Tell Me About Infinity

Tell Me About Infinity

Jonas Reitz https://openlab.citytech.cuny.edu/members/jreitz/

Mathematics/ School of Arts and Sciences

MAT 2675 Calculus II https://openlab.citytech.cuny.edu/2012spr-mat1575-reitz/

Activity Description: Provide a brief description of the activity

In this low-stakes writing assignment, students create a blog post exploring the concept of infinity. The post must respond to one of several prompts focusing on personal experiences of infinity, and must include a photo that illustrates infinity in some way. Extra credit is offered for providing a thoughtful comment on another student’s post.

Learning Goals: What do you aim to achieve with this activity?

This activity is introduced in the course MAT 2675 Calculus II as we prepare to embark on the study of infinite sequences and series, the first rigorous introduction of infinity in a mathematical context. Before students begin to wrestle with the (challenging!) technical details of the subject, I want them to reflect on their preconceptions about this pervasive and slippery notion of “infinity”. I want to give them the opportunity to make connections between infinity as it appears in other areas of life – philosophy, art, religion – and as it appears in the curriculum. In addition, I use this activity to build or reinforce technical skills – how to create a blog post, upload images, and add tags. I want to get students writing in a low-stakes environment, where their focus is on the content. Finally, I want to give students a chance to respond to one another, building community and trust in my class.

Timing: At what point in the lesson or semester do you use this activity? How much classroom time do you devote to it? How much out-of-class time is expected?

This activity is tied to a particular topic in Calculus II, infinite sequences and series, which traditionally makes up the last third of the course. The assignment is given just before we begin this topic, around week 9 or 10, and it is due two weeks after it is assigned. I spend 5-10 minutes discussing the project in class when it is assigned, and in subsequent classes I will provide a little time for students to ask questions or raise concerns. I expect students to devote 2-4 hours to this activity, over the course of 2 weeks.

Logistics: What preparation is needed for this activity? What instructions do you give students? Is the activity low-stakes, high-stakes, or something else?

I post the assignment, including detailed instructions, on the course OpenLab site (see below). I will spend a very short time in class discussing the assignment and answering questions – but I will NOT go over every detail (they are expected to carefully read the assignment and follow all instructions). I try to make the assignment stand-alone, with links to appropriate resources (including, for example, how to create a blog post, how to upload an image, and so on).

High-Impact Educational Practices: Which of these practices based on George Kuh’s High Impact Educational Practices (and other innovative approaches) does this activity incorporate? Choose all that apply.

Open Digital Pedagogy (the OpenLab), Wrriting-intensive projects/assignments

Assessment: How do you assess this activity? What assessment measures do you use? Do you use a VALUE rubric? If not, how did you develop your rubric? Is your course part of the college-wide general education assessment initiative?

The assignment includes a list of 5 specific expectations (“You should create a new blog post including the following”), and I use this as a checklist. The assignment is worth a certain number of points, and a student’s score is based solely on the checklist. I want this to be low-stakes in terms of writing — grammar and spelling are not evaluated, and the structure and content of the written work need only loosely fit the instructions. I write a response to each student’s post, and while I don’t share their point score at that time, I will point out if there are significant problems or missing items and encourage the student to make revisions.

Reflection: How well did this activity work in your classroom? Would you repeat it? Why or why not? What challenges did you encounter, and how did you address them? What, if anything, would you change? What did students seem to enjoy about the activity?

This has been one of my most successful writing prompts – I was excited and impressed with the variety of creative and thoughtful responses. Asking them to write about their personal experience provided freedom to talk about the subject without fear of “being wrong,” and gave a rich source of material from which they could draw. Many posts spurred great comments, and I noticed in several cases the comments developed into real conversations (although the extra credit offered for commenting on another post did not extend to multiple comments).
I think this assignment could adapt quite easily to many disciplines. It is often the case that certain words, familiar from our daily lives, take on a specific and technical formal meaning in an academic context which gives students trouble – especially as the “formal” and “informal” definitions may be at odds with one another. I can imagine this activity applying to many such cases – by asking students to explore their existing experience of a word or concept, they begin to focus on the meaning of it in an intentional way, which prepares them to compare and contrast their informal definition with the formal usage.

Additional Information: Please share any additional comments and further documentation of the activity – e.g. assignment instructions, rubrics, examples of student work, etc. These could be in the form of PDF or Word files, links to posts or files on the OpenLab, etc.

Link to Assignment: https://openlab.citytech.cuny.edu/2012spr-mat1575-reitz/2012/04/04/openlab-assignment-7-tell-me-about-infinity/

Link to Student Work Examples: https://openlab.citytech.cuny.edu/2012spr-mat1575-reitz/?s=infinity

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