Calculus Refresher Course for Math Teachers

Catalog Description – This module is a calculus refresher course designed for math teachers. It covers a review of the topics covered in differential and integral calculus with an emphasis on reform. The course covers the material using the content and pedagogy of Calculus&Mathematica, as run on Mathematica.

Calculus&Mathematica is a modern calculus course based on an interactive, electronic text. It is currently offered on campus at a number of universities, and by distance education at many high schools.
Credit: 3 grad. sem. hrs. or 9 CEU’s

Students in this course will review first semester calculus and submit a final project based on teaching calculus and the NCTM standards.

Detailed Description

Using the reform electronic based text, Calculus&Mathematica, this course takes an intuitive, graphical and hands-on approach to reviewing the topics of differential and integral calculus. Topics covered include: Growth, Natural logs and Exponentials, Instantaneous Growth Rates, Rules of the Derivative, Using the Tools of the Differential Equations of Calculus, Parametric Plotting, Integrals for Measuring Area, the Fundamental Formula of Calculus and Measurements using Integrals.

Calculus&Mathematica is a complete, modern calculus course developed at the University of Illinois and Ohio State University. The course, which is based on an interactive electronic text written as a series of Mathematica notebooks, fully integrates the numeric, symbolic and graphic capabilities of Mathematica as tools to explore calculus concepts, methods and applications. As such, it differs markedly in content emphasis and organizational style as well as in its underlying pedagogy from "traditional" calculus courses. Calculus&Mathematica (C&M) is a college-level course that is taught at a number universities and high schools throughout the country.

The goal of this module is to review calculus skills using a reform approach to the material and to tie the material learned to the NCTM standards.

Required Materials

In addition to the general requirements for
participating in the Math Teacher Link Course Module Program, this module also has the following requirements:

Mathematica
To complete this program, you mucst have Mathematica installed on the computer that you will use to complete the coursework. We recommend that new students use Mathematica 8.0, but legacy support can be provided for earlier versions.
Graduate credit students will get the best pricing by obtaining Mathematica from the University. Once you have a University of Illinois NetID (which will be sent to you after enrolling) go to http://webstore.uiuc.edu to obtain the software. This software costs about $25 plus shipping. It will need to be renewed after September 1 for another $25.

Continuing education students will need to contact Wolfram and will choose from a Standard Edition, or a time limited edition. If you purchase Mathematica directly from Wolfram, be sure you don't get the teacher's edition because it will not work with our lessons. Let them know that you are a teacher and that you are taking a Math Teacher Link course. To order by phone, please call (800) 441-MATH (6284) in the U.S. To find out more about Mathematica, please e-mail Wolfram Research Inc. at info@wolfram.com or check out its homepage at http://www.wolfram.com

More information on Mathematica, including some sample applications, called demos, may be found on the Wolfram webpage at http://wolfram.com . The requirements for running the Mathematica software may also be found on that site.
Courseware
All of the Calculus & Mathematica lessons for the first two semesters of calculus are available on a single CD that serves as our electronic textbook.
Graduate credit students can get the Courseware lessons by going to the University of Illinois WebStore http://go.illinois.edu/NetMath234Courseware . The cost is about $25 and you will download the lessons directly from the WebStore.

Continuing education students should purchase the lessons from: https://www.makershed.com/ProductDetails.asp?ProductCode=MMUI220 .

Step By Step

Registration information for this course may be found at http://mtl.math.uiuc.edu/register.php .

This module is estimated to take around 130 to 140 hours to complete. Follow the steps below:

Step #1 Make sure that you have installed Mathematica on your computer

See Required Materials if Mathematica is not installed on your computer.

Step #2

Make sure that you have installed the Calculus& Mathematica courseware from MathEverywhere.com

Step #3 Download the Pre-Assignment

Log in to the course management system at http://cm.math.uiuc.edu/classcomm and download the pre-assignment. Open the file in Mathematica, save the file and submit it to the homework section of Classcomm. Send an e-mail to

$calcref [at] mtl [dot] math [dot] uiuc [dot] edu$

Step #4

If you are not familiar with Mathematica, download the Feel of Mathematica:

Mathematica 5.x

0.FeelofMathematica

Mathematica 6.0

6.0/FeelOfMathematica.zip

Play around with that for an hour or so. You can skip this step if you are already comfortable with Mathematica. You may also download an INTRO to CALCULUS AND MATHEMATICA tutorial from here:

All versions

tutorial

Step #5

Review the document called "introtoc_m.doc." It will guide you though the format of the lessons which reside on your courseware CD from MathEverywhere.

Step #6

All homework assignments are from the Give It a Try and Literacy Sheet sections. The assignments are as follows:

1.01 - G2, G4, G6, G7a, L1,L3,L7,L14,L15,L16
1.02 - G1, G2, G3a, G4a, L2,L4,L6,L9,L17,L18
1.03 - G1a,b, G2, G3, G4a, L1,L4,L5,L8,L9,L11
1.04 - G1, G2a,b,d,e,j, G3, G7a,c, L1 c,d,f,g,h,k,L6,L10,L13
1.05 - G1, G2a,b, G3a, G5a, G7, L1,L2,L5,L7,L9,L10
1.06 - G1, G2b, G3 and either 6a or 6b--your choice, L1,L2,L4,L7,L10,L12
1.07 - G1, G2b, G6, L1, L4, L5, L7, L11, L12, L13
1.08 - G1, G2, G5, G6, L1,L4,L5
1.09 - G2a, G3, G4a,b,c,d, G.5, L6,L7,L8,L9
2.01 - G1, G3a, G5a,b, G6a, G8a, L1,L4,L8,L11,L12,L13
2.02 - G1a,b, G2, G3a, G5, G6, G7a,b, G9a.i, L1,L2,L3b,c,e,g,l,L11,L12
2.03 - G1a,b.i,b.ii, G2a,b,c,d, G3, G4a.i, G8, L1,L2,L6,L7,L11,L14
2.04 - G1, G2a.i, G3, G4, G5, G10, L1,L3,L5,L6,L10,L11
2.05 - G1, G6, G7, L3,L4,L7,L9,L13
2.06 - G1a, G2a.i,ii,iv,v, G5, G7, G9, L1,L2,L4,L6a,b,L9

Step #7 Final Project

Read the NCTM - Principles and Standards, Chapter 7: Standards for grades 9-12, and write a four page paper where you "Compare and Contrast how Calculus & Mathematica vs. a Traditional Calculus course align with the NCTM standards."

If you don't own a printed copy of the NCTM-Principles and Standards, you can access them online at http://standards.nctm.org/ .

E-mail your paper as an attachment to

$calcref [at] mtl [dot] math [dot] uiuc [dot] edu$

Step #8 See handin system for further assignments and projects.

If you are enrolled for graduate or continuing education credit, submit the graded student homework file through the Module Hand-In System using your MTL login and password. You have just completed the module. Congratulations!