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?

Shouldn’t the bridge supports be a catenary, rather than a parabola? Has anyone analyzed the picture to see if it is a parabola?

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.

“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.

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.

*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?”

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.”

“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.

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.

#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.

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.

I enjoy the great irony of Dan’s “marker” #3 and the move to a new thread of the parabola v. catenary debate

Dan: When you see someone love something you find completely unloveable, it’s hard to relate to that person.

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.

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.

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.

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?

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.

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?

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 :-)

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.

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!”