Tuesday, June 30, 2009

The formula for changing math education

at 6/30/2009 12:20:00 PM · 4 comments

Listen to Arthur:

2 min 59 sec

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Thursday, May 14, 2009

Calculus Made Easy

at 5/14/2009 11:15:00 PM · 2 comments

Cover of "Calculus Made Easy"Cover of Calculus Made Easy

Considering how many fools can calculate, it is surprising that it should be thought either a difficult or tedious task for any other fool to learn how to master the same tricks.

By far the best opening line for a math text ever written. Now released from copyright restrictions you can download a copy, visit the scribd.com version, or read it here.

I think I'm going to use this as the text for my High School Calculus class next year and perhaps as a supplemental text for my AP Calculus students.

Thanks to Denise for the tip. ;-)

Calculus Made Easy, by Silvanus P. Thompson Calculus Made Easy, by Silvanus P. Thompson q2
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Saturday, May 02, 2009

Weekly Math Links (weekly)

at 5/02/2009 07:36:00 PM · 0 comments

Was it a good idea to auto-publish this as a blog post?


Posted from Diigo. The rest of Math Links group favorite links are here.

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Monday, April 13, 2009

My Class Blogs: Part 5

at 4/13/2009 09:39:00 PM · 1 comments

I'm publishing this one out of order. It's my blog, so there.

What Came Before

    Part 1: Before Meeting the First Class
    Part 2: The First Class
    Part 3: Digital Ethics (coming soon)
    Part 4: Delicious and Flickr Assignments (coming soon)
    Part 5: Wiki Solution Manuals (that's this post)

Three years ago I first started having students create Wiki Solution Manuals as part of their exam preparations. The AP Calculus AB exam is coming on May 6 and so, year four of our wiki wonderland begins.

Some students have already started solving and annotating their problems tonight. Feel free to watch how it unfolds on the wiki.

Over this past weekend I created a new wiki and seeded it with exam level problems. The details are posted on the front page of the wiki, but in brief, the assignment comes in two parts done over two weeks:



A Significant Contribution or Week 1

Solve a problem completely. Annotate well enough so that an interested learner can learn from you. Make the layout clean, clear, and complimentary to the articulation of the solution.

Students often think this is the hard part of the assignment. I think it's the easy part. It's more or less like a Scribe Post focusing on a single problem. Granted, some of the problems are challenging, but the timeline for this, 1 week, is supposed to make it a low pressure sort of thing. Unless they leave it for the last possible moment; most don't some do. I mean, they have a week to do something that could reasonably be assigned as an overnight homework assignment.



A Constructive Modification or Week 2

This time next week the real fun begins. (The real metacognitive work.) Each student must scan through the entire wiki looking at each solution their mates have done, find one that has an error, and fix it. They must edit someone else's work, not their own.

Week 1 was just a set up for this; this is where I think the real learning happens.

As they read through several solutions looking for errors they have to decide what is right or wrong and why. They question each line of every solution verifying each other's thinking as they read through. The hardest part for me, as the teacher, is to not say anything.

This all ties in with one of the three guiding principles I always think of as I design learning experiences for my students: Make Thinking Transparent. This is particularly well illustrated in this assignment.



Refinements or The Nuts and Bolts

The sidebar of the wiki has links to:

» the class blog.

» the grading rubric (feel free to copy it if you like, it's quite simple).

» an index of all the problems/units seeded on the wiki.

» the sitmo Google Gadget for create point & click LaTeX equations. (This makes it real easy to write math on the web.)

» equplus.net, a database of copy & paste LaTeX equations & expressions for those kids that really want to rock and roll with LaTeX.

Next in this series (when I've caught up with the backlog) is Part 6: Developing Expert Voices or Learning To Do What Mathematicians Do: create mathematics.

Photo Credit: Create by flickr user Darren Draper
Wistful thinker... by flickr user carf

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Saturday, April 11, 2009

Rules To Live By

at 4/11/2009 11:23:00 AM · 1 comments

I've become more and more interested in visual design as it pertains to teaching. I see a lot of teachers new to using a SMARTboard creating long, text heavy slides in their lessons. For myself, I've started a collection of feeds in my reader called Visual Thinking and it's had a dramatic impact on my own slide design process.

If you watch TED Talks you may have noticed that the visuals used by speakers at this years conference are qualitatively superior to those used in the past. TED has hired Duarte Design and assigned each speaker a small stipend to have their visuals given a makeover by the folks at Duarte. You can really see it in the visuals used in these two talks:

Barry Schwartz: The real crisis? We stopped being wise

Here's the backstory to Barry's slide makeover.

Bruce Bueno de Masquita: Three predictions on the future of Iran, and the math to back it up

Here's the back story to Bruce's slide makeover. (Seems to be offline; wonder what happened? Here's the Google Cache of the page. You can also find it on my Shared Items page.)

The post ends with this:

Rules We Live By

  » Break apart big ideas into smaller bite-sized pieces.
  » Simplify the message (even when you’re talking about using game theory to predict the future!)
  » Give a message space to stand out and contrast to focus attention.
  » Use more visuals and less words.
  » Use clear, easy-to-read charts with simple shapes and colors to add texture and clarity.

If you're new to using an Interactive White Board (IWB) in your class I think this is an excellent list to use as a starting point for slide design. When designing slides for classroom instruction these are the ideas I use as guidelines. I'm working hard at evolving how I present information to my students daily. Particularly when teaching more conceptually difficult material.

This is how I introduced statistics the first time with the SMARTboard:

Applied Math 40S Slides Mar 12, 2007
View more presentations from dkuropatwa.

This is how I did it this year:

Applied 40S March 20, 2009
View more presentations from dkuropatwa.

There's still lots of room for improvement in that second set of slides above. I'd genuinely appreciate any suggestions you may have about improving this particular slide deck or my approach in general. Can you suggest a specific image that might fit nicely into this lesson?

I'm going to keep trying to increase my use of visual images and since SlideShare added the ability to embed YouTube videos in each slideshow I've been trying to have at least one instructional video inserted into every day's set of slides.

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Monday, March 30, 2009

What are Our Kids Doing Online @ CJOB

at 3/30/2009 11:11:00 PM · 0 comments

Chris Harbeck and I will be guests tomorrow morning on the Richard Cloutier Reports show at our local radio station, CJOB.

The topic is "What are our kids doing online?" but I can see us talking about adults as well as how some sites are changing the way we connect socially, personally, and professionally at all ages.

You can listen live, streamed over the internet, but we'd rather have folks participate in the chat room we've created or via twitter. We're using the hash tag #cjob.

Chris has a much more detailed post up than I do. Head over there and check it out.

Hope to see you online and on the radio. ;-) The fun starts at about 9am central time in North America.

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What's the Value Added?

at 3/30/2009 05:56:00 PM · 9 comments

Cross posted from a ning community I'm in.

Watch this first:

OK, so this is going to sound weird coming from a math teacher — I'm liable to be run out of the club for saying it — but, in most subjects, does every kid have to learn exactly the same stuff?

Here's what I'm thinking (and I don't think it's an original thought):

Don't send them home to read and listen to the lecture, send them home to take in a short (10-15 min video) or even a micro lecture. Then change the classroom into more of a lab or studio environment. Each kid produces a paper or other artifact of what they've learned and shares it with the rest of the class either face-to-face or online; they become expert in the area they've chosen to explore and at the same time develop the research skills to learn related content when needed.

The question I try to ask myself is: What is the value added for my students by being in the same room with me? If I recorded my lecture (video or audio) and they watched it at home, did the assignments and handed them in, would they be missing something by not being here physically?

I do think my students gain value by being in the same room with me, but most often when I speak very little. I let them work through the problem(s), debate and defend their work with each other, and only towards the end, when they've collectively sucked the marrow from the bones of the problem do I either ask another question that fires them all up again or draw their attention to the finer points of how best to share their thinking on paper.

This is what the video I embedded above suggests to me. I know I'm not there yet, but man! I'd like to be.

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