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.

Common Core Standards for Mathemtical Practice that are emphasized include:

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 and the Common Core Mathematics Standards.

Required Materials

In addition to the general requirements for participating in the Math Teacher Link Course Module Program, this module also  uses the Making Math online system. 

There is no separate textbook required to take this course -- only an account ($99) in the Mathable system. This system fully integrates three things:
1) Courseware designed to help students learn by dynamic exploration and visualization,
2) A web-based interface to the computer algebra system Mathematica for students to perform calculations and write full explanations of their solution process,
3) A Learning Management System to streamline administration of the course and promote communication between students, instructors, and mentors.

You will be given information about how to sign up for an account in Mathable after you enroll in the course. NOTE: Because Mathable is a web based service, students will need to be able to work with a consistent internet connection. In addition, Mathable is currently only supported on Firefox and Chrome web browsers, so students must download and install the latest version of Firefox or Chrome.

For more information, and to see an overview of the Mathable system, please visit and preview the "How it Works" tab.

Step By Step

Registration information for this course may be found at .

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

Step #1 Make sure that you have set up your U of I email account.

Before you begin the course, please set up your University of Illinois email account using your NetID and password. Directions for the setup can be found in the email you received from OCE upon registration. 


Step #2: Create a Mathable Account

2)  Create a Mathable account by following the Mathable link in your welcome email.  You can use this same URL once you've created your account to log into your course. (Mathable must be accessed through the most recent version of the Mozilla Firefox Browser, available at or with the most recent version of Google's Chrome Browser, available at ). 

This webpage will walk you through the registration steps; you will be asked to provide your Illinois email address.  

Step #3: Getting the Feel of Mathable

If you are not familiar with Mathematica, sign into your "Mathable" account and you will find a unit titled "Getting Started" that contains lessons which explain the system, work through these lessons to become familiar with how to use Mathematica.

Play around with that for an hour or so. You can skip this step if you are already comfortable with Mathematica.

Step #4: Starting the Lessons

Proceed to Unit 1 in "Mathable".  You will find each unit to be composed of two parts, the problem set and the literacy sheet. You will do the problem sets in Mathable, and will find your literacy sheet assignments in your Moodle course at:

 You should receive your moodle log in information with your welcome email at the beginning of your course.


After units 1.05 and 2.01 you will find short writing assignments.  You will complete the writing assignments in Moodle, as you do the literacy assignments.

Step #5 Final Project

Reflecting on how calculus taught with Mathematica relates to the math standards.

Here you have an option, you can either write towards the National Council of Mathematics Standards (option 1) or you can write towards the Common Cores State Standards Initiative (option 2 ).

Option 1:

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 .

Option 2:

The Common Core State Standards Initiative inclues a component called Standards for Mathematical Practice .  Read through those standards and write a four page paper where you "Compare and Contrast how calculus taught with Mathematica vs. a Traditional Calculus course align with the Common Core Standards for Mathematical Practice."

When you are finished, upload your completed assignment to the Moodle hand in site.   

Step #6 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!