Ed. Note
I've published this post several times. Sorry about that. It's been written over a week and I seem to keep stumbling over the words. I've been editing it not to remove content but to remove the repetitive bits.

The last four weeks have been crazy busy. I haven't blogged and have accumulated a backlog of unanswered email which I've been catching up on over this past week. I haven't been blogging here but I have been blogging on my class sites (here, here and here and the podcast.).

Among the many things that have occupied my time has been this year's Third Annual Mystery Coin Hunt. I stayed late at work last Thursday and finished assembling all the clues for the hunt. The coin hunt is one of the ways that we celebrate π Day. (We also eat a lot of pie and tell dumb math jokes. ;-)) The hunt usually begins on March 14. This year the hunt began on March 20. I'll write more about it in a future post. ;-)

I've also been working on the Developing Expert Voices assignment that I've been writing about here. I've finally written out the assignment in concrete form. I suspect it's transferable to other domains (see below).

It has moved away from my original idea of connecting individual kids across classes and grade levels and evolved into something where students have choice over every aspect of the assignment ... except whether or not to do it. ;-) (Although I guess they could choose not to do it ... one or two of them, unfortunately, just may do that.) I have set an absolute latest due date (May 31) and advised the students that they should not be choosing that date. I created a Google Calendar for each class. Each student has chosen their own due date and it has been added to the class calendar. Using the Google Calendar Viewer Gadget (one of many Google Gadgets) I have added the calendar for each class to the sidebars of their blogs. (In one class, we also whimsically added upcoming birthdays to the calendar as well. ;-))

About ten days ago I created a new Google Doc for the students in all my classes to collaborate on building the assessment rubric for the project, much like I did with their flickr assignments. I also invited my three blog mentors (Lani, Emina and Roland) to participate as well. [Roland just joined the team of mentors working with my classes. We're lucky to have him. Roland actually "met" one of my classes in a spontaneous skype call we did. It was captured in the class podcast here at 25 min 25 sec.] In total there were about 60 people invited to work on this document. (We have about a 10% participation rate; which, it turns out, is not great but "good enough.") The mentors role is similar to what it is on the blogs: asking pointed questions, making helpful suggestions and clarifying and/or summarizing the students thinking. The students started working on the rubric on last Friday and had until today (March 23) at 9:00 am to finish their collaboration. I've collated all their suggestions, assembled the final document and published it here and on all the class blogs.

There is still a possibility that some of my students will collaborate with another class but those conversations are ongoing and nothing has been finalized yet. There is also a possibility that some students will outsource the online publication of their work to students in another class, but that too is still in the works.

There are several pedagogical goals attached to this assignment. Here is a quick short list off the top of my head:

• » Another modality to bring the paradigm of "watch it, do it, teach it" into the classroom. It is one thing to know a thing; quite another to teach it. Real learning comes from teaching. In order to provide our students with authentic learning experiences I think we should try to get them to "teach" as much of what they are learning as possible. It's important for students to experience that kind of deep learning.
• » Collaboration is an important skill and becoming more so in our rapidly changing society. I think teachers should do all they can to best prepare students to work in collaborative environments as that is the way all sectors of our economy our moving -- it is a more realistic experience and preparation for the kind of professional work kids will have to do in the future work force. (This will be particularly true for those students who "outsource" their work to others for the "Presentation" part of the assignment.)
• » Having to present their work to a global audience not only increases motivation (via the fact of the large audience) but has another advantage: Publishing student work online gives it life beyond the end of our courses or the limits of our classroom walls. The ideas don't die; they grow wings. Student work published on a blog can be commented on by visitors at any time (weeks, months, years) after the work is done. If they have a question students may come back, reply and continue teaching and learning -- this kind of work fosters lifelong learning.

Over the next week I am planning to build a new blog with a unique and attractive template where we will publish all the students Developing Expert Voices (DEV) assignments. I will show them how to subscribe to the comments on their individual posts. If they get comments beyond the life of the class they will know about it and be able to reply.

Anyway, here's the assignment as it was published to my class blogs. If you adapt it, or part of it, for use in your class let me know. I'd be interested in how it plays out in other classrooms.

The Assignment
Think back on all the things you have learned so far this semester and create (not copy) four problems that are representative of what you have learned. Provide annotated solutions to the problems; they should be annotated well enough for an interested learner to understand and learn from you. Your problems should demonstrate the upper limit of your understanding of the concepts. (I expect more complex problems from a student with a sophisticated understanding than from a student with just a basic grasp of concepts.) You must also include a brief summary reflection (250 words max) on this process and also a comment on what you have learned so far.

Timeline
You will choose your own due date based on your personal schedule and working habits. The absolute final deadline is May 31, 2007. You shouldn't really choose this date. On the sidebar of the blog is our class Google Calendar. You will choose your deadline and we will add it to the calendar in class. Once the deadline is chosen it is final. You may make it earlier but not later.

Format
Your work must be published as an online presentation. You may do so in any format that you wish using any digital tool(s) that you wish. It may be as simple as an extended scribe post, it may be a video uploaded to YouTube or Google Video, it may be a SlideShare or BubbleShare presentation or even a podcast. The sky is the limit with this. You can find a list of free online tools you can use here (a wiki put together by Mr. Harbeck and myself specifically for this purpose). Feel free to mix and match the tools to create something original if you like.

Summary
So, when you are done your presentation should contain:

(a) 4 problems you created. Concepts included should span the content of at least one full unit. The idea is for this to be a mathematical sampler of your expertise in mathematics.

(b) Each problem must include a solution with a detailed annotation. The annotation should be written so that an interested learner can learn from you. This is where you take on the role of teacher.

(c) At the end write a brief reflection that includes comments on:

• Why did you choose the concepts you did to create your problem set?
• How do these problems provide an overview of your best mathematical understanding of what you have learned so far?
• Did you learn anything from this assignment? Was it educationally valuable to you? (Be honest with this. If you got nothing out of this assignment then say that, but be specific about what you didn't like and offer a suggestion to improve it in the future.)

Experts always look back at where they have been to improve in the future.

(d) Your presentation must be published online in any format of your choosing on the Developing Expert Voices blog. url: tba.
Experts are recognized not just for what they know but for how they demonstrate their expertise in a public forum.

Levels of Achievement
Instead of levels 1-4 (lowest to highest) we will use these descriptors. They better describe what this project is all about.

Novice: A person who is new to the circumstances, work, etc., in which he or she is placed.

Apprentice: To work for an expert to learn a skill or trade.

Journeyperson: Any experienced, competent but routine worker or performer.

Expert: Possessing special skill or knowledge; trained by practice; skillful and skilled.