020. Caroline attended the North Carolina Governors School in Choral Music in 2024, and she is President of her schools A Cappella Club. She also is a member of her churchs Worship Team, the chair of her middle schools Young Alumni Council, and the President of her schools Public Forum Debate Team. Caroline hopes to go into educational policy and help create a better system for the next generations.

Dear Readers Part 1: Personalizing Tutoring Chapter 1: Building Relationships Chapter 2: Diagnosing Strengths and Needs Chapter 3: Reducing Math Anxiety Part 2: Planning Your Time Chapter 4: Designing Successful Sessions Chapter 5: Launching Effective Sessions Chapter 6: Excelling at Remote and Virtual Tutoring Part 3: Implementing the Art and Science of Effective Tutoring Chapter 7: Setting High Expectations and Building Self-Confidence Chapter 8: Asking the Right Questions Chapter 9: Honoring Mistakes Chapter 10: Incorporating Alternative Approaches and Multiple Representations Part 4: Reflecting on Tutoring Sessions Chapter 11: Providing Feedback Chapter 12: Reflecting to Revise Plans for the Next Session Part 5: Math Tips and Word Problems Chapter 13: Our Best Ideas for Teaching the Biggest Ideas of Mathematics Chapter 14: Strategies for Tackling Word Problems Conclusion Appendix 1: Parents as tutoring partners for their children Appendix 2: National Council of Teachers of Mathematics Eight Mathematics Teaching Practices Appendix 3: Great websites for lesson launch activities, lesson tasks and engaging activities Appendix 4: Questions to launch a tutoring session Appendix 5: Tutoring session planning template