New Calculus Research Lab!


TELEPHONE (516) 377-9269 FAX (516) 377-3764


Title of Proposal:
Calculus Research Lab
(final revision 4 – new title, free software, free textbooks,

Calculus (AB or BC)

Persons Preparing this Proposal:
A. Jorge Garcia

This proposal represents a:
new course or program;

Anticipated outcome of this proposal. (Exactly what will the district have at the conclusion of this project which it did not have before?)
The outcome of this proposal is a laboratory class dedicated to using computers to solve mathematical problems involving real world applications.

Who will be using the outcome or product of this project?
The intended audience for this course is the students enrolled in AP Calculus.

Why is the project necessary?
Most of the students in AP Calculus will be pursuing majors related to math, science or technology. Many of the colleges these students will be attending will require the use of a Scientific Computing or Mathematical Programming Environment. This course is intended as an introduction to such an environment.

What Board of Education or building-level goals or objectives will be met through development and implementation of the program?
The emphasis of this course will be enrichment. Each laboratory will be devoted to learning how to use SAGE to solve real world problems thereby enriching the AP Calculus curriculum. SAGE is Free Open Source Software (FOSS) very much like Mathematica, Maple and MATLAB.

What makes it significant enough in scope to place it outside of the professional periods wherein curriculum development projects are assigned throughout the school year or semester?
A Scientific Computing or Mathematical Programming Environment such as SAGE has never been used in our school. Significant time will be needed to develop teaching materials that meet the goals mentioned above and for teacher training.

What are the program and/or school goals or objectives which will be more effectively met as a result of creating or revising the curriculum or, put differently, what are the specific goals of the project?
By meeting the goal of enrichment as described above, these students will be more successful when they take the AP Calculus exam!

Please provide the following information about the proposed project and attach any supportive materials which will help in reviewing this proposal.
TextBook: Teacher developed lab materials and free online textbooks.

Number of Hours needed to complete the project:
Curriculum Development: 30 hours

Rationale for determining that number of hours:
Determined by previous Math curriculum writing projects.

Program Credit (if applicable):
0.5 credit

Staffing Requirement(s):
one teacher who will teach 1 lab (every other day) or 2 labs (everyday) depending on the enrollment.

Anticipated related costs (e.g., textbooks, supplies, equipment, transportation, etc.):
SAGE: Software for Algebra and Geometry Exploration is available at and This software will be installed on the Linux clients in Room 429. The textbooks are free online pdfs:


Timeline for implementation (Please detail when, if necessary, the program will appear in the "Course Offerings Booklet" or when it will be implemented into the regular school program. How will students be selected for the program? Is this heterogeneous or homogenously grouped? Staff Development - What is requested relative to training to deliver this program? etc.):
September 2009.
Students that take this course will have a co-requisite of AP Calculus AB or
AP Calculus BC.

Evaluation Procedures (Specifically, how and when will this program be evaluated? Give criteria for evaluation.):
Students will be evaluated by using weekly programming projects. We will evaluate the success of the course by enrollment and the number of students passing the AP Calculus exam.

Date of anticipated completion of the project:
May 2009

Outline for the content of the project: (Please be as specific and complete as possible)
The teacher will choose labs from the following free online textbooks as time permits:

Quarter I
Differential Calculus and SAGE (DCS)
DCS101: Collection of Formulae
DCS102: Variables and Functions
DCS103: Theory of Limits
DCS104: Differentiation
DCS105: Derivative Rules
DCS106: Applications of Derivatives
DCS107: f’, f’’, f’’’
DCS108: Extrema and Inflection
DCS109: Differentials
DCS110: Related Rates
DCS111: Change of Variables
DCS113: Mean Value Theorem

Quarter II
Integral Calculus using SAGE (ICS)
ICS101: The Integral
ICS102: Applications
ICS103: Polar Coordinates
ICS104: Integration Techniques
ICS105: Sequences and Series
ICS106: Intro to Ordinary Differential Equations

Quarter III
Differential Equations using SAGE (DES)
DES101: First Order Ordinary Differential Equations
DES101: Second Order Ordinary Differential Equations
DES101: Systems of First Order Ordinary Differential Equations
DES101: Intro to Partial Differential Equations

Quarter IV
AP Review
Numerical Computing with MATLAB or Octave using SAGE (NCM)
NCM101: Linear Equations
NCM102: Interpolation
NCM103: Zeros and Roots
NCM104: Least Squares
NCM105: Quadrature
NCM106: Ordinary Differential Equations
NCM107: Random Numbers
NCM108: Fourier Analysis
NCM109: Eigenvalues and Singular Values
Experiments with MATLAB or Octave using SAGE (EXM)
EXM101: Iterated Functions
EXM102: Fibonacci Sequences
EXM105: Matrices and Transformational Geometry
EXM106: Fern – An Iterated Fractal System
EXM109: 2D Cellular Automata and the Game of Life
EXM110: Benoit Mandelbrot’s Fractal
EXM115: Predator vs. Prey and Simultaneous Ordinary Differential Equations Models
EXM116: Hydrodynamics and Partial Differential Equation Models
Simple R for Statistics using SAGE (SRS)
SRS101: Data
SRS101: Univariate Data
SRS101: Bivariate Data
SRS101: Multivariate Data
SRS101: Random Data
SRS101: Simulations Data
SRS101: Exploratory Data Analysis
SRS101: Confidence Interval Estimation
SRS101: Hypothesis Testing
SRS101: Two-sample Tests
SRS101: Chi Square Tests
SRS101: Regression Analysis
SRS101: Multiple Linear Regression
SRS101: Analysis of Variance