Listen to an Expert Voice

4/12/2007 11:26:00 pm

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. ;-)

You Might Also Like


  1. Darren,
    Kudos on this project! The two that I have seen/read have been very interesting. I think grey-m was incredibly insightful in his reflections and his project was fantastic. That is a tribute to his hard work, intellect, and desire to succeed, as much as it is to a teacher enabling/empowering students to achieve.
    I have struggled with many of the same concerns that grey-m raised in my own teaching (being considered a tough teacher who stresses deeper understanding versus an easier 'A') and have always hoped that I was able to have my students make the connections that he so eloquently made. The difference for me is that you allow your students, no demand that your students, think about these issues. It is the total picture that I have been so amazed by with your teaching, and I applaud your attention to cognition as much as your attention to content.

  2. Darren, Absolutely incredible. Grey-m's work should be published as an example of higher order thinking in math. (I guess it is published as it's on your blog.) I'm really impressed and can only hope that my kids have a math teacher like you.

  3. Anonymous24/4/07 16:42

    Thanks fellas ... the consequences of this project are only beginning to unfold. Just today two students told me that they've been using flickr as a way of asynchronously sharing work they are doing on a project in another class.

    Also, the kids that have pushed themselves to expert level problems shared with me that they have learned more then they ever had before. They said it was one of the hardest projects they've ever done, but now that it is done they are glad they did it. There's more to share about all this ... in a future blog post. ;-)