Learning mathematics is the central goal of mathematics education, yet it is the least frequently addressed of the National Council of Teachers of Mathematics' (NCTM's) Principles and Standards. With an increasing population of English language learners and the inclusion of students with learning disabilities into the regular mathematics classroom, how can all the differentiated needs be met in one classroom? What is the balance between focusing on developing concepts and memorization of certain facts and rules? NCTM's sixty-ninth yearbook furthers the discourse on learning with five main areas: how students learn, students' learning in school contexts, measuring and interpreting students' learning, teachers' learning of mathematics, and reflections on mathematics teaching and learning. Twenty-two chapters are presented in five parts. Part 1, Perspectives on How Students Learn is introduced by W. Gary Martin and includes: (1) Changes through the Years: Connections between Psychological Learning Theories and the School Mathematics Curriculum (Diana V. Lambdin and Crystal Walcott); (2) Teaching the Meaning of the Equal Sign to Children with Learning Disabilities: Moving from Concrete to Abstractions (Ruth Beatty and Joan Moss); (3) Is "Just Good Teaching" Enough to Support the Learning of English Language Learners? Insights from Sociocultural Learning Theory (Jennifer M. Bay-Williams and Socorro Herrera); and (4) Learning with Understanding: Principles and Processes in the Construction of Meaning for Geometric Ideas (Michael T. Battista). Part 2, Issues Related to Students' Learning in School Contexts, is introduced by W. Gary Martin, and includes: (5) The Learning Environment: Its Influence on What Is Learned (Gladis Kersaint); (6) Examining School Mathematics through the Lenses of Learning "and" Equity (Celia Rousseau Anderson); (7) Academically Productive Talk: Supporting Students' Learning in Mathematics (Suzanne H. Chapin and Catherine O'Connor); (8) Engaging Students in Collaborative Discussions: Developing Teachers' Expertise (Jeffrey Choppin); (9) Putting It All into Context: Students' and Teachers' Learning in One Mathematics Classroom (Jon D. Davis); (10) Shared Reflection in an Online Environment: Exposing and Promoting Students' Understanding (Debra M. Dosemagen); and (11) Amplifying Students' Learning in Mathematics Using Curriculum-Embedded, Java-Based Software (Eric Hart, Christian R. Hirsch, and Sabrina A. Keller). Part 3, Measuring and Interpreting Students' Learning, is introduced by Marilyn E. Strutchens, and includes: (12) When Getting the Right Answer Is Not Always Enough: Connecting How Students Order Fractions and Estimate Sums and Differences (Kathleen Cramer and Terry Wyberg); (13) Learning about Fractions as Points on a Number Line (Geoffrey B. Saxe, Meghan M. Shaughnessy, Ann Shannon, Jennifer Garcia de Osuna, Ryan Chinn, and Maryl Gearhart); and (14) Beyond Puzzles: Young Children's Shape Composition Abilities (David C. Wilson). Part 4, Teachers' Learning of Mathematics, is introduced by Marilyn E. Strutchens, and includes: (15) Mathematics Teachers' Beliefs about Mathematics and Links to Students' Learning (Denise S. Mewborn and Dionne I. Cross); (16) Creating an Equitable Learning Environment for Teachers of Grades K-8 Mathematics (Valerie A. DeBellis and Joseph G. Rosenstein); (17) Prospective Teachers' Use of Concrete Representations to Construct an Understanding of Addition and Subtraction Algorithms (John F. McAdam); and (18) Making Sense of Decimal Fraction Algorithms Using Base-Ten Blocks (Lillie R. Albert and John F. McAdam). Part 5, Reflections on Mathematics Teaching and Learning, is introduced by Marilyn E. Strutchens, and includes: (19) Affecting Affect: The Reeducation of Preservice Teachers' Beliefs about Mathematics and Mathematics Teaching and Learning (Peter Liljedahl, Katrin Rolka, and Bettina Rosken); (20) Learning from the "Unknown" in Mathematics Teacher Education: One Teacher Educator's Reflections (Eileen Fernandez); (21) Under the Microscope: Looking Closely at One's Own Teaching and Learning (Sue Tinsley Mau); and (22) Learning to Learn Mathematics: Voices of Doctoral Students in Mathematics Education (Dan Chazan, Sarah Sword, Eden Badertscher, Michael Conklin, Christy Graybeal, Paul Hutchison, Anne Marie Marshall, and Toni Smith). [For 68th Yearbook, see ED495233.]