Let’s trick ‘em into learning!

© 2006 Gary S Stager

A friend called a few months back and asked me to tell him my most dangerous idea. What a great question! My answer, “Curriculum is bad.”

Allow me to make the case.

I can turn to almost any page in a textbook, article or website and find an outlandish, inaccurate or confusing idea some curriculum writer thought was brilliant. Even the most well intentioned efforts at relevance or context stretch credulity, often in a hilarious fashion.

Indigestion
recent article in Edutopia (July 2006) presented a new method for making connections between art and math, called Aesthetic Computing. The following example demonstrates how the method might be used to teach teens about slope intercept form.

Aesthetic computing attempts to reach those frustrated by traditional math instruction by presenting abstract mathematical concepts in a more creative and personal way… For example, a standard equation for graphing lines on a slope such as y = mx + b might become a hamburger, with y representing the whole burger, m referring to the meat, and x standing in for spices. Multiplication is indicated by the fact that the meat and spices are mixed together, and b is added to represent hamburger buns. Students then write a story about the burger or draw a picture of it.

What? How is drawing a burger related to slope? One abstraction (slope) is replaced by even greater abstractions. The concept of variable is muddled and equations are presented wrongly as recipes. Worst of all, this is referred to as a hands-on project when it’s just coloring. (Note: If you think this is just one out-of-context example, I encourage you to read the primary sources on aesthetic computing. There you will find profoundly confusing examples of pedagogical tricks masquerading as constructivism.)

Fumble!
Corporations often write curriculum tie-ins to their products. Some are shameless marketing ploys while others are more altruistic. The NFL recently announced a $1.5 million marketing campaign to get kids more active and fight obesity –  a noble public service gesture. It’s not their fault that curriculum is bad. They’re just playing along.

A language arts lesson has students create and perform a rap that demonstrates action verbs. A science lesson has kids play scooter tag, with one group of students representing cholesterol and another representing healthy hearts. (Associated Press, 10/19/06)

The NFL might solve two problems simultaneously. The Kansas City Chiefs can become the Cholesterols and the Redskins, the Healthy Hearts. Racist mascots could be replaced with scientific models while local school kids rap about vascular plaque. Multiple-choice comprehension questions appear on the Jumbotron.

Lola Falana Math
Textbook publishers use graphics and word problems to recycle old content. Units often begin with “real-life” content to help students make “connections.” One 7th grade math text has a photo of Walter Matthau dressed as Einstein. I know what the curriculum designers are thinking. Kids are just nuts for Walter Matthau!

The text below the photo reads something like, “In the classic motion picture, I.Q., Matthau plays Albert Einstein. Meg Ryan is his niece and Tim Robbins is a mechanic with a crush on her… Later in the film Tim Ryan’s character asks the niece, ‘How old is your uncle?’ Einstein overhears the question and yells from the other room, ’10 times 2 to the third.’”

Get it? They’re teaching exponents. What a hoot! All of the film stuff was unnecessary trivia that distracts from what should have been a simple arithmetic problem – not that anyone would ever express their age in exponential form.

The point of exponential notation is what? How does it work? Why?

Surely, the mere invocation of Einstein in the passage makes this a science lesson too.

I Know What You’re Thinking
Gary is against “bad” curriculum like the examples above. No, I oppose all of it. Curriculum is the arrogant folly of adults who don’t know the children who will play cholesterol scooter soccer, yet are self-ordained to prescribe what those students should know and when they should know it. Curriculum is the weapon of choice for ranking, sorting and labeling children. It is indifferent to individual needs, talents or desires. Worst of all, curriculum creates an impermeable barrier between teacher and student. Without curriculum, failure would be more difficult as would the assorted pathologies of discipline problems, drop-out rates and violence that plague far too many schools.

Last Friday afternoon I experienced one of the most joyous moments of my thirty years in education. I took three fifth grade girls (along with their classroom teacher chaperone) out to lunch. That’s right. We walked right out the front gate of the school, into the sunlight, crossed the street, walked down the block and had a leisurely 90-minute lunch at the restaurant of their choice – regrettably the crime against gastronomy (and pizza), California Pizza Kitchen.

A few weeks earlier, I had challenged the 5th graders to write a computer program in MicroWorlds EX that would draw fractional representations of a circle for any fraction a user requested. Feeling a bit cheeky, I said that I would buy lunch for the first kid or group of kids to write a successful program. After a few class sessions dedicated to the challenge, three fifth grade girls were the first to succeed.

I know. I’m a hypocrite.

I reject behaviorism and its evil friends; grades, punishment, bribes and rewards. However, this felt different. The kids were going to join me for lunch like colleagues celebrating an accomplishment. Best of all, their classmates continued working on the programming challenge, without hard feelings, even after “winners” had emerged. Perhaps they knew that their turn would come. I routinely bring treats from my travels into the classroom. If I worked in an office, I might stop occasionally and buy Dunkin Munchkins for my co-workers. I do the same with my students. Why not?

I loved telling the girls that they could order anything they wanted and learning about their dietary habits and favorites. Conversation covered sick babies, interior decorating, roller coasters, face blindness and Khan Academy. The last two topics were introduced by a girl who matter-of-factly stated, “I watch 60 Minutes.” I was jealous of their classroom teacher who knew more about their parents, siblings, friends and neighbors than I do, but a good time was had by all. The genuine gratitude expressed by the girls (including their teacher) made it all worthwhile.

Perhaps the highlight of our lunch was watching the girls color their kid’s menus at a lunch celebrating their computer science prowess.  Once again, Seymour Papert is correct.

Below is the program the girls wrote. It required figuring out how to “teach the turtle” to draw a circle and utilized a bunch of mathematical concepts, including radius, fractions, variables and angle.

For those of you lacking the skills of a 5th grader and can’t read a Logo program, I’ve included a video demonstrating their program at work.

to Pie
 repeat 360 [fd 3 rt 1]
 end
to fraction :n :d
 cg
 setc "black
 pd
 Pie
 pu
 rt 90
 fd 172
 rt 90
 pd
 repeat :d [fd 172 bk 172 rt 360 / :d]
 repeat :n [rt 360 / :d fillit ]
 end
to fillit
 setc color + 5
 pu
 rt 5
 fd 20
 fill
 bk 20
 lt 5
 end
to mem
 repeat :n [fillit pu rt 1 fd :l / :d lt 1]
 rt 1
 bk :n / :d * :l lt 1
 end

 .

An old friend of mine, Dr. Barry Newell, is an astrophysicist who was was the Administrator (in the NASA sense) of Mount Stromlo and Siding Spring Observatories of the Australian National University. He now works on the dynamics of social-ecological systems. In his spare time (back in 1988), he wrote two classic books on Logo programming and mathematics, Turtle Confusion and the accompanying book for educators, Turtles Speak Mathematics. Turtle Confusion features 40 challenging turtle geometry puzzles in a mystery format and Turtles Speak Mathematics helps educators understand the mathematics their students are learning.


I was reminded of the books when Sugar Labs, the folks behind the operating system for the One Laptop Per Child XO laptop, featured the challenges as an activity to accompany TurtleArt software on the XO.

Screenshot of the XO Turtle Confusion Activity

The books’ author, Dr. Barry Newell, gave me permission to share digital copies of the book for personal, educational and non-commercial use. Click here to go to the download page.

These books are best used with versions of Logo such as MicroWorlds EX or Berkeley Logo. Some of the puzzles are very difficult or impossible to solve in Scratch, but it’s worth trying if that is all you have. SNAP! is another potential option. TurtleArt is another possibility. Although, mathematical programming is often easiest and best achieved through the use of textual language (IMHO). A bit of dialect translation might be necessary. For example, CS is often CG (in MicroWorlds EX).

A few weeks ago, I quietly launched a new site, The Daily Papert to bring Seymour Papert’s powerful ideas to our short attention-span culture. I am gratified by the response The Daily Papert has received and hope you will take a few minutes to read the posts already on the site AND subscribe to its RSS feed.

Three provocations inspired the creation of this site honoring the work and powerful ideas of Dr. Seymour Papert.

First provocation
In August, 2010, I attended the Constructionism 2010 conference in Paris. The conference gathered hundreds of educators, researchers and scholars in a celebration of the theory of constructionism originated by Seymour Papert. Old friends, colleagues and disciples who never met Dr. Papert spent several days sharing their knowledge and 40+ years of recollections, but one person was missing – Seymour.

Seymour Papert was in Maine where he continues recuperating from a terrible accident he experienced in 2006. However, his presence at the conference was unavoidable. As each of the esteemed conference attendees presented their work formally during sessions or informally over meals, the enormity of Papert’s influence overwhelmed me. Each of us and our work represents but a tiny fraction of Papert’s legacy. It might take thousands of us to assemble the quilt that is the life and legacy of Seymour Papert.

Second Provocation
On more than one occasion I have been accused of making an argument based on Papert’s work. Colleagues have exclaimed, “The answer to every question in education isn’t Seymour Papert.” However, Papert was so ahead of his time, so thoughtful, prescient, bold, creative and often times right, that I do find that he either predicted current problems confronted by educators or offered solutions. In many cases, he did so decades ago.

Third Provocation
While Papert’s innovation, scholarship and wisdom is widely recognized across the globe and among scientists, his half century of contributions to his major field of choice, education, is largely invisible. It is not that educators disagree with Papert’s theories or recommendations, they just ignore him entirely. This “idea aversion” (a term of Papert’s) is manifest by Papert’s absence from teacher education texts, educational technology publications and school reform literature.

I hope that this site offering bite-size nuggets of Papert wisdom will inspire educators, parents, scholars and citizens to investigate more of Papert’s work in years to come.

It is the least I can do for a friend, mentor and colleague who has transformed my thinking and given purpose to my life for three decades.


Many thanks to Chris Craft who generously spent hours debugging the site (there are still a few left) after I lost my sanity and patience.

This past Fall, one of my oldest friends, veteran mathematics educator Ihor Charischak, hosted me for a Math 2.0 live webinar.

The webinar featured a freewheeling discussion about the state of math education, the role of computers in mathematics learning, school reform, constructionism, Seymour Papert, Web 2.0 and a host of other topics. If you missed the original webinar, you can watch or listen to it now and read the comments posted by attendees.

Replay the webinar


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