# Discovering Advanced AlgebraAn Investigative Approach

## An In-Depth Look

### Inquiry-based Algebra curriculum offers real-world applications and cooperative learning

Changes in society and the workplace require a careful analysis of the algebra curriculum that we teach. The curriculum, teaching, and learning of yesterday do not meet the needs of today's students.

### Mathematics in Real-Life Contexts

• Students work with real data, real-life situations, and real-world applications to realize the value and enjoyment of learning mathematics.
• Innovative classrooms incorporate investigations, experiments, and cooperative learning.
• Students approach traditional and contemporary algebra topics from many different perspectives, exploring concepts informally and intuitively before seeing algebra in its abstract, symbolic representations.
• Students use technology, such as graphing calculators, computers, and electronic data-collection devices, to explore problems, ideas, and concepts from different viewpoints in a learning environment that encourages a spirit of discovery.
• The coherent nature of the content structure enables students to see the connections between families of functions.
• Students use both technology-related and paper-and-pencil problem-solving tools.
• Explorations and investigations emphasize symbol sense, algebraic manipulations, and conceptual understandings.
• Students make sense of important algebraic concepts, learn essential algebraic skills, and discover how to use algebra as a practical and flexible tool.

### Important Benefits of Discovering Advanced Algebra

• Encourages students to make sense of numbers, variables, expressions, equations, and algebraic "laws" in contextual situations
• Prepares students for additional study of mathematics, science, and courses rich in data analysis and statistics, in high school and beyond
• Allows students to work with real-life data, situations, and applications
• Integrates algebra with geometry, statistics, data analysis, functions, probability, and trigonometry
• Emphasizes inquiry, problem solving, mathematics investigation, writing, discussion, and cooperative learning
• Integrates graphing calculator technology, with specific instructions for the Texas Instruments TI-83 Plus, TI-84 Plus, TI-Nspire, and TI-Nspire CAS graphing calculators, to develop a powerful, meaningful, and useful mathematics content and process
• Provides optional opportunities for in-depth explorations using Dynamic Mathematics software, with specific instructions for The Geometer's Sketchpad® and Fathom® Dynamic Data software
• Provides a hands-on, investigative approach that is easily adapted for multiple periods or block scheduling, sustaining students' interest for 90 minutes, as they set up, complete, and discuss the investigations
• Embodies an algebra curriculum that is consistent with the NCTM Principles and Standards for School Mathematics
• Is highly adaptable to different teaching styles and curricular needs