Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning

Rich tasks, collaborative work, number talks, problem based learning, direct instruction…with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one―it’s about when―and show you how to design high impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school.

That’s a high bar, but with the amazing K 12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the 
effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. 

Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: 

Surface learning phase: When―through carefully constructed experiences―students explore new concepts and make connections to procedural skills and vocabulary that give shape to developing conceptual understandings.

Deep learning phase: When―through the solving of rich high cognitive tasks and rigorous discussion―students make connections among conceptual ideas, form mathematical generalizations, and apply and practice procedural skills with fluency.

Transfer phase: When students can independently think through more complex mathematics, and can plan, investigate, and elaborate as they apply what they know to new mathematical situations. 

To equip students for higher level mathematics learning, we have to be clear about where students are, where they need to go, and what it looks like when they get there. Visible Learning for Math brings about powerful, precision teaching for K 12 through intentionally designed guided, collaborative, and independent learning.

John Hattie, PhD, is an award-winning education researcher and best-selling author with nearly thirty years of experience examining what works best in student learning and achievement. His research, better known as Visible Learning, is a culmination of nearly thirty years synthesizing more than 2,100 meta-analyses comprising more than one hundred thousand studies involving over 300 million students around the world. He has presented and keynoted in over three hundred international conferences and has received numerous recognitions for his contributions to education. His notable publications include Visible Learning, Visible Learning for Teachers, Visible Learning and the Science of How We Learn, Visible Learning for Mathematics, Grades K-12, and 10 Mindframes for Visible Learning.

Douglas Fisher is a professor and chair of educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. Previously, Fisher was an early intervention teacher and elementary school educator. In 2022, he was inducted into the Reading Hall of Fame by the Literacy Research Association. He has published numerous articles on reading and literacy, leadership, and curriculum design, as well as books such as Your Introduction to PLC+, Welcome to Teaching, How Feedback Works, Teaching Reading, and RIGOR Unveiled. Fisher loves being an educator and hopes to share that passion with others.

Nancy Frey is a professor of educational leadership at San Diego State University and a teacher leader at Health Sciences High and Middle College. Her published titles include The Courage to Learn, The Art and Science of Coaching, How Scaffolding Works, and The Illustrated Guide to Visible Learning. Frey is a credentialed special educator, reading specialist, and administrator in California and learns from teachers and students every day.

Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, Linda M. Gojak directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics.

Sara Delano Moore is an independent mathematics education consultant at SDM Learning.  A fourth-generation educator, her work focuses on helping teachers and students understand mathematics as a coherent and connected discipline through the power of deep understanding and multiple representations for learning. Sara has worked as a classroom teacher of mathematics and science in the elementary and middle grades, a mathematics teacher educator, Director of the Center for Middle School Academic Achievement for the Commonwealth of Kentucky, and Director of Mathematics & Science at ETA hand2mind. Her journal articles appear in Mathematics Teaching in the Middle School, Teaching Children Mathematics, Science & Children, and Science Scope.