Calculus & Mathematica for Mathematics Teachers

Calculus & Mathematica is a university credit, 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.  This module introduces teachers to the content and pedagogy of the Calculus&Mathematica course. This module is suitable for any mathematics teacher interested in teaching, or simply learning more about, the Calculus&Mathematica course. Credit: 1 grad. sem. hr.

Common Core Standards for Mathemtical Practice that are emphasized include:

Calculus & Mathematica for Mathematics Teachers was written by Tony Peressini and Debra Woods from the University of Illinois during January 1996. It was updated by Tom Anderson for Mathematica Version 10.0 in April 2016.

Detailed Description

Calculus & Mathematica is a complete, modern calculus course developed recently 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 familiarize you with the Calculus&Mathematica course as well as how it is taught and the way in which student performance is evaluated.

Because you are a mathematics teacher who is familiar with calculus, the best way to achieve this goal is to have you go through some sample lessons in the course and do some homework from these lessons just as C&M students do. This will not be as boring as it might sound because, as noted above, Calculus & Mathematica presents calculus in a manner that is usually quite different from the way that you and we learned it (or taught it) before. Some of these differences may please you as welcome changes from traditional approaches; others may annoy or worry you. In either case, we think that they will prompt you to rethink and perhaps modify your views of how calculus can and should be taught.

We will also have you look at some sample homework from high school students and then look at how it was graded. That will help you to understand the homework grading philosophy for the course.

After this, we will ask you to grade one "real" homework set for one or our current C&M students.

Although this module was initially developed for high school mathematics teachers who served as local coordinators for the Calculus & Mathematica NetMath Distance Education Program in their schools, we believe that any mathematics teacher will find it to be a good, thought provoking introduction to the content and pedagogy of the C&M course and, more generally, to the recent calculus reform movement.

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:

Step By Step

Registration information for this class may be found by clicking the "Registration" Link above.

Materials for the module for Mathematica Version 10.0 may be downloaded by clicking on the Version 10.0 attachment link below.

Materials for the module for Mathematica Version 8.0 may be downloaded by clicking on the Version 8.0 attachment link below.

For Mathematica beginners, it is likely that it will require about 45 hours to complete this module.
After you have completed and submitted your on-line registration form, you will be directed to download the necessary files for this module. After you have downloaded the appropriate module files folder for your operating system (PC or Macintosh) and your copy of Mathematica has been installed, you are ready to begin. Proceed as follows:

AttachmentSize
Mod1download_V10_Moodle HandIn.zip2.15 MB
Mod1download_v8_Moodle.zip2.16 MB

Step #1

The lessons that you are required to review are in the Sample Lessons folder in the download folder. Review the three lessons listed below and do the problems that are listed as Teacher Homework. These problems are a subset of the student homework listed for each lesson. As you finish each lesson, review the corresponding comments in the Highlights file in the download folder. Share your views with us by adding them to the Highlights file.

We would suggest that you read the Basics and Tutorials sections of each lesson actively (that is, try some variations on the given examples) and then skim the student homework for that lesson. Then start the Teacher Homework problems and refer back to the Basics and Tutorials as needed. We have purposely assigned only two or three problems from each lesson so that you will have time to write detailed solutions (including explanations of procedures and results) to these problems. That is what we expect (and usually get) the C&M students to do and we would you to have a taste of that too!

Lesson 0: Feel of Mathematica
This one is optional. It serves as an introduction to Mathematica for the students in the course. If you are already using Mathematica, you probably won't find anything new here. It may be interesting to skim the lesson anyway just to see how C&M students are being introduced to the use of Mathematica.

Pre-Assignment: Open the file called preassign.nb and follow the instructions within. Submit the assignment to the Module Working Environment under the Homework button using your MTL login and password.

Lesson 1.01 Growth;
Student Homework Assignment: G.1; G.2; G.4. a); G.5; G.6. b), c); G.8. a), d).
Teacher Homework: Do G.2 and G.8 and copy your solution to these two problems in the Assignment 1.1 notebook in the Module download folder.  Your solution will be embedded in the problem, so you will in effect be copying both the problem and your solution simultaneously.

Lesson 1.05 Tools;
Student Homework Assignment: G.1 a), d); G.2 c); G.3; G.4;
G.5.a) ,b); G.6; G.7; G.9 a) ,d).
Teacher Homework: Do G.1 a), d) and G.7 and copy your solution to these two problems in the Assignment 1.1 notebook in the C&M Module download folder.

If you are enrolled for graduate or continuing education credit, submit Assignment 1.1 through the Module Working Environment under the Homework button using your MTL login and password before you go on to Step 2.

 

Step #2

Review the four lessons listed below and do the problems that are listed as Teacher Homework. As you finish each lesson, review the corresponding comments in the Highlights file. Share your views with us by adding them to the Highlights file.

Lesson 1.06: Differential Equations
Student Homework Assignment: G.1.a), b), d), e); G.2. b); G.3; G.4;
G.5 a), c), d); G.6.b); G.8
Teacher Homework: Do G.2 b) and G.3 and copy your solution to these problems in the Assignment 1.2 notebook in the C&M Module download folder.

Lesson 1.09 Parametric Plots

Student Homework Assignment: G.1; G.2; G.3; G.4; G.5; G.6; G.11
Teacher Homework: Do G.3, G.6 and G.11 and copy your solution to these problems in the Assignment 1.2 notebook in the C&M Module download folder.

Lesson 2.01: Measuring Area

Student Homework Assignment: G.1; G.2 a), b), d); G.3; G.4 a), b), c), e);
G.5; G.6; G.8 a); G.9.
Teacher Homework: Do G.4 a), b), d); G.6 and G.8 and copy your solution to (all parts of ) these problems in the Assignment 1.2 notebook in the C&M Module download folder.

Lesson 2.03: Measurements
Homework Assignment: G.1 a); G.3; G.5; G.7
Teacher Homework: Do G.1 a); G.3; and G.5 and copy your solution to these problems in the Assignment 1.2 notebook in the C&M Module download folder.

If you are enrolled for graduate or continuing education credit, submit Assignment 1.2 through the Module Working Environment under the Homework button using your MTL login and password before you go on to Step 3.

Step #3

Review the contents of the Sample Student Homework (SampleHW) folder and comment on the sample homework and its grading in the Highlights notebook in the C&M Module download folder.

This folder contains sample homeworks from former C&M students, most very good and some just OK. Reviewing these files should help you to get a feel for the work that the better C&M students do. You will also see how the homework was graded by their undergraduate C&M mentors. We have removed all student and mentor names from the samples to respect the privacy of the individuals involved. Again, we invite you to comment on the homework and its grading in the highlght.nb file.

If you are enrolled for graduate or continuing education credit, submit Assignment 1.3 through the Module Working Environment under the Homework button using your MTL login and password before you go on to Step 4.

Step #4

Grade a homework assignment from one of our current C&M students.

Please e-mail us at candm@mtl.math.uiuc.edu when you are ready to do this. We will select a current homework file and send it to you as an e-mail attachment. You should grade the homework and insert comments to the student as you see fit.

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! Those of you enrolled for continuing education credit will be sent feedback on the three assignments that you were required to submit.