Developing Expert Voices Rubric v1.1

I should have stuck to my instincts.

When we were putting this rubric together the students argued strongly that the "Solutions" and "Annotations" categories should be combined into one. I felt they should be two. Now, as I assess their work I have students who have written Expert Level annotations. If I find even one error, according to the rubric that would move them down to Journeyperson Level.

We discussed it and we're splitting them back into two different categories. We felt that the annotation should be weighted significantly more heavily than the solutions because that's where the real teaching part of the assignment comes into play.

So, here it is, updated in progress, DEV Rubric version 1.1 ... in eternal beta. ;-)

Oh, and BTW, check out some of the amazing work they've been doing ... the leaving of comments is greatly appreciated and strongly encouraged. ;-)

Teaching mathematical concepts is the main focus of this project; so we can teach other people and learn at the same time.

Achievement Descriptors
Instead of levels 1-4 (lowest to highest) we 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; a beginner.
Apprentice: One who works for an expert for instruction or to learn a skill or trade.
Journeyperson: Any experienced, competent but routine worker or performer.
Expert: One who possesses special skill or knowledge; trained by practice; skillful and skilled.

Mathematical Challenge (25%)
Annotation (40%)
Solutions (15%)
Presentation (20%)
Novice Problems illustrate only an introductory knowledge of the subject. They may be unsolvable or the solutions to the problems are obvious and/or easy to find. They do not demonstrate mastery of the subject matter. Explanation does not "flow," may not be in sequential order and does not adequately explain the problem(s). May also have improper mathematical notation. One or more solutions contain several errors with insufficient detail to understand what's going on. Presentation may or may not include visual or other digital enhancements. Overall, a rather uninspired presentation. Doesn't really stand out. It is clear that the student has invested little effort into planning their presentation.
Apprentice Problems are routine, requiring only modest effort or knowledge. The scope of the problems does not demonstrate the breadth of knowledge the student should have acquired at this stage of their learning. Explanation may "flow" well but only vaguely explains one or more problems. Some parts of one or more solutions are difficult to follow. May include improper use of mathematical notation. One or more solutions have a few errors but are understandable. The presentation style is attractive but doesn't enhance the content; more flashy than functional. It is clear that the student has invested some effort into planning their presentation.
Journeyperson Problems showcase the writer's skill in solving routine mathematical problems. They span an appropriate breadth of material. One or more problems may require careful thought such as consideration of a special case or combine concepts from more than one unit but not necessarily. Explanation "flows" well and explains the problems step by step. Solution is broken down well and explained in a way that makes it easy to follow. May have minor use of improper mathematical notation. May point out other ways of solving one or more problems as well. All solutions are correct and easy to understand. Very few or no minor errors. The presentation may use multiple media tools. The presentation style is attractive and maintains interest. Some of the underlying message may be lost by some aspects that are more flashy than functional. It is clear that the student has given some forethought and planning to their presentation.
Expert Problems span more than one unit worth of material. All problems are non-routine. Every problem includes content from at least two different units. Problems created demonstrate mastery of the subject matter. Showcases the writer's skill in solving challenging mathematical problems. Explanation "flows" well, explains the problems thoroughly and points out other ways of solving at least two of them. All solutions correct, understandable and highly detailed. No errors. The presentation displays use of multiple media tools. The presentation style grabs the viewer's or reader's attention and compliments the content in a way that aids understanding and maintains interest. An "eye opening" display from which it is evident the student invested significant effort.

Creativity (up to 5% bonus)
The maximum possible mark for this assignment is 105%. You can earn up to 5% bonus marks for being creative in the way you approach this assignment. This is not a rigidly defined category and is open to interpretation. You can earn this bonus if your work can be described in one or more of these ways:

  • unique and creative way of sharing student's expertise, not something you'd usually think of;
  • work as a whole makes unexpected connections to real world applications;
  • original and expressive;
  • imaginative;
  • fresh and unusual;
  • a truly original approach; presentation method is unique, presented in a way no one would expect, e.g. song, movie, etc.

A Twittering Hypocrite

I've avoiding signing up for a twitter account. I don’t see the attraction at all. I don’t see the value in it; personally or as a tool I can use with students. I can't imagine anyone being interested that I'm drinking chocolate milk as I write this (Chocolate Caramel Quick, and lots of it, actually).

Twitter has spread quickly across the blogosphere and I've been uncomprehending as I've watched this happen. Alan has been writing a lot about twitter. In a recent post I asked him about it and he wrote a great reply. (Thanks for that.)

The tipping point for me was Alan's comment: "you cannot really talk about the game of ed tech as a spectator."

So, now I've got a twitter account. To properly appreciate the twitter experience you need a friends list. So, I started off "befriending" a number of people. Given my recent post about Friends, I guess this makes me a hypocrite.

I'm also thinking that twitter has at least one potential benefit to the classroom. It also provides a means to get students using their cell phones in an educationally meaningful way. Using twittercamp to display people's twits (?) (if that's the right vernacular it's most unfortunate ;-)) can be a way to give voice to the quieter students in class. If I have them working in groups on a problem and at least one student in the group has a cell phone, they can twit their ideas and we can have them displayed for all the class to see on the SmartBoard. (Any type of projection screen should work just as well.) This also aligns well with the the atelier model I've been working hard to bring into my teaching.

I guess I'd need them to all get twitter accounts and teach them how to use their cell phones to twit but I think there's some potential here. Hopefully it's not a long distance call to twit.

Double Click to Learn

Here's a cool tool: Answer Tips (see the badge at the bottom of the sidebar). As of right now if you double click on any word on this blog that isn't a link a bubble will appear to teach you something. ;-)

I can think of scads of circumstances where this would be beneficial on my class blogs. For now, it's just here for a couple of days as I experiment with it ... I don't think the experimentation phase will last very long. ;-)

Thanks to Jan Nordgreen of Think Again! for the link.

Update: April 29, 2007
I've been thinking about how this tool works since I first saw it. I think it has tremendous implications for how we read, write and learn in a linked environment. Essentially, Answer Tips drenches every text posting to a blog or wiki in content. Every single word is clickable to learn; how to pronounce it, what it means, examples of it's use, explore the meaning in greater depth and more.

Part of learning in any domain involves acquiring the specific vocabulary associated with the content. The implications here for learning math, science, social studies, geography, English as another language, etc. are endless.

With a tool like this a teacher can simply publish a vocabulary list to the class blog and:

  • assign the students to learn the meaning of each one, maybe test them on it in their next class.
  • preview the content that will be covered in class the next day.
  • ask students to post pictures of examples for each word (science, geography) to bring another modality to help solidify their learning.
  • publish to a staff development blog where teachers can thrash out together the best way to teach a network of related concepts.
  • ... add your ideas in the comments below. I'm sure there are many more I'm missing. ;-)


I've recently joined (and created) a few ning social networks; mostly as a result of different projects I'm involved in. The networks are typically small; made up of people I know or people whose work I'm familiar with. In most cases we've been invited by a third party to collaborate.

Anyway, shortly after becoming part of these networks I started getting "friend requests" from different people on the network. Now in these small groups that we're working in, where some of us are meeting for the first time, working together on a larger project, it sort of makes sense to me that everyone is just being friendly and wants to be friends with everyone else. I like that. I like working in collegial environments.

Some of these invitations to friendship are from people I've never come across which is kind of flattering. The thing is, one of the invitations came from a person who, in their profile, said that they know nothing about the network they had joined. They just wanted to see what develops in the space. When I look at the profiles of some of the folks inviting me to friendship I see 500, 600+ friends in their personal network. 500 friends? Who has 500 friends? Maybe my definition of "friend" is too restrictive but, as a friend of mine pointed out the other day, these folks may just be building mailing lists. (Smells like spam.)

I suspect this is the sort of group Graham was talking about a while back. There's also a distant echo here from Bud's recent post.

... are these meaningful, two-way partnerships, or are we lowly teachers being taken advantage of a little bit?

Photo source: IMG_8118.

Reading Again

I haven't read much from my Bloglines account in months. The accumulation was overwhelming. I've just downsized from 181 feeds to 20. It wasn't easy ... until I changed my attitude. I asked myself what sources educate me the most? Not "What am I interested in?" My interests are diverse and I tend to immerse myself in them. When I shifted focus to those sources that push my thinking and teach me new things it became easier.

Doing this has inspired me to read my feeds again. I'm eager. It's been a long time since I felt that way ... reading had become a chore. I've also switched from Bloglines (although I'm hanging on to the account ... I'm thinking I'm going to use it to store feeds as references or examples to cite when talking to other teachers about the read/write web) to Google Reader. The tipping point was Alan's latest post about all it's ajax gooodness.

Photo source: untitled.

Listen to an Expert Voice

I've been slow to blog for lots of reasons. One of them is a feeling (self imposed and, as a result, particularly paralyzing -- does anyone else ever feel this way?) that there are things that I have to write about; but I just read something that I really want to share.

On Monday the first two Developing Expert Voices projects were published to the project blog. Two more will be published next week and the week following will see a steady stream of projects published until June 4.

Ivy was the second student to publish her project. If you look at it you'll see she worked hard on her presentation but struggled with the content. This led to her talking with me about ways she could go back and review the content she had difficulty with. Many students who struggle in math are happy to wait for a difficult unit to pass, put it behind them and forget about it. I think Ivy's renewed interest in relearning the content she had trouble with is a direct result of this project. The idea is to "teach other people and learn at the same time." They do this by creating their own problems and explaining the solutions as clearly as possible. The students are learning that making up good problems is no easy task. Writing well written solutions is also hard work.

One student, Graeme, told me he learned more doing this project than anything he's ever done before. Graeme published his project first. It uses text, graphics, a SlideShare slideshow, and several explanatory podcasts. Lani was struck by what he wrote in the Reflection section of his project and asked him about it:

Hi Grey-M,

The podcasts really help to contribute to understanding the content. Your voice, tone, and easy speak were a very good listen!

I am very interested in your reflection especially when you say: "When I did the problems I knew exactly what I was doing but when explaining them the words escaped me. I almost think that it would have been worth doing journeyman level questions for the boost in the mark of annotation because I don't know if my answers are going to get through to everyone. I know what I mean but others may not. With an easier question that you have a stronger foundation in you'll be able to explain it much better."

This first question may be unfair-- Do you think you would have learned as much had you chosen journeyman level questions? Is this really all about the marks?

Do you think, now that you have experienced difficulty in explaining what you feel you really know (that has happened to me alot!) that perhaps you didn't know it as well as you thought? And that in composing an explanation you've really extended your understanding?


We're so fortunate to have Lani "in" our class. Not being a math specialist she focuses on helping the students stay focused on their learning. And she asks just the right questions in just the right way. ;-) (Emina, a professor of mathematics, has also been doing some great mentoring. In Vincent's scribe post the comments hold a great discussion pushing Vince to clarify his thinking again and again and again.) I was particularly struck by Graeme's reply to Lani, for several reasons ...

Hi Lani,

I must say that doing the harder level questions did by far extend my understanding but as the project description says it is not just our understanding, it is everyone who wants to learn the materials understanding that counts as the point of this is to assume the role of the teacher while teaching ourselves. Doing the expert questions taught me more but in doing so may have given the other people less in comparison to a journeyman question that would have given me less but with their explanations given others more. Then again if people get my explanations completely then the expert questions are the way to go because they'd be teaching yourself as much as the other person.

Graeme really groks the purpose and intent of the assignment. He goes on to contrast the value of learning with the value, validity and fairness associated with grading student work ... (my emphasis added)

As for your other question the marks are important to me but it is merely a byproduct of the hard work invested into the teaching of ourselves and others in this case as that is the main goal. If you don't achieve that goal you won't get the marks as it is based on how well you teach and apply concepts. (and a high mark in Mr.K's class is a badge of honor as he has the most wicked hard tests you can imagine as most questions aren't routine and truly test your understanding. A mark of say 70 in Mr.K's class is probably and 80 or 85 in other math teachers classes.). But I must say that marks do unfortunately matter. A University is going to choose the person with the higher marks if all the rest is equal (even though certain teachers are easier to pass then others so I don't see it as a fair process). In the end though I think that understanding trumps marks. I failed an identities test but I understand that concept completely, foolish errors caused by going to fast and the stress of the test. In the end that will get me farther than if I had fluked the questions and got a high mark without understanding what I did completely.

[I really didn't know I was considered such a "tough" teacher. ;-)] Here's a student who has gotten everything out of this assignment that I could have hoped and dreamed for all my students. He articulates the tension between learning and grading so well and concludes "that understanding trumps marks." He finishes by talking about a particular moment of clarity he had that came about not from creating a problem but from the act of explaining (teaching) the solution ...

Explaining the work in words and diagrams so that others can understand it made my understanding of it become rock solid. I may have known methods to merely complete them before but to be able to explain them is to be able to fully grasp problem and see the nuances and intricacies that you may not have seen before leading to a better way. Like the last slide on the velodrome question. I never saw that until I had explained everything.

As Mr.K would say... cheers!


I think we're going to do this sort of work again in my class. ;-)

It's Elementary: Web 2.0 in the elementary classroom

Some friends of ours send their kids to a local Jewish parochial school. Over the spring break I was invited to speak to the staff at the school about web 2.0 in education. There are about 10 teachers in the school, including the principal, and none of them had ever heard of web 2.0, blogs, wikis or podcasts before except as buzzwords in the mainstream media.

By far the highlight of the morning was Kathy Cassidy. Kathy graciously made herself available to skype in to our workshop and chat live with the teachers. Many of them had never seen or heard of skype before. It was a powerful experience for them. They had seen Kathy's presentation from K12 Online and after hearing how a self described "non-techie" teacher leverages the power of web 2.0 tools to foster enthusiasm and excitement for learning in her students, they were juiced.

By the end of the day we had six new blogs started. The principal really "gets" the possibilities inherent in blogs, wikis and podcasting for his school, teachers and students. One family is leaving the school for a year to live in Israel, the teachers are planning to keep in touch and maintain connections between the students and their school via a blog.

After we had chatted with Kathy, he announced that when they get back from their break next week each teacher will be required to maintain a blog. They will publish a minimum of one post per week about anything they like as long as it relates to what is going on in their classrooms. He's also made a commitment to find 15-20 minutes in their instructional week to free them up to do this. We're going to collect the feeds from all the blogs and create a Protopage (linked to the school's website) so that parents can see what's going on throughout the school at a glance.

Here are the slides from the presentation on SlideShare and here's the link to the video of the first half of the workshop. We used the second half of our morning together to build new blogs for each of the teachers in the workshop.

Full screen version here.

The links embedded in the slideshow aren't working on the web hosted versions so I've added the list of links, organized by slide, below:

Slide 1: George Siemens, link, Alan Levine,

Slide 2: photo source.

Slide 3: video source.

Slide 4: Go2Web2.0.

Slide 5: The Weblog Project.

Slide 6: Nancy White, video source.

Slide 7: A Difference, Applied Math 40S (Winter '07).

Slide 8: Wikipedia, 1000 Names wiki.

Slide 9: The Important Thing About a Wiki.

Slide 10: What is a Wiki?, Heavy Metal Umlaut: the movie, John Udell.

Slide 11: Ask A Ninja, video source.

Slide 12: What is a Podcast?, How to Podcast.

Slide 15: video source, Visit K12 Online.

Slide 16: Class Blogmeister, Flickr, Audacity, video tutorial, BubbleShare, Wikispaces.

Slide 17: The Story of Eddie.

Slide 18: The Language of Math.

Slide 19: Eddie and Intro to Trig Modeling and Flickr.

Slide 20: A Good Day.

Slide 21: There's Something Happening Here.

Slide 22: Tell The Stories.

Slide 23: Great Day in Georgia.

Slide 24: One Drop of Water.

Slide 25: photo source.

Slide 26: small voices, Kathy Shields.

Slide 27: EduBlogs Star Award, Duck Diaries.

Slide 28: Trout Blog.

Slide 29: Mark Ahlness, The Mighty Writers Blog.

Slide 30: Al Upton and the miniLegends.

Slide 31: EduBlog Award Winners 2006, Have Fun With English 2.

Slide 32: Room 613 Student Blogs 06-07, Room 613 Student Blogs 05-06.

Slide 33: Clarence Fisher, Excellence and Imagination, International Teen Life Project.

Slide 34: video source.

Kids Are Amazing!

Run, don't walk, over to Chris Harbeck's class blog to learn about his un-Project and see what his kids have done. Most of it is published on the Un-Project wiki but some un-projects have been published to the blog as well. My favourite so far is this one. ;-)

Look what's possible when we give kids an open ended (un)project and the tools to publish their work online for a wide audience.

Developing Expert Voices - The Blog

Over the spring break I hacked (just a little bit) together a new blog where my students will be publishing their Developing Expert Voices projects. The blog is here and the first projects will be published on Monday. I know of at least two students that are planing to include podcasts as part of their presentations. Many of my students have started reading this blog and it turned out to be a good thing. Some of the content here includes podcasts and links to online presentations in a variety of formats which modeled for my students what can be done with a blog. I'm really looking forward to what they're going to publish.

For anyone who is interested in doing something similar with their students you can read all the posts I've written here on this project and how it has evolved.

photo source: Wait and Hope