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Changing the world### Open Course Library Discussion

one course at a time…

Melonie Rasmussen

David Lippman

Tyler Wallace

Dale Hoffman

Federico Marchetti

What is the OCL Project?

Design 42 high-enrollment courses for face-to-face, hybrid, or online delivery

Reduce cost of course materials (< $30)

New resources for faculty to use in their courses

Creating ready-to-use course modules

This is NOT

Mandated curriculum

Canned courses

An effort to force classes to go online

------

The courses will be digital and modular so faculty can take the pieces they want to use and ignore the rest

What we will be doing

Finding, compiling, or creating* a low-cost book or book alternative for under $30

And then…

*writing a book is not what this grant is funding

What we will be creating

- A syllabus with clear learning outcomes
- Course curriculum & instructional materials
- Formative and summative assessments
- Surveys
- Grading rubrics
- Cover letter describing tips and tricks of how to teach the course
- Cover letter for licensing

Who’s doing what?

Tyler Wallace, Big Bend CC

Introductory and Intermediate Algebra

Federico Marchetti, Shoreline CC

Intro Statistics, Math& 146

Melonie Rasmussen & David Lippman, Pierce CC

Precalculus 1 and 2, Math& 141/142

Dale Hoffman, Bellevue College

Calculus 1, 2, and 3, Math& 151/152/153

Precalc 1 and 2

Planned approach:

- Contextual motivation
- Mix of plenty of drill with interesting applications that don’t exactly match examples
- A function exploration approach: With each new function we study: the graph, important features, domain/range, transformations, finding equations from sufficient data, solving equations, modeling, applications.
- Link graphical, verbal, numerical, and algebraic representations

Precalc 1 and 2

- Functions
- Functions and Function notation
- Basic Tool Kit functions
- Domain and Range and graphing and Piecewise
- Composition of functions
- Transformations
- Inverse functions
- Linear functions
- Linear functions (finding equations, rates of change, domain/range)
- Graphs (intercepts, parallel/perpendicular, relating words & tables to graphs)
- Solving equations and inequalities *maybe distribute to 1 & 4
- Linear models (applications, extensions)
- Fitting lines to data
- Absolute value functions (transformations, graphs)
- Solving absolute value equations and inequalities

Precalc 1 and 2

- Polynomial and Rational functions
- Polynomial functions (power functions, form, domain/range, turning points, long run behavior)
- Quadratic graphs (vertex, intercepts, transformations)
- Solving quadratic equations and inequalities
- Polynomial graphs (intercepts, graph to/from equation)
- Rational functions (asymptotes, intercepts, domain/range)
- Solving polynomial and rational equations and inequalities
- Applications of polynomial and rational functions
- Exponential and Logarithmic functions
- Exponential functions (form, finding equations)
- Graphs (asymptotes, intercepts, transformations, domain/range)
- Exponential models (applications, continuous growth)
- Fitting exponentials to data
- Logarithms (def as inverse, use to solve basic exponentials)
- Log properties (properties, use to solve more difficult exponentials)
- Graphs (asymptotes, intercepts, transformations, domain/range)
- Solving exponential and log models (solving applications)

Precalc 1 and 2

- Trig functions
- Angles (degrees / radians / reference angle)
- Right triangles (define sin/cos/tan as right triangle proportions)
- Unit circle (relate triangles to unit circle, special angles to memorize, pythagorean identity)
- Trig graphs (transforms, domain/ranges)
- Reciprocal functions (graphs of sec/csc/cot, domain range, defs)
- Solving trig equations (basic solving using unit circle values. define inverse functions, domain/range, simple solves)
- Applications of trig equations (modeling)
- Changing Amplitude & Midline
- Non-right triangles (law of sines/cosines with applications)
- Simplifying trig expressions (use identities)
- Proving trig identities
- Solving equations using identities
- Applications of trig
- Polar coordinates
- Vectors
- Applications of vectors
- Polar form of complex numbers
- Parametric equations

Statistics

Planning on working with Carnegie Mellon’s Open Learning Initiative

http://oli.web.cmu.edu/openlearning/

Calculus 1, 2, and 3

- How to Succeed in Calculus
- 0.1 Preview
- 0.2 Lines
- 0.3 Functions
- 0.4 Combinations of Functions
- 0.5 Mathematical Language
- 1.0 Slopes & Velocities
- 1.1 Limit of a Function
- 1.2 Limit Properties
- 1.3 Continuous Functions
- 1.4 Formal Definition of Limit
- 2.0 Slope of a Tangent Line
- 2.1 Definition of Derivative
- 2.2 Differentiation Formulas
- 2.3 More Differentiation Patterns
- 2.4 Chain Rule (!!!)
- 2.5 Using the Chain Rule
- 2.6 Related Rates
- 2.7 Newton's Method
- 2.8 Linear Approximation
- 2.9 Implicit Differentiation

Calculus 1, 2, and 3

- 3.1 Introduction to Maximums & Minimums
- 3.2 Mean Value Theorem
- 3.3 f' and the Shape of f
- 3.4 f'' and the Shape of a f
- 3.5 Applied Maximums & Minimums
- 3.6 Asymptotes
- 3.7 L'Hospital's Rule
- 4.0 Introduction to Integration
- 4.1 Sigma Notation & Riemann Sums
- 4.2 The Definite Integral
- 4.3 Properties of the Definite Integral
- 4.4 Areas, Integrals and Antiderivatives
- 4.5 The Fundamental Theorem of Calculus
- 4.6 Finding Antiderivatives
- 4.7 First Applications of Definite Integrals
- 4.8 Using Tables to find Antiderivatives
- 4.9 Approximating Definite Integrals

Calculus 1, 2, and 3

- 5.0 Introduction to Applications
- 5.1 Volumes
- 5.2 Length of a Curve
- 5.3 Work
- 5.4 Moments and Centers of Mass
- 5.5 Additional Applications
- 6.0 Introduction to Differential Equations
- 6.1 Differential Equation y'=f(x)
- 6.2 Separable Differential Equations
- 6.3 Growth, Decay and Cooling
- 7.0 Introduction
- 7.1 Inverse Functions
- 7.2 Inverse Trigonometric Functions
- 7.3 Calculus with Inverse Trigonometric Functions

Calculus 1, 2, and 3

- 8.0 Introduction
- 8.1 Improper Integrals
- 8.2 Finding Antiderivatives: A Review
- 8.3 Integration by Parts
- 8.4 Partial Fraction Decomposition
- 8.5 Trigonometric Substitution
- 9.1 Polar Coordinates
- 9.2 Calculus with Polar Coordinates
- 9.3 Parametric Equations
- 9.4 Calculus with Parametric Equations
- 9.5 Conic Sections
- 9.6 Properties of the Conic Sections

Calculus 1, 2, and 3

- 10.0 Introduction
- 10.1 Sequences
- 10.2 Infinite Series
- 10.3 Geometric Series & the Harmonic Series
- 10.4 Positive Term Series: Integral Test & P-Test
- 10.5 Positive Term Series: Comparison Tests
- 10.6 Alternating Sign Series
- 10.7 Absolute Convergence & Ratio Test
- 10.8 Power Series
- 10.9 Representing Functions as Power Series
- 10.10 Taylor and Maclaurin Series
- 10.11 Approximation Using Taylor Polynomials
- 11.0 Introduction: Moving Beyond Two Dimensions
- 11.1 Vectors in the Plane
- 11.2 Rectangular Coordinates in Three Dimensions
- 11.3 Vectors in Three Dimensions
- 11.4 Dot Product
- 11.5 Cross Product
- 11.6 Lines and Planes in Three Dimensions

Calculus 1, 2, and 3

- 12.0 Introduction to Vector-Valued Functions
- 12.1 Vector-Valued Functions and Curves in Space
- 12.2 Derivatives & Antiderivatives of Vector-Valued Functions
- 12.3 Arc Length and Curvature of Space Curves
- 12.4 Cylindrical & Spherical Coordinate Systems in 3D
- 13.0 Introduction to Functions of Several Variables
- 13.1 Functions of Two or More Variables
- 13.2 Limits and Continuity
- 13.3 Partial Derivatives
- 13.4 Tangent Planes and Differentials
- 13.5 Directional Derivatives and the Gradient
- 13.6 Maximums and Minimums
- 13.7 Lagrange Multiplier Method
- 14.1 Double Integrals over Rectangular Domains
- 14.2 Double Integrals over General Domains

Questions / Discussion

What would make you want to use one of these OCL courses?

What kind of course supplement materials are important to you?

How important is the book itself? Could videos, Powerpoints / lecture notes, worked out examples, exercise sets suffice?

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