Learn Mathematical Thinking From the Wrong Answer

I recently saw this video clip from an old Abbott and Costello film (thanks to my Twitter network). It reminds us that math isn’t simply about learning a computational process, or getting the right answer. It’s pretty clear that Lou Costello has learned the wrong algorithm, and he defends his approach it with great determination.  See the same mathematical thinking by Ma and Pa Kettle

We learn math skills so that we can apply mathematical thinking to the problem solving we will need in our lives. Thus, much can be learned from the procedures we use to generate both the “correct” and the “incorrect” answer. Sharing our thinking with others allows us to negotiate a deeper understanding of algorithms and their application in the real world.

The video clip neatly “illustrates” a teaching strategy from Teach Like Your Hair’s On Fire by Rafe Esquith. The book details Esquith’s fifth grade teaching methods in a rough LA neighborhood. Esquith shows us what students can learn from the wrong answer and his process can be easily applied across the curriculum. While it makes for an excellent test taking strategy, its real power is that gives students an engaging perspective to think more deeply about teaching and learning.

Esquith writes,  “Let’s say I’m teaching addition. Just before I give the kids their own problems, I put one more problem on the board:

63 + 28 = 

Rafe: All right, everybody. Let’s pretend this is a question on your Stanford 9 test, which as we all know will determine your future happiness, success, and the amount of money you will have in the bank. (Giggling from the kids) Who can tell me the answer?

All: 91.

Rafe: Very good Let’s place that 91 by the letter C Would someone like to tell me what will go by the letter A?

Isel: 35.

Rafe: Fantastic! Why 35, Isel?

Isel: That’s for the kid who subtracts instead of adds.

Rafe: Exactly. Who has a wrong answer for B?

Kevin: 81. That’s for the kid who forgets to carry the 1.

Rafe: Right again. Do 1 have a very sharp detective who can come up with an answer for D?

Paul: How about 811? That’s for the kid who adds everything but doesn’t carry anything.

In Room 56, the kids come to learn that multiple-choice questions are carefully designed. It is rarely a matter of one correct answer and three randomly chosen incorrect ones. The people who create the questions are experts at anticipating where students will go wrong. When a kid makes a mistake somewhere in the course of doing a problem and then sees his (incorrect) answer listed as a potential solution, he assumes he must be correct. My kids love to play detective. They enjoy spotting-and sidestepping-potential traps.

When students in Room 56 take a multiple-choice math test with twenty problems, they see it as an eighty-problem test. Their job is to discover twenty correct answers and sixty incorrect ones. It is hysterical to listen to the sounds of the class when the students take a standardized math test. The most common sound is a quiet giggle of recognition. The kids love to outsmart the test and can’t help laughing as they discover one trap after another.”

Inspire Your Students To Tell A Story With Prezi

I've been using Prezi in my workshops and have written a few posts illustrating it's features – brainstorming with Prezi and embedding Prezi in your blog.

Enjoy "Create a Prezi" – a fine video that demonstrates the process in under 5 minutes. (No, I didn't create it!) It will inspire your students and give them a chance to break out of the lineal / PowerPoint style. (Thanks for the tip – Twitter/ashleyproud)

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Use Wiffiti to Engage Your Audience – Big Screen Live Presentation of Feeds from Twitter, Flickr and Text Messages

I’m always looking for ways to make my presentations more engaging and interactive. (A must if you’re advocating more student-centered instruction.) I’ve been using a TurningPoint ARS for years with great results and have tried live blogs at my larger workshops. As a convert to Twitter, I thought it was the logical next step. 

I’ve experimented with Twitter visualizers on my blog- StreamGraph,  TwitterCloudExplorer, and most recently, Wiffiti. When I saw how good Wiffiti looked on my blog, and I realized it would be a great way to capture the backchannel at workshops. Users can interact with Wiffiti from their mobile phones or the web. It looks great on the big screen – plus it can feed from Twitter, Flickr and text messages.  

I opened a free account and gave it a trial run at my recent workshop in Moriarty-Edgewood SD, New Mexico. It was easy to create a new Wiffiti screen with custom background. (I selected a local landmark neon sign from old Rt 66 in Moriarty.)  I set up the Wiffiti screen to capture Tweets tagged with my Twitter user name @edteck.

The evening before the presentation, I posted a Tweet asking for greetings – “Say good morning to my teachers’ workshop on old Rt 66 in NM. Where are you from? Why do you Twitter?”  As participants arrived in the workshop,  they were greeted on the big screen with encouraging words from all over the world. Pretty impressive when you’re talking about the impact of technology on teaching and learning!  Special thanks to all that sent greetings – it was an powerful demonstration of the new landscape of information and a display of the power of Twitter / social media!

I shot a bit of video to give you and idea what it looked like.  
 (Remember, the live version of this screen no longer has Tweets relevant to the workshop.)

New Wiffiti messages are instantly displayed center screen and are easily viewable from a distance. Older messages then fade back and move as an animated cloud. Updates from both mobile and web are displayed synchronously across all screens subscribing to the same tags, encouraging the creation of a wide, cross-channel audience.

 Using Wiffiti in Breakout Sessions

I also created a second Wiffiti screen to use during break outs. This one was designed to capture text messages from participants. For those that did not have cells, we set up computer stations where they could make comments directly from the Wiffiti website.

Here’s some sample comments – a nice mix of thoughtful observations, fun comments and a few critiques. (Note: I kept it real and I ran my system unmoderated, but it is possible to have someone monitor comments.) 

“School is where kids go to watch old people work really hard”

“My Brain Hurts!”

“Let’s get going!”

“disequilibrium, change, and freedom”

“same old stuff, different day!”

“the table in the back rocks!!”

“English teachers and librarians rule -all others drool!”

“having a blast!”

“science is over here.”

“This is a great workshop!”

“Enjoying the presentation Peter. Especially the film clips!”

“Rigor and Relevance for the English Department: Rigor: Apply knowledge and skills in complex ways to analyze and solve real problems…”

My bottom line? Wiffiti is a great way to harness back channel workshop comments. The free version works well and paid versions offer more opportunities to customize and monitor comments. 

Innovative Teaching is to Sustainable Farming as Test Prep is to _____?

Recently I spoke at a project-based learning conference in Wisconsin. I had been reading Michael Pollan's "The Omnivore's Dilemma,” so I had farming on my mind as I drove from the Milwaukee airport to Janesville WI past vast cornfields punctuated by enormous grain silos.

Pollan observes that high-yield corn is a product of genetically identical plants that can be densely planted without fear of any stalks monopolizing resources. As corn dominated the midwestern landscape, the region became an agricultural monoculture of expansive corporate cornfields – pushing out other crops and more diverse family farms. Cheap corn created the "Concentrated Animal Feeding Operation," where never-ending truckloads of feed are used to fatten cattle in the least time possible. "Big" corn and cattle production are artificially supported by vast, but unsustainable, industrial inputs of fossil fuels, petro-chemicals, and an elaborate transportation system.

And somewhere on the drive to Janesville, I got thinking that Pollan's indictment of corporate agriculture might be extended to some aspects of education. The testing regime is turning our kids into a high-yield, uniform commodity. Rows and rows of competent, standardized students, that can be delivered according to employers' specifications for a "skilled workforce.” Children “force fed” in test prep programs in efforts to quickly “fatten” the scores to meet AYP. Like the cornfields and feedlots that are disconnected from local ecosystems, the movement toward national educational standards erodes at local control and innovation.

Fortunately when I got to the conference I saw another side of contemporary education – innovative teachers. It was like walking into a sustainable farmers' market.

The conference was held at the TAGOS Leadership Academy and hosted by Project-Based Learning Systems, the developer of Project Foundry, a web-based management tool for innovative learning environments. Teachers had come from across the country – Chula Vista CA to Waterville ME. Like sustainable farms, their schools were deeply rooted in their communities, each closely tied to its unique local social ecology. Their programs fostered interdisciplinary learning, like the symbiotic polyculture of a farm based on a rotational interplay of crops and animals.

PF-plans The PBL approach is based on the notion that rather than simply apply bodies of knowledge to problems, the exploration of problems can generate new bodies of knowledge. Teachers didn't attend the conference to simply “sit and get,” they were there to share. After my introductory talk and a planning session using my audience response system, the teachers self-organized into a series of peer-teaching sessions that took them through most the rest of the conference. 

The next day I headed home feeling upbeat. I had met many fine teachers and instructional leaders who reminded me of why I went into education. Most of all, I thought about the scores of teachers across the country, working in innovative schools (or perhaps subversively innovating in traditional schools), committed to raising a “crop” that can sustain itself through a life time of learning.