Core Symbol Manipulations

The apps consist of lessons created as multiple-choice questions, and when you answer a question, you receive an immediate response. Unlike multiple-choice tests, the app lessons use multiple-choice questions as a teaching tool. The “Algebra through Function” series contains five (5) apps and has 41 embedded lessons.

Since the primary mode of operation of the brain is pattern generalizing, almost all of the lessons are structured as pattern-building activities. Users are encouraged to generalize the patterns because when you do, the brain creates a memory of the pattern. To help you generalize the patterns, it is strongly suggested that you write any algebra from the question on paper and next to it write the correct answer. As the questions progress, you should see a pattern developing toward a mathematical goal.

When appropriate, the apps use function as the underlying theme to teach the included algebra. When users connect new algebraic concepts to existing long-term memories of previously learned algebra, the brain understands the new concept or procedure in the lesson. Function representation and function behaviors connect all of the algebra.

Audience:
The apps are designed for students in first or second year algebra, and college students in remedial algebra courses. While the lessons are teaching in nature, they are also for review in preparation for midterm tests.

Technology Requirements:
The graphing calculator is required and is used to help develop patterns and provide visualizations of the algebra in the lessons. It is crucial as a learning tool because visualizations lead to understanding. In addition, the graphing calculator processes function representation and function behaviors, which are at the core of learning algebra through function.

The Content Author:
The author has 16 years of experience writing multiple-choice questions for college mathematics placement tests, for end-of-year exit exams, and for pre-service teacher proficiency tests. See www.redbankpublishing.com for more information about the author.

Symbol Manipulations in Algebra
1. Symbol Manipulations in Algebra: Polynomial Addition
2. Symbol Manipulations in Algebra: Polynomial Multiplication
3. Symbol Manipulations in Algebra: Factoring 1
4. Symbol Manipulations in Algebra: Factoring 2
5. Symbol Manipulations in Algebra: Factoring 3
6. Symbol Manipulations in Algebra: Exponents
7. Symbol Manipulations in Algebra: First Law of Exponents
8. Symbol Manipulations in Algebra: Second Law of Exponents
9. Symbol Manipulations in Algebra: Third Law of Exponents
10. Symbol Manipulations in Algebra: Simplifying Square Roots
11. Symbol Manipulations in Algebra: Multiplying Square Roots
12. Symbol Manipulations in Algebra: Addition and Subtraction of Square Roots