Technology Supporting Innovative Pedagogy

by Brian Katz

There have been some recent developments in educational technology that can be used in math courses including adaptive individualized online algebra instruction, clickers, and Wolfram Alpha. You have probably heard about these or their cousins before, but I have been experimenting with two less obvious tools: Wikis and a LiveScribe audio/visual capture pen. For me, these technological developments have allowed information to flow between members of the class community in ways that were just not possible before, allowing exciting new pedagogical opportunities that I’d like to tell you about.

Wikis:
I have used Wikis in two different kinds of math classes, and the structure is different enough to describe both here. I in each case, the Wiki functions like a textbook for the class, so I will refer to it as the WikiTextbook.

Calculus
In my Calc II course this spring, each student was responsible for taking notes during lecture (more on this in the LiveScribe section below). The student then posted a condensed version of the lecture as a chapter in the WikiTextbook. In addition, each student was responsible for preparing 2-3 problems and presenting them to their peers in discussion; once presented, these problems were also added to the WikiTextbook by the presenter. I build in a requirement that they post a draft in a timely fashion and then edit in response to my feedback.

Each of these activities is really a study skill that the students need to practice, but it’s hard to get them to do so unless you can point to a future use/value. The students notice that they perform strongly on the quiz relating to material that they worked with in either capacity. I also give take-home exams mostly, and I allow the students to use the WikiTextbook as a resource during that time. In addition, the students are now able to read a version of the lecture from another student’s perspective and to see examples that are worked using the exact structure modeled in class.

Proofs
My proof-based courses are taught using an inquiry-based course design. This means many things to many people, but the most critical here is that I don’t lecture and there is no textbook for the course; instead there is a scaffolded sequence of questions/theorems that the respond to and prove for homework. Class is then spent on student presentations and further conjecturing. As a result, much of the written work is done before the students have talked to anyone about the material; they need a chance to parse the feedback from class (for maximal learning) and a chance to get a more reliable grade (or they will get mad fast).

This term, my Modern Geometry class built a WikiTextbook, which transformed the scaffold of questions/theorems into a readable document. There are an almost infinite number of questions to think about before jumping into this application, but the main points for me are that (1) everyone was required to submit regular work, and (2) I did give feedback and grades on the WikiTextbook. At the end of the term, I exported the WikiTextbook (from our online course management system) to a zip file that the students will be able to keep forever. Many of them will eventually teach geometry at the high school level in the next 5 years.

I used Wikis in second manner in this class. Instead of submitting their work on paper, the students published their individual work to a wiki that only I could see. The work was due an hour before class started, which allowed me to adapt my plan in response to the understanding that the students are going to bring with them to class that day.

There are so many opportunities with Wikis, ranging from hyper-linking and group editing to saved versioning! I will be talking about Wikis (with another teacher-user) at the RLMoore Legacy Conference in DC in June if you’d like more detail.


LiveScribe Pen:
The LiveScribe pen is, well, a very special pen. In addition to writing on a piece of paper, it simultaneously captures audio and syncs it with the writing. The details are important but confusing, but it’s much faster to look at an EXAMPLE, which is a supplement to the first day of Calc II. Be sure to expand to the full page view and click on the document to see some of the features. The audio may take a few seconds to buffer even after the video is ready.

I believe that these pens were originally created to help administrative staff take better notes during meetings, but it has also been marketed to doctors for dictation and now to educators. The top of the line pen was less than 200 dollars. It requires special paper, which you can buy in bound notebooks or print from a high quality printer.

One of my colleagues uses his LiveScribe pen to give short pre-lectures in order to reserve class time for more nuanced details and questions. He sits in his office and essentially dictates a mini-lecture. If this application excites you, look in Camtasia as well, because it allows your laptop’s webcam to embed video as well as audio and power-point into these pre-lectures.

Calculus
In my calculus class, I have been using the pen by having students rotate taking notes during lecture. The student that takes notes is the one responsible for publishing the chapter to the WikiTextbook described above. It takes about 3 minutes after class to upload the file so that the whole class has access. By the time the WikiTextbook is complete, the students will have access to the original textbook’s development, my development from lecture, their notes from class, another student’s notes from class, a polished version of the main ideas from lecture, and several examples worked by peers as resources. While I haven’t researched carefully, some of the lectures were viewed many times during the term.

Proofs
As mentioned above, my proof-based courses are inquiry-based. For many students, this means that it is very difficult to take notes in class. In addition, some student presenters struggle to express their ideas and remember the feedback they have been given. So, in these classes, I ask a student who is not presenting to take notes during the presentation. This captures the audio well enough for most purposes, but it is challenging to write a complete proof in time with an oral presentation. As a result, the role of the rest of the class is to pick out the key ideas and help the note-taker make a summary. The notes from Geometry usually look like a diagram drawn in time followed by a list of the key ideas. These summaries are a critical part of the WikiTextbook as well. In addition, sometimes we have a discussion that is not represented in the scaffolding notes, and the pen makes it possible to come back to these later when the themes re-emerge.

I used the LiveScribe pen for two other purposes in Geometry, both related to the exams. First, I recorded the students’ oral exams using the pen. While they presented, I could take in-the-moment notes about errors. If you’ve ever talked with a student about a presentation, you know how difficult it is to explain your feedback; this allowed them to connect the comments with the exact words that they used. In addition, it provided a single-page list of the major changes that they need to make before submitting the written version of the test.

Once the students submitted the written versions of their tests, I decided to try dictating my feedback instead of writing it in the margins (or inserting it into the file). I think it took about the same amount of time but was orders of magnitude more likely to make sense. It’s hard for me to write enough to explain why “Let” was the wrong choice, but I can say it pretty quickly. However, it was tiring. I did not pre-grade the papers and then give only the summary; this saved me time but meant that the feedback could seem like an onslaught of information and criticism for the students. Warning them o this seemed to work well enough with this particular group of students. In addition to dictating, I was taking short notes, which helped me sum up the major themes at the end.


I feel like I’ve just scratched the surface of what can be done with these tools. However, it is clear to me that they are allowing me to ask more analysis/synthesis of my students by providing the information that they need to succeed. You may already have access to these tools in your institution, so I hope you’ll give them a try. And feel free to leave comments with other uses for technology!

(If you’re curious, I prefer the Wiki in Moodle because it handles LaTex the best for my purposes and because the security issues are already handled by someone else.)

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