Building Thinking Classrooms in Mathematics, Grades K-12

Building Thinking Classrooms in Mathematics, Grades K-12

Author: Peter Liljedahl

Publisher: Corwin Press

Published: 2020-09-28

Total Pages: 454

ISBN-13: 1544374844

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A thinking student is an engaged student Teachers often find it difficult to implement lessons that help students go beyond rote memorization and repetitive calculations. In fact, institutional norms and habits that permeate all classrooms can actually be enabling "non-thinking" student behavior. Sparked by observing teachers struggle to implement rich mathematics tasks to engage students in deep thinking, Peter Liljedahl has translated his 15 years of research into this practical guide on how to move toward a thinking classroom. Building Thinking Classrooms in Mathematics, Grades K–12 helps teachers implement 14 optimal practices for thinking that create an ideal setting for deep mathematics learning to occur. This guide Provides the what, why, and how of each practice and answers teachers’ most frequently asked questions Includes firsthand accounts of how these practices foster thinking through teacher and student interviews and student work samples Offers a plethora of macro moves, micro moves, and rich tasks to get started Organizes the 14 practices into four toolkits that can be implemented in order and built on throughout the year When combined, these unique research-based practices create the optimal conditions for learner-centered, student-owned deep mathematical thinking and learning, and have the power to transform mathematics classrooms like never before.


Visible Learning for Mathematics, Grades K-12

Visible Learning for Mathematics, Grades K-12

Author: John Hattie

Publisher: Corwin Press

Published: 2016-09-15

Total Pages: 209

ISBN-13: 1506362958

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Selected as the Michigan Council of Teachers of Mathematics winter book club book! 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.


Teaching Math at a Distance, Grades K-12

Teaching Math at a Distance, Grades K-12

Author: Theresa Wills

Publisher: Corwin Press

Published: 2020-10-12

Total Pages: 194

ISBN-13: 1071837125

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Make Rich Math Instruction Come to Life Online In an age when distance learning has become part of the "new normal," educators know that rich remote math teaching involves more than direct instruction, online videos, and endless practice problems on virtual worksheets. Using both personal experience and those of teachers in real K-12 online classrooms, distance learning mathematics veteran Theresa Wills translates all we know about research-based, equitable, rigorous face-to-face mathematics instruction into an online venue. This powerful guide equips math teachers to: Build students’ agency, identity, and strong math communities Promote mathematical thinking, collaboration, and discourse Incorporate rich mathematics tasks and assign meaningful homework and practice Facilitate engaging online math instruction using virtual manipulatives and other concrete learning tools Recognize and address equity and inclusion challenges associated with distance learning Assess mathematics learning from a distance With examples across the grades, links to tutorials and templates, and space to reflect and plan, Teaching Math at a Distance offers the support, clarity, and inspiration needed to guide teachers through teaching math remotely without sacrificing deep learning and academic growth.


Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12

Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9-12

Author: Thomas J. Cooney

Publisher:

Published: 2010

Total Pages: 109

ISBN-13: 9780873536233

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Are sequences functions? Why can’t the popular “vertical line test” be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? How much do you know… and how much do you need to know? Helping your high school students develop a robust understanding of functions requires that you understand mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to functions, this book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.


Teaching Mathematics in Grades 6 - 12

Teaching Mathematics in Grades 6 - 12

Author: Randall E. Groth

Publisher: SAGE Publications

Published: 2012-08-10

Total Pages: 513

ISBN-13: 1452256020

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Teaching Mathematics in Grades 6 - 12 by Randall E. Groth explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows preservice mathematics teachers the value of being a "researcher—constantly experimenting with methods for developing students' mathematical thinking—and connecting this research to practices that enhance students' understanding of the material. Ultimately, preservice teachers will gain a deeper understanding of the types of mathematical knowledge students bring to school, and how students' thinking may develop in response to different teaching strategies.


FTCE Mathematics 6-12 (026) 3rd Ed., Book + Online

FTCE Mathematics 6-12 (026) 3rd Ed., Book + Online

Author: Sandra Rush

Publisher: Research & Education Assoc.

Published: 2018-10-20

Total Pages: 482

ISBN-13: 0738612405

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REA's FTCE Mathematics 6-12 (026) Test Prep with Online Tests Gets You Certified and in the Classroom! Updated Third Edition This new third edition of our FTCE Mathematics 6-12 test prep is designed to help you master the competencies tested on this challenging exam. It's perfect for teacher education students and career-changing professionals who are need certification to teach mathematics in Florida's secondary schools. Written by Sandra Rush, M.A., math test expert, author, tutor, and private test-prep coach, our test prep covers all the relevant topics, with expert score-raising strategies developed just for the FTCE Math test. Our targeted review covers the 10 competencies tested: knowledge of algebra, advanced algebra, functions, geometry, coordinate geometry, trigonometry, statistics and probability, calculus, mathematical reasoning, and instruction and assessment. End-of-chapter practice reinforces key concepts and helps you evaluate your overall understanding of the subject. An online diagnostic test pinpoints your strengths and weaknesses so you can focus your study on the topics where you need the most review. Two full-length practice tests (available in the book and online) offer realistic practice and are balanced to include every type of question and skill tested on the actual exam. Our online tests are offered in a timed format with automatic scoring and diagnostic feedback to help you zero in on the topics and types of questions that give you trouble now, so you can succeed on test day. This test prep is a must-have for teacher certification candidates in Florida! REA's book + online prep packages are teacher-recommended and are proven to be the extra support teacher candidates need to pass their challenging certification exams.


Open Middle Math

Open Middle Math

Author: Robert Kaplinsky

Publisher: Taylor & Francis

Published: 2023-10-10

Total Pages: 193

ISBN-13: 1003839886

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This book is an amazing resource for teachers who are struggling to help students develop both procedural fluency and conceptual understanding.. --Dr. Margaret (Peg) Smith, co-author of5 Practices for Orchestrating Productive Mathematical Discussions Robert Kaplinsky, the co-creator of Open Middle math problems, brings hisnew class of tasks designed to stimulate deeper thinking and lively discussion among middle and high school students in Open Middle Math: Problems That Unlock Student Thinking, Grades 6-12. The problems are characterized by a closed beginning,- meaning all students start with the same initial problem, and a closed end,- meaning there is only one correct or optimal answer. The key is that the middle is open- in the sense that there are multiple ways to approach and ultimately solve the problem. These tasks have proven enormously popular with teachers looking to assess and deepen student understanding, build student stamina, and energize their classrooms. Professional Learning Resource for Teachers: Open Middle Math is an indispensable resource for educators interested in teaching student-centered mathematics in middle and high schools consistent with the national and state standards. Sample Problems at Each Grade: The book demonstrates the Open Middle concept with sample problems ranging from dividing fractions at 6th grade to algebra, trigonometry, and calculus. Teaching Tips for Student-Centered Math Classrooms: Kaplinsky shares guidance on choosing problems, designing your own math problems, and teaching for multiple purposes, including formative assessment, identifying misconceptions, procedural fluency, and conceptual understanding. Adaptable and Accessible Math: The tasks can be solved using various strategies at different levels of sophistication, which means all students can access the problems and participate in the conversation. Open Middle Math will help math teachers transform the 6th -12th grade classroom into an environment focused on problem solving, student dialogue, and critical thinking.