Creative Writing is Experiential Learning!

Abstract: Creative writing gives students a chance to experience a topic in a new way and lets students try on an alternate persona. Also, I muse about how to include creative writing in a math class.

At the Experiential Learning Lunch on October 21, 2015, we had a lively discussion about creative writing and why it is such a powerful tool in experiential learning.

Keren Dali (Library and Information Science) explained that creative writing is a great way to inject energy into the classroom. She has students choose from writing a screenplay, a letter to the editor, a blog post, a love story, etc. It allows the students to change their voice by playing a role, which allows students to take risks that they wouldn't take from their usual position. For example, a student might learn about the background of an author and do some reflective writing about them. This would help the student to connect better with the author's writing because the students place themselves in the author's shoes.

Yves Cloarec (English) voiced the concern that standard writing assignments often have the students writing what they think the instructor wants to hear. An example was given in which students did background work or research that supports one conclusion and they write that it supports an opposing conclusion because that is what they think is what the research was supposed to say!

Yves also talked about the process he uses to have the students get the most out of their creative writing. His assignments often have two parts. There is the creative writing part, but there is also an academic writing part. For every two pages of creative writing that the students submit, they are also expected to produce one page of academic writing explaining the thought process behind their creative writing. The students would discuss the research that went into their work, giving citations for theoretical resources or showing analogous constructions in other works they have read. This left a strong impression on me because I often think of "creative writing" as something that is difficult to grade objectively and fuzzy in some sense, but by requiring students to theoretically justify their creativity, you can see the thought process behind the project, and see that the students actually put thought into their work.

There was a discussion about having students learn about the writing process by having the students first think about all the steps involved in making toast---it sounds easy until you go into all the steps. The students are asked not to write the steps but instead use symbols to draw the steps of the process. Once the students have tripped over themselves they are supposed to learn that writing is a process as well. That writing entails first thinking about what they want to write, organizing their thoughts, starting to write, and rewriting (multiple times).

This exercise made me think about a recent blog post that I read about teaching students how to write mathematical proofs, where every step from start to finish must be explained with no gaps in logic. The activity in question involved having the students write down the sequence of events that are necessary to make a peanut butter and jelly sandwich. (Watch a Fun music video non sequitur.) Then an outside actor "PB&J guy" comes in and does exactly what the students have written, which is not at all what the students meant. This is an exercise in getting students to think carefully and write precisely. And then in class it is possible to refer to gaps in logic in a very handy way by referencing "PB&J guy" throughout the semester. Unfortunately I can't find the original post; if anyone finds it, I will update this post. (Here is a nice handout about such an activity.)

I'm trying to figure out how to incorporate more creative writing into my own mathematics classroom. Would that mean writing a paper from the point of a view of a mathematician so that the theorem they just proved is understood more in context? I have already had students research mathematicians and write papers or edit Wikipedia on them, but this would take that to another level. Would that mean writing a play or story that had as its basis some mathematical theory or computer science algorithm? (In fact, our class acts out the Gale-Shapley algorithm in Graph Theory.) Would this involve having the students explain their thought processes when they are writing their proofs or having students submit not just their proofs but also their proof drafts and including a discussion about why they had to change their original reasoning? I will be able in incorporate one of these ideas next semester in my Math with Mathematica class. I will make sure to have my students write the thought process they went through to create their mathematical art, so student's aren't just "making art"—they are being thoughtful in the choices they make along the way.

This blog post is part of the Queens College Teaching Circle blog; it is cross-posted on my personal teaching blog, Math Razzle.

Experiential Learning Lunch on 21 Oct 2015

Abstract: We highlight a few of the innovative teaching techniques that were presented in October's Experiential Learning Lunch.

On Wednesday, October 21, 2015, twenty-eight members of the Queens College community assembled for a lunch discussion devoted to Experiential Learning. (Learn more about our group.) I had asked participants to prepare a 2-3 minute discourse about something that they tried recently and a self-evaluation of what went well and what could be improved in the future.

In this post I would like to highlight some of the discussions we had.

Zahra Zakeri (Biology) shared the idea of the "experimental essays" that her students are required to write on various topics throughout the semester. The students must develop an experiment that would test certain hypotheses, such as "How would we know whether two twins are monozygotic?", and justify why their experiment is a valid way to test their hypotheses. By having to design this experiment the students have to gain a deeper understanding of the material in her classes instead of simply memorizing facts.

Elena Mancini (German Language and Literature) highlighted how she is taking ideas she is learning in the theater techniques workshop and integrating them into her class. She asks groups of students to analyze a text passage for tone, emotions, believability, and perspective. The gropu takes this information to create a play about the passage using props. This live reinactment of the passage infuses energy into the classroom and is widely regarded as a fun and engaging assignment. This discussion initiated a more general conversation about creative writing, which I feel merits its own blog post. So keep tuned for that!

Keren Dali (Library and Information Science) was happy to share how most of the courses in their department are experiential. For example, if the students are learning cataloging, they need hands-on experience in learning how to catalog. Keren was especially proud of how she helps to take experiential education to the next level—into the community. Her class partners with libraries in the community; each student group spends time with a librarian to find challenging areas for which the libraries don't have the staff or resources to address. The students work out a solution to the problem in a group and present it to the librarian by the end of the semester. Many of these solutions are then implemented by the community libraries. The students get real-world experience and the libraries have made strides toward improving their services. It sounds like a great program!

Lightning round! One-sentence summary of some other presenters:

Joe Pastore (Mathematics) uses the software GeoGebra to exhibit mathematical concepts dynamically in class, which allows his high-school-teaching students to integrate this technology directly into their own classes.

Adam Kapelner (Mathematics) has programmed software called Gradesly which integrates directly into Google Sheets to provide students and instructors with up-to-date information about course grades.

Eva Fernandez (Provost's Office and CTL) talked about the Queens Memory Project, which collects an audio and visual history similar to Story Corps.

Jack Zevin (Education) talked about this simulation game in which students play city council members and gain first-hand experience with the legislative process.

It is always great to hear the ideas others are trying on campus. In many of these situations, students are initially reluctant to participate in these "non-standard" assignments but by the end of the semester these assignments are what the students rave about on their teaching evaluations.

The topic that generated the most amount of buzz was about technology in the classroom. Should students be allowed to use their phones in the classroom? How can we integrate technology into the classroom in a thoughtful and educationally beneficial way? What works well in different size classes? I think we have found the topic of December's Experiential Learning Lunch!

I was especially pleased and proud that three of my math department colleagues came and participated. It's nice to be building a local network supporting innovation in mathematics instruction!

This blog post is part of the Queens College Teaching Circle blog; it is cross-posted on my personal teaching blog, Math Razzle.

The Experiential Learning Group at Queens College

Abstract: This post is a quick introduction to our college's experiential learning group. What is experiential learning? What happens in a group meeting?

I've been participating in a teaching and learning group at Queens College focused on Experiential Learning since it was founded in 2012 when Grace Davie (QC History) was taking the lead. This group of like-minded educators spans many disciplines and provides a refreshing sense of community on a commuter campus where people in different departments rarely interact. While the faculty members participating in the various events changes each time, the value of attending the group is always very high since the self-selecting members inevitably care about teaching.

What is experiential learning? "Excellent question!" We spent many of our first meetings trying to determine a good working definition for our group. Should the focus be on social justice work of our students that happens off campus? Should the focus be on college-sponsored internships where students learn skills ``on the job''? Should the focus be on active learning activities that happen in the classroom where students engage with and experience the material instead of passive non-participation? We ended up deciding to not decide. We wanted our group to be an umbrella group that allowed people with disparate interests to come together and share their innovative teaching practices.

At the beginning our group met in multi-day workshops to which were invited outside speakers to discuss teaching pedagogy and mindfulness. More recently I have been carrying the torch of our Experiential Learning group by organizing and serving as the moderator of lunchtime discussion sessions, sponsored by the Queens College Center for Teaching and Learning. I tend to favor round-table discussions where we each get to bring in ideas from our teaching, and that is the focus of today's lunch, where I have asked participants to prepare a 2-3 minute discourse about something that they tried recently and a self-evaluation of what went well and what could be improved in the future.

The most positive aspect about this format is that we are exposed to many different ideas and we get to see the diversity of techniques that are available and in practice at Queens College. This helps to give a sense that we are a college where good teaching by our peers is happening and is valued. The most negative part about this format is that for everyone to talk, people get at most five minutes, so it is impossible to get into the nitty gritty details about the module's implementation or give constructive feedback to the presenter, or have a deeper philosophical discussion about the module. These points were better addressed under the multi-day workshop format, which takes much more preparation by the organizers.

Today's session has an additional undercurrent of supporting the administration's need to collect information about experiential learning that happens through Queens College to comply with the City University of New York's task force, required by a new New York State law to increase experiential or applied learning opportunities for undergraduates. One personal goal of mine will be to have people contribute their experiential learning modules to the collection effort.

I'm sure that today will be as invigorating as always! We have another lunch scheduled for December 2, 2015. If you are around and would like to participate, make sure to join us! You can email me at chanusa@qc.cuny.edu to be added to my email distribution list about Experiential Learning at Queens College.

This is the third blog post that I am writing as part of the Queens College Teaching Circle blog; it is cross-posted on my personal teaching blog, Math Razzle.

Announcing The MathZorro Podcast

Abstract: In Fall 2014, I recorded podcasts with my Combinatorics students and they are now ready for consumption.  You can read descriptions of the episodes, or subscribe on iTunes or Stitcher.

One of my core teaching philosophies is that students are the most motivated to learn and internalize the concepts they are learning best when they are invested in a project.  (This would be my framing of the idea of experiential learning.)  All my upper-level classes involve some project-based component.  In my Combinatorics class, I supervise parallel research projects, where students work either by themselves or with a partner to investigate a counting question they have found somewhere in the real world.  For example our most recent crop of projects included analyzing the New York Knicks' basketball shooting possibilities, counting ways to place chess pieces on a chessboard, and investigating the collection of collectable cards (such as Pokemon or baseball cards).

I like to end the semester with a poster session; the students complete their research, determine the main results of their work, and organize this information on poster board.  The posters are all set up in a room and students share their work with their peers informally and more formally in a presentation to the class.  It is a fantastic capstone to the semester because it is an informal setting in which the student get to show off their hard work.  Moreover, the students get to see all the techniques that they learned in the class applied to a wide variety of topics.  (Here is a screencast discussing the poster session.)

In Fall 2014, I realized that there was a part of the project's deliverables that I wanted to improve.  I really like the poster session, but I also find it important for the students to compile a summary of their work where they address the most important take-away messages from their work.  In previous incarnations of the course, the students would write a page-long summary, I would skim it, and ... it would go no further.  Since the poster session was the last meeting of the semester, students wouldn't get any feedback and they wouldn't think more deeply about it.

I wanted to change the "throwaway" aspect of this summary, so I decided to move the poster session a bit earlier in the semester, and during Finals Week I would invite my students into my office to record an interview with me about their research.  After editing, this would be published as a podcast.  I provided my students with the same basic thought exercises that I had previously had them write about, but instead of summarizing the important points in written form, the students recorded answers to these questions orally.

This was excellent in multiple ways.   First, the students had invested so much time in the work over the semester---they had honed their projects and received feedback and guidance in class and in office hours.  Moreover, they had already had to think about organizing their information to be displayed on a poster and to be presented to the class at the poster session.  In effect, this recording session served as a time for project debriefing---the students had one final chance to share their excitement for their project and the process with me.

What I really value about these podcasts is that my students' research can be shared with a much larger audience.  I always got to the end of the semester and felt like more people should see the amazing work that my students had done.  Sure, a few non-student peers had always attended, as had our very supportive department chair and some fellow faculty members (math and non-math), but I knew that the quality of much of my students' work was quite good and should be better preserved.  I had always posted image galleries of the posters online; but now with a podcast, the students' work is able to be preserved in multiple media formats.

I am happy to announce that as of this month, the fruits of the my students' labor are available for listening as a podcast: The MathZorro Podcast.  Follow that link to see detailed descriptions of all 15 episodes.  Here are also links to subscribe on iTunes or Stitcher.

The podcasts turned out great.  You will be able to hear the enthusiasm my students had for their work, and the variety of questions that they addressed.  I had two students who were recent immigrants and they included a message in Chinese to share with family in China.  One special feature of each podcast was when I asked my students to share a favorite number that appeared in their research.  It was fun to hear what they chose and why---some gave a final answer to their question, some gave a number that seemed to appear multiple times, and some found a way to avoid giving one answer to this question.  (This feature was inspired by two podcasts I like: the Marketplace Tech Report and the Slate Money Podcast)

I am proud of the work my students did, and I am especially happy to be able to produce more mathematical content to share with the world.  If you are looking for one episode to try out, I would suggest listening to one of the first six episodes (Card Collecting through Basketball).  If you are not a mathematician, perhaps a nice first episode would be #5 Lattice Paths?

I would love to record some more podcasts with mathematicians of all stripes.  If you'd be interested in trying it out, drop me a line!

This is the second blog post that I am writing as part of the Queens College Teaching Circle blog; it is cross-posted on my personal teaching blog, Math Razzle.

Teaching students Mathematica

Abstract: Mathematica has amazing capabilities, and my students have started to harness its power to investigate and create mathematics.

This Spring 2015 semester I am teaching MATH 213: Math with Mathematica. I last taught this course in Fall 2009, and this was the last time it was taught at Queens College. Back then I had less experience with Mathematica and I tried to base the class around a course packet written by the previous instructors. Moreover, it was my third semester at Queens College, so I was still learning the ability level of the students. By the end of that semester I was a bit disappointed by the amount of material that we had covered, I was discouraged by the performance on the assessments, and I realized that I did not find the course packet as motivating as I had hoped. On the other hand, I was happy that the students had gained some ability with Mathematica and I enjoyed the diversity of projects that my students had created. With these thoughts in mind, I revised the syllabus at the beginning of this semester. In this post, I'll talk about the program Mathematica, the course setup, and the beginning of this semester.

Mathematica is a computer program that one can use to do simple and very complex mathematical calculations, to write and run complex computer programs, and to generate mathematical structures algorithmically. There are a number of different competitors to Mathematica, including Maple, MATLAB, and SageMath. SageMath is open source and would be my second choice, especially since a number of researchers in my field use and contribute to it. There are three important reasons why I choose Mathematica to teach to my students and for my own research. (I switched from Maple around 2007.) First, the syntax of the commands is very natural to a mathematician. When you want to plot the graph of a function where x ranges from 0 to 10, then you type Plot[f[x],{x,0,10}]. Second, the documentation that accompanies the program in its Documentation Center is excellent. Not only does it provide the syntax and the options that are allowed for each built-in command, there are scores of examples highlighting each of the capabilities of the command along with some "Neat examples" to see what is possible with advanced techniques. The Documentation Center also gives suggested related commands which makes it easy to explore all the things that Mathematica can do. (It's the same principle behind getting lost in Wikipedia.)

The last capability that takes the cake and keeps me from switching away is Mathematica's amazing visualization capability. Not only is it easy to generate and analyze data, it is possible to easily visualize large amounts of data instantly and dynamically, and export it in a flash. Do you want a histogram? a scatterplot? 3D charts? Mixed with its mathematical backbone, this allows for some great visualization of mathematical objects, not to mention visualization of the amazing amount of curated information that is available for direct import from the Wolfram servers --- including up-to-date and historic financial, geographic, demographic, scientific, etc. data. (If you've ever played with Wolfram Alpha, you have some idea of the scope.) I especially love the Manipulate command, which introduces sliders allowing for an easy and instantaneous change of one or multiple parameters, such as size of 3D objects, or time-frame of demographic data, or list of chemical compounds, etc. I have created a number of animated gifs using Mathematica that you can see on my webpage and in this gallery. (One of them has received over 35,000 views on Google+)

Now about my MATH 213 class. My goal at the beginning of the semester is to hook the students on Mathematica and give them the basic building blocks that they'll need as they progress through the semester. I have found that these classes have a wide range of ability levels, and as such work best when the course is run using tutorials. I put in a large amount of time creating a tutorial for each class focusing on multiple related topics. The students follow along in class; when they run into issues they can either talk to their neighbors or I am able to provide assistance. The quality and self-sufficiency of the tutorials is important so that I can address the concerns of the fifteen students in the class and I am not spread too thin. (This is a lesson I learned the hard way when I first tried to teach Maple to Mathematical Modeling students as a post-doc in 2006.) Throughout the tutorials are sets of Comprehension Questions where the students work to master the presented concepts by creating or modifying Mathematica code. One issue that I have run into is that a number of students often do not come to class because the class is early (8:45am at a commuter school) and the tutorials are available online. (Perhaps they do not need or think they need assistance?) To make the classes more relevant and instructive, I have started requesting that students post a question about recent tutorials to the discussion board; I start class each day responding to these questions, which leads on some interesting tangents into the intricacies of Mathematica.

The class assessments include three major projects and in-class quizzes that happen after every few tutorials. The first two quizzes were only on paper and were 20-30 minutes each. The first quiz focused on the creation and modification of lists (the key data structure in Mathematica) while the second quiz focused on the creation and application of functions and patterns. The most recent quiz (on the creation and manipulation of 2D and 3D primitives) ended up needing one hour and allowed the use of computers to generate specific 2D and 3D graphics and debug non-working code. I am happy with these quizzes (even if I am less than happy about the students' grades) because they are testing if the students have internalized Mathematica's syntax and understand how certain commands work. For instance, I will ask students to write a paragraph explaining how a certain command works (syntax, inputs, outputs), and to understand what a written command will output.

The projects are the most important part of this class. I feel that students learn best when they are motivated by an end goal that is student-driven and faculty-guided. On campus we have a faculty group devoted to Experiential Learning; these projects fit into that framework. For their first project this semester, students were asked to create their own Mathematica tutorial that helps students with coursework from another class. Full project details are here. Behind this project is the idea that students will be able to use basic knowledge of Mathematica to understand a topic from another math class that they found difficult. Not only will they get more practice in this complex topic, but they are also learning how to use Mathematica to solve their own problems. Moreover, they must work to convey their understanding in complete sentences, which is an important step in the learning process. Ideally we would upload and publish these tutorials to a centralized server and make them available to current students in those classes, but maybe that will be one of the requirements in a future iteration of the class.

For this and future projects, I give the students a detailed timeline and set of expectations that the students had to follow. I find it very important to give detailed specifications because I give the students complete freedom in choosing their topic. Once they determine the subject, I help them refine the scope of the project so that it is feasible to be done in the given time frame and is neither too difficult or too simple. I ask the students to prepare and present a five-minute presentation of their projects to the class, and gather feedback from their classmates for them to revise their projects one more time before submission for grading. A few of the projects from students this semester included understanding conservative vector fields from Multivariable Calculus), solving differential equations, and understanding the cycloid curve. I enjoyed the many comments from students about how amazed they are about the capabilities of Mathematica, and how they now use it in their other classes.

I will stop writing here and devote the next blog post to discussing the second project which involves creating and printing 3D mathematical art. Write you next time!

This is the first blog post that I am writing as part of the Queens College Teaching Circle blog; it is cross-posted on my personal teaching blog, Math Razzle.