Algebra Intervention: Aim for Algebra^TM Curriculum & Professional Development

Who Should Participate in Aim for Algebra?

• Teachers of algebra, algebra intervention, and algebra readiness courses
• After-school, extended day, and summer school algebra teachers
• High school exit exam preparation classes
• District/site personnel responsible for mathematics curriculum and programs

What Is the Algebra Intervention Curriculum, Aim for Algebra, All About?

Aim for Algebra is a standards-aligned, concept-based supplemental/intervention curriculum developed by WestEd with funding from the U.S. Department of Education's Institute of Education Sciences. The curriculum program is a coherent set of materials, conceptual in nature, rather than a collection of individual worksheets on isolated topics.

In this curriculum, WestEd researchers have identified and addressed specific areas that most often become barriers to learning algebra. This targeted curriculum helps students better understand essential math topics by providing learning experiences that reinforce, refresh, or reteach these important concepts.

Aim for Algebra has a modular format for easy implementation, flexible programming, and individualized student placement. The content-specific modules may be accessed as a complete set, or individually, or as replacement materials, allowing teachers to provide students a variety of experiences in regular, intervention, or readiness algebra classes.

Aim for Algebra lessons are based on cognitive research and learning theory that optimizes understanding and retention, and enables students to bridge the conceptual gaps created by traditional algebra curricula:

• A focus on the typical barriers to success in algebra
• Purposeful sequencing and scaffolding of ideas to deeper comprehension
• Multiple strategies to reduce student misconceptions
• Manipulatives for hands-on learning for students with varying learning styles

What Is Included in the Aim for Algebra Curriculum?

The following six modules have been published through Its About Time publishing:

Signed Number Operations
Concept 1: Numbers Less Than Zero
Concept 2: Models to Illustrate Signed Number Operations
Concept 3: Applying Signed Numbers

Variables and Expressions
Concept 1: Variables
Concept 2: Writing, Translating, and Evaluating Algebraic Expressions
Concept 3: Creating Algebraic Expressions

Ratio and Proportion
Concept 1: Ratios — Comparing Quantities
Concept 2: Similarity and Scale
Concept 3: Proportions

Patterns
Concept 1: Numerical Patterns and Sequences
Concept 2: Patterns Describing Numeric and Geometric Relationships
Concept 3: Connecting Geometric and Algebraic Patterns

The Coordinate Plane
Concept 1: Parts of the Coordinate Plane/Identifying/Locating
Concept 2: The Equation of a Line–Graphing/Interpreting/Finding Slope
Concept 3: Using the Coordinate Plane in Algebra

Inequalities
Concept 1: Basics of Inequalities
Concept 2: Inequalities in One Variable
Concept 3: Inequalities in Two Variables

Each module includes a student workbook, lesson-by-lesson facilitator guide, pre/post tests, answer keys, and appropriate manipulatives. Additional modules will be available in 2009:

• Number Theory for Algebra
• Exponents
• Rational Numbers
• Proportional Reasoning
• Equations and Formulas
• Data and Probability

Why Does This Algebra Intervention Curriculum Work?

Aim for Algebra lessons and activities help students understand underlying algebraic concepts in a deep way, organize their thinking, work with multiple representations, and learn incrementally. The following seven principles guided the development of the curriculum:

1. Reflects connections to algebra with targeted curriculum
   • Creates connections between prerequisite concepts and algebra, so students recognize what they will know and be able to do as they master the concepts and skills.
   • Focuses on specifically chosen traditional barriers to success in algebra.
   • Uses algebraic expressions and models, and carefully deconstructs the ideas to help students in their mathematical comprehension.
2. Establishes conceptually based foundations for learning
   • Uses links from prior knowledge of arithmetic operations to help students understand algebraic procedures with a conceptual foundation.
   • Uses varied contexts to encourage application of ideas, not merely a set of worksheets, increasing accessibility due to gender, language, and geography.
3. Embeds instruction and develops organizational skills
   • Designs instruction to be interactive to help students stay focused and engaged in ongoing instruction.
   • Uses icons, labeled examples, and less text to encourage self-direction.
   • Provides guidance for organizing, displaying, and explaining the mathematics through key questions and models.
4. Sequences and scaffolds ideas purposefully
   • Uses careful scaffolding of essential ideas to increase access, encourage incremental learning, and diminish the reinforcement of wrong ideas.
   • Provides sequencing of established, quality tasks that is essential to the program's proven success with students, rather than isolated exercises.
5. Uses mathematically precise language and concrete models
   • Uses appropriate, precise mathematical vocabulary and terminology, helping students make connections to core texts and mandated tests.
   • Uses multiple representations of math ideas and asks students to provide multiple responses to deepen mathematical understanding.
   • Encourages use of manipulatives to create models and written responses.
6. Embeds formative assessment
   • Uses multiple checks for understanding through guided practice.
   • Encourages self-checking while doing mathematics by substitution and error analysis.
   • Includes pre- and post-assessments with items from mandated tests.
   • Provides detailed lesson plans for facilitators that indicate higher-order thinking questions, assessments, and homework.
7. Supports differentiated learning
   • Allows for flexible implementation due to modular format.
   • Uses Universal Access Strategies to ensure student understanding — applicable for diverse student populations.

What Were the Field-Test Results?

The materials were field-tested during the 2005-06 school year with more than 1,000 students in grades 7-10. Students who received instruction using Aim for Algebra modules exhibited substantial, statistically significant increases in student achievement, and the data showed no ceiling effect, meaning that continued student improvement could be expected. Teachers rated Aim for Algebra better at engaging students and helping them understand algebraic concepts than curriculum materials they had used in the past.

Professional Development Services: What Is the Format and Cost?

On-site implementation seminars with flexible dates are available for school or district teams. The on-site institutes take place over three days: an initial two-day implementation seminar and a one-day follow-up later in the year. The on-site institutes cost $7,500 per site, for up to 35 participants. Multiple-day seminars, on-site coaching, and technical assistance services are also available.

The curriculum can be purchased through Its About Time publishers: 888.698.8463 or www.its-about-time.com/aim/aim.html.

Contact Information

Kimberly Viviani
650.381.6429
kviviani@wested.org