Introduction to Algebra is a complete one-year course for 8th graders who are preparing for algebra. It fully meets the requirements for an “Algebra Readiness Program” as described in Appendix E in the 2006 California Mathematics Framework, and includes most of the standards on California’s General Mathematics Standards Test.

The UCLA Math Content Program for Teachers and Students developed this program. This is a mathematics-education group within the UCLA Department of Mathematics, Curtis Center for Mathematics and Teaching, and we have been developing content programs since 1999. By combining the expertise of classroom teachers with mathematicians, MCPT created a mathematically solid and pedagogically appropriate program for students.

Introduction to Algebra is organized as a two-semester program. It includes 8 units (4 weeks per unit), and the instructional materials are organized by weeks (32 weeks). During the week, students complete two lessons that emphasize concept development and one lesson that emphasizes skill development. To provide maximum flexibility for use, the program can be reorganized into “clusters” that center around topics necessary for algebra readiness. This is because each lesson within the program is being carefully constructed to flow as part of a comprehensive program and also as part of a program that targets specific skills.

This program is most effective for 8th grade students who have struggled to learn California’s 6th or 7th grade standards. It is especially appropriate for students identified as “far below basic” or “below basic” on the California Standards test, for struggling English language learners, and for others with special needs.

The writing team chose to organize the program into weekly packets because we felt this would be an easy system for teachers to implement, and a successful organizational structure for low-achieving students. Each week the students receive a packet, which includes all the work for the week. This format gives students a fresh start for success each week with a manageable amount of work. It also allows for an easy transition into the class for transient students.

YES. The “Foundational Skills and Concepts” and the “Algebra Readiness Standards” identified in Appendix E are organized into 31 topics, identified as “highlighted review.” These skills are carefully developed in lessons, which are typically followed by three to five weeks of intensive and intermittent practice.

Five types of formative assessment are available for Introduction to Algebra: Pre-assessments for each semester, weekly quizzes, weekly knowledge checks, home-school connections, and questions embedded in lessons that are designed to assess student understanding.

• Pre-assessments: Diagnose strengths and weaknesses with assessments in Weeks 0 and 00. Item analyses and suggestions for their use are in the Teacher guide.
• Knowledge Check: Diagnostic information specific to the lessons for the week.
• Weekly Quiz: Monitor student progress on topics introduced during the week.
• Home-School Connection: Additional questions to monitor student progress, provide review for the weekly quiz, and to keep parents informed.
• Comprehension questions: Bold italic print questions in the teacher guide help teachers monitor student progress during class. 

In addition, the Pre-Algebra Readiness Test (PA) and the Algebra Readiness Test (AR), which were developed by the UC/CSU Math Diagnostic Testing Project, align to the program. These assessments can be ordered online directly from MDTP   

Each week a highlighted review skill is identified and tested as part of the weekly quiz. Typically summative assessment of this skill takes place after 3-5 weeks of study, intensive practice, and intermittent practice. For students who do not show mastery on a highlighted review skill, more practice, and a second form of the summative assessment are available.

Quarterly assessments, which are composed of highlighted skills, give students a second chance to demonstrate knowledge of the algebra readiness standards.

• Highlighted Review Quizzes: Thirty-one essential skills for algebra readiness target the essential skills needed for algebra. Students practice these skills for several weeks prior to a summative assessment, which is the second part of each weekly quiz. For students who do not demonstrate competency on the summative quiz, a reproducible highlighted review worksheet is provided, along with a second form of the quiz in the Teacher Resource Binder.
• Periodic Summative Assessments: (by quarter or trimester) These assessments cover highlighted review topics for an 8-10 week period. Questions are aligned with the algebra readiness standards, and they have been carefully constructed, field-tested, and refined with the help of an independent evaluator. Solution and item analyses are located in the Teacher Guide.
• Periodic Assessment Scoring Service: Teachers can get tests scored and obtain detailed feedback from an independent evaluator.
• A Periodic Assessment Upload License: A CD-ROM includes all periodic assessments, solutions, item analyses correlated to CA Mathematics Content Standards, and permission to use with any test scoring software for scoring and analysis.

Introduction to Algebra addresses these issues directly with its program design and support materials. Specific strategies special needs learners, and English learners, are included in the Teacher Guide, and essays with research-based guidance are in the Teacher Handbook. Here are some other ways Introduction to Algebra addresses these challenges:

1. Weak computational skills
   Carefully selected numbers within problems allow students to learn and generalize new concepts as they continue to develop fluency with computation
2. Low work completion rate
   Low achieving students complete colorful student packets because they are a manageable amount of work, and eliminate the need to carry a heavy textbook.
3. Poor motivation
   Meaningful activities, good teacher questioning strategies, and reliance upon cooperative learning engage students.
4. Inconsistent attendance
   • Skill Builders give students who miss class substantial opportunities to catch up.
   • Weekly packets give students a fresh start each week.
5. Lack of confidence in mathematical ability
   As students experience success with small chunks of weekly work, their ability and confidence to do mathematics grows.
6. Poor Attention
   Simple black-and-white page layouts keep students focused on the tasks.
7. Unwilling or unable to write out complete solutions
   Graphic organizers, problem templates, and adequate white space minimize the need for copying problems.
8. Different learning needs and strengths
   • Emphasis on representing mathematical ideas visually, numerically, symbolically, and verbally (the fourfold way) gives students multiple ways to communicate their mathematical knowledge.
   • Repetitious and intermittent practice on highlighted skills offers students multiple opportunities to develop competency on skills essential to algebra.
9. Poor test-taking skills
   Opportunities to practice test-taking in small doses (Test Preparation, Weekly Quizzes, Highlighted Review Quizzes), and at extended intervals (Periodic Assessments), give students multiple ways to practice test-taking skills and to show what they know.
10. Poor conversational or academic language skills
    • Weekly packets include Focus on Vocabulary activity.
    • The Student Handbook is organized as a topical glossary with diagrams and examples.
    • Cooperative learning establishes a safe environment for practicing mathematical communication.

While Introduction to Algebra focuses on the needs of struggling students, some students will flourish and be ready for more challenging problems. To differentiate instruction, a weekly Knowledge Challenge is available in the Teacher Resource Binder, and the Teacher Resource Binder CD-ROM includes additional challenging problems.

Professional development and support are essential to this program, and we want every teacher to be comfortable with the content and pedagogy within the program. The Center for Mathematics and Teaching, Inc and local professional development providers have teamed up to deliver first-class professional development to California teachers at regional sites. Because of its importance, we expect first-time users to participate in 2-3 days of professional development prior to beginning the program, and then 5-6 additional days throughout the year.

Yes, Introduction to Algebra is a state adopted text for Algebra Readiness Program.

No. Introduction to Algebra materials are copyrighted and must be purchased on a per student basis.

The program is appropriate for students struggling to learn skills and concepts essential for success in algebra. Some uses include a second course for low achieving 7th, 8th, or 9th graders, as an intersession course for middle or high school students, or a summer bridge course for entering high school students. However, the MathLinks program might be a better choice for a second course.

Studies of student achievement and teacher satisfaction are underway. Public Works, Inc. is currently collecting and analyzing student achievement data using quarterly assessments and the California General Mathematics Standards test in a quasi treatment-control design. Field researchers are gathering information about the program through classroom observations, interviews of teachers, students, and administrators, and analysis of student work.

Shelley Kriegler - 818-995-8685 - for program design information

Cynthia Raff  - 310-569-8258 - to establish a contract and to arrange for professional development

Theresa Lee - 310-310-4948 - with general program questions