Algebra Survival Guide’s Approach
Supported by Research
What the RESEARCH says about ANALOGIES, METAPHORS, and STORIES:
Students struggling to understand abstract concepts benefit from metaphors, analogies and stories that simplify and clarify concepts. By using analogies, teachers build bridges between familiar concepts and new, perplexing concepts. Once students understand the concepts, they can quickly transition to solving problems with fewer errors.
The Algebra Survival Guide (ASG) follows this research model by using real-life analogies to present abstract algebraic concepts.
Examples:
Negative numbers are likened to both debt and below-zero temperatures. (ASG, pp. 38 – 41) Cartoons give life to these analogies.
To help students make sense of the mixed-sign rule, the ASG uses the analogy of a tug-of-war. (ASG, p.41) A “positive” team and a “negative” team pull on opposite sides of the rope, and the team with more people always wins. Again, a cartoon enhances the explanation, making the concept memorable through a visual representation.
What the RESEARCH says about STEP-BY-STEP INSTRUCTION:
Students benefit from looking at examples of specific problem-solving strategies offered in a detailed way.
The Algebra Survival Guide provides step-by-step instruction for all problems that require more than one step. Even problems as simple as -2 + 5 are broken down into four steps with clear instruction right next to each step. (ASG, p. 40)
What RESEARCH says about the ONE-CONCEPT-AT-A TIME APPROACH:
For students struggling to grasp abstract concepts, it’s important to avoid memory overload and confusion by teaching information in small, understandable chunks.
In the Algebra Survival Guide, each page presents only one concept. The concept is first identified with a question at the top of the page, then immediately explained at the bottom of the page. Both the page layout and the one-concept-per-page format help students isolate and grasp the concept they are learning.
What the RESEARCH says about FOCUSED PRACTICE PROBLEMS:
To prevent students from mixing up concepts, students need practice problem sets that cover just one concept at a time. Only after students demonstrate understanding of a distinct concept should the teacher provide practice problems covering a variety of concepts.
On almost every page, the Algebra Survival Guide provides practice problems that test for understanding of that particular concept. This way teachers and students can check for understanding before moving to the next concept. Tests that cover multiple concepts appear only at the end of each chapter.
As an additional resource, the Algebra Survival Guide Workbook provides many more practice sets, each set testing for one specific concept.
What the RESEARCH says about EVERYDAY LANGUAGE:
Use everyday language as much as possible.
The entire Algebra Survival Guide is written as a conversation between perplexed student and friendly teacher. This approach eases math anxiety and fosters understanding.
What the RESEARCH says about TEXTBOOK DESIGN…
…for special needs students: Special needs students require a variety of organizational aids to avoid feeling overwhelmed when faced with written material.
The Algebra Survival Guide helps students navigate a text by using a variety of organizational aids. Each page incorporates borders, shadowboxes and icons to help students differentiate between various types of information. For example, practice problems are set off from the rest of the page by a border and marked with an icon.
Each page of the Guide also presents the same type of information in the same place, making it easy for students to locate what they’re looking for. For example: on pages using the Q&A format, the question is always in the top half of the page and the answer is always in the bottom half.
…for teenagers: Bold patterns and pictures attract a teenager's attention. Imagery that may appear “busy” to an adult actually helps a teen focus.
The Algebra Survival Guide makes use of "cool" graphics to make the page inviting without being overwhelming. It balances design concepts that organize and identify information with design concepts that create visual interest. The end result is a unique design that keeps students engaged.
DOCUMENTATION:
Glynn, S.M.; Methods and strategies: The Teaching-With-Analogies Model, 44(8), pages 52-55, Copyright 2007, Science and Children.
Jaye, Daniel & Posamentier, Alfred; What Successful Math Teachers Do, Grades 6-12; pages 102 – 103, Research-Based Strategies for the Standards-Based Classroom; Copyright 2005, Corwin Press.
Kenyon, Rochelle; Accommodating Math Students with Learning Disabilities, Copyright September 2000, Focus on Basics, Connecting Research & Practice, Volume 4, Issue B.
Mercer, Cecil D., David M. Miller (University of Florida) & Bradley S. Witzel (Winthrop University); Teaching Students with Learning Difficulties: An Investigation of an Explicit Instruction Model, Learning disabilities Research and Practice, 18(2), pages 121-131, Copyright 2003, The Division for Learning disabilities of the Council for Exceptional Children.
Mercer, Cecil D., David M. Miller & Bradley S. Witzel; Teaching Algebra to Students with Learning Difficulties: An Investigation of an Explicit Instruction Model, pages 121 – 131, Copyright 2003, Learning disabilities Research and Practice 18.
Tyree, Rhonda Beach; Instructional Materials for Diverse learners: Features and Considerations for Textbook Design, Remedial and Special Education, Volume15, pages 363-377, Copyright November 1994, Remedial and Special Education. |
