## Multimedia Inoculates Pseudocontext, Ctd.

Here’s what I’m trying to say. It’s easy enough to write the following pseudocontextual problem:

Dan shot a basketball from the three-point line. The ball followed the path given by the equation:

.

How many units high will the ball be at its highest point?

Try to commit that pseudocontext to a photo, though. It isn’t impossible, but it’s much, much harder.

That’s all I meant. Not that I think Star Wars is real.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

1. #### Dina

November 24, 2010 - 1:33 pm -

Better, Dan, but not good enough. :)

Here’s what I see.

In “My Favorite Orange,” you make this comment about its pseudocontext:

“Some kids will respond positively to the absurdity of it. Some kids will respond positively to the historical context. Some kids will respond positively to their energetic teacher… None of that reassures me.”

In “Toaster Regression,” however, you make the following case to Jen, who wonders if the toaster video is also pseudocontextual:

“If a question arises naturally from a video and if the answer to that question has also been filmed, I’m not sure the accusation sticks… {through WCYDWT} you are encouraging them to invest in the problem. They will want to know the answer. They won’t let you move on.”

So haven’t you just contradicted yourself? How can you place a premium on student interest in Toaster Regression, and dismiss it so completely in My Favorite Orange?

Given the presence of student interest in *both* problems (either intrinsic or teacher-elicited), there’s only one variable that differs between the two: its physical presentation. Therefore, there’s only one answer to the question above: you think kids as a whole learn better through the magic of video because it “eliminates” pseudocontext. And there’s only one problem: You have no proof for this assertion at all.

I think this both exposes your technological bias, and brings home the larger, better point you’ve made in the past: that we’re still all trying to figure this out.

For an example: what *is* pseudocontext? Here’s just a sample of answers I see from scanning the comments here, and your own words.

1) Pseudocontext is present a question which uses information irrelevant to daily life.

2) Pseudocontext is present in a question which uses information in which a student has no intrinsic interest.

3) Pseudocontext is present in a question which manipulates scientifically verifable facts.

And as you can see, the permutations and combinations of these three statements which still can be defined as “pseudocontext” are legion.

Additionally, as many commenters have noted, the situation is complicated by the fact that the amorphous concept of “multimedia” is in no way immune to any of these definitions.

More broadly, pseudocontext, really, is just “What are we supposed to teach in schools, and how are we supposed to teach it?” dressed up as a critical question about math, which why I love it.

But to then make a bald, sweeping statement about multiamedia with the moral and teleological force of “it makes it very, very hard to lie”, as in your last post? Well, it is a pretty phrase (with single syllable words in a magic group of three for the ending punch, don’t you know!)– but it’s also irresponsible.

If you stood in front of a class of smart preservice teachers and asked them to buy into this type of premise while simultaneously asking them to inquire genuinely into the nature of pseudocontext, there’s a distinct chance they would consider you at best a thoughtless wordsmith, and at worst a fraud. Seriously. With pseudocontext so elusive at the moment, I would not go down that road with a sack of elven lammas bread and Bear Grylls for a boyfriend.

To put it simply: you need to know what pseudocontext IS, before making any judgements about whether– and which–technological approaches in the classroom work counteract it– or not.

And have a great Thanksgiving.

2. #### Jason Dyer

November 24, 2010 - 1:45 pm -

What if the same picture was made with the graph tacked on but without the balls in the air? (I’ve seen this before as a way to “cheat” through the multimedia in a problem before.)

I’d sneak in an extra couple words:

Using multimedia that records an entire action makes it hard to create pseudocontext.

3. #### Shawn Cornally

November 24, 2010 - 3:02 pm -

Dan’s right. The silliness that books pass off as context is usually so unnatural that to capture it with rich media requires Photoshop, final cut pro, and a sadistic need to seem “tech savvy.”

In the end: get excited about the lesson, show kids stuff that scream good questions, and make sure they can extend it beyond the book’s toy practice problems.

Love,
Cornally

4. #### Ian H.

November 24, 2010 - 3:51 pm -

I’m with you, Dan. Not that images and multimedia make it hard to lie, necessarily, but that the lies of pseudocontext become that much more obvious when made visual. Their foundations are revealed as evidently false, which may or may not happen for students simply searching a word problem (as long as we’re talking about math) for relevant information.

There did seem to be a push for a while in textbook writing to try to “trick” the student by including more information than is necessary for the problem, which may be what has bled into the modern textbooks’ penchant for pseudocontext.

5. #### Z. Shiner

November 24, 2010 - 5:09 pm -

In response to Dina’s point:

“How can you place a premium on student interest in Toaster Regression, and dismiss it so completely in My Favorite Orange?”

The way I see it, there is a very big difference between the two. There is some sort of naturally occurring pattern (and an inherent question about that pattern) involved in the toaster regression problem. The irony is that people thought it would be linear and when in fact it was not, and as a result, they were sucked into their own WCYDWT problem. Do you not find yourself asking questions about it? I don’t think it is necessary that the mathematics naturally rises from the question, but the mathematics is inherent to the toaster’s settings. In the ‘My Favorite Orange” problem there is a mathematical question being asked, but it is in no way related to the orange.

I think one way to isolate pseudocontext (if we define it as context which is unrelated to the mathematics) is to ask yourself if this question could be asked by a curious individual. I can imagine someone toasting bread and wondering about the times for the different settings (read: David Cox). However, I cannot imagine someone holding an orange and wondering what the weight of the orange would be if it weighed nine tenths of what it weighed and another nine tenth’s of a pound.

From my understanding, multimedia dissuades pseudocontext because it inspires students to ask a question rather than forcing the question upon the students. The context in a WCYDWT problem brings students to mathematics. The context of a text book problem brings mathematics to students, sometimes in places where it doesn’t belong.

6. #### Dan Meyer

November 24, 2010 - 7:31 pm -

Dina: Better, Dan, but not good enough.

Whew! Glad to know where I stand.

Dina: So haven’t you just contradicted yourself? How can you place a premium on student interest in Toaster Regression, and dismiss it so completely in My Favorite Orange?

I don’t place the premium on interest. I place it on the natural connection between question and context. (eg. the first clause from your quote: “If a question arises naturally …”) Do linear equations arise naturally from toaster settings? Does a one-variable equation arise naturally from an orange? These are the questions that concern me, the questions that pseudocontext fails.

Jason: Using multimedia that records an entire action makes it hard to create pseudocontext.

Solid addition. I tried to dig at that in the last two sentences of the previous post:

How do you take a picture of a premise that is false? Even harder, how do you take a picture of the conclusion of that false premise in a way that doesn’t belie the premise itself?

Zac: I think one way to isolate pseudocontext (if we define it as context which is unrelated to the mathematics) is to ask yourself if this question could be asked by a curious individual.

I’m running in the other direction. “Would someone be reasonably interested in this question?” begs a definition of “reason” and “curiosity,” both of which have been annoyingly hard for me to pin down. It seems like every installment of Pseudocontext Saturday has some passionate defender saying, “Well, I’m interested in the problem.” (For instance, Sean in My Favorite Orange.) How do we measure this?

7. #### Cason Bang

November 24, 2010 - 8:27 pm -

Is psuedocontext a scale or an absolute? Can the orange problem be *more* pseudocontextual than the toaster problem?

8. #### Numbat

November 25, 2010 - 2:49 am -

Is there somewhere a discussion on whether pseudo context is better than no context? I was trying to discuss the danger of pseudo context with some colleagues today and they were trying to convince me that pseudo context was better than no context. Being new to all these ideas I was at a loss to counter their arguments in a meaningful way. Can anyone point me in the right direction here?

Ta muchly,
Chris.

9. #### Brendan Murphy

November 25, 2010 - 3:56 am -

If math is inherent in everything around us then perhaps the need to contrive some sort of math problem is pseudocontext.
I am naturally drawn to the parabolic arc of the basket ball, I am naturally drawn to the linear regression of the toaster (I am surprised to find that it isn’t and drawn even further into the problem – at least at the high school level). I didn’t realize there was a right angle in the dog’s bandanna and I really can’t see it even when looking. The orange would have made a great mind puzzle if it weren’t so absurd.

I think I would define psuedocontext as creating an unnatural mathematical context to explain a specific situation.

I do agree with Dina though that making a blanket statement about multimedia is a dangerous proposition.

10. #### Dina

November 25, 2010 - 5:12 am -

You can add “naturally arising questions” to your list of Annoyingly Difficult Concepts to Pin Down (reason/ curiosity), I think. In fact, don’t– because I’m 99% sure they’re the same thing. And therefore (once again) I find it suspect when folks speak so confidently in this conversation about what pseudocontext is and isn’t.

Consider this as an example. As a “wordie” with little to no intrinsic interest in math, no questions whatsoever naturally arise for me from the toaster regression. Have never done. (I do have a toaster, unlike a definition of pseudocontext.) Nor do I burn to investigate the bouncing ball, the jar of pennies, or the escalator, even if they’re prettily glowing on a video screen. I’m just not that into you, you know?

So if your definition of pseudocontext rests on “naturally arising questions,” every WCYTWT is pseudocontextual to me– because I don’t ask mathematical questions naturally.

And I’m pretty sure that this cretinous math reality of mine is the one to which you need to pay the most attention as a teacher. Your commenters have vastly self-selected as people with long and abiding interests in math. Your students will have done no such thing.

Given this, your argument may be that WCYDWT– the potent combination of multiple sensory input, the application of theory to objects kids see daily, teacher guidance, and proper questioning– is a superior tool for *eliciting* curiosity/reason/naturally arising questions. This, to my mind, is a far better defense for WCYDWT than to argue that multimedia facilitates curiosity, or scientifically verifiable problems, or learning a priori, given the voluble evidence that it doesn’t.

But even with this better defense, there are concerns you will need to answer.

First, the “WCYDWT as a superior tool” defense presupposes the creation of the catalytic presence of student interest, which you continue to dismiss, oddly.

Second, what then distinguishes WCYDWT as a tool from the plain old skills of good teacher? A skilled, sensitive teacher will *create* context– help me be interested in the possibility of a nine pound orange, perhaps even a heck of a lot more than a boring old toaster– since a Martian orange is quite interesting. (Admit it.)

Thirdly, if your corollary argument is that WCYDWT is “real world,” then why on earth aren’t you physically bringing this stuff into class– or the kids to it– instead of putting it one remove from the kids in a video? (Your historical schematic defense here– because it would be too complicated and messy for the typical math teacher– can be equally applied to learning Mac Pro and securing a digital projector in the inner city, so I don’t know how much water that holds.)

Finally, what about your argument that “math is its own context?” Why is the worth and value of math pinned only to what I can find in my bathroom? And haven’t you eliminated entire realms of curriculum (calculus?) otherwise?

That’s enough for now, I think.

11. #### Rhett

November 25, 2010 - 8:54 am -

I triple-dog-dare some publisher to put this question in their textbook. That would be so awesome.

12. #### Z. Shiner

November 25, 2010 - 1:45 pm -

So if your definition of pseudocontext rests on “naturally arising questions,” every WCYTWT is pseudocontextual to me— because I don’t ask mathematical questions naturally.

I think there’s a big difference between “naturally arising questions” and “questions which I might ask.” The first is about the question while the second is about the person asking it. Perhaps one the difficulties in defining pseudocontext is the fact that we are weaving the individual into the definition. I can always find someone who will not ask a mathematical question, but in my opinion, that doesn’t make the question pseudocontextual.

I think that a mathematical question which arises naturally, whether interesting or not, is not pseudocontext (if pseudocontext asks students to use operations that have nothing to do with the given context). For example, someone could ask the question “what is the arc a basketball makes as I shoot a hoop?” Though some (most?) people would not be interested in tackling the mathematics inherent in this question, the mathematics does exist. I can ask the question “what is the maximum height of a shoot I make?” This question asks for information people probably don’t care about, but there is mathematics involved in answering the question, and the mathematics used complements the way which the real world works.

On the other hand, the question “what is the highest point of a basketball if the ball moves in the motion of an absolute value function?” Would never be asked because basketballs don’t work like that. The question “what is the weight of this orange if the orange weighs nine tenths of its own weight plus nine tenths of a pound?” would never be asked because no one calculates the weight of an orange as a function of the weight of the orange. Pseudocontext asks people answer a question which would never be asked in the first place (and I mean asked by anyone, not just the “wordies”).

The question of “would someone reasonably ask this question?” is different from “would someone be reasonably interested in this question?” which is very different from “would my students ask this question?”

The first question is about the questions people ask as a whole. It does not rely on an individual asking a specific question, but rather on the collective curiosity of people in general. Again, you can always find someone who wont ask a question, but it’s a matter of whether or not the question would naturally be asked. If someone (anyone) naturally formulates the question (read: wants to know the answer as opposed to merely trying to ask a math question) then the context is authentic.

The second question really says nothing about context. As we’ve seen, someone will always be interested in answering a question. However, I see pseudocontext as whether or not someone would ask the question in the first place rather than whether or not someone wants to answer it.

The third question seems like a WCYDWT question. It is related to the first, but puts the focus on the specific audience rather than the question itself. If students naturally ask the question then they have satisfied the criterion for a problem to be not pseudocontextual. However, if the students don’t ask the question it doesn’t necessarily imply the problem is pseudocontext, merely that the information did not trigger the asking of a question.

This how I see the relationship between WCYDWT and pseudocontext. A WCYDWT problem gets students to ask a question which requires mathematics to solve. By virtue of the question arising naturally (and again, I’m defining ‘naturally’ as ‘without the sole intent of creating a math problem’) then it is not pseudocontext.

13. #### Curmudgeon

November 25, 2010 - 2:38 pm -

Here’s my definition of pseudo-context: It’s a question that is written specifically for, and intended to be solved with, mathematical ideas and/or methods that are inherently wrong to the question, e.g. the absolute value projectile question. Additional characteristics include falsifying the data to fit the solution and the inclusion of both genders and multiple ethnicities in an attempt to be “real.”

Kids reject these questions as fallacy. If the attempt at “real-world” offends them, then you have pseudo-context.

A ball CAN move in that particular path, by the way. You just need to change your frame of reference – look vertically down on a ball hitting a wall and label your axes accordingly. Or think of the bouncing logo on the Office tv.

14. #### Chris Sears

November 25, 2010 - 6:56 pm -

Dina:

Finally, what about your argument that “math is its own context?” Why is the worth and value of math pinned only to what I can find in my bathroom? And haven’t you eliminated entire realms of curriculum (calculus?) otherwise?

Calculus is usually where you leave pseudocotext behind in the traditional curriculum. Algebra is chock full of it.

@Z. Shiner Well said.

15. #### Dan Meyer

November 25, 2010 - 10:45 pm -

Dina: So if your definition of pseudocontext rests on “naturally arising questions,” every WCYTWT is pseudocontextual to me— because I don’t ask mathematical questions naturally.

The natural rising I describe isn’t from the context to the mind of the student but from the context to the question. Questions of parabolic motion arise naturally from the context of the flight of a basketball. The absolute value question in the body of this post does not.

Dina: This, to my mind, is a far better defense for WCYDWT than to argue that multimedia facilitates curiosity, or scientifically verifiable problems, or learning a priori, given the voluble evidence that it doesn’t.

Where have I asserted that video or photos accomplish any of this a priori or in absolute terms. Multimedia makes it “really, really hard” to lie – not “impossible.”

Dina: First, the “WCYDWT as a superior tool” defense presupposes the creation of the catalytic presence of student interest, which you continue to dismiss, oddly.

Now I’m struggling all of the sudden to figure out if you have any idea what WCYDWT is. It’s weird I have to explain how this isn’t just mathemagical fairy dust I sprinkle on my students’ heads to make interesting math happen.

WCYDWT starts with an image or video that either immediately or over its duration connects with a student’s prior experience. (eg. Everyone has tossed a ball; Everyone has filled a vessel with water.) That leads to a question that is both concise and guessable, a question that requires no mathematics to answer. The risk of investment is low, in other words, and the promised payoff to the student is that we will be able to verify whose intuitive guess was closest by playing the end of the video.

From my own anecdotal experience and the reports of others, this works as it’s intended. No one is presupposing student interest.

Dina: Second, what then distinguishes WCYDWT as a tool from the plain old skills of good teacher? A skilled, sensitive teacher will *create* context– help me be interested in the possibility of a nine pound orange, perhaps even a heck of a lot more than a boring old toaster– since a Martian orange is quite interesting. (Admit it.)

It’s difficult to make an appeal to student intuition with pseudocontext, since pseudocontext (by my wobbly current working definition) disrupts intuition. If I show you the first four toaster settings, you can guess with some confidence at the eighth. If I write about an orange that is one half more than three times etc etc, you can guess at the orange’s weight but it’ll be an arbitrary guess (since the operation doesn’t naturally arise from the context – def’n #2), and worse, your knowledge of oranges will screw you over here because this is a pseudocontextual orange that weighs nine pounds (def’n #1).

Incidentally, you seem confused about the order of events in the favorite orange problem. The teacher doesn’t generate interest with a nine-pound Martian orange. The nine-pound orange is the conclusion of the problem, not the premise. The premise is the pseudocontextual equation.

Dina: Thirdly, if your corollary argument is that WCYDWT is “real world,” then why on earth aren’t you physically bringing this stuff into class– or the kids to it– instead of putting it one remove from the kids in a video? (Your historical schematic defense here– because it would be too complicated and messy for the typical math teacher– can be equally applied to learning Mac Pro and securing a digital projector in the inner city, so I don’t know how much water that holds.)

WCYDWT requires a means for capturing media and a means for getting that media in front of your students. That’s all and if that’s impossible to procure, then no judgment from me, but let’s be real about the expense of this particular intervention relative to the expense of other technological interventions.

There are certainly instances where the digital representation of the thing isn’t as good as the thing itself, in which case, perhaps my digital video can still serve as one of Grossman’s representations of practice (2009)*, a guide for your physical representation. That’s still value added.

* dy/dan, now with research.

But in many instances, it isn’t just “too complicated and messy for the average teacher” to bring the real, physical stuff into class, it’s impossible. For any teacher. Tell me how we examine the use of angles in the construction of the Eiffel tower. Tell me how we talk about the speed of the trap-jaw ant.

Dina: Finally, what about your argument that “math is its own context?” Why is the worth and value of math pinned only to what I can find in my bathroom? And haven’t you eliminated entire realms of curriculum (calculus?) otherwise?

If [concept x] has an application to the world, let’s do as much justice to that application as we can. I have nothing better than WCYDWT for that, which isn’t to say that nothing better exists. If there isn’t an application for [concept x] let’s not force one with pseudocontext. That’s basically it.

16. #### Jonas

November 25, 2010 - 11:25 pm -

> “Try to commit that pseudocontext to a photo, though. It isn’t impossible, but it’s much, much harder.”

I think it would be even harder in video.

In a photo, you can cheat and “paste” the ball at all the right points. In a video, it’s much harder.

For one, there’s a large number of frames (100 per 4’ish seconds modulo NTSC/PAL) so it’s a lot more work to doctor a video.

Secondly, if the video is just a little bit shake, it becomes much harder to paste the ball each shot, because where it has to be pasted and at what angle depends on how the immediate context around the ball has changed on a frame-to-frame basis. Fudging this, I think, is something human visual processing is good at picking up.

(But I haven’t read the scientific litterature on visual perception, so don’t take me without some sodium chloride.)

[OT @Dan: where can I find a list of the markup I can use in your comment system? Could you put a link to that next to the Post-A-Comment field, that’d be swell :)]

17. #### Joe Henderson

November 26, 2010 - 6:14 am -

Dan, your last response here really clarified the WCYDWT teaching strategy for me. It’s definitely something I have struggled to understand in the past in this space, so thanks for that.

One thing though. You write:

“The natural rising I describe isn’t from the context to the mind of the student but from the context to the question. Questions of parabolic motion arise naturally from the context of the flight of a basketball.”

Curious leverage of “natural” here, as if such a process is objective. Whose questions “arise naturally” from the flight of a basketball? Your questions? The students’ questions? Both? How do you facilitate this discourse process with your students in a way that allows them to have ownership? Do they have ownership, especially in shaping/creating the context?

I guess this is why I continue to struggle with “pseudocontext” as you are using it. It seems to me that there’s an assumption of contextual relevance (which you rightly critique textbooks for). But what’s to stop a teacher from making the same assumption, just in the form of a slick multimedia WCYDWT?

Am I missing something here? Help me out.

18. #### Brendan Murpy

November 26, 2010 - 9:11 am -

@Dina and @Dan

I like the questioning of WCYDWT.

In my job I work with a few math teachers in middle school. Always, there seems to be pressure on the teachers to finish curriculum. The temptation is there to show and practice procedures often enough, with enough word problems mixed in, that the students will recognize when to use the correct procedure and apply it correctly. All this in an effort to be measured as competent in math.

Some students love this, they love putting numbers and letters into a machine and pressing buttons and dials until finally the right answer pops out. These students are considered smart and good at math.

When faced with an object in the real world these students do not connect it with math because math is numbers and letters and rules.

There are also teachers who struggle to find the math they teach in the real world. (I’ll raise my hand here).

I don’t see WCYDWT as a way to bring math to the real world. Just the opposite I see it as a way to explain why we invented math in the first place. We don’t have parabolas because they make cool graphs and have some consistent properties we have them because this is the way the world functions. “What goes up must come down”

I have seen through my own experience that when students start looking for patterns and asking questions about life that often those students who are “bad” at math lead the way. They lead because they aren’t looking for the right equation, but are just trying to figure out what they heck is happening.

Consider this, a math student looking at the basketball might start by trying to figure out the linear equation for the ball going up and the linear equation for the ball going down and push them together. The math curriculum s/he knows is y=mx+b. s/he might spend a long time and finally give up because s/he knows eventually the teacher will give up and tell the answer. Later s/he can memorize the new information.

The non-math student will see that the ball is moving in and arc and look for the high point and draw a nice curve up and mirror it down. With no calculations at all s/he will say the ball fails to go in because the left and right side of the curve have to be equal and his shot is just a bit off.

Then we can play with graphing calculators to regress to the correct equation. If we want we can try this with a bunch of canned examples and figure out what happens when we change coefficients.

The hope is that even wordies can see the symmetry and patterns so even if they don’t remember the exact math they will at least remember the keywords “parabola and quadratic equations” so their google search is a bit faster.

19. #### Curmudgeon

November 26, 2010 - 10:16 am -

I would like to point out one thing we all need to remember when it comes to “The Real World.” It took centuries to figure some things out. It will take years to figure out some others.

The RW isn’t clean all the time and we need to be careful about how we assume student understanding. It may be perfectly clear to them … and wrong.

WCYDWT needs to promote discussion but also accept that not everyone will have a clear idea of what’s going on.

20. #### Jim Ellis

November 26, 2010 - 11:33 am -

Just for fun historical conversation to Brendan’s post and other similar posts…

Algebra went through three main stages of development over several thousand years:

First – Rhetorical Algebra – found primarily in Arabic and Asian cultures (the solving of problems with written/spoken language)
Second – Syncopated Algebra – (the solving of problems with written/spoken language with symbolism and symbols taking an important place)
Third – Symbolic Algebra – created in the early 20th century (fully symbolic, and frequently) abstract

The way I look at what Dan is doing, would be to see similarities in algebraic development over thousands of years. Both of their chronology look rather similar to me.

It’s also worth mentioning that this historical perspective is something I teach directly to my 7th graders and we commonly use rhetorical, syncopated and symbolic to describe the stages we find ourselves in when solving problems.

Jason: “Using multimedia that records an entire action makes it hard to create pseudocontext.”

-I’d prefer to look into what multimedia will show clearly back to my students regarding their own problem solving regarding their own rhetorical, syncopated and symbolic steps they took. Not what it will prevent from creating (pseudocontext).

21. #### Dan Meyer

November 26, 2010 - 2:01 pm -

Joe: Curious leverage of “natural” here, as if such a process is objective.

Can you make a subjective case that an absolute value equation (specifically that absolute value equation) pertains to the flight path of a basketball? I don’t think I’m assessing the situation subjectively when I say that quadratics pertain and absolute value equations don’t.

Joe: Whose questions “arise naturally” from the flight of a basketball? Your questions? The students’ questions? Both?

This is veering a little bit towards Dina and Zac’s measurement of “interest” and I need to clarify again that students can be interested in pseudocontext; students can be uninterested in real context. Student interest is a separate, very important deal, but it’ll only cloud this discussion.

(As a clarification of the WCYDWT protocol, though, your first step after displaying the media is to solicit student questions about it. It’s step one.)

Joe: It seems to me that there’s an assumption of contextual relevance (which you rightly critique textbooks for). But what’s to stop a teacher from making the same assumption, just in the form of a slick multimedia WCYDWT?

Nothing. My WCYDWT lesson on rugby strategy will fall flat on a crowd that cares nothing of rugby. I’m a pretty enthusiastic advocate of the protocol but show me where I promise that WCYDWT will be relevant to every student all the time.

Maybe this is the confusion: “multimedia inoculates pseudocontext” doesn’t mean “multimedia makes everything interesting to everybody.” Seems like that should go without saying, though.

22. #### Dina

November 26, 2010 - 2:42 pm -

But it doesn’t go without saying, Dan, and especially to teachers, who are bombarded with the false promises of technology every single day. To throw around catchy vagueness like your multimedia statement puts the good work of WCYDWT at risk. Since pseudocontext, in your words, consists of problems that are “boring, irritating, and alienating,” isn’t your inoculation statement easily interpreted as another way of stating that multimedia is interesting, a priori? Seems that way to me. You’re going to require a few more (a lot more?) specific parameters on how to use multimedia to make your case, a la Jason Dyer.

As for student interest, you seem to continue to contradict yourself on the importance of such a thing in your protocol. Either it’s nice, conversation-clouding side-bonus, as in “I don’t place the premium on student interest”– or it’s necessary, as in “WCYDWT uniquely encourages students to invest in math problems, and therefore learn math.” We need to know which it is.

Why is this important? Because the question “What is pseudocontext for math?” in turn begets this much harder question: “What is a *real* context for math?” And that’s what I’m struggling with. If a real context is not defined by student investment, by what is it defined? If a real context is not delineated as something a student cares about, then what is it?

Which is where the orange problem comes in, and others like it. I understand that the nine-pound element is the answer. Have you never hooked student interest in solving the problem by foreshadowing the answer? You can still use it, in otherwords, to create real context (which I’m assuming here is, again, created via student interest). Isn’t my interest in the question, as a student, the thing that makes it real *for me*?

23. #### Dina

November 26, 2010 - 2:51 pm -

And by the way re: the usefulness of multimedia for bringing Eiffel Tower-type questions into the classroom–

Yeah, you’re right. But this is also a straw man. The fundamental aspect of WCYDWT is that, in your words, it “either immediately or over its duration connects with a student’s prior experience,” which delineates material far more prosaic than the Eiffel Tower- indeed, available at the grocery down the street– 99% of the time. So once again: why remove it from the kids’ direct experience with digital imagery?

Have you actually compared the efficacy, academic effectiveness, material requirements, engagement, ancillary and direct benefits, of getting ten rolls of tickets and having groups work with them, versus WCYDWT? What happens? What value is added by the tech in these situations? Where do the costs in all arenas outweigh the benefits, and vice versa? Do that in an impoverished district which needs to closely question a digital camera and projector because they can’t afford to get the asbestos out of its walls, and you’ve got yourself some real evidence.

24. #### Kathy sierra

November 26, 2010 - 4:29 pm -

So much to think about in this (and the previous pseudo context threads).

My husband and I have our own still-fuzzy way of evaluating whether something one of our authors does is pseudo-context: if the scenario/example creates cognitive overhead because the learner is spending brain cycles thinking (even if barely at a conscious level)’ “yeah, but… What idiot would do it that way when you could just…” then there is a pseudo-context problem. We have not found arguments over what is and is not “real world” or even “interesting” to be as easy to pin down, so rather than say what IS a non-pseudo/good context, we just try to weed out the ones that make people furrow their brow over the scenario itself. We want furrowed-brow (scarce resource neurons firing) energy to be going to thinking about the problem, and any mental energy spent thinking it’s a totally bulls*** scenario is a learning hit.

Actually in our case, it may also be a financial hit… though this is wildly speculative, I bet if I mapped pseudo context use to book sales just within our series, I am pretty certain we’d see a relationship. The problem for us, though, is also that the authors who blow the context in this way also tend to have other, equally-damaging problems in their teaching approach.

We blame these problems (pseudo-context, especially) on the author’s lack of understanding of and/or respect for their
audience/learners.

Another way we think about pseudo-context is to use a filmmaking model… We do not care so much whether the scenario is real-world vs. fantasy; we care only whether the audience can suspend disbelief (if needed) and thus be fully engaged in what we REALLY want them to care about and focus on.

Films and novels can be as non-real-world as one could imagine, but what matters most for engagement is whether the world presented is internally consistent. Plausible can sometimes be more important than “relevant”, because once they are on the journey with you, relevance can emerge naturally as the viewer maps the not-quite-OUR-real-world experience into their own world. This sometimes happens only *after* and as a result of their participation, so we do not equate real-world with relevant for our books, as long as the learner can imagine how this thing-they-learn might actually morph or scale into something they COULD imagine using one day.

So perhaps part of the problem with pseudo-context is the violation of internal consistency… It asks you to imagine a world that does not make sense, period. A world where the fictional participants who have this “problem” are not constrained or curious, just… Lame.

Toaster example would not be pseudo-context for me… because it does not seem to inspire the “but only an idiot would actually do it that way” cognitive overhead. In fact, I love the toaster thing and I am not even sure why. All I know is it got me thinking about many different questions. And I am not Math Girl.

25. #### Dan Meyer

November 26, 2010 - 4:35 pm -

Dina: As for student interest, you seem to continue to contradict yourself on the importance of such a thing in your protocol. Either it’s nice, conversation-clouding side-bonus, as in “I don’t place the premium on student interest”— or it’s necessary, as in “WCYDWT uniquely encourages students to invest in math problems, and therefore learn math.” We need to know which it is.

It’s only a contradiction if you conflate two different concepts and misunderstand one of them.

“WCYDWT” and “multimedia” aren’t equivalent, though multimedia is an aspect of WCYDWT.

“Pseudocontext” and “uninteresting” aren’t equivalent, though the two correlate pretty well.

“WCYDWT” and “pseudocontext” aren’t opposite. The post to which you originally responded directly concerned pseudocontext and multimedia. It had only a wispy connection to WCYDWT.

I place a high premium on student interest in my WCYDWT curriculum development but student interest doesn’t factor into my assessment of pseudocontext. You continue to conflate two concepts whose association, frankly, isn’t even yet clear to me.

Because you misunderstand the three syllogisms in the first paragraph, when I say, “multimedia inoculates pseudocontext (under circumstances I elaborate on if you’ll kindly read past the title of the post)” you read “Dan thinks multimedia is equivalent to student engagement.”

Dina: The fundamental aspect of WCYDWT is that, in your words, it “either immediately or over its duration connects with a student’s prior experience,” which delineates material far more prosaic than the Eiffel Tower- indeed, available at the grocery down the street— 99% of the time. So once again: why remove it from the kids’ direct experience with digital imagery?

Two things:

One, we are now off the path of “what is pseudocontext?” and onto the path of “things that bug Dina Strasser about WCYDWT.” That’s totally cool. I just don’t want to confuse anybody here. This has nothing whatsoever to do with pseudocontext.

Two, this is bizarre. Are you positive you aren’t being overly exclusive in your definition of a “student’s prior experience?” I don’t even know where to start.

Wait. I do. Speed. Speed is part of every student’s prior experience. Every student has run or watched someone run. The number of contexts within which you can explore the math of speed are innumerable and far more diverse than what the teacher can physically bring into the classroom or what a student has picked up at a grocery store.

For instance, some scientists at Berkeley filmed super-slow video of a trap-jaw ant snapping its jaws shut. Its jaws are moving at something like a million miles per hour. I couldn’t afford to create that video myself but someone created it for me. All I need now is a digital projector and my students and I have some engaging and challenging math ahead of us.

There are plenty of counter-propositions where that one came from.

Dina: Do that [comparison] in an impoverished district which needs to closely question a digital camera and projector because they can’t afford to get the asbestos out of its walls, and you’ve got yourself some real evidence.

I can’t compare the differential effectiveness between the digital and physical representations with the trap-jaw ant because the physical representation is impossible for me to obtain. And even if I could bring a trap-jaw ant into the classroom (or one for every student) it’d be useless to us because its jaws move too fast for measurement without Berkeley’s high-speed camera. The physical fails me here.

So what do I do with this video that will engage many (if not all) of my students and lead to some challenging math? Not use it out of sympathy for the classroom that can’t afford a \$300 projector? Or use it and not advocate the intervention for the same sympathetic reason?

The bar you’ve set for “blogger should advocate an intervention” is really hard to take seriously.

26. #### Kathy sierra

November 26, 2010 - 4:48 pm -

Oh, on the video/multimedia topic… Still thinking about that. I am thinking of many of the most horrific pseudo-context examples in our books (including some of my own cringe-worthy just-shoot-me code scenarios) and imagining whether multimedia could or would have stopped it. I *feel* like it would have, but I am not sure until I really have a chance to study them. *shudder*

27. #### Dina

November 26, 2010 - 5:07 pm -

For now I’ll just laugh at you yelling at me for conflating multimedia and WCYDWT, when I’m trying to tell you that This Is What You’re Doing. When you say things like “Multimedia Inoculates Pseudocontext.” WCYDWT might; and it might not (see again Jason Dyer’s reworking), but that clarity is exactly what you’re sacrificing for a pithy phrase, and teachers don’t need that crap around tech. S’all I’m saying.

28. #### Dan Meyer

November 26, 2010 - 5:34 pm -

Dina: For now I’ll just laugh at you yelling at me for conflating multimedia and WCYDWT, when I’m trying to tell you that This Is What You’re Doing. When you say things like “Multimedia Inoculates Pseudocontext.”

Hoisted on my own petard! Humor me, though. Where in this post do I reference WCYDWT?

Kathy: Another way we think about pseudo-context is to use a filmmaking model… We do not care so much whether the scenario is real-world vs. fantasy; we care only whether the audience can suspend disbelief (if needed) and thus be fully engaged in what we REALLY want them to care about and focus on.

The filmmaking model helps me out here. A lot of your Head First texts seem to carry a single scenario through the entire book. The 3D Geometry book I was reviewing awhile ago featured an outer-space hook that the author expanded in each chapter. The initial hook wasn’t real, but once you accepted it (in the same way you accept that Doc Brown’s DeLorean travels through time when it hits 88 mph) the author played fairly within those constraints.

The problem with chapter-length or problem-length scenarios (which are the WCYDWT stock-in-trade) is that I don’t profit from the suspension of disbelief. There’s no time for it.

29. #### John

November 26, 2010 - 5:42 pm -

Dina, I teach science and math, and my wife is one of the two science lab assistants at our school who sets up all the experiments for all the classes. The lab assistants work full time setting up our experiments and managing the resources of the laboratory. We regularly have to go and purchase things outside school hours so that experiments can be done.

Let us for a moment assume that the math teachers of our school were to as a group adopt the WCYDWT methods and do all those for which it is possible practically. We have 10 to 20 math lessons happening every period of the day (its a big school with 5 year levels and 4 70 minute lessons a day). To support every teacher doing WCYDWT practically would require the equivalent of the science prep-room for the math department as well. That is 1 or 2 assistants employed full time to manage and maintain the equipment and have the resources ready for class use.

That is simply less practical than our math department investing in 1 digital video camera, and 4 data projectors and laptops to go with them. It is also far more expensive: \$30K for a lab assistant vs \$10k for the mulitmedia needs.

Videos also have the advantage that if we find a one online, we can simply download and use it, no need to acquire new physical resources as we have all that we need. In other words a new video we find online is immediately usable in a class!

Editing videos is relatively simple in Windows Movie Maker which is free. Worst case you might need to get another free program to convert file formats so they are compatible.

Considering that a data projector and laptop combo can be moved from room to room, and used for far more than running WCYDWT lessons, the overall value (ie cost vs usefulness) of acquiring them is much greater than building a huge pile of physical resources.

In fact this is exactly what I have found! I purchased a data projector and use it in every lesson basically because I can do so much more with it being reliably available to me. If I want to do the “water tank fill” WCYDWT, I download and run the video. I can make the tank 2m tall on the wall and every one of my 28 students can see it clearly. We can get a ruler up there and make measurements that everyone can see as well. I have a data projector and a laptop. I don’t have a water tank and a hose. Makes multimedia a pretty clear winner in my book.

30. #### Dina

November 26, 2010 - 6:44 pm -

Thanks, John. I loved this post, long on specifics as it is.

I would push back on two things.

a) The very fact that you purchased a digital projector (out of your own pocket, I assume) illustrates the access/cost/material issues that still surround the vast majority of technology even in solvent schools (which, with the hiring of multiple full time lab assistants making 3/4 of my salary, I am also assuming yours is). Correct me if I am wrong. This, admittedly, is not WCYDWT’s problem. But it is Dan’s.

b) As I indicated above, you’ve narrowly defined “value” by two terms: cost, and materials. From the management perspective, I understand and appreciate this. From the educator’s, I find it too simplistic. Multimedia *has no inherent educational value.* It is only a tool. If its use cannot be proven in a multiple-dip rubric of “effectiveness,” running from money to time to quantifiable learning to retention to student engagement and back, I don’t buy it– literally or figuratively.

WCYDWT, as a very specific subset of multimedia, might be a superior use of that tool. It might not. I’m not sold yet. You can probably tell.

31. #### John

November 26, 2010 - 7:41 pm -

I purchased one because I wanted to always have it available. The school actually has 3 or 4 data projectors for the math department (hey I never need to borrow them so I don’t know).

I think you are misinterpreting “usefulness” in order to support your position. What is useful to you as a teacher? Isn’t it things that are “effective” in improving “learning retention” and “student engagement” etc? The quality of useful is determined by the circumstance of use, not by an absolute criteria.

The whole concept of “inherent educational value” applied to resources is a false one. Resources are only as good as their ability to be used to create good educational outcomes. A toaster is no better as an educational resource than a video of a toaster if the teacher attempting to use it as a resource is unable to draw educational outcomes from the lesson for the students.

Multimedia has the advantage of consistency of experience, lower long term costs (in time in particular), wider support from a funding perspective by governments, and in particular in safety for the members of the class.

Consider this: if I showed you a video of a flower growing in a language class what would I want to do with it? If I showed the same video in science would I want you to do the same thing? What would the differences be?

When I show a video of a ball throw in math I want students to think about the curve, and how that might be described mathematically (we are in math class after all). If we go out and shoot hoops, that is what their focus will be on, the physical elements. By controlling their experience I can appropriately direct their attention to the area I want them to focus on, and draw the science, math, language or whatever my lesson is about from that point.

I teach science, and sometimes experiments are good for teaching concepts, but sometimes distancing the student from the task is the best way of getting their attention on what you want them to learn. The difference between learning how to shoot a hoop, and the math that describes the motion of the ball.

32. #### Greg Kochanski

December 6, 2010 - 1:10 am -

The vertical bars of the absolute value function don’t show up in you image, so it may be a bit confusing for some people.