Fostering Algebraic Thinking

Fostering Algebraic Thinking
Author: Mark J. Driscoll
Publisher: Heinemann Educational Books
Total Pages: 176
Release: 1999
Genre: Education
ISBN:

Fostering Algebraic Thinking is a timely and welcome resource for middle and high school teachers hoping to ease their students' transition to algebra.

Fostering Geometric Thinking

Fostering Geometric Thinking
Author: Mark Driscoll
Publisher: Heinemann Educational Books
Total Pages: 144
Release: 2017-05-12
Genre: Education
ISBN: 9780325093130

The Trends in International Mathematics and Science Study has shown that American schools have consistently helped students understand algebraic and statistical concepts, leading to high achievement internationally. Now it's time to do the same for geometry. Mark Driscoll, author of the powerful and popular Fostering Algebraic Thinking, takes up the challenge and leads you to new, research-based ways to improve how your students conceptualize and apply geometric ideas. With Fostering Geometric Thinking any math teacher can discover essential, practical ideas for helping students cultivate geometric habits of mind that lead to success in this crucial mathematical subject. The book focuses on rigorous, problem-based teaching that encourages students to deepen their thinking in three key geometric strands: geometric properties geometric transformations measurement of geometric objects. Fostering Geometric Thinking shows you how the interplay of these strands helps students devise multiple solutions and develop a broader sense of geometric principles. It's loaded with helpful resources, including: engaging problems to use in your classroom examples of student solutions to these problems transcripts of classroom interactions online resources featuring in-the-field footage of students working through open-ended problems highlighted in the book. Geometry is a vital component of mathematical understanding, and it's time that it received the same attention that algebra and statistics do. With engaging problems and straightforward suggestions that can help students deepen, recognize, and describe their thinking, Fostering Geometric Thinking is the resource you need to ensure that when it comes to geometry, your students know all the angles.

Routines for Reasoning

Routines for Reasoning
Author: Grace Kelemanik
Publisher: Heinemann Educational Books
Total Pages: 0
Release: 2016
Genre: Education
ISBN: 9780325078151

Routines can keep your classroom running smoothly. Now imagine having a set of routines focused not on classroom management, but on helping students develop their mathematical thinking skills. Routines for Reasoning provides expert guidance for weaving the Standards for Mathematical Practice into your teaching by harnessing the power of classroom-tested instructional routines. Grace Kelemanik, Amy Lucenta, and Susan Janssen Creighton have applied their extensive experience teaching mathematics and supporting teachers to crafting routines that are practical teaching and learning tools. -- Provided by publisher.

Algebra and the Elementary Classroom

Algebra and the Elementary Classroom
Author: Maria L. Blanton
Publisher: Heinemann Educational Books
Total Pages: 228
Release: 2008
Genre: Education
ISBN:

Algebra in the Elementary Classroom provides the support we need as teachers to embed the development of students' algebraic thinking in the teaching of elementary school. - Megan Loef Franke Coauthor of Children's Mathematics and Thinking Mathematically How do you start students down the road to mathematical understanding? By laying the foundation for algebra in the elementary grades. Algebra and the Elementary Classroom shares ideas, tasks, and practices for integrating algebraic thinking into your teaching. Through research-based and classroom-tested strategies, it demonstrates how to use materials you have on hand to prepare students for formal algebra instruction - without adding to your overstuffed curriculum. You'll find ways to: introduce algebraic thinking through familiar arithmetical contexts nurture it by helping students think about, represent, and build arguments for their mathematical ideas develop it by exploring mathematical structures and functional relationships strengthen it by asking students to make algebraic connections across the curriculum reinforce it across the grades through a schoolwide initiative. No matter what your math background is, Algebra and the Elementary Classroom offers strong support for integrating algebraic thinking into your daily teaching. Its clear descriptions show you what algebraic thinking is and how to teach it. Its sample problems deepen your own algebraic thinking. Best of all, it gives you ideas for grade-specific instructional planning. Read Algebra and the Elementary Classroom and prepare your students for a lifetime of mathematical understanding.

The Fostering Geometric Thinking Toolkit

The Fostering Geometric Thinking Toolkit
Author: Mark J. Driscoll
Publisher: Heinemann Educational Books
Total Pages: 0
Release: 2008
Genre: Education
ISBN: 9780325011479

"Based on the popular Fostering Geometric Thinking, the Toolkit's 20 two-hour sessions provide a year's worth of math PD for middle and secondary teachers. Its facilitator and particpant-friendly sessions cover the key topics of Fostering Geometric Thinking: geometric properties, transformations and measurement. With the Fostering Geometric Thinking Toolkit, you'll lead teachers through hands-on opportunites to: develop new understandings of middle and secondary students' geometric thinking through a field-tested geometric habits-of-mind framework. Broaden and express their own geometric thinking by solving rich problems. Observe students' thinking and problem solving through in-the-classrom footage. Practice analyzing student work. Apply all they've learned in the sessions to engage students' thinking more effectively."--PUBLISHER'S WEBSITE.

Rings, Fields, and Vector Spaces

Rings, Fields, and Vector Spaces
Author: Bharath Sethuraman
Publisher: Springer Science & Business Media
Total Pages: 210
Release: 1996-11-26
Genre: Mathematics
ISBN: 0387948481

Using the proof of the non-trisectability of an arbitrary angle as a final goal, the author develops in an easy conversational style the basics of rings, fields, and vector spaces. Originally developed as a text for an introduction to algebra course for future high-school teachers at California State University, Northridge, the focus of this book is on exposition. It would serve extremely well as a focused, one-semester introduction to abstract algebra.

Early Algebraization

Early Algebraization
Author: Jinfa Cai
Publisher: Springer Science & Business Media
Total Pages: 631
Release: 2011-02-24
Genre: Education
ISBN: 3642177352

In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.

Mathematical Thinking and Communication

Mathematical Thinking and Communication
Author: Mark Driscoll
Publisher: Heinemann Educational Books
Total Pages: 0
Release: 2016
Genre: Education
ISBN: 9780325074771

Language is deeply involved in learning mathematics as students both communicate and think about mathematical ideas. Because of this, teachers of English learners have particular challenges to overcome. Mathematical Thinking and Communication addresses perhaps the most significant challenge: providing access to mathematics for these students. For all students-and English learners in particular-access means finding effective, authentic ways to make language clear and thinking visible so they can reason more, speak more, and write more in mathematics. Based on extensive research and collaboration with teachers, coaches, and schools, Mark Driscoll, Johannah Nikula, and Jill Neumayer DePiper outline four principles for designing instruction that creates this kind of access: challenging tasks, multimodal representations, development of mathematical communication, and repeated structured practice. Starting from the perspective that English learners are capable of mathematical thinking (even as they are learning to express their ideas verbally), the authors highlight techniques for using gestures, drawings, models, manipulatives, and technology as tools for reasoning and communication. By embedding these visual representations into instruction-and encouraging their regular use-teachers support engagement in problem solving, facilitate mathematical dialogue, and notice evidence of students' thinking that propels them to create more engaging and equitable instruction. Enhanced by an extensive online collection of companion professional development resources, this book highlights classroom-ready strategies and routines for fostering mathematics success in all students and helping them recognize their potential.