I’m trying to remember when I was 12 how I would react to We Use Math.

I was in New York last month consulting on a project intent on improving students’ perception of mathematics. We were spitballing around the table when someone pulled up this poster which was designed by NCTM:

Everyone in the room fawned over it, myself included. Then I pulled up this photo on my iPad.

I said I found the differences between the two images provocative. One person said, “Right. Basketball. Kids like basketball more than bridges.”

Is that it?

Let’s look at We Use Math, a project triple-teamed by Brigham Young University, the Mathematical Association of America, and the American Mathematical Society. Clearly that consortium brought a lot of resources to the table. The site features polished quotations from happy and well-paid professionals testifying to the usefulness of math in their careers. There’s a career tracker which lists dozens of high-paying careers, their salaries, their employers, the math required, and the ways math is used. Here’s the flyer for chemists [PDF], for instance. There’s stock photography of pretty people who (presumably) also use math, as well as a T-shirt store.

Engagement is a funny, fickle thing. On the subject of how to excite children about math in the same way it excites me, I have more questions than answers. Let me try to lay out a few markers, though:

**There is a difference between***showing a picture*of the math of parabolas and*provoking a question*which can be answered using the math of parabolas.**“If you manage to endure maybe nine more years of math you dislike, life will reward you with a well-compensated job doing math you like.”**That’s a tough sell for a twelve year-old. That’s over half her entire existence you’re asking her to bet on extremely speculative odds. (See also: “Doing the Math to Find the Good Jobs“; interviews with professionals in textbooks.)**When you see someone love something you find completely unloveable, it’s hard to relate to that person.**It’s hard not to think they’re insane.

Venturing out farther on the creaky limb of engagement, here is some advice I give myself:

**Don’t promise students they’ll enjoy the math they hate now in a career later. Let them experience math they enjoy now.**PBS does this effectively with Get the Math. It features interviews with musicians, fashion designers, and video game engineers talking about how great math is, how much math they use, etc, but it also gives students something to*do*. It puts them in a position to experience that math now.**Show don’t tell**. Instead of*testifying*to math’s power,*show*them math’s power. The CME Project features sidebars all throughout its textbooks with promises like:- You can use the polynomial function that describes the frog’s motion to predict the time the frog will land.
- You can use vectors to describe the magnitude and direction of the wind, currents, and movement of the ship.
- You can use a matrix to organize a large amount of information, such a a bus schedule.
- You can use triangle relationships to measure the width of the glacier.

If you’re going to brag about math’s power to do [x], let’s

*do*[x].(That’s setting aside the trickier issue of whether or not [x] interests students in the first place.)

**An ounce of perplexity is worth a pound of engagement.**Give me a student with a question in her head, one that math can help her answer, over a student who’s been engaged by a poster or a celebrity testimonial or the promise of a career. Engagement fades. Perplexity endures.

Perhaps it comes to this: rather than remembering your *own* tastes as a twelve-year-old, empathize with the tastes of a twelve-year-old who *isn’t anything like you*, one who has experienced only humiliation and failure in mathematics. What does math have to offer *that* student?

**BTW**: Here are three more PR projects. I like the odds on one of them way more than the other two.

**2011 Oct 21**. Great piece from Jason Buell on the extremely variable and personal definitions of “real world.”

**2011 Nov 06**. Jan Nordgreen links up a remark from Alfred North Whitehead in 1929:

Whatever interest attaches to your subject-matter must be evoked here and now; whatever powers you are strengthening in the pupil, must be exercised here and now; whatever possibilities of mental life your teaching should impart, must be exhibited here and now. That is the golden rule of education, and a very difficult rule to follow.

**Featured Comment**

But another approach – since you used the word “enjoy” – is to simply consider math as an opportunity for puzzle-solving in interesting ways. After all, there is virtually NOTHING “personally relevant” in many of the games and pursuits people find so compelling, like, for example, Sudoku. Even chess. Or Angry Birds. Whether math is useful/relevant RIGHT NOW is a worthy and challenging goal.

## 49 Comments

## Ben

October 17, 2011 - 10:03 am -This speaks HEAVILY upon the relevance portion of the whole RR framework (http://www.leadered.com/rrr.html). Sure, a beautiful bridge like that is relevant to a child’s life in that they have to drive over them, or they might be a good place to hide underneath while trying to hide their experiments with nicotine, but it’s not the right kind of relevance.

Although, having mulled over your writing, and the RR framework for a few minutes, I’m wondering if the whole relevance aspect of the framework too often overlooks the immediate relevance to the student in favor of the relevance to the curriculum, thus reinforcing really pretty images and quotes, but doing little to motivate students.

What are your thoughts about turning an opportunity like this into a challenge based experience in that you show students the power of math [x = parabolas in bridge construction], and then challenge them to create their own bridges using parabolas?

## Boyce

October 17, 2011 - 10:10 am -I was observing a 4th grade math lesson at a high-performing charter school in NYC recently. The teacher (a good friend of mine) opened his math block by asking students how they wanted to “lead the world” (an over-all theme of the classroom), and then how math might help them with this. The kids spent the most time connecting math to one student’s goal of being an NBA/NFL player.

I saw the answers falling on to a scale:

1. The superficial.

These answers cast math as something that has to do with numbers. It may not make sense or be important–but there are numbers in the world. This is the domain of pseudocontext: “He will want to measure the area and perimeter of the basketball court.”

2. The applicable.

These answers come from students who see math as being basically useful for specific tasks. So, “He needs math to keep score of the game.” Math here is something that comes up in the world, and when you see it you have to be prepared for it.

3. The transformative.

These answers cast math as something that truly changes your relationship to the world. Not many fourth-graders can answer this way, and no one in this class did. The closest was, “he needs to know how many touchdowns he makes per year,” and I think this stuck out to me just because I had recently watched Moneyball. What I wanted to hear: “He can’t truly understand who he is as a basketball player unless he can measure and analyze his performance.” Math is a way of seeing that’s essential to truly understanding the world.

The point of all of this is that most math PR examples are pushing students to fall into category 2. Rarely do we try to sell math as something that is transformative–often, I think, because a lot of our teachers themselves don’t see math as transformative.

## gasstationwithoutpumps

October 17, 2011 - 11:13 am -Shouldn’t the bridge supports be a catenary, rather than a parabola? Has anyone analyzed the picture to see if it is a parabola?

## gasstationwithoutpumps

October 17, 2011 - 11:17 am -I think that the physics facts will have the most impacts. The pictures of people are boring and irrelevant, and the math posters are way too busy and hard to read. They might work in the intended environment (people waiting for a subway train with nothing else to look at), except that the fonts are a bit small and people can’t cross the tracks to look at them more closely.

## Phil

October 17, 2011 - 11:31 am -The “we use math” website clearly sees money as a motivator for doing math as they have the website designed to make that show up right away.

While kids will talk about music/sports stars and the millions they hope to make, my conversations have always been much more deep and they want to “do something fun”.

I agree with Dan and many others who say, let it be fun now. Give them the tools to answer their own questions and create during their most formative and creative years. We are throwing millions of cognitive surplus down the drain every year by showing students math they’ll use someday rather than letting them solve our biggest problems collectively or at least begin to understand them.

We underestimate what they are capable of and marvel at stories of what high school dropouts invent.

## John Chase

October 17, 2011 - 11:35 am -I agree. The bridge should be a catenary, not a parabola. I could be wrong, but I thought bridges & arches were catenaries (just like hanging chains). Is this an exception?

## Laura

October 17, 2011 - 12:11 pm -“There is a difference between showing a picture of the math of parabolas and provoking a question which can be answered using the math of parabolas.”

This is where I get stuck as a teacher of mathematics to 12 year olds (8th grade Pre-Algebra & Algebra). I can teach the math – the calculations, the formulas, the mechanics, etc. However, I cannot for the life of me figure out how to apply this math to anything other than very superficial circumstances (textbook math and pseudocontext). My students see through me before the first 5 minutes are up!

I need help, too. I hope I’m not the only one… How do I use linear functions? They don’t care about cell phone contracts, which is what I’m always shown when I bring this up in department meetings. Is anything REALLY a linear function? Is anything that is really a linear function of interest to 12 year olds?

I want help devising the situations in which my kids can ask the questions that can be answered using the math. I just don’t think I know enough math to make them interesting situations and I don’t think the people who know enough math can make them interesting, either.

## luke hodge

October 17, 2011 - 1:54 pm -That is quite the poster from the NCTM – a three line non sequitur in a hybrid alphabetic-pictorial language.

## Kathy Sierra

October 17, 2011 - 1:55 pm -Wow.

“let them experience math they enjoy now.” Yes, yes.

I do like to imagine a continuum of “reasons to be engaged” and the PR FAIL that is WE USE MATH is at the end, only one imperceptible step beyond NO REASON (though the use of stock photography models as the “users of math” might have a DEmotivating effect, oh well). On the far opposite end, where total engagement lives, is a completely immersive scenario where math is firmly embedded in a deeply intrinsically rewarding activity. A game developer coding a challening game lives there.

Somewhere between those two we find something more realistic. One realistic/useful approach is to find things where math really IS relevant to their lives, RIGHT NOW. This is super difficult and often results in pseudo-context. You are one of the true masters here. But another approach — since you used the word “enjoy” — is to simply consider math as an opportunity for puzzle-solving in interesting ways.

After all, there is virtually NOTHING “personally relevant” in many of the games and pursuits people find so compelling, like, for example, Sudoku. Even chess. Or Angry Birds. Whether math is useful/relevant RIGHT NOW is a worthy and challenging goal. But perhaps it is also useful to consider ways in which math is a wonderful platform for crafting “flow” experiences (in the Mihaly / Optimal Experience sense). This was the required text to study when I worked for Virgin Sound and Vision (at the time, a division of Virgin Games focused on kid’s and educational games).

Just as a good novel or film or even game can suck you in *despite* having a theme you are NOT interested in (eg. I loved several golf and baseball themed movies despite a pathological disinterest in both sports) and will never, ever use. We already know that only a small percentage of kids will make the leap to a form of motivation needed to stay focused on tasks because of “some future payoff”. Getting a payoff NOW is what matters.

The form of that payoff can vary a lot, but having it be at least partly *intrinsically rewarding* is a good goal, as is finding a way to connect what they are learning to something they do, right now, care about quite a lot.

The problem with the we future payoffs is that they almost never work. For example, among all demographics, when people are told they must make lifestyle changes following a coronary bypass or they MAY DIE A PAINFUL DEATH, virtually everyone is convinced that of COURSE they would make those reasonably do-able changes. Yet the research shows that only 1 in 9 people actually make the change. If we cannot get people to do behaviors when their very LIFE is at stake, we certainly have little hope motivating young people about some distant career.

Motivation, according to Self-Determination Theory, for education needs one or sometimes two things: either intrinsically rewarding activities (they are fun for their own sake, no other reason) and/or they are directly connected to something that in my mind and heart I personally care about and believe in… Where doing it becomes part of who I am *in spite of the fact that it is not an intrinsically pleasurable activity*.

The same themes described in Dan Pink’s TED talk keep showing up in motivation research: you need autonomy, mastery, and purpose. Most math education may have the potential for mastery, but is a total FAIL on autonomy (defined as something I believe I am doing on my own volition, even if it was required… It is not an autonomy-killer that someone else told you to do it as long as you perceive that you WANTED to do it because it aligns with who you are and what you want) and a total FAIL on Purpose.

If I am writing an educational thing these days, I try a simple checklist for each page/topic:

1. Does it support the learner’s autonomy, mastery, and purpose?

2. Does it have the three Ps: a point, a pulse, and a payoff?

Sorry for writing a novel here, Dan. I am just doing this to help clarify my own thoughts around the thing I fear MOST in education today: the move toward “gamification” (the use of extrinsic rewards / operant conditioning to build “engagement”). Way too much scary research around THAT.

## blink

October 17, 2011 - 3:46 pm -I agree with the spirit of your post, but find your reference to the CME text ironic. I don’t think a published curriculum exists with *fewer* ostentatious graphics, etc. detracting from the mathematics. Your selective quoting of surface details is exactly the same as those who dismissed your example with a quick, “eh, it’s basketball.” I hope others see the substance of your problems rather than being swayed by the gloss, and I hope that you do the same.

## Jen

October 17, 2011 - 6:36 pm -*is to simply consider math as an opportunity for puzzle-solving in interesting ways.

After all, there is virtually NOTHING “personally relevant” in many of the games and pursuits people find so compelling, like, for example, Sudoku. Even chess. Or Angry Birds. Whether math is useful/relevant RIGHT NOW is a worthy and challenging goal. But perhaps it is also useful to consider ways in which math is a wonderful platform for crafting “flow” experiences *

This. This times a lot. The truth is that I really didn’t like math in school — but I liked getting good grades and I liked not feeling like an idiot. So, I listened in class and I did the problems and I looked back at the book if I didn’t get it and I did more problems. I created my own reward/relevancy out of a bigger picture desire to be “smart” and to “do well.”

From that perspective (which changed at some point in my early 20s when I finally sort of got the “fun” of math) none of these relevancies is particularly interesting or relevant. I get that some people think so, just like I get that while I like reading horrible true life stories from the paper to my family, they do not want to hear them.

Now, I do like the ideas and questions, and that came about through what? Maturation? Time for things to percolate? Suddenly all those concept-y things that really hadn’t stuck came back and made sense. Had I not done the “following directions to get a good grade” stuff before though, I wouldn’t have had the capacity for that switch over, right?

So. It comes back to finding some in to a flow or enjoyment experience. For some kids it may be checking off a checklist of problems done correctly to get to a new level or to get a prize or have some level of recognition. And honestly? I don’t have a problem with that. I used to, but now I guess I’m more jaded!

I used to tell very far behind grade-level 7th grade students that learning math meant not getting ripped off or conned nearly as often. That it’s easy to take the money of someone who isn’t able to think about numbers. That actually seemed to work as a unifying theme…most any problem could be rephrased as “is this fair to you?” or “do you trust him?”

## Paul Salomon

October 17, 2011 - 6:37 pm -That first one is probably a catenary though, right? Like the Saint Louis Arch?

## Chris Sears

October 17, 2011 - 7:31 pm -I totally want to find a gecko right now.

When I was an undergraduate, I wound up on a panel about “positive norming” on the university’s image with the student body. (It’s funny how positive norming is a spin term for spin.) The point of the panel was to discuss how to highlight to students that there was more to do on the college campus than drinking. Out of that panel came my favorite example of statistics that say more than was intended.

One of the fliers that was presented at the panel had the following: “69% of all college students have 0 – 4 drinks per week.” That was scary to me because it said that 31% of students were getting drunk. That is spin gone wrong.

I think you’ve made a good point on the ineffectiveness of these PR materials. They do make math seem more mysterious and intimidating. We, as math teachers, already see the beauty of it, but we haven’t prepared our students for it.

I am still learning how to get mathematics to relate to my community college students. They measure every class on how it will prepare them for their chosen program, and they don’t like anything that will not make them a better nurse or HVAC technician. I would be very happy with a set of materials that featured blue-collar workers with the caption “I use math every day.”

## Susan

October 17, 2011 - 8:02 pm -I too struggle with making math interesting and fun. I do my best and differentiate my indtruction as best as I can. Since I teach Math and Science, I try to relate them as best as I can so that they can at least see where else Math is useful. I just got the question of when will I ever use this in my life in reference to exponents. It is hard to give children the anwer to that question because a 10-11-12 year old does not really want to hear one. I do try to relate the problem solving aspect of Math to solving problems in life. Math as many strategies that can help students become life-long problem solvers.

## Dan Meyer

October 17, 2011 - 9:19 pm -That’s a great question. If there were some way for students to experience the mathematics inherent to building bridges, to successfully build a small bridge

withmathematics after having struggled to build onewithoutmathematics, that’d be worth our time. I suspect that kind of application is beyond the reach of the kind of student that would be studying parabolas, though.I tend to agree with you.

One of the more interesting outcomes of our #anyqs experiment is that

someteachers testify to a new, mathematical lens on life. Overnight. They can’t help problematizing their world mathematically. That doesn’t get us all the way to “using math transformatively in their own lives” but “asking mathematical questions about their own lives” is a prerequisite and, given how simple the exercise is to start (take a picture or a video, share it), I’m encouraged. How else do teachers change?You aren’t the only one. And good call on the sketchy application of math to cell phone contracts. That’s the litmus test right there to pick out teachers who sorta comprehend that some students want mathematics that’s relevant to their lives but who don’t really get students at all. “Cell phones! Kids like cell phones! Let’s get some math in there!”

More seriously, IMO, the best thing you can do for yourself is to

somehowrecord the math you see around yourself. Write it down. Take a photo. Take a video. Leave yourself a voice memo. I do all of those and most of the time those notes go nowhere. But 20% of them turn into something more interesting and 10% ofthoseturn into fun and challenging activities for kids. 10% isn’t much at first but pretty soon you can’t turn your mathematical notetaking off. You’re leaving a dozen notes to yourself every week. At that point 10% ain’t nothing.More immediately, here are two applications of linears I like a lot: Stacking Cups & Air Travel.

Jenzeros in on that quotation also. Lately I find it easier to talk about “perplexity” instead of “relevance” or “application” or “engagement” for reasonsKathydescribes. The term cuts around the real world v. fake world distinction which trips a lot of us educators up and which is simultaneously totally self-imposed.Are you perplexed? Great. So long as math can help you resolve that perplexity, it doesn’t matter to me if it came from the world outside your front door, the textbook on your desk, or some hypothetical that hopped out of your head.

You’ll have to read my critique again. It had nothing to do with “ostentatious graphics detracting from the mathematics.” And just because a text gets a lot right (which CME does) doesn’t put it beyond criticism.

That’s encouraging. I wonder, though, how much more thrilled they’d be to experience some of that math themselves, in the safety of the classroom, with your help.

## Bowen Kerins

October 18, 2011 - 12:44 am -Absolutely a justified criticism of CME Project in my opinion. The purpose of these sidebars appears to be to pass a “flip test” for people who select a program based on its real-world applicability. I have yet to find even one student who is hooked by these kinds of carrots, so that means these graphics aren’t being created for students.

I think CME does a decent job in the bang-per-sidebar count, but there is still plenty to improve.

Inside baseball: the manuscripts we submitted for CME Project did not include any of the examples you cite. They were added by Pearson, with an eye toward book sales. On the plus side, they are easily ignored or covered with white-out!

I actually like quite a bit of the artwork they added, including these little cartoon characters acting out problems in the book. But there are definitely a few that make me wonder. For example, there’s a breakdancer on the Algebra 2 cover… um, what?? We have started calling that book “Algebra 2: Electric Boogaloo”.

On a positive note, this post reminds me of the materials developed as companions to the TV show “Numbers”. They were quite good, varied, and pitched at the right level. The website is gone but some things remain, such as these TI activities:

http://teachers.olatheschools.com/~pflynnoe/Professional%20Writing/Numb3rs.html

There are a few duds, but overall these activities do a better job of introducing “real math” than WeUseMath.org can.

Oh, and shouldn’t that NCTM poster say “I (heart) cardioids”?

## Matt E

October 18, 2011 - 6:06 am -“When you see someone love something you find completely unloveable, it’s hard to relate to that person. It’s hard not to think they’re insane.”

Was it you that pointed me to this, Dan? http://www.brianjaystanley.com/aphorisms/everything-is-interesting

I find it to be all kinds of true, and something I wish I’d learned earlier in my life–the idea that people who are passionate about something can (if I allow them) broaden my perspective on life by sharing that passion with me. I most often apply it now to music; if a particular artist has a rabid fan base, I consider it more likely that I am missing something than that they are all cretins, and take more listening time to figure out what that something might be. Sometimes I wind up joining their throng (Bjork) and other times I eventually give up (Phish), but I always give it a shot. This is one of the many things I want to impart to my students that is not explicitly math.

## Sean

October 18, 2011 - 6:12 am -Dan:

“But 20% of them turn into something more interesting and 10% of those turn into fun and challenging activities for kids.”

Whoa that’s like 2 percent. So 1 out of every 50 things you film, photo, or take note of ends up publishable. You started a feature a while ago- “it got away” or something like it- that cemented this. I forgot until just now.

That’s crazy inspiring. Chip away relentlessly.

## Kathy Sierra

October 18, 2011 - 8:00 am -Ooooooh. Perplexity. Love it.

If the brain science is valid, the right level of perplexity can be an irresistible seduction. How many times has someone posed a question that — almost against your will — you found yourself unable to stop thinking about?

Not to compare kids to animals, but as a horse trainer, there is much discussion around the science of motivation for learning applied to animal training lately, for two reasons: operant conditioning does not work where creativity, innovation, sustained thinking is required and, of course, punishment is often risky and carries nasty side-effects. Also, many of us are aware that it is easier/safer to reach three pounds of brain vs. 1000 poinds of muscle and bone. So today, many are beginning to use strategic perplexity to invite animals to *enjoy* solving puzzles. You get far more motivated behavior than asking for compliance/obedience which, in the end, leaves you with phoned-in behavior.

Now that I think about it, as the parent of two twenty-somethings, kids as teens share a lot in common with young stallions. You cannot manufacture motivation and engagement, but you can surface what is already in their nature. And that includes a deep desire to discover and master challenges in their environment. On their own terms. In other words, they all want to be just a little more bad-ass.

## Dan Meyer

October 18, 2011 - 8:01 am -Coming as a surprise to absolutely no one:

@

Matt E, I think I tweeted that link awhile back. I love the piece. Maybe this is different, though. In this case, if you don’t fully master the ins and outs of Bjork’s discography, if you don’t memorize the names of all the instruments offMedulla, if you can’t plunk out the melody to “It’s Oh So Quiet” at someone else’s whim, you fail Bjork and you don’t go to college and you don’t get a rewarding, well-paying career.Disaggregating that a little more, the odds of publication go way up if I pull out a camera. It’s the quick written observations that tend to accumulate and drive the overall percentage down.

## Dave L. Renfro

October 18, 2011 - 8:07 am -#3, #6, #13: The situation is a little different for suspension bridges. Rather than a catenary, they’ll be parabolas, assuming negligible cable weight. This can often be found in texts for an elementary differential equations course (a fairly standard course, along with multivariable calculus and linear algebra, that one can take after first year college calculus or after high school BC ap-calculus). See the following google-books search.

## hillby

October 18, 2011 - 8:38 am -Are you serious? Dan’s making a major point about the PR for math, and you’re debating catenary vs. parabolic?

That kind of stupid nitpicking is part of the reason I still hesitate to call myself a math teacher.

Just to make Dan’s point even more solid. If I was designing a bridge, and I NEEDED to know what a catenary curve was, THEN I would care. You know what I think a catenary curve is for all intensive purposes? A fancy parabola.

## Dan Meyer

October 18, 2011 - 8:47 am -Now The Great Parabola v. Catenary Debate of 2011 has its own thread.

## David

October 18, 2011 - 9:14 am -“You know what I think a catenary curve is for all intensive purposes? A fancy parabola.”

I’m glad you’re not my math teacher.

## blink

October 18, 2011 - 9:26 am -Cosmic justice: It appears you are feeling the force of my earlier point even if you disagreed with it. Inconsequential though it may be, the Catenary-Parabola debate is at least as relevant to the point at hand as your fault-finding with textbooks based on (utterly inconsequential!) surface features.

As something of a role-model, you need to set the bar higher. If you want others to treat your arguments serious — which I certainly agree they merit — please model it yourself.

## David Wees

October 18, 2011 - 10:54 am -One issue which I think is important to bring up is that this notion of relevance is culturally based.

My students actually ENJOYED learning about the relationship between cell phone plans and linear functions (when we worked on a long project to examine the question: what’s the best cell phone plan for Mr. Wees).

It seems clear to me that what is relevant is very much dependent on the community and culture of the people being taught. It probably also depends on their individual preferences as well…

## blaw0013

October 18, 2011 - 11:42 am -I enjoy the great irony of Dan’s “marker” #3 and the move to a new thread of the parabola v. catenary debate

## timstudiesmath

October 18, 2011 - 7:04 pm -Sometimes I get sad when I think about all the fascinating things I wish I learned from a curious, capable, interested math teacher.

I never heard of a focus and directrix until cramming for the GRE subject test. But back in ‘this is x^2 land’ if someone showed me how amazing it is to put a light bulb at the focus of a parabola made of mirrors and watch every emanating ray be reflected parallel to each other like in a single beam of a flashlight, I might be much happier dredging through weeks of mindless calculating associated with ‘learning’ about that function family. Or, conversely, if we talked about how that satellite dish is shaped to collect parallel rays at a single point. Or if I was given a piece of paper, drew a line across one edge, put a dot in the center of the paper, and folded that paper 20 ways such that the dot rested somewhere on the line each time (I’ll let you know how this goes with my students in the spring).

They’re shapes, and the things those particular shapes do are amazing to me. Respect!

## Alexandra

October 19, 2011 - 5:17 am -Hm, I guess I’m only interested in commenting after the thread has derailed.

Kids love bridges. Correction: kids love building bridges. I can’t make them stop using West Point Bridge Builder.

## James

October 19, 2011 - 8:52 am -@ hillby: Or my English teacher: The phrase is “for all intents and purposes.”

## James C.

October 20, 2011 - 7:09 am -I’m arriving in this conversation a little late, but I think we’re comparing apples and oranges. The basketball throw is intriguing because it poses a problem. The bridge is intriguing because it poses an application. These have two very different uses in the classroom. Don’t you guys remember elementary school when your teacher told you to go around the room looking for examples of circles or triangles or other shapes? That’s the use the bridge picture has. I wouldn’t pose any kind of problem with the bridge picture but I would include it as part of a quadratic theme. For example, a poster on the wall with all kinds of pictures of quadratics, or a picture in a textbook on the first page of the chapter. Brain-based learning type stuff to get people used to the idea of the quadratic pattern.

## John B.

October 20, 2011 - 5:11 pm -With these PR examples, I see a lot of extrinsic motivators (i.e. “being good at math will help you make more money”), but very few non-cheesy attempts at inspiring students to enjoy math for its own sake. Ask any person who is truly passionate about the study of mathematics why he/she studies it, and few of them will say, “Oh, it’s for applying it to the world around me.” Many of them will say (including myself) that mathematics should be studied for its own sake. Sometimes it will yield a practical application; other times not. We aren’t at liberty to decide that, particularly when the Heisenberg Uncertainty Principle comes into play. We study mathematics for its own sake, and its applications for humans’ sake.

As a teacher, I have had the most success with students (achievement and motivation) when teaching mathematics through the Paideia method of instruction. Through shared inquiry seminars grounded in readings written by historical mathematicians, scientists, and philosophers; coached projects that focus on a blend of mathematical laws and observations such as Dan’s basketball problem; and minimal didactic instruction – students’ interest (as well as my own!) in mathematics has truly blossomed, right along with their state test scores. In fact, my most successful instructional year was one in which I taught without the use of a text book, supplanting the formally researched problems and ideas with my own action research-based ideas. I had a lot more ownership over every problem, and building them myself to span all levels of Bloom’s Taxonomy gave me entirely new insights about the depth of that which seems so very simple. Of course, it helped that students were discussing the depth as well, finding patterns in numbers and algorithms that I had never before seen. True mathematics is often taken for granted, and from what I have seen, the worst culprits are often math teachers…

## Den Rattee

October 20, 2011 - 8:00 pm -This is an advertisement for math; and advertising works! Whether catenary or parabolic it’s a cool math shape that may make kids pause and consider math differently for a moment, or it may plant a seed to help them grow that different perspective in the future. I certainly was struck by the aesthetic and mathematical beauty of the bridge. Also, the bridge is only a model of the mathematical function at the core of it’s design; in reality it is not exactly congruent to either function. So model away. Frankly I would be thrilled if some of my student modelled it with a circle and a couple of tangent lines.

As for engaging kids in a mathematics classroom, I have only found one truth. Math is only fun for the people doing the thinking. As math teachers, we have an opportunity to present the only curriculum in school that students can figure out for them selves. We need to find tasks that challenge our students at the right level and them help them generalize their ideas to envelop the curriculum. As soon as we try to provide memorized solution processes, we turn the best subject in school into the worst.

## Dan Meyer

October 21, 2011 - 9:19 am -Agreed that they’re different things. One, a question. The other, an application. But they aren’t equally effective motivators. If I hate math, showing me applications of math won’t do much to change my perception of math. More effective is to help me use math to answer questions that matter to me.

Always?

## Sue VanHattum

October 21, 2011 - 12:53 pm -Den, I love this: Math is only fun for the people doing the thinking. As math teachers, we have an opportunity to present the only curriculum in school that students can figure out for them selves.

I’d like to quote you in a book I’m putting together. Can you email me at mathanthologyeditor, on gmail?

## Jason Dyer

October 21, 2011 - 1:23 pm -Den: This is an advertisement for math; and advertising works!Dan: Always?I dunno about the bridge poster but I’d say the other posters in the series

I (heart) spherical analogs of truncated icosahedrons

and

I (heart) hyperbolic cosines

just make math sound nerdy.

## James C.

October 21, 2011 - 1:35 pm -How about not so much as a motivational technique, but as a learning technique, to customize students to the parabolic pattern? Granted, this may not have been the original intention of the publishers of the poster, but I still think it has potential if it is used this way. Isn’t it kind of telling how little we make this connection if a room full of math teachers were fawning over it?

## Dan Meyer

October 21, 2011 - 1:50 pm -Sure. Nowhere am I saying they’re useless. I’m saying their usefulness is limited for one particular purpose.

Right. They’re tribal symbols, basically, and tribal symbols have strange and unpredictable connotations for people who aren’t members of the tribe.

## louise

October 21, 2011 - 3:24 pm -Looks like the pure vs. applied math debate to me (again). Maybe the Math equivalent of writers vs. editors? Artists vs. art critics? (stirring the pot?) I do know that, when I was in grad. school, the math/physics continuum was

pure mathematicians, theoretical physicists, applied mathematicians, experimental physicists. You got to take your pick on which was the “top end” depending on your own interests. I am very happy that people on this discussion understand that the only reason for doing Math is as a minion to help with experimental physics, but I do know some mathematicians who are pretty horrified. Of course they mostly don’t stoop to teaching middle and high school students :-)

## Dan Meyer

October 21, 2011 - 3:38 pm -I don’t this particular post has that character. Rather it addresses the question, “If we’re going to make the claim that math applies to the world, how best do we do that?”

## luke hodge

October 21, 2011 - 4:53 pm -I am not so sure how many students really believe that the math they learn today will even be helpful to them in a few days, weeks, or months down the road in that very same math class, let alone in the world outside school. I think that many students, with justification in some instances, view math as a string of largely unrelated two week units.

School is very much the “real world” for students – real work to get done, real stress, etc. I wish I could do a better job of marketing the fact that working for a better understanding today really will make a difference in a student’s “real world” experience in the classroom in future months (more success and less stress) — and make sure that the marketing isn’t false advertising.

## Jan Nordgreen

November 6, 2011 - 1:19 am -Alfred North Whitehead said the same in 1929.

More: https://plus.google.com/u/0/108840294486623374565/posts/ayyYJdWLqVd

## Mr. Vaudrey

December 15, 2011 - 3:14 pm -Have we arrived here yet?

http://www.youtube.com/watch?v=xyowJZxrtbg

To save you 12 minutes, Bennett contends that upper-level math is really only necessary for a career in math instruction.

Further, he contends that the type of abstract reasoning taught by Algebra can be taught just as easily with puzzles, logic, and games.

Interesting, but I’m not on board just yet. I think the idea of perplexity runs in this same vein, but tangential to the movement of “Overthrow the Standardized Test!”

## James C.

December 15, 2011 - 4:54 pm -It’s a little hard to take a math teacher like Bennett seriously when he simplifies finance to the most basic financial transactions (e.g. leaving a tip on your meal cost), and suggests only math teachers and engineers need “higher” math. If he’s suggesting that maybe we’re not teaching the right topics in math, he may have a point. But even if the chosen math topics are not to his liking, at least a curriculum means there is progression and we don’t leave it up to teachers to re-invent the math wheel every year.