Insights Into Algebra 1: Teaching for Learning
This video workshop for middle and high school teachers presents strategies for improving how typical Algebra 1 topics are taught.
A video workshop for middle and high school teachers; 8 one-hour video programs, workshop guide, and website.
Insights Into Algebra 1: Teaching for Learning is an eight-part video, print, and web-based professional development workshop for middle and high school teachers. Participants will explore strategies to improve the way they teach 16 topics found in most Algebra 1 programs. In each session, participants will view two half-hour videos that showcase effective strategies for teaching mathematical topics. Then, led by the workshop guide, participants will engage in activities designed to help them examine their teaching practice, incorporate what they are learning into their practice, share their experiences with other teachers, and reflect on their ongoing development.
Individual Program Descriptions
Workshop 1: Variables and Patterns of Change
In Part I, Janel Green introduces a swimming pool problem as a context to help her students understand and make connections between words and symbols as used in algebraic situations. In Part II, Jenny Novak’s students work with manipulatives and algebra to develop an understanding of the equivalence transformations used to solve linear equations.
Workshop 2: Linear Functions and Inequalities
In Part I, Tom Reardon uses a phone bill he received to help his students deepen their understanding of linear functions and how to apply them. In Part II, Janel Green’s hot dog vending scheme is a vehicle to help her students learn how to solve linear equations and inequalities using three methods: tables, graphs, and algebra.
Workshop 3: Systems of Equations and Inequalities
In Part I, Jenny Novak’s students compare the speed at which they write with their right hand with the speed at which they write with their left hand. This activity enables them to explore the different types of solutions possible in systems of linear equations, and the meaning of the solutions. In Part II, Patricia Valdez’s students model a real-world business situation using systems of linear inequalities.
Workshop 4: Quadratic Functions
In Part I, Tremain Nelson and his students use a basketball toss as a launching point to learn how the constants in the equation y = a(x – h)2 + k transform the parent function y = x2. In Part II, Tremain and the students apply what they learned in the previous lesson to model several bounces of a ball dropped below a motion detector.
Workshop 5: Properties
In Part I, Tom Reardon’s students come to understand the process of factoring quadratic expressions by using algebra tiles, graphing, and symbolic manipulation. In Part II, Sarah Wallick’s students conduct coin-tossing and die-rolling experiments and use the data to write basic recursive equations and compare them to explicit equations.
Workshop 6: Exponential Functions
In Part I, Orlando Pajon uses a population growth simulation to introduce students to exponential growth and develop the conceptual understanding underlying the principles of exponential functions. In Part II, a scenario from Alice in Wonderland helps Mike Melville’s students develop a definition of a negative exponent and understand the reasoning behind the division property of exponents with like bases.
Workshop 7: Direct and Inverse Variation
In Part I, Peggy Lynn’s students simulate oil spills on land and investigate the relationship between the volume and the area of the spill to develop an understanding of direct variation. In Part II, they develop the concept of inverse variation by examining the relationship of the depth and surface area of a constant volume of water that is transferred to cylinders of different sizes.
Workshop 8: Mathematical Modeling
This workshop presents two capstone lessons that demonstrate mathematical modeling activities in Algebra 1. In both lessons, the students first build a physical model and use it to collect data and then generate a mathematical model of the situation they’ve explored. In Part I, Sarah Wallick’s students use a pulley system to explore the effects of one rotating object on another and develop the concept of transmission factor. In Part II, Orlando Pajon’s students conduct a series of experiments, determine the pattern by which each set of data changes over time, and model each set of data with a linear function or an exponential function.
Getting the Materials
The workshop guide is available for download as a PDF.
If you are participating in a group session, your facilitator will give you a copy of the print guide or request that you print the PDF for yourself from this website. Your facilitator will give you any instructions concerning meeting time and place, what you should bring to sessions, and work you should do outside the group sessions.
Using the Materials
The print guide and website provide background, activities, discussion questions, homework assignments, and resources to supplement the workshop session programs and provide a robust professional development experience. They also provide information for facilitators to plan and structure group sessions.
Workshop sessions generally are held weekly for at least two hours. The workshop guide describes pre- and post-viewing activities and discussion to fill out the remainder of the session. The guide also provides homework to expand on what you have learned and prepare you for the next session.
If you are leading a group session, please review the Facilitator Information below and the Workshop Guide for more information on planning and facilitating this workshop.
Insights Into Algebra 1: Teaching for Learning is a production of Thirteen/WNET New York. Copyright 2004, The Annenberg Foundation. All rights reserved.
A major American cultural and educational institution for nearly four decades, Thirteen/WNET supplies more than one-third of all primetime programs aired on PBS, including acclaimed cultural, science, and public affairs series and specials. The award-winning Children’s and Educational Programming group is a leading and innovative provider of programming for a variety of projects, from teacher professional development to instructional television and interactive multimedia. Broadcast series that further the station’s educational mission include the daily animated PBS Kids math program Cyberchase, the history series for families Freedom: A History of US, ZOOM Local/National, What’s Up in the Environment/Technology/Factories?, and In the Mix specials. Many projects promote implementation of national and state education standards. These include The Expanding Canon: Teaching Multicultural Literature in High School, Science … Simply Amazing, Learning Science Through Inquiry for Annenberg Media, and PBS TeacherLine, Mathline, and Scienceline.
Thirteen is also a trusted source of Web-based content for educators. Thirteen Ed Online, an award-winning Web site that features classroom materials, resources and support for teachers, and professional development workshops, reaches thousands of teachers, teachers-in-training, administrators, and others involved in pre-K-12 instruction. Ed Online workshops are currently used by professors and students at Harvard University, Teachers College at Columbia University, and in school districts throughout the country. Ed Online also produces education companion pieces to national series’ Web sites and original online content to complement Thirteen’s educational initiatives. Projects include Human Rights 101, Teaching Heritage, Afterschool Exchange, Cyberchase Parents and Teachers, Innovation, Religion & Ethics NewsWeekly, The Rise and Fall of Jim Crow, and Wide Angle.
Website Production Credits
Brigitte Magar Matsuoka, Executive Producer
Sandy Goldberg, Producer
Jesse Gale, Associate Producer
Laura Leung, Project Coordinator
Patrick Vennebush, Writer
Fred Longhart, Writer
Karen A. Longhart, Math Content Director
L. Carey Bolster, Math Content Consultant
Jill Peters, Project Director
Naomi Edelson, Editorial Supervisor
Todd Schindler, Copy Editor
Daniel T. Dolan
Carol R. Findell
Janis M. Palkowski
Math Content Reviewers
Michael B. Scott
Interactive and Broadband Unit:
Anthony Chapman, Director of Interactive and Broadband
Mikki Monkolchayut, Technical Producer
Ana Giron, Production Assistant
Jeremy Hinsdale, Production Assistant
Sabina Daley, Art Director
Karen Mattson, Designer
Ruiyan Xu, Graphics Production
Brian Santalone, HTML Implementation
Ben Chappel, Interactive Programming
Brian Lee, Technical Director
Supplemental Curriculum Materials provided by
Kendall/Hunt Publishing Company
Key Curriculum Press
Video Production Credits
Math Content Director
Karen A. Longhart
Project Officer, Annenberg Media
Deborah A. Batiste
Math Content Consultant
L. Carey Bolster
Project Advisory Board
Daniel T. Dolan
Carol R. Findell
Janis M. Palkowski
Mary Ann Toman
Matthew G. Monroe
Elizabeth de la Garza
Original Music Composed by
Special Thanks to:
Aptos High School, Aptos, CA
Austintown Fitch High School, Austintown, OH
Bel Air High School, El Paso, TX
Hastings High School, Houston, TX
The International School, Bellevue, WA
River Hill High School, Clarksville, MD
Walt Whitman High School, Huntington Station, NY
West Yellowstone High School, West Yellowstone, MT
Director of Children’s and Educational Programming
Karen A. Longhart, Math Content Director
A mathematics teacher for 22 years, Karen Longhart has served on the board of directors at both NCTM and the Montana Council of Teachers of Mathematics (MCTM), where she was also president. Recently she has been a presenter of algebra professional development institutes for the NCTM Academy. Karen was a Presidential Awardee for Excellence in Mathematics and Science Teaching, and has been named to the Mathematical Sciences Education Board for 2000-2003. MCTM honored her as Teacher of the Year. Karen is a prolific writer of mathematics curricula, including material for Texas Instruments’s Eighty Something, and the Systemic Initiative for Montana Mathematics and Science (SIMMS).
Karen has contributed considerably to improving the use of technology in mathematics teaching. A recipient of National Science Foundation grants to study technology and teaching methods, she has written numerous successful grants to fund professional development and technology for teachers all over the state of Montana. She piloted SIMMS projects that promoted the use of technology, cooperative learning, and authentic assessment while teaching mathematics using real-world contextual situations.
L. Carey Bolster, Math Content Consultant
Carey Bolster has been vitally active in mathematics education throughout his career. He served as Coordinator of Mathematics for Baltimore County Public Schools, Vice-President and President of the National Council of Supervisors of Mathematics (NCSM), initiated the “Activities” section of The Mathematics Teacher, co-directed the State Institute for Leaders in Mathematics and Science sponsored by MSEB, consulted with the National Academy of Sciences development of its online project, and is an author for Scott Foresman.
Carey has been an innovator in bringing professional development to mathematics teachers through video and online productions. Currently he serves as co-mathematics director for the PBS mathematics adventure cartoon show, Cyberchase. As director of PBS Mathline, Carey developed over 72 videos and an extensive online interactive professional development network involving thousands of teachers. As co-principal investigator of the Modeling Middle School Mathematics Project (MMM), he developed video and online activities highlighting exemplary mathematics curricula. Carey served as senior mathematics consultant for PBS Teacherline, an online initiative for math teachers. He initiated MathWeb 2000 and 2001, the first 100% online math conferences. He is president of Bolster Education, Inc., which specializes in creating content for videos, the Web and other technologies used in professional development.
G. Patrick Vennebush, Writer
Patrick Vennebush never met a math problem he didn’t like. With over a decade of experience in education, he has held positions as a middle school teacher in Mercer, PA, as curriculum coordinator for MATHCOUNTS, and as an associate director for PBS TeacherLine. Patrick has written problems for the American Mathematics Competition, the Polya competition, the Mathematics Teacher “Calendar,” and the Mathematics Teaching in the Middle School “Menu of Problems.” In addition, he has written online lessons and courses for MathSoft, Infinity Software Development, and Thirteen/WNET New York. Patrick serves on the MAA Committee for Local and Regional Competitions, is the editor of the “Media Clips” column in the Mathematics Teacher for 2003-05, and is a developer for the Professional Development Group at ETS.
Fred Longhart, Writer
Fred Longhart retired in 2002 after a 30-year teaching career, the last 20 of which were spent at Flathead High School in Kalispell, Montana. He is currently teaching part-time at Flathead Valley Community College. Fred was President of the Montana Council of Teachers of Mathematics and is currently a member of the Affiliate Services Committee at the National Council of Teachers of Mathematics. Fred has extensive experience as a professional developer. He was a Teachers Teaching with Technology instructor from 1994-2002, and a presenter at two NCTM Professional Development Academies from 2002-2003.
Janel Green, Walt Whitman High School; South Huntington, New York
Janel Green realized she was gifted in the field of mathematics at a very young age, and as a child, she tutored and assisted her siblings and friends in their math studies. A native of Brooklyn, NY, Janel received a bachelor’s degree in mathematics from Queens College of the City University of New York, where she was the recipient of the Herbert Fremont Award, and went on to complete a master’s of science degree in education. Currently, she is working toward an administrative degree at Queens College. She has taught mathematics at Walt Whitman High School for the past six years.
Peggy Lynn, West Yellowstone High School; West Yellowstone, Montana
Peggy Lynn has been teaching mathematics at West Yellowstone K-12 Schools for eighteen years. For the last nine years, she has been using a standards-based integrated curriculum that is context-oriented and incorporates the use of technology. She has become a firm believer in this approach for teaching mathematics. Outside of school, Peggy is a board member and secretary for the Montana Council of Teachers of Mathematics, a board member and treasurer for the West Yellowstone Ski Education Foundation, and team coordinator for the USSA Intermountain/Northern Region junior cross-country ski committee.
Mike Melville, Aptos High School; Aptos, California
Mike Melville has been teaching for 17 years. He has taught mathematics using traditional texts and curricula as well as reform-based strategies. In between his years of teaching, Mike spent 11 years working for a franchising company, becoming a manager in charge of franchise operations. From this experience, he realized how important it is that what students learn be connected to how they live in some meaningful way. As a teacher of mathematics, he received training in the reform pedagogy needed for the Interactive Mathematics Program (IMP) and has also trained other teachers in this curriculum. At Aptos High School, Mike has been a department chair and has worked on various committees to improve the math education for college-bound students.
A. Tremain Nelson, Hastings High School; Houston, Texas
While working as a performance engineer with NASA, Tremain Nelson realized that his true passion was helping children succeed in school, and he decided to become a math teacher in the Houston area public school system. During this time, he had the opportunity to teach using the Cognitive Tutor™ mathematics curriculum and become a certified implementation specialist for Carnegie Learning, Inc. He is currently serving as the Director of K-12 Community for Carnegie Learning and works closely with math supervisors and fellow educators nationwide to help them increase their students’ understanding of Algebra I, Geometry, Algebra II, and Integrated Math.
Jenny Novak, River Hill High School, Clarksville, Maryland
Jenny Novak is a fourth-year teacher and is involved in many professional development activities for the Howard County public schools in Maryland. She has been a member of the curriculum development team for Algebra I and has served as the lead for the Algebra II writing team. Jenny has co-taught an intermediate course on graphing calculators for teachers, and for the last two summers, she has led an “Algebra Institute” course for Howard County’s new teachers. She has presented at county in-services and the N.S.A. Mathematics Symposium, and has co-presented at the Governor’s Academy in Maryland.
Orlando Pajon, Bel Air High School; El Paso, Texas
Orlando Pajon is working as a Math Staff Developer for the Ysleta Independent School District in El Paso, TX. Previously he spent five years teaching mathematics at Bel Air High School. He completed the alternative certification program at the University of Texas at El Paso in 1999. Formerly an electrical engineer, Orlando received his Master of Science degree from L’vov Order Lenin Polytechnical Institute (now known as L’vov Polytechnical University) in L’vov, Ukraine. Orlando was born and raised in Cuba.
Tom Reardon, Fitch High School; Austintown, Ohio
Tom Reardon is the mathematics department chair at Austintown Fitch High School and a mathematics instructor at Youngstown State University. Tom has given numerous presentations at National Council of Teachers of Mathematics (NCTM) national and regional conferences and at Teachers Teaching with Technology national and regional conferences. He earned the Presidential Award for Excellence in Teaching Mathematics in 1997, the Radio Shack National Teacher Award in 2000, and the Toyota TIME grant from NCTM in 2003. He earned National Board certification in 2000. Tom has authored textbooks and worked with Texas Instruments on software development projects.
Sarah Wallick, The International School; Bellevue, Washington
Sarah Wallick is currently in her third year of teaching at the middle and high school levels in a Washington State public school. She is also pursuing a master’s degree in Educational Leadership and Policy Studies at the University of Washington, and is working toward administrative certification to become a principal. Sarah is a trainer for The College Board’s “College Success Initiative,” which aims to improve math and language arts studies at the middle school level so that students will be better prepared to succeed in those subjects when they enter college. Before moving to Washington, Sarah taught mathematics in California. She holds a Bachelor of Science degree in Applied Mathematics from California State University, Stanislaus, where she also received her teaching certification.
Patricia Valdez, Aptos High School; Aptos, California
Patricia Valdez teaches mathematics in English and bilingually in English and Spanish. She has been a staff developer for the Interactive Mathematics Program (IMP) for ten years, and has taught other IMP staff developers nationally. Patricia has taught at the prestigious California Academy of Mathematics and Science (CAMS) and in the Los Angeles Unified School District. Patricia was the first person to earn a mathematics degree with a bilingual cross-cultural credential from the California State University at Long Beach. She was born in Mexico City.
Diane Briars is the senior program officer for mathematics and science education for the Pittsburgh public schools, and co-director of the Pittsburgh NSF Urban Systemic Program PRIME PLUS (Pittsburgh Reform in Mathematics Education and in Programs for Learning and Understanding Science). She was a member of the National Commission on Mathematics and Science Teaching for the 21st Century, headed by John Glenn; a member of the advisory committee for the Education and Human Resources Directorate of the NSF; and a former director of the National Council of Teachers of Mathematics.
Frances R. Curcio
Dr. Frances Curcio is a professor in the Department of Education and Youth Services at Queens College of the City University of New York. She is permanently certified as a secondary school mathematics teacher and administrator and spends part of her teaching time at the Louis Armstrong Middle School in East Elmhurst, NY. A former member of the NCTM board of directors, she served on a special panel appointed by the New York City schools chancellor to investigate and report on the state of mathematics education in New York and to provide recommendations for improvement. Currently she is co-principal investigator of a project to develop scenario tasks as a means to assess teachers’ mathematical and pedagogical content knowledge.
Dr. Miriam Leiva is director of MATHink and Project Excel MATH, professional development programs at the University of North Carolina at Charlotte that link classroom teachers and schools. She is the Bonnie E. Cone Distinguished Professor of Mathematics Emerita at UNC and was one of the first Hispanic-American women for whom English is a second language to receive a doctorate in mathematics and mathematics education in the United States. Dr. Leiva is serving as the first president of TODOS: Mathematics For All, a national organization designed to support and assist educators in teaching mathematics, particularly to Hispanic-Latino students. She will lead the first U.S.-Cuba Mathematics Education Conference in Havana in 2004.
Carol Malloy is an associate professor of mathematics education at the University of North Carolina at Chapel Hill. She has served on the NCTM board of directors and was member of the NCTM Standards 2000 team. Dr. Malloy’s research interests include mathematics learning, the influence of culture on the cognitive development and mathematics learning of African-American students, and teacher-student interactions that lead to understanding in mathematics. Prior to becoming a professor, she was the associate director for programs, as well as director of the pre-college program, at the University of North Carolina Mathematics and Science Education Network.
Beatrice Moore-Harris is the associate mathematics manager for Project Grad Houston. Her consulting clients include Glencoe/McGraw-Hill Publishing Company, the Bureau of Education and Research, the Texas Association for Supervision and Curriculum Design, and the Texas Rural Systemic Initiative. She was a board member of the National Council of Teachers of Mathematics (NCTM) and is the past president of the Benjamin Banneker Association. She has published numerous articles, and has worked on several educational committees and projects at the national level.
Anthony Piccolino is Associate Professor of Mathematics at Montclair State University, and a co-project director for an NSF-funded Systemic Initiative for teachers and administrators in grades K-8 in the Newark Public Schools. Prior to this, he was a middle and high school teacher and supervisor of mathematics in the New York State public school system. A co-author of the high school textbook series Integrated Mathematicspublished by McDougall Littell, he has served as a consultant in AP Mathematics for the College Board during the past 20 years. Past directorships include: President of the Association of Mathematics Teachers of New York State and the New York State Association of Mathematics Supervisors, and First- and Second-Vice President and Eastern Regional Director for the National Council of Supervisors of Mathematics.
Jane F. Schielack
Dr. Jane F. Schielack is a Professor of Mathematics at Texas A&M University. Recently she served as academic advisor as well as writer on several professional development institutes for middle school mathematics teachers. Her other experiences include designing the on-line Mathematics TEKS Framework for supporting implementation of the Texas Essential Knowledge and Skills in K-12 mathematics. Currently she is Director of Information Technology in the Science Center for Teaching and Learning at Texas A&M University. The Center seeks to replenish the nation’s supply of education specialists in science, mathematics, and technology through learner-centered opportunities involving scientists, mathematicians, education researchers, and education
David C. Webb
David Webb is the executive director of the Freudenthal Institute USA, an international research collaborative for mathematics education, as well as an associate researcher at the Wisconsin Center for Education Research. His research focuses on teachers’ classroom assessment practices and the design of professional development resources to support teacher learning. Recent research projects have focused on teacher modification through classroom assessment, the impact of reform curricula on student learning and achievement, and the design of formative assessment tools. David received his Ph.D. in curriculum and instruction from the University of Wisconsin, Madison.
Daniel T. Dolan, director, PIMMS (Project to Increase Mastery of Mathematics and Science), Wesleyan University; Middletown, Connecticut
Carol R. Findell, clinical associate professor, Curriculum and Teaching, Boston University; Boston, Massachusetts
Ana England, teacher, Lakeview Middle School, Watsonville, California
Janis M. Palkowski, teacher, East Junior High School, Traverse City, Michigan
Annenberg Learner professional development workshops and courses provide teachers with content and pedagogical learning to strengthen their professional credentials. Teachers may use Annenberg Learner’s workshops and courses with a study group of colleagues or at regular professional development sessions to review subject content. To support these uses of the materials, each course and workshop has a workshop or facilitator’s guide found on the accompanying website that provides information on the course or workshop structure as well as a script for running professional development sessions. A chapter corresponding to each video includes —
background questions for the participants,
video discussion questions,
hands-on group activities, and
references for further study.
Any teacher or administrator can step into the role of facilitator. One does not need extensive experience running a workshop for teachers. Just follow the guide and let the group work through the questions and activities. For several series, the correct answers to problems posed are located in the guide, too.
Tips for preparing for and running sessions smoothly —
Create a meeting schedule
A typical schedule includes weekly meetings of two-and-a-half hours. During the first hour, the group watches and discusses the video. During the second hour and beyond, smaller working groups can engage in learning activities as described in the workshop or course guide or they can use the time to connect the content to their own curricula. Groups and facilitators should feel free to design a meeting schedule that works best for them.
Access the video
Video programs are streamed on-demand at www.learner.org. Search for the series you want by title or choose from subject headings on the home page. Note that the video stream image will be less sharp when projected for a group to watch.
Provide readings, handouts, and worksheets to participants
Many of these are printable documents from the course or workshop website. Participants can print their own copies or the facilitator can print copies for the group. Readings should be completed before the workshop session.
Make note of other materials needed for the session
These include manipulatives, large pads, whiteboards, etc. Specific materials needed are listed in the workshop guide.
Workshop 1 Variables and Patterns of Change
In Part I, Janel Green introduces a swimming pool problem as a context to help her students understand and make connections between words and symbols as used in algebraic situations. In Part II, Jenny Novak's students work with manipulatives and algebra to develop an understanding of the equivalence transformations used to solve linear equations.
Workshop 2 Linear Functions and Inequalities
In Part I, Tom Reardon uses a phone bill to help his students deepen their understanding of linear functions and how to apply them. In Part II, Janel Green's hot dog vending scheme is a vehicle to help her students learn how to solve linear equations and inequalities using three methods: tables, graphs, and algebra.
Workshop 3 Systems of Equations and Inequalities
In Part I, Jenny Novak's students compare the speed at which they write with their right hands with the speed at which they write with their left hands. This activity enables them to explore the different types of solutions possible in systems of linear equations, and the meaning of the solutions. In Part II, Patricia Valdez's students model a real-world business situation using systems of linear inequalities.
Workshop 5 Properties
In Part I, Tom Reardon's students come to understand the process of factoring quadratic expressions by using algebra tiles, graphing, and symbolic manipulation. In Part II, Sarah Wallick's students conduct coin-tossing and die-rolling experiments and use the data to write basic recursive equations and compare them to explicit equations.
Workshop 6 Exponential Functions
In Part I, Orlando Pajon uses a population growth simulation to introduce students to exponential growth and develop the conceptual understanding underlying the principles of exponential functions. In Part II, a scenario from Alice in Wonderland helps Mike Melville's students develop a definition of a negative exponent and understand the reasoning behind the division property of exponents with like bases.
Workshop 7 Direct and Inverse Variation
In Part I, Peggy Lynn's students simulate oil spills on land and investigate the relationship between the volume and the area of the spill to develop an understanding of direct variation. In Part II, they develop the concept of inverse variation by examining the relationship of the depth and surface area of a constant volume of water that is transferred to cylinders of different sizes.
Workshop 8 Mathematical Modeling
This workshop presents two capstone lessons that demonstrate mathematical modeling activities in Algebra 1. In both lessons, the students first build a physical model and use it to collect data and then generate a mathematical model of the situation they've explored. In Part I, Sarah Wallick's students use a pulley system to explore the effects of one rotating object on another and develop the concept of transmission factor. In Part II, Orlando Pajon's students conduct a series of experiments, determine the pattern by which each set of data changes over time, and model each set of data with a linear function or an exponential function.