Transcript Open Course Library, WAMATH 2010

Changing the world
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
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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
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Precalc 1 and 2
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Functions
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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
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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)
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Precalc 1 and 2
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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
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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
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Polar coordinates
Vectors
Applications of vectors
Polar form of complex numbers
Parametric equations
Intro and Intermediate Algebra
Statistics
Planning on working with Carnegie
Mellon’s Open Learning Initiative
http://oli.web.cmu.edu/openlearning/
Calculus 1, 2, and 3
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How to Succeed in Calculus
0.1 Preview
0.2 Lines
0.3 Functions
0.4 Combinations of Functions
0.5 Mathematical Language
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1.0 Slopes & Velocities
1.1 Limit of a Function
1.2 Limit Properties
1.3 Continuous Functions
1.4 Formal Definition of Limit
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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
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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
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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
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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
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6.0 Introduction to Differential Equations
6.1 Differential Equation y'=f(x)
6.2 Separable Differential Equations
6.3 Growth, Decay and Cooling
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7.0 Introduction
7.1 Inverse Functions
7.2 Inverse Trigonometric Functions
7.3 Calculus with Inverse Trigonometric Functions
Calculus 1, 2, and 3
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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
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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
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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
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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
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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
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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
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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?