Copyright Policy
Archive of Reform Calculus Resources Since 1993!
Compiled* by Harel Barzilai.
(* and authored, where not otherwise stated)
As featured on UTK Math Archives and CollegeBoard.com's APCentral

 ∞ ♥ ❀  Educational non-profit use with proper citation is allowed and encouraged! ❀  ♥   ∞ 
If you have questions or have used or modified feel free to drop me at note at barzilai at gmail dot com


Quick jump to:
- Activities -
Explorations; usually for in-class (can finish for HW)
Suited for cooperative learning (group-work).
- Projects - Long-term (multi-week) in-depth investigations, outside of class
Normally in small groups. Use math plus writing/exposition.
- Capsules - Tutorials, mini-lectures, and discovery-based intro to topics.
- Resources - Handouts for students: How to work in groups in class; how to work on projects outside of class; & more. For instructors sample syllabus and course structure as pioneered at Cornell in mid-1990s; adaptable for your 21st century needs, just modify, say "mash-up" and go!

"Hello! I am a high school Calculus teacher in Las Vegas. I 've been using some of your projects in my class...Thank you for your wonderful problems!"
[See also College Algebra Resources (in preparation)]
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Listings indexed by section in Calculus: Concepts and Contexts  by James Stewart.
If there is enough interest, I will create other indexes. Planned: on-the-fly indexes by keyword.

In-Class Activities


  • (Stewart 0.0)
         
  • Graph Your Story
         
  • A Week in the Life of Sue
         
  • Estimating the Mile Record     [ Guidelines and Solutions]
         (Preview of Calculus)(Functions)

  • For more "preparing the ground" activities on algebra/precalculus topics, see my smaller page with activities in those areas.
  • (Stewart 1.1)
         
  • Estimating the Mile Record    [ Guidelines and Solutions]
         (Preview of Calculus)(Functions)
  • (Stewart 1.2)
         
  • Composing Functions [Broken link]
         (Composition of Functions)
  • (Stewart 1.4)
         
  • Air Traffic Controller
         (Polar)(Parametric)
         
  • A Crash Course in Calculus
         (Polar)(Parametric)
  • (Stewart 1.5)
         
  • Generating the Generations: Modeling Exponential Growth
         (Exponential Functions)(Exponential Identities)(Exponential Growth)
  • (Stewart 2.1)
         
  • The Car Trip    [ Solutions to The Car Trip]
         
  • Designing a Speedometer and A Second Train
         (Tangents)(Velocities)(Rates of Change)(Derivative)
  • (Stewart 2.5)
         
  • Limits with Infinity
         (Limits)(Infinity)
  • (Stewart 2.6)
         
  • The Car Trip   [ Solutions to The Car Trip]
         
  • Designing a Speedometer and A Second Train
         (Tangents)(Velocities)(Rates of Change)(Derivative)
  • (Stewart 2.7)
         
  • The Car Trip    [ Solutions to The Car Trip]
         
  • Designing a Speedometer and A Second Train
         (Tangents)(Velocities)(Rates of Change)(Derivative)
  • (Stewart 2.8)
         
  • From f' to f
         (Derivative)(Graphical)(Antiderivatives)
  • (Stewart 2.9)
         
  • Estimating the Square-Root of 10    [Discussion of one subtlety] --------------format fixed, in 2012!
         (Linear Approximation)
  • (Stewart 2.10)
         
  • From f' to f
         (Derivative)(Graphical)(Antiderivatives)
  • (Stewart 3.2)
         
  • Graphical Differentiation (needs fixing)
         (Product Rule)(Quotient Rule)(Chain Rule)(Graphical)
  • (Stewart 3.4)
         
  • Mathematical Muscle-building: Inverse Trigonometric Functions
         (Trigonometric Functions) (Inverses)
  • (Stewart 3.5)
         
  • Graphical Differentiation (needs fixing)
         (Product Rule)(Quotient Rule)(Chain Rule)(Graphical)

         
  • The Chain Rule and an Interesting Derivative
         (Chain Rule)(Exponential Functions)(Logarithmic Functions)
         
  • Chain of Reasoning
         (Chain Rule)(Mathematical Reasoning)
  • (Stewart 3.6)
         
  • Mathematical Muscle-building: Implicit Differentiation
         (Implicit Differentiation)
  • (Stewart 3.7)
         
  • A Very Fast-Growing Function
         (Exponential Functions)(Logarithmic Functions)(Logarithmic Differentiation)(Max/Min)
  • (Stewart 3.8)
         
  • Estimating the Square-Root of 10    [Discussion of one subtlety] --------------format fixed, in 2012!
         (Linear Approximation)
  • (Stewart 4.1)
         
  • The Balloon
         (Related Rates)
  • (Stewart 4.2)
         
  • A Very Fast-Growing Function
         (Exponential Functions)(Logarithmic Functions)(Logarithmic Differentiation)(Max/Min)
         
  • I Challenge You   (Directions)
         (Max/Min)(Curve Sketching)(Inflection)
         
  • Analyze the Function
         (Curve Sketching)(Max/Min)(Concavity)(Inflection)
  • (Stewart 4.3)
         
  • I Challenge You   (Directions )
         (Max/Min)(Curve Sketching)(Inflection)
         
  • Analyze the Function
         (Curve Sketching)(Max/Min)(Concavity)(Inflection)
  • (Stewart 4.6)
         
  • Save the Pups!   [Solutions to Save the Pups!]
         (Application)(Max/Min)
         
  • The Case of the Perfect Cans
         (Application)(Max/Min)
  • (Stewart 4.9)
         
  • From f' to f
         (Derivative)(Graphical)(Antiderivatives)

         
  • Maglev Train
         (PREPfor: Definite Integral)
  • (Stewart 5.1)
         
  • Sigma Detectives
         (Sigma Notation)(PREPfor: Definite Integral)
  • (Stewart 5.2)Definite Integrals: graphically
         (Definite Integral)(Graphical)
  • (Stewart 5.2)Definite Integrals: numerically
         (Definite Integral)(Table of Values)(Properties of Integrals)
  • (Stewart 5.2)Definite Integral: Estimation with rectangles from Table and from Explicit Formula
         (Definite Integral)(Table of Values)(Estimation)(Approximation)
  • (Stewart 5.2)
         
  • Bare-hands Integration
         (Definite Integral)(Sigma Notation)(Limits)
         
  • Series, Integrals and Hidden Patterns
         (Infinite Series)(Definite Integral)(Sigma Notation)(Limits)
  • (Stewart 5.8)
         
  • Surface Area of a Pool
         (Numerical Integration)
         
  • Sherlock Holmes' Train Adventure
         (Numerical Integration)(Lefthand Approximation)
         
  • Sherlock Holmes' Real Train Adventure
         (Numerical Integration)(Midpoint Approximation)(Trapezoid Approximation)
         (Simpsons Rule)
  • (Stewart 7.5)
         
  • The General Spore (External Link; by Annalisa Crannell)
         (Exponential Growth and Decay)(Separable Differential Equations)
  • (Stewart 8.1)
         
  • A discovery-based Introduction to Infinite Sequences
         (Sequences)
         
  • Exploring Infinite Sequences, Part II
         (Sequences)
         
  • How Do Your Favorite Sequences Stack Up?
         (Sequences)(Foreshadow: Series and Convergence Tests)
  • (Stewart 8.2)
         
  • A discovery-based Introduction to Infinite Series
         (Infinite Series)
         
  • Series, Integrals and Hidden Patterns
         (Infinite Series)(Definite Integral)(Sigma Notation)(Limits)
         
  • The Race
         (Sequences)(Infinite Series)(Geometric Series)
         
  • Medical Dosage
         (Sequences?)(Infinite Series)(Geometric Series)(Application)
  • (Stewart 8.3)
         
  • How Do Your Favorite Sequences Stack Up?
         (Sequences)(Foreshadow: Series and Convergence Tests)

  • (Stewart 8.5) (Stewart 8.6) (Stewart 8.7)
         
  • Taylor Series Cookbook    [1995 Student Feedback on Taylor Series Cookbook]
         (Power Series)(Taylor Series)(Interval of Convergence)
  • (Stewart 8.9)
         
  • The Calculator Puzzler
         (Infinite Series)(Taylor Series)(Estimation)
         (Error Approximation)(Taylor's Theorem with Remainder)
  • (Stewart Appendix G: Polar Coordinates)
         
  • Air Traffic Controller
         (Polar)(Parametric)
         
  • A Crash Course in Calculus
         (Polar)(Parametric)
  • Volume II:
         
  • Steamboat Captains
         (Vectors)(Vector Addition)
         
  • Airline Passenger
         (Vectors)(Vector Addition)(Trigonometry)
         
  • Sail Away   [Student Feedback on Sail Away]
         (Vectors)(Vector Addition)(Vector Components)

    Long-Term Student Projects

    Unlike the Activities section and most of the Capsules and Tutorials section, I am not the author of any of these long-term (multi-week) projects and links are usually to external websites.

    Guidelines for students


  • (Stewart 2.*)(Stewart 4.*)
         
  • The Case of the Crushed Clown
         (Parametric Curves)(Differentiation)(Parametric Differentiation)
  • (Stewart 4.6)
         
  • An Illuminating Project...
         (Max/Min)
  • (Stewart 5.8)
         
  • Tunnel Vision, Inc.
         (Numerical Integration)
  • (Stewart 6.2)
         
  • Houdini's Escape
         (Volumes)(Definite Integral)
         
  • The Case of the Murky Well
         (Volumes)(Definite Integral)
  • (Stewart 7.*)(Stewart 8.*)
          Tripple Trouble    [Sample Grading Scheme for Tripple Trouble]
         (Sequences)(Infinite Series)(Differential Equations)
         (PREPFOR: Power Series)(PREPFOR: Taylor Series)
  • (Stewart 8.*)
         Pi in the Sky    [ Sample Grading Scheme for Pi in the Sky]
         (Infinite Series)(Taylor Series)(Estimation)(Error Approximation)
         (Taylor's Theorem with Remainder)

    Capsules & Tutorials

    By Harel Barzilai except "If only..." by Marshall Cohen and "Power Maths" by Sidney Schuman.


  • (Stewart 1.1)
         
  • Mini-lecture on Functions
  • (Stewart 1.2)
         
  • Mini-lecture on Functions
  • (Stewart 1.* through 4.3)
         
  • Review Problems (Covers Stewart Chapter 1 through 4.3)
  • (Stewart Chapters 2 & 4)
         
  • Power Maths
         (Derivative)(Antiderivatives)(Powers)
  • (Stewart 6.2)
         
  • Tutorial: How to Compute Volume Integrals
         (Volume)(Definite Integral)
  • (Stewart 8.1)
         
  • A discovery-based Introduction to Infinite Sequences
         (Sequences)
         
  • Exploring Infinite Sequences, Part II
         (Sequences)
  • (Stewart 8.2)
         
  • A discovery-based Introduction to Infinite Series
         (Infinite Series)
  • (Stewart 8.*)
         
  • If Only Every Function Were A Polynomial Introduction/Overview of Taylor Series.
         (Infinite Series)(Power Series) and (Taylor Polynomials)

    See also the Taylor Series Cookbook in the Activities section which includes a mini-lecture for students, on strategies (Finding Power Series / Taylor Series for Functions)


    Resources


    For Instructors:
         

  • Some Good Cartoons (MAA Film Series) for teaching Volumes (Stewart 6.2).
         
  • A sample second-semester calculus course with in-class groupwork activities,
         projects, and student oral presentations.
  •        
  • Course Structure
         
  • Hypertext Syllabus
         
  • Some Notes on Using the Hypertext Syllabus
  • For Handing out to Students:

          A sample Flyer to Advertise Reform Sections of Calculus

          Sample Course Information Sheet for Day 1.
         

  • Flyer: Some Suggestions on Working in Groups for Day 1.
    [Praise for Harel Barzilai's handout, "Some Suggestions on Working in Groups" by Dr. Jackson back in 1996]
    (Today she is VP for Learning and IT, Chief Information Officer, and Associate Provost at the University of IL)


          Guidelines for Students for working on Projects.

         
  • Project Evaluation Questions which students complete & hand-in with final Project.

         

  • Some sample Topics for Student Oral Presentations

         

  • Additional Course Evaluation Form for reformed calculus sections.
         
  • [Student Feedback]


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    URL: http://barzilai.org/archive/     Contact: barzilai at the domain gmail.com or hxbarzilai at the domain salisbury.edu

    I first became interested in groupwork as a graduate student at Cornell, where I was involved
    in instigating a reform initiative (http://math.cornell.edu/~projcalc/
    → click on "Spring 1995 Projects Calculus" and "A Cross-Referenced History")
  • Project InterMath has some projects as well.