# Calculus I: A Guided Inquiry

Edition: 1

Pages: 248

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Students learn when they are activity engaged and thinking in class. The activities in this book are the primary classroom materials for teaching Calculus 1, using the POGIL method. Each activity leads students to discovery of the key concepts by having them analyze data and make inferences.  The result is an "I can do this" attitude, increased retention, and a feeling of ownership over the material.

If you are interested in having instructor resources, please reach out to Danielle Schlichtmann (DSchlichtmann@kendallhunt.com).

Kendall Hunt is excited to partner with The POGIL Project to publish materials in a variety of disciplines that are designed for use in active learning, student-centered classrooms.

POGIL is an acronym for Process Oriented Guided Inquiry Learning. Because POGIL is a student-centered instructional approach, in a typical POGIL classroom or laboratory, students work in small teams with the instructor acting as a facilitator. The student teams use specially designed activities that generally follow a learning cycle paradigm. These activities are designed to have three key characteristics:

• They are designed for use with self-managed teams that employ the instructor as a facilitator of learning rather than a source of information.
• They guide students through an exploration to construct understanding.
• They use discipline content to facilitate the development of important process skills, including higher-level thinking and the ability to learn and to apply knowledge in new contexts.

Functions
F1: Review of Functions
F2: Characteristics of Functions
F3: Compositions of Functions

Limits
L1: Limit of a Function
L2: Limit Laws
L3: Precise Definition of a Limit
L4: Continuity

Derivatives
D1: Velocity, Introduction to Derivatives
D2: Derivative at a Point
D3: Derivative as a Function
D4: Differentiability
D5: Second Derivative

Differentiation Techniques
DT1: Power, Constant Multiple, Sum and Difference Rules
DT2: Product and Quotient Rules
DT3: Derivatives of Exponential Functions
DT4: Derivatives of Trigonometric Functions
DT5: the Chain Rule
DT6: Derivatives of Inverse Functions
DT7: Implicit Differentiation

Differentiation Applications
DA1: Related Rates
DA2: Linear Approximation
DA3: Mean Value Theorem
DA4: Maximum and Minimum Values
DA6: Optimization

Integration
I1: Area and Distance
I2: Riemann Sums
I3: Definite Integrals
I4: Fundamental Theorem of Calculus
I5: Antiderivatives and the Fundamental Theorem of Calculus
I6: Indefinite Integrals

The POGIL Project

Kendall Hunt is excited to partner with The POGIL Project to publish materials in a variety of disciplines that are designed for use in active learning, student-centered classrooms.

POGIL is an acronym for Process Oriented Guided Inquiry Learning. Because POGIL is a student-centered instructional approach, in a typical POGIL classroom or laboratory, students work in small teams with the instructor acting as a facilitator. The student teams use specially designed activities that generally follow a learning cycle paradigm. These activities are designed to have three key characteristics:

• They are designed for use with self-managed teams that employ the instructor as a facilitator of learning rather than a source of information.
• They guide students through an exploration to construct understanding.
• They use discipline content to facilitate the development of important process skills, including higher-level thinking and the ability to learn and to apply knowledge in new contexts.

Andrei Straumanis

Andrei Straumanis has a B.A. in Chemistry from Oberlin College and a Ph.D. in organic chemistry from Stanford University. During a three-year NSF-supported post-doctoral fellowship in SMET education, Dr. Straumanis developed and tested materials for guided inquiry organic chemistry. Since 1997, he has given numerous talks and workshops on active learning in organic chemistry and the use of guided inquiry in large classrooms.

Catherine Bénéteau

Catherine Bénéteau is an associate professor in mathematics and statistics at the University of South Florida. She was educated in Canada at McGill University where she earned her bachelor's and master's degrees in mathematics. She obtained her Ph.D. in 1999 at the University at Albany, under the supervision of Boris Korenblum. Her main research interests are in complex function theory and mathematics education.

Zdenka Guadarrama is an associate professor and chair of the department of mathematics at Rockhurst University. She is passionate about mathematics education and outreach, with her work currently focusing on mathematics curriculum development through inquiry, and the intersections of mathematics with other fields, particularly the arts.

Jill E. Guerra

Jill E. Guerra is a preceptor of mathematics at Harvard University. She earned her B.S. from the University of Buffalo and her Ph.D. from the University of Arkansas.

Laurie Lenz

Laurie Lenz is currently a professor of mathematics at Marymount University. She has done research in the field of combinatorial group theory, a blend of group theory and topology. She is currently studying college algebra and calculus reform, the use of technology in the classroom, and research and assessment of teaching methodologies. She earned her B.S., M.A., and Ph.D. from the State University of New York Albany.

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