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Algebra ConnectionsCalifornia Edition
A Presentation to Teachers for the
California Mathematics Adoption
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Background of CPM
• Supported by research in methodology and studies of student results, available at
www.cpm.org
• CPM has developed curriculum for 18 years
• Written with the help of California classroom teachers based on their experience of what effectively develops both procedural skills and conceptual understanding.
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Research Base
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Research Support:
• Social interaction increases the ability of students to learn ideas
• The integration of knowledge is best supported by engaging in a wide array of problems around a single idea.
• Long-term retention and transfer of knowledge are best-supported by spaced learning.
Research Summary
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Examples of California data:
• Students in California CPM schools scored 6 - 10 percentage points above the state average for grades 9-11 on the SAT-9 test for 1998 - 2002.
• 8th Grade CST scores for 2002-2007 in CPM schools are 59% above the state average.
• Students in both low-performing and high performing schools score higher than matched groups of comparison schools.
• Reports are posted at www.cpm.org.
Program Components
The Algebra Connections Program for this review includes:
CA Edition Student text
Teacher binder with assessment
Extra Practice workbook
Parent Guide
Homework help (hotmath.com)
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Examining a LessonThe Structure of the Teacher
MaterialsWe will examine a lesson developing the content for Standard 9.0:
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9.0: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables to sketch the solution sets.
Lesson 6.2.3
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Lesson Objective:
Students will develop the Elimination Method for solving systems of equations.
Lesson 6.2.3
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Suggested Lesson Activity:
Description of lesson and strategies for implementation, such as questions for students
Lesson 6.2.3
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Closure:
Every lesson contains closure strategies for teachers.
Introduction:
• Motivates learning
• Gets students active
• Challenging
Lesson 6.2.3
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Conceptual Development:
When appropriate, manipulatives (such as algebra tiles) are used to help students move from concrete to abstract understanding.
• Structured lesson
• Problem-based learning
Lesson 6.2.3
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Socratic Method:
Questions that students answer to develop a new concept
• Requires students to be actively thinking
• Outlines a process for solving the problem
Lesson 6.2.3
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Practice:
Embedded in classwork
Context:
Focus on solving word problems.
Lesson 6.2.3
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Explicit Notes:
Following most lessons is a “Math Notes” box containing:
• Formal definitions
• Solved examples
• Multiple strategies
• Explanation of special cases
Effective Learning Strategy
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Students develop and practice topics in study teams:
• Research-based
• Structured problems with clear objectives
• Active engagement with the lesson
• Mathematical discourse
Homework
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Review & Preview Icon designates where homework starts.
Homework includes:
• Spaced practice with previous work
• Practice with current work
• Extensions and enrichment
Hotmath Help
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Help with Homework:
Students have access to free tutorial help with hints and solutions to all homework questions.
Teacher & Student Interaction
Forms of Teacher Interaction:• Targeted lectures
• Clarifying instructions
• Checking for understanding
• Testing student results
• Questioning student processes
• Providing closure
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Multiple Assessment Resources
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Assessment Handbook• Individual tests• Team tests• Participation quizzes• Student presentations• Portfolios
Chapter Assessment Plans
Tests and Problem Bank
Student and class observations
Universal Access
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Solved Examples:
Additional resource containing solved examples of content with complete explanations.
Teacher Intervention
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Extra Practice:
Offers multiple practice problems (with answers) for use in class or at home.
Answers:
Answers are provided so that students can get instant feedback on developing skill.
Parental Support
Parent Guide
To help parents help their children
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Reading Level
Flesh-Kincaid:
Using the Flesh-Kincaid scale of readability, the student Algebra Connections scores are:
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7.4 64.0
Grade Level Reading Ease
Ways of Thinking
• Justifying
• Generalizing
• Applying and Extending
• Making Connections
• Reversing Thinking
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Algebra Connections focuses attention on five “ways of thinking” mathematically:
Chapter Closure
• Reflective activities
• Key vocabulary
• Graphic organizers
• Practice problems with answers for self-assessment
• Ways of Thinking
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Each chapter offers extensive closure opportunities, including:
Use of Algebra Tiles
• “Legend” reminds students and teachers which tiles are positive and negative
• “Minus” region negates the tiles in that region, helping students represent the opposite of a negative.
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Symbolic manipulation is developed through use of concrete tools
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2x − x +1− (2 − 3)