The Fostering Algebraic Thinking Toolkit Introduction And Analyzing Written Student Work

Part of the Fostering Algebraic Thinking series, this module gives participants an opportunity to analyze students' written work for evidence of algebraic thinking.

This set of professional development materials helps teachers identify, describe, and foster algebraic thinking in their students. The toolkit features classroom video, four complete modules containing notes for facilitators, and reproducibles for workshop participants. Each module concentrates on a different kind of classroom evidence to share and analyze with colleagues: Analyzing Written Student Work Asking Questions of Students Documenting Patterns of Student Thinking Listening to Students

Participants will find in this module more written student work to analyze, but the focus, instead, is on patterns of thinking across a class of students.

Together with the accompanying video, this module offers a change both in the type of student data considered--from written to real time--and in the emphasis of the module--from understanding to fostering student thinking.

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

This participant book, in combination with the facilitator's guide, forms a comprehensive professional development program designed to improve the efforts of site-based mathematics leadership teams for middle and high schools. Secondary Lenses on Learning prepares leaders to explore concepts in middle and high school algebra as a window into content, instruction, and assessment. You will learn how to assess the strengths and needs of your mathematics programs, set goals, and generate plans for ongoing improvement by engaging in extended explorations and conversations based on readings, problem-based activities, cases, and videos.

This New Edition collects and brings together in one place what has been learned from professional developers efforts across the country in order to make the framework, principles, and strategies of the first edition come to life. This edition deepens our understanding of professional development through further research and new resources. The original purpose of this book to put a competent and caring teacher in every classroom has yet to be fulfilled and is more urgent now than ever. The authors provide one-stop shopping for busy practitioners that incorporates the most up-to-date research gleaned from the broadest possible research base as well as robust and rich descriptions of effective professional development programmes. It incorporates the growing knowledge base about learning, teaching, the nature of science and mathematics, professional development, and change. The authors scanned the field of professional development in mathematics and science over the last five years, noting what has changed and what has not, dissected the original framework, updated examples, incorporate what authors have learned as well as advances in the field. This essential primer offers a framework that considers key inputs and combines strategies uniquely tailored to their environment and goals; summarizes key knowledge and best practices; provides guidance on assessing one′s context; describes strategies that go beyond most common workshops and institutes; provides real-life examples of how elements of the framework were used to create professional development initiatives; offers references and resources for further exploration and inquiry. Highlights of the Second Edition include: - New design framework that incorporates standards, student learning data, and evaluation techniques - More guidance for assessing context using data - More strategies for professional development, including lesson study, aligning and selecting curriculum, and demonstration lessons. - Stronger real-life examples, including new uses of technology and data-driven designs An essential resource for educators who design, conduct, and support professional development for teachers of mathematics and science, including staff developers, principals, teacher leaders, curriculum supervisors, and leadership teams. College and university faculty in education, science, and mathematics will also find this to be a useful compendium of ideas for improving mathematics and science education.

Algebra is the gateway to college and careers, yet it functions as the eye of the needle because of low pass rates for the middle school/high school course and students’ struggles to understand. We have forty years of research that discusses the ways students think and their cognitive challenges as they engage with algebra. This book is a response to the National Council of Teachers of Mathematics’ (NCTM) call to better link research and practice by capturing what we have learned about students’ algebraic thinking in a way that is usable by teachers as they prepare lessons or reflect on their experiences in the classroom. Through a Fund for the Improvement of Post-Secondary Education (FIPSE) grant, 17 teachers and mathematics educators read through the past 40 years of research on students’ algebraic thinking to capture what might be useful information for teachers to know—over 1000 articles altogether. The resulting five domains addressed in the book (Variables & Expressions, Algebraic Relations, Analysis of Change, Patterns & Functions, and Modeling & Word Problems) are closely tied to CCSS topics. Over time, veteran math teachers develop extensive knowledge of how students engage with algebraic concepts—their misconceptions, ways of thinking, and when and how they are challenged to understand—and use that knowledge to anticipate students’ struggles with particular lessons and plan accordingly. Veteran teachers learn to evaluate whether an incorrect response is a simple error or the symptom of a faulty or naïve understanding of a concept. Novice teachers, on the other hand, lack the experience to anticipate important moments in the learning of their students. They often struggle to make sense of what students say in the classroom and determine whether the response is useful or can further discussion (Leatham, Stockero, Peterson, & Van Zoest 2011; Peterson & Leatham, 2009). The purpose of this book is to accelerate early career teachers’ “experience” with how students think when doing algebra in middle or high school as well as to supplement veteran teachers’ knowledge of content and students. The research that this book is based upon can provide teachers with insight into the nature of a student’s struggles with particular algebraic ideas—to help teachers identify patterns that imply underlying thinking. Our book, How Students Think When Doing Algebra, is not intended to be a “how to” book for teachers. Instead, it is intended to orient new teachers to the ways students think and be a book that teachers at all points in their career continually pull of the shelf when they wonder, “how might my students struggle with this algebraic concept I am about to teach?” The primary audience for this book is early career mathematics teachers who don’t have extensive experience working with students engaged in mathematics. However, the book can also be useful to veteran teachers to supplement their knowledge and is an ideal resource for mathematics educators who are preparing preservice teachers.

Teaching our children to think and reason mathematically is a challenge, not because students can't learn to think mathematically, but because we must change our own often deeply-rooted teaching habits. This is where instructional routines come in. Their predictable design and repeatable nature support both teachers and students to develop new habits. In Teaching for Thinking, Grace Kelemanik and Amy Lucenta pick up where their first book, Routines for Reasoning, left off. They draw on their years of experience in the classroom and as instructional coaches to examine how educators can make use of routines to make three fundamental shifts in teaching practice: Focus on thinking: Shift attention away from students' answers and toward their thinking and reasoning Step out of the middle: Shift the balance from teacher-student interactions toward student-student interactions Support productive struggle: Help students do the hard thinking work that leads to real learning With three complete new routines, support for designing your own routine, and ideas for using routines in your professional learning as well as in your classroom teaching, Teaching for Thinking will help you build new teaching habits that will support all your students to become and see themselves as capable mathematicians.