Web 2.0 Math Reflections - Collaborating and Blogging

A few months ago, with the talk of political protests making travel to school difficult, my co-teacher and I started a project in ESL-support-for-Math-Science class to simulate working from home. We set the stage with the words: "The protesters have filled the streets. The traffic is terrible. It's not possible to get to school. School will go online. Are you ready?"

Our goal was three-fold. First, work with students on a topic that would prepare them for an upcoming assignment in math class -- writing a math reflection about fraction division. Second, collaborate and interact with a partner to complete part of the assignment jointly. And third, use information technology to collaborate exclusively online as if students were working from home.

The first two are run-of-the-mill goals as far as execution, but the online collaboration was basically artificial. After all, how can two students in the same class restrict their during-class collaboration to the web? It turns out we had the luxury of two classrooms that we regularly use to divide students since we have 20 ESL students in the class. We assigned partners across classrooms so no two members of a team were in the same physical space. Again, we designed this artificial online collaboration to simulate a Virtual School situation.

The assignment was as follows. Working with a partner by chatting online, jointly create an a realistic story problem that requires a solution using fraction division. The example should be constructed in Google Docs. Then independently use this problem as an example of a math reflection describing when and how to use fraction division. The reflection should also be done in Google Docs in collaboration with the teacher for the purpose of feedback. Finally, post the reflection to one's school blog.

We tried out the various applications to make sure we ourselves could perform the tasks we were assigning and used our examples as models for the students, with the exception of chat for which students had the option of Google Apps or our school Moodle, PantherNET.

The link to the Google Doc presentation file that we used to model joint construction of the realistic story problem is here.

The link to the Google Doc document file that we used to model independent reflection writing is here.

And the link to the blog we used to model a published post is here.

Ultimately, we were able to carry out the project as we planned, but not without some surprises. Some of those surprises were the limitations of chat in Google to the Gmail application. It would have been better if available in Google Docs. We also discovered that using Google Docs in Internet Explorer resulted in the loss of Google Docs' menu bar, essentially disabling the application. We learned that some images created in a Google presentation file could not be copied directly to a Google document file. And we found that some students could not see their images in their blog posts when copied from Google Docs to Word Press. Except for the last issue, we were able to work around all problems, albeit if somewhat tediously.

We were pleased to see students negotiating their ideas by chatting online, using Google Docs to collaborate with each other and with us, and publishing their reflections to their blogs. We initially lamented the technology glitches along the way and going over-budget on the days devoted to the project. We later appreciated the fact that some of the glitches catalyzed meaningful, authentic and highly-engaging student interaction in problem solving far beyond the interaction of our own design, and that students students' learning extended beyond our most narrow goal of English for Math class.

Both of these last points were brought to our attention by two colleagues who observed various points of the project during Looking for Learning visits. One was our ISBangkok Dean of Learning, Andy Davies, who commented after interviewing students that some were so engaged and focused that they would not stop working to have a conversation with him about their learning. And the other was the Middle School educational technology specialist, Kim Cofino, who interviewed students and observed me from a educational technology perspective as part of my final project for ISBangkok's Certificate of Educational Technology and Information Literacy series of courses.

In the end, we had a day of Virtual School because of a State of Emergency declared by the government, but it fell on a Friday before a week vacation, so it did not involve extensive work for students. However, the possibility continues in Bangkok for more Virtual School. The school recently asked that teachers show students how to use their Gmail accounts and Google Apps. Thanks to our Virtual School simulation, our students already do know how.

Instant Feedback Online Math Homework via Moodle

This year's new Math program, CMP 2 (Connected Mathematics Project) brought with it some concerns about how to handle going over homework. At the beginning of the year, we settled on the following system: on the due date of the homework, students compare answers with each other at the start of class, and we review one or two of the most challenging problems as a whole class. That evening on our class management software, PantherNet (our schools form of Moodle), we post the answers to the homework problems we did not review as a whole class. Students correct and check their own work before handing it in for a score. This was our Math teams attempt to provide feedback while not cutting into lesson time. Prior to this system, we had found that it was possible to spend half of class or more going over the homework.

Nevertheless, I wasn't satisfied with the fact that students were doing so many problems for homework in Math that I wasn't able to give direct feedback to. I found also that students were either: 1. not correcting their homework with the answers the teachers were posting, or 2. just copying the answers straight from the key. That wasn't very satisfying either.

At the same time, I was frustrated by the organizational challenges for myself and the students of the daily homework assignments and grading. This motivated me to explore online submission of homework. I was aware of PantherNet's modules for online quizzes through my wife's, Carole Henriot's, exploration of this feature in her French classes (Intro, A and B). So I decided to trial it myself. What I quickly realized is that the Moodle quiz module allowed for immediate feedback in terms of accuracy as well as any comments I might want to make in response to students' answers or scores.

I have used the Moodle quiz module for online homework for about a semester now. In it's current form, I allow students to redo the homework as many times as they want, and I take the highest score for their grade. (It is actually possible for students to get a perfect score even after multiple attempts by correcting incorrect responses.) I also choose settings that allow students to keep previous correct answers on any new attempts (so they don't redo problems they worked correctly initially) while reworking only problems they have missed. There is also a handy feature that allows students to check the accuracy of their answer before submitting the assignment for a grade. From the teacher side of the module, I can see all of students answers and how they have adjusted them as they learn they are incorrect. I have been amazed to see how many students can correct an incorrect answer simply from being told that it is incorrect. Students rework the problem and appear to find their error and correct it. I have been amazed to see that no student settles for submitting an incorrect answer without trying to correct it at least 3 times. I have also been amazed to hear that students begin to work with their parents to find the correct answers. My sense is that using an online scored homework assignment has transformed the process of homework practice from one of simply trying to get through the homework as quickly as possible regardless of accuracy to one of multiple passes with multiple resources. I frequently hear students say something to the effect of not having understood a problem and not having attempted it. Papers with blank problems is not unusual. But online homework problems with blank problems IS unusual. I attribute the occurence of students' editing/revising of homework and the increased number of attempted and completed problems as resulting from the instant feedback nature of the homework. When a student knows BEFORE SUBMISSION that a blank problem is counted against them or a that an answer is incorrect, the student is motivated to solve the problem correctly, at least moreso that in the traditional homework format.

In terms of organization and management, it has reduced that amount of paper that both I and the students keep track of. It has taken the same or less time to create the online assignments than to grade the hard copy equivalent. And the time investment now will pay great dividends in future years when the assignment is already online for future classes, essentially requiring no more time on my part. Great advantages for management.

With that said, there are some cautions about online self-correcting homework. 1. It only lends itself to problems with discrete answers. Explanations cannot be scored automatically. 2. It requires the teacher/programmer to imagine various possible forms of the answer in order that the teacher/programmer enters all variations as acceptable correct answers. 3. The syntax of the answers must be exact to be accepted as correct, for example, spacing, labels, place value, etc. 4. It may promote a concern for a score rather than a concern for understanding.

Nevertheless, I have found the process worthwhile. It has also led me to ask if students' ability to self-correct their work when told an answer is inaccurate could result in better test performance. During a test early in the year, before ever thinking about online homework, I circulated around the classroom tell students to double check their work because a certain problem was incorrect. In many (most?) cases, I found students were able to correct their work once I told them it was incorrect. I don't think it's unfair to score students' tests after giving them a chance to correct themselves. Perhaps knowing which problems are incorrect provides motivation for checking their work. Otherwise, they seem to do it very little. And isn't this a worthwhile skill in itself, besides the understanding of content?

Next school year, I will attempt to conduct a more systematic study of the effects of online self-correcting homework to determine what effects it has on students homework completion, accuracy, parent interaction, and understanding as measured by tests. I'd like to be able to determine that such homework results in greater rates of attempt, greater completion, greater accuracy, greater collaboration, and greater understanding. Ambitious, definitely, but also worth a systematic study!