Teaching calculus with Mathematica

[Michael_Morrison]

I've spoken to some professors that introduce Mathematica for part of their calculus sequence (for example, second-semester calculus or calc II) and I'm curious to hear if others do that as well, or if Mathematica is introduced at the beginning of the sequence.

[mfitch]

I demonstrate Mathematica usage in first semester calculus starting with derivatives. However I only ask them to use it to check their work on derivatives and anti-derivative and definite integral problems. They also use a provided Mathematica worksheet for one project (Newton-Raphson method).

More students are beginning to use these tools (Mathematica usage is optional in my class), especially since Wolfram Alpha went live.

[Michael_Morrison]

I demonstrate Mathematica usage in first semester calculus starting with derivatives. However I only ask them to use it to check their work on derivatives and anti-derivative and definite integral problems. They also use a provided Mathematica worksheet for one project (Newton-Raphson method).

Thanks! Anyone else care to weigh in?

[Bruce_Torrence]

We have "Calculus with Mathematica" and "Calculus" (without Mathematica) sections available for semesters I and II. Students can freely choose which section to take, and we allow (but don't encourage) students to switch from one flavor to the other at the beginning of each term. Calc III is only offered with Mathematica, so at the end of the day, any student who completes the full sequence has to use Mathematica. This organizational structure demands that the professor has to expect new users at the beginning of each semester. While this seems like it would be difficult, in fact it has run very smoothly (we've been doing this for about a decade). In the first semester, of course, all students get the introduction. But in semesters II and III, there are a mix of students who know and who don't know Mathematica, and we use this as an opportunity to get the students talking to each other and learning from each other. It promotes the sort of productive engagement and interactivity that we like to see from our students, and it happens right at the beginning of the term when it can really do them some good. They are then in a good position to work together on both mathematical and Mathematica issues as they arise over the course of the semester.

[Jose_Luis_Gomez]

Next link contains one of the Mathematica activities I use in my "Calculus 1" course. This particular activity at the begining of the course, when working with piecewise-defined functions, before Limits. Later in the course I refer again several times to their results, because a good Coke bottle made of a piecewise defined functions needs continuity of the function and the first derivative:

http://homepage.cem.itesm.mx/lgomez/chess6/activity.htm

I hope you find it useful
Jose
Mexico

[ron.bannon]

The University of Illinois has an online mathematics program called NetMath <http://netmath.uiuc.edu/> that uses Mathematica as an instructional aid. It would be wonderful to have courses similar to NetMath's offerings, but designed and hosted by Wolfram. Getting a publisher to sign on would be helpful, and having a team of content experts to validate the courses would aid in adoption.

Wolfram needs to see an opportunity here. I'd love to see Wolfram become more of a course publisher, possibly reinvigorating the field of mathematics education.

[Kathy_Bautista]

The University of Illinois has an online mathematics program called NetMath <http://netmath.uiuc.edu/> that uses Mathematica as an instructional aid. It would be wonderful to have courses similar to NetMath's offerings, but designed and hosted by Wolfram. Getting a publisher to sign on would be helpful, and having a team of content experts to validate the courses would aid in adoption.

Wolfram needs to see an opportunity here. I'd love to see Wolfram become more of a course publisher, possibly reinvigorating the field of mathematics education.

Thanks for the good suggestion, Ron! I'll bring it up in my next meeting to see if we can start the ball rolling with this idea. Do you envision these as self-paced courses, like NetMath, where students individually register and complete the course, including locally-proctored quizzes and exams? Or would you prefer to see downloadable notebooks that faculty can obtain to use in their courses and distribute to students?

What do others think?

On a related note, several of my colleagues were involved in teaching before joining Wolfram, and put together some sample primary/secondary school math lessons with Mathematica. I just wrote a post about it here, in case you're interested:
viewtopic.php?f=11&t=46

-Kathy

[ron.bannon]

The University of Illinois has an online mathematics program called NetMath <http://netmath.uiuc.edu/> that uses Mathematica as an instructional aid. It would be wonderful to have courses similar to NetMath's offerings, but designed and hosted by Wolfram. Getting a publisher to sign on would be helpful, and having a team of content experts to validate the courses would aid in adoption.

Wolfram needs to see an opportunity here. I'd love to see Wolfram become more of a course publisher, possibly reinvigorating the field of mathematics education.

Thanks for the good suggestion, Ron! I'll bring it up in my next meeting to see if we can start the ball rolling with this idea. Do you envision these as self-paced courses, like NetMath, where students individually register and complete the course, including locally-proctored quizzes and exams? Or would you prefer to see downloadable notebooks that faculty can obtain to use in their courses and distribute to students?

What do others think?

On a related note, several of my colleagues were involved in teaching before joining Wolfram, and put together some sample primary/secondary school math lessons with Mathematica. I just wrote a post about it here, in case you're interested:
viewtopic.php?f=11&t=46

-Kathy

There's already a product from Math Everywhere, Inc. that is the foundation of NetMath, but many schools are going to need something that's centrally managed. For example, Cengage publishes a product called Course360 where they provide content online, and host the system on their managed LMS. It sure would be nice if Wolfram (or someone else) provided such a service. That is publish a package (including a limited time copy of Mathematica) where the courseware would be provided via an LMS. Teacher would need to be trained, and I'd certainly like to see some standardized assessments to measure what is happening.

[Aaron_Naiman]

Hi all. I would like to weigh in on this subject -- and I will try to keep it short.

Overall, I agree with Ron. I have been teaching college mathematics (linear algebra, calculus and numerical methods) and computer science (C++ programming) since 1995. When I started, I looked for textbooks I liked, which also included teacher's manuals, solution manuals, etc., and lecture slides. Those aspects would really sell me on a textbook. Note that this was not due to laziness, but rather -- why reinvent the wheel??

I did not find the lecture slides, so I spent a lot of time creating my own numerical methods and C++ slides. (For whomever is interested: http://jct.ac.il/~naiman.) I have a pretty well-greased system, including generating test questions and homework assignments. But ...

Recently I noticed, while teaching multi-variable calculus, that even though I am using very snazzy slides from Thomas' Calculus, with great 3-D pictures, and even though I really enjoy the material, it is not enough to grab most of the students.

So, if a picture is worth a thousand words, then animations are worth at least a megabyte. I took a look at a few of Cliff Hastings online presentations -- in a word: excellent -- thanx! I used to be a real Mathematica evangelist while doing my PhD (in Applied Mathematics), but that was only in order to perform very heavy symbolic computations. I knew very little about the new niceties like Manipulate[].

(Gee, this is longer than I had wanted -- I hope you are still reading!)

Bottom line: I would love to have all -- not just the ability to add some of the already prepared Mathematica projects or demonstrations here or there, but rather complete (math) courses, with lecture slides in the slide presentation format, with all of the yummy animation goodies thrown in, the ability to easily create homework assignments or tests, from pools of questions, etc..

Please note that this can be envisioned either accompanying a popular text (e.g., for calculus: Thomas' or Stewart), or perhaps without. (Personally, I favor the former, as: why not use these excellent, tried-and-true resources?)

That would see me -- and I bet many others -- on the use of Mathematica (and a specific textbook) in the course and in the classroom.

Thanx for listening!

Aaron

[Salim_Salem]

Hi all,
In my department, students are obliged to register on a Symbolic Mathematical software course, But this is not an independent course, it is in fact a part of a calculus, algebra, mechanics and electricity courses. What I would like really to see is not a course managed by Wolfram, but some of the great applications of Mathematica on these subjects .