How to teach Mathematica

Question

Preface

A few weeks back I asked in the chat whether other users had any experience preparing and teaching a class/lab on Mathematica as general programming and problem solving tool. I received but two messages about my post so I though I'd give it a try as a question here on meta instead.

Talks with other students and an interested professor at my university who himself is a Mathematica user led to the idea of teaching a Mathematica class/lab. At our university there has been a class for engineers that teaches Matlab for several years and thus most students have at least some proficiency with it. However come work on their thesis or some other hands-on seminar they tend to struggle at lot with sometimes trivial data-exploration tasks. I think Mathematica is a excellent tool in that regard that it makes exploration of data and models really easy and is currently underrepresented outside maths/physics.

I had a look at the new book from Stephen Wolfram available as free online version and the fast introduction for programmers and really liked them for teaching basic syntax and programming concepts in Mathematica that might be foreign to people only familiar with procedural programming (read: Matlab). At the same time I don't think that a lecture on syntax and rule-/pattern-/function-based programming is very engaging in itself.

Question to the community: Which questions here on Mathematica.SE would you recommend as examples worth discussing in such a class (either for being really helpful for beginners or as interesting examples of what can be done in Mathematica, that might be adapted into a kind of guided exercise/exploration task).

Examples:

• Helpful material for beginners: What are the most common pitfalls awaiting new users

• Interesting, self contained problem: Recognizing integers in an image

Answer 1

I'll second m_goldberg's concerns regarding the scope of the question as asked; however, getting students more acquainted with Mathematica such that they can use this tool to solve problems important to them is a task about which I feel very strongly.

Because I view Mathematica as a tool (one I enjoy using), I view your question similar to this one: How to teach Hammer. Grammatical liberties aside, my point is that tools are objects used within the context of something bigger, and are rarely, if ever, taught as standalone skills. Consider how you might entitle a course that contains a module on how to use a hammer; for example, Intro. to woodworking. The course is indirectly about how to use a particular set of tools to create something out of wood.

Likewise, I find it is much more productive to teach Mathematica with a purpose in mind. In my case, I want students to use Mathematica to visualize and process data collected in their (real and virtual) Chemistry laboratory experiments. Since they have a goal (e.g. create a plot of your first order kinetics data including a linear regression line), they have a clear path guiding them towards their goal. Mathematica is huge, it's syntax is not intuitive to those unfamiliar with programming, so it is very easy for beginners to get lost.

Others will disagree with my perception of Mathematica as a tool rather than a language and point to a standard Computer Science curriculum, where courses in programming C, Java, Python, etc. proliferate. It's also clear that WRI wishes for us to accept the Wolfram Language branding. My primary issue with this approach is that I do not believe teaching someone how to program in the Wolfram Language is as valuable as helping them learn how to solve problems.

In summary, if my students were asked the question, "How comfortable are you with using Mathematica?", I would like them to be able to answer with something similar to, "I used Mathematica to analyze data that shows how bleach will remove blue food coloring at twice the rate as it does red food coloring" rather than a generic "I can use it to perform linear regressions".

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Off the soap box, answering the question

Here are a few examples of times where I have exposed my students to Mathematica.

1. Using custom-made CDFs and objects from the Wolfram Demonstrations site: Students gain an appreciation for the power of Mathematica, and based on how well the CDF is designed, are able to meet the learning objectives of the module. Naturally, they gain zero understanding of how Mathematica was used to design/present the information. Nonetheless, I use this platform most often as it is best suited for my student-base, which is typically computer-programming illiterate.

2. Formal instruction. I create videos and worksheets for students to view and follow in order to complete their project objectives. Even the stronger students in my classes tend to treat these materials as cookbook instructions, and the weaker students inevitably "borrow" notebooks to plug in their own data.

3. Opportunistic instruction. In several instances, I have had students ask me how to do something in Mathematica. Most recently, given that my institution has decided not to renew its license, is how to use the Cloud/Development platform. I started some screen-capture software and walked the students through the process, then gave them access to the screencast. Two of the three students continued to use the Cloud for other projects.

4. Independent learning spaces. My research students make use of Mathematica in their work, and since they have very varied projects, it is difficult to have a one-size-fits-all worksheet/introduction. Instead, I teach them about the resources available such as Stack Exchange and how to effectively use the documentation. It is a tedious process; however I see the most improvement in Mathematica proficiency in these students.

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The short version

Now that I've worked through my ideas (hopefully for someone else's benefit, but I suspect this exercise was most beneficial for me), I think I can more succinctly answer your original question.

There is no one set of questions/resources that I find most beneficial for teaching students how to use Mathematica. I prefer a problems-based approach in which the students have a problem to solve and learn how to use tools (in this case, Mathematica) to solve the problem. In my instructional delivery, I help students learn how to search the available resources for guidance. I encourage students to "'Google' linear regression in mathematica" rather than pointing them directly to a particular Q&A or documentation page. Students then benefit not only from the in-context-learning, but also gain tangential experience in searching for and critically assessing resources available to them. It also has the added benefit of removing some biases in my instructional delivery, since I am suggesting resources as an experienced user trying to remember how I felt at the start of the journey.

Answer 2

I think this could be a fruitful Meta question, but I have reservations.

1. I have an issue with the phrasing of your question. I feel that in

   Which questions/answers here on mathematica.SE or other material would you recommend for teaching

   the phrase "other material" makes your question too broad and takes it out of the meta area. I would be much happier with something like

   Which questions here on Mathematica.SE would you recommend as examples worth discussing in such a class.

2. Although I have many favorite questions on Mathematica.SE that I think would make good class material, I am also worried that any recommendation I would make would be inappropriate for your purposes because I don't have a accurate mental picture of the particular class you envision. I would like to be better informed about the kind of content you are seeking before investing time into gather up a list of examples.

Update

Based on Sascha's comments I recommend

• How to draw timing diagram from a list of values?