Douglas Fisher

Nancy Frey

John Hattie

Sara Delano Moore

William Mellman

Linda M. Gojak

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.

What Works Best to Optimize Student Learning

Visible Learning for Mathematics, Grades K-12

Linda M Gojak

John A. Hattie

Douglas B. Fisher

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 Math, 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.

Kimberly Morrow-Leong

Help students reveal the math behind the words Solving problems is about more than computation. Students must understand the mathematics of a situation to know what computation will lead to an appropriate solution. Mathematize It! shares a reasoning approach that helps students dig into the problem to uncover the underlying mathematics, deeply consider the problem’s context, and employ strong operation sense to solve it. This user-friendly resource for Grades K-2 · Offers a systematic mathematizing process for solving word problems · Provides specific examples of questions and explorations for addition and subtraction of whole numbers as well as early thinking for multiplication and division · Demonstrates the use of concrete manipulatives to model problems with dozens of short videos

Going Beyond Key Words to Make Sense of Word Problems, Grades K-2

Mathematize It! [Grades K-2]

Kimberly Rimbey

Put math manipulatives to work in your classroom and make teaching and learning math both meaningful and productive. Mastering Math Manipulatives includes everything you need to integrate math manipulatives—both concrete and virtual—into math learning. Each chapter of this richly illustrated, easy-to-use guide focuses on a different powerful tool, such as two-color counters, linking cubes, base ten blocks, fraction manipulatives, pattern blocks, tangrams, geometric solids, and others, and includes a set of activities that demonstrate the many ways teachers can leverage manipulatives to model and reinforce math concepts for all learners. It features: • Classroom strategies for introducing math manipulatives, including commercial, virtual, and hand-made manipulatives, into formal math instruction. • Step-by-step instructions for 75 activities that work with any curriculum, including four-color photos, printable work mats, and demonstration videos. • Handy charts that sort activities by manipulative type, math topic, domains aligned with standards, and grade-level appropriateness.

Hands-On and Virtual Activities for Building and Connecting Mathematical Ideas

Mastering Math Manipulatives, Grades K-3

Sara Delano Moore

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