Syllabus

M302: Calculus Throughout the Curriculum

Syllabus
Spring Semester, 2006-2007

Instructor:
Greg Mongold
IU Math Ed Adjunct Faculty
Math Dept Chair – Bloomington HS North
Phone: Home: 332-2694
Electronic Mail Address: gmongold@indiana.edu

Office Hours:
By appointment in Ed 3274 before or after class. Feel free to phone at any time.

Resources:

Indiana Academic Standards: http://www.indianastandardsresources.org/
NCTM Principles and Standards of School Mathematics: http://www.nctm.org/
Conceptual Building Blocks of Calculus K-12 (from New Jersey): www.state.nj.us/njded/frameworks/math/math13.pdf
AP Central: official instructor site of AP Calculus with resources: http://apcentral.collegeboard.com/

One must register but it's free and this site has the official AP Calculus curriculum guide as well as many years of previously released free response questions along with the official scoring standards. The site also has other supporting documents about developing free response questions (such as "the amusement park problem") and other essays about teaching and learning calculus.

Calculus Textbooks

OnCourse CL:

Tools within Oncourse CL (https://oncourse.iu.edu/portal) will be used on regular basis to communicate class announcements, to answer students' questions, and to encourage peer discussions. Students will also use OnCourse CL group spaces and discussion forums to collaborate on their group projects. All students should become familiar with the use of OnCourse CL during the first week of classes. You may want to enroll in one of the OnCourse workshops to learn more about the available tools: http://ittraining.iu.edu/workshops/schedule_by_group.aspx?group=22

Attendance:

I expect you to attend each class. If you must miss class for a school function or religious celebration, let me know at least two weeks in advance. See comments on attendance in the Assignments and Grading sections.

Grading:
This is a Pass/Fail course. You will pass if you miss no more than three classes, complete your project hours and other assignments, and have a group project that meets the criteria listed above, by the end of the semester.

Assignments
You will be responsible for the production of a course web site that will be available to teachers across the state, country, and world. You will select a major theme (see next section for a list of possible themes) that cuts across the grades 7-12 curriculum, and you will join a group of four students to develop web-based projects centered on that theme. Each student will contribute 15 hours of work, outside of class, toward the web-based project. Your load will increase by 4 hours for every class that you miss. You will also be looking at a great many specific problems and their solutions to illustrate and to help us reach our goals. Contributions may include (but are not limited to):

Challenging and interesting lesson tasks or problems that you have created.
Annotated synthesis of web resources related to your theme.
Analysis and evaluation of teaching ideas from books like Beyond Numeracy, Dr. Euler’s Fabulous Formula, The Universe and the Teacup: The Mathematics of Truth and Beauty, Fermat’s Enigma, The Golden Ratio: The Story of Phi, The Lady or the Tiger by Raymond Smullyan, or any of the other many wonderful books about mathematics in the math sections of Borders or Barnes and Noble OR journal articles from The Mathematics Teacher or The College Journal of Mathematics.
Mathematical computer applications, using graphing calculators or software, such as GSP (Geometer’s Sketchpad), or Excel.
Java scripts, graphs, tables or other representations of data and mathematical concepts.
Audio or video productions relevant to your group’s theme.

You will arrange your plans for contributions with me ahead of time, by meeting with me as a group, so that we can determine the number of hours your individual pieces will require. I may ask you to revise or rewrite pieces that need more work or contain mistakes (typographical, grammatical or mathematical). Try to spread the work evenly over the semester. Your first draft for all pieces must be turned in by ? Only revisions will be accepted after that date.

You may want to look at past projects for the algebra linking course (http://www.indiana.edu/%7Evong/), but note that those projects were in algebra and they were also different in that they were completed individually and were not centered on a particular theme. You are encouraged to use any and all other web resources to build your project. Be sure to reference and link to original web pages. In addition, your group’s project should be closely aligned with Indiana curriculum and state standards (http://www.indianastandardsresources.org/).

You will need to meet with your group at least every other week to design plans and share progress toward your group, web-based project. You will need to communicate more regularly by email, through OnCourse discussion forums and group spaces. During the last two weeks of classes, your group will present its project with the class.

Other course assignments will include completing short readings relevant to class discussions and continuing class discussions in OnCourse discussion forums outside of class.

Calculus Themes

The following are a list of themes from which your group can choose for the web-based project. Keep in mind that each theme should be developed with vertical connections between grades 7 and 12 and we are often interested in seeing the ideas graphically, numerically, analytically, and verbally

Area / Definite Integral
Rate of Change / Derivative
Movement and time (velocity, speed, acceleration, distance traveled, net change in position)
Riemann sum approximations and trapezoid approximations in various area application situations
Optimization (maxima and mimima)
Volume (volume of objects with known cross-section)
Slope fields (rates of change – geometric interpretations)
Functions and their graphs and their relationships to calculus concepts and how to use them to help learning (zeros, maxima, minima, end behavior, continuity)
Finding averages – average value of function – Mean Value Theorem
Approximating solutions to equations (graphing calculators, Newton – Raphson Method, Intermediate Value Theorem, how does “solver” actually work)
Polynomials – zeroes, Rolle’s Theorem
Exponential Growth (before and after solving differential equation dy/dt = ky
Length of a straight line – length of a curve
Understanding and proving a calculus theorem – proof / justification before and after the geometry course
Why is .999… = 1? (rationale without calculus / rationale with calculus) (why do students almost never question that .333… = 1/3
The need for algebraic reasoning in becoming an informed citizen
e^(i * pi) + 1 = 0
The Fundamental Theorem of Calculus in the secondary school curriculum
Work with one of the released AP Calculus free response questions and analyze / develop how earlier math courses can support the learning necessary for success with that specific problem

Criteria for Acceptable Projects

All acceptable group projects must meet the following criteria by the end of the semester:

Group projects will align with all course goals and several learning objectives as listed on the first page of the syllabus.
The projects will include a page articulating the vertical connections made across grades 7-12 (A template for this page will be provided to you).
All relevant connections to the NCTM and Indiana standards will be made explicit within the various components of the group project.
The various components of the group project will be integrated so that they offer a consistent and coherent presentation of the theme.
Group projects will incorporate a variety of resources that will be useful and attractive to math teachers across the state of Indiana.
The final draft will be free of all grammatical and mathematical mistakes.