Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Insights Into Algebra 1 - Teaching For Learning
algebra home workshop 1 workshop 2 workshop 3 workshop 4 workshop 5 workshop 6 workshop 7 workshop 8
Topic Overview Lesson Plans Student Work Teaching Strategies Resources
Workshop 3 Systems of Equations and Inequalities Resources
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Tool Box
Journal
Graphing Calculator
Channel-Talk
NCTM Standards


The links below are to pages within stable sites and are current as of the date of publication of this workshop. Due to the ever-changing nature of the Web, it is possible that some links may change. Should you reach a non-working link, we recommend entering a couple words from its description into the site's search function, or into a Web-based search engine.


Related Standards
Systems of Equations, Systems of Inequalities, and Linear Programming
Building Understanding
Teaching English Language Learners
Books

Related Standards:

NCTM Middle Grades Algebra Standard
http://standards.nctm.org/document/chapter6/alg.htm
This Web page describes what students should know and be able to do algebraically in grades 6-8, and offers suggestions for the type of classroom activities necessary to develop conceptual understanding.

NCTM High School Algebra Standard
http://standards.nctm.org/document/chapter7/alg.htm
This Web page describes what students should know and be able to do algebraically in grades 9-12, and offers suggestions for the type of classroom activities necessary to develop conceptual understanding.

Systems of Equations, Systems of Inequalities, and Linear Programming:

Understanding Distance, Speed, and Time Relationships Using Simulation Software
http://standards.nctm.org/document/eexamples/
Example 5.2 includes a software simulation of two runners on a track. Students can control the speeds and starting points of the runners, watch the race, and examine a graph of the time-versus-distance relationship. The computer simulation uses a context familiar to students, and the technology allows them to analyze the relationships more deeply by manipulating the environment and observing the changes that occur. This applet could be used as an introduction to solving systems of equations.

High School Operations Research
http://www.hsor.org/
High School Operations Research develops instructional materials for use in high school mathematics classrooms. This site has some examples of linear programming problems.

Figure This!
http://www.figurethis.org/index40.htm
The "Figure This!" site provides a growing set of challenges intended to promote students' problem-solving ability. The site is designed to entice parents and other adults to do mathematics problems with middle school kids and thus understand the high-level mathematics problems that are part of the middle school curriculum. There are currently 80 challenges. In this particular challenge, students are presented with a diagram depicting the "cost" of various combinations of frowns, smiles, and neutral expressions on a face. They are asked to determine how much is a smile worth. In order to answer the question, students may either use the method of guess/check or rely on patterns to develop systems of equations.

Exploring Linear Functions: Representational Relationships
http://standards.nctm.org/document/eexamples/
Example 7.5 presents a series of explorations based on two linked representations of linear functions. The grades 9-12 section on the "Problem Solving Standard" also includes a helpful description of how a teacher engaged her students in problem solving and reasoning with tasks such as those presented on the site.

Quick Math
http://www.quickmath.com/
This Web site gives students access to a powerful online computer algebra system. It provides such algebraic manipulations as expanding, factoring, and simplifying expressions, as well as combining rational expressions and generating partial fractions. It can solve almost any equation or inequality a high school student will encounter, giving exact answers when possible and approximations in other cases. Matrix operations and beginning calculus are also within its grasp, as is graphing of two-dimensional functions and relations. There is almost nothing it can't do, and the site responds to requests very quickly!

Building Understanding:

Olson, Steve and Susan Loucks-Horsley (eds). Inquiry and the National Science Education Standards: A Guide for Teaching and Learning. Committee on the Development of an Addendum to the National Science Education Standards on Scientific Inquiry, National Research Council; 2000.
This book deals with the challenges of teaching science and math, and is available for free online at http://www.nap.edu/

How People Learn: Brain, Mind, Experience, and School (Expanded Edition). Committee on Developments in the Science of Learning, 2000.
This book makes important connections between classroom learning and everyday activities. It contains additional material from the Committee on Learning Research and Educational Practice, National Research Council, and is available for free online at http://www.nap.edu/

Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools. Committee on Programs for Advanced Study of Mathematics and Science in American High Schools, National Research Council; 2002.
This book is available for free online at http://www.nap.edu/

Teaching English Language Learners:

TESOL (Teachers of English to Speakers of Other Languages)
http://www.tesol.org/index.html
This is a well-organized site with lots of curricular, practical, professional, and social information.

The National Association for Bilingual Education (NABE)
http://www.nabe.org/
The site provides access to the Bilingual Research Journal Online, NABE publication that focuses on issues in the bilingual education field. Users can also access NABE News, the Association's official news magazine. Published articles and research papers provide further support and information.

Dave's ESL Café
http://www.eslcafe.com/
One of the most popular sites for ESL teachers, Dave's Café offers materials and ideas for the classroom, helpful resources, and opportunities for ESL teachers to communicate with one another.

Books

August, Diane and Kenji Hakuta (eds). Educating Language-Minority Children. Committee on Developing a Research Agenda on the Education of Limited-English-Proficient and Bilingual Students, National Research Council and Institute of Medicine; 1998.
This book is available for free online at http://www.nap.edu/

August, Diane and Kenji Hakuta (eds). Improving Schooling for Language-Minority Children: A Research Agenda. Committee on Developing a Research Agenda on the Education of Limited English Proficient and Bilingual Students, National Research Council and Institute of Medicine; 1997.
This book is available for free online at http://www.nap.edu/

Cummins, Jim. Empowering Minority Students. Sacramento: California Association for Bilingual Education, 1989.

Ladson-Billings, Gloria. "Culturally Relevant Teaching." The College Board Review, 155 (1990): 20-25.

Tate, William F. "School Mathematics and African American Students: Thinking Seriously about Opportunity-to-Learn Standards." Educational Administration Quarterly, 31 (1995): 424-48.

Changing the Faces of Mathematics: Perspectives on Multiculturalism and Gender Equity. Reston, VA: National Council of Teachers of Mathematics, 2000.
This book contains volumes of articles written by authors who are committed to the goals of the mathematics education reform movement. Each chapter offers a compelling narrative about a specific issue.


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