Second, as what may be called a “committed constructivist”, I want to remind all that constructivism is a theory for how people learn, or better stated–a theory for knowing. It very certainly says nothing as a theory for teaching; at best it may suggest what might be more powerful. In very brief summary, as a theory for learning constructivism states that no matter what method of instruction used by the classroom teacher, the student–or better the students’ minds–“construct” meaning (a way of knowing) from the experience. Piaget: “The mind organizes the world by organizing itself.”

Your rhetoric reminds me of ed seminars I’ve been in that talk only of “staying positive” and “setting a high bar for the students” without getting into any details on how these things are done (“actionable”, to be jargonlike). Finding actionable methods is not a trivial task, not something that can’t be waved away with “I’m sure you’ll figure it out”.

I’ll take it for granted there must be at least some aspect of WCYDWT made simpler, WCYDWT-lite so to speak, for it to work with students. The boiling down for students may make it more appropriate to call the thing something else.

I’m willing to try my magazine example above some time and see what happens, but I’d love to get a more concrete structure down to raise the probability of student success.

To what extent should all curricula apply to a student’s daily life?

I would argue that all of it should, at least as a starting point. Yes, we should have standards. Yes, teachers should navigate those with the students. Yes, we should assess understanding in a transparent way. But education fundamentally isn’t about us, it’s about the students. This is NOT to remove teachers from the equation, quite the opposite. Imagining education as student-centered makes our job that much more difficult and I empathize with the struggles articulated over the course of this thread. But, at a very basic level, you cannot experience these struggles unless you cede some authority over the learning process to the students, and that is something that people seem very unwilling to do as this thread has evolved. I find that interesting and am not really sure what to say to that.

So, guys, I’m out. I’ll leave you with a little Dewey from 1900:

“From the standpoint of the child, the great waste in the school comes from his inability to utilize the experiences he gets outside the school in any complete and free way within the school itself; while on the other hand, he is unable to apply in daily life what he is learning in school. That is the isolation of the school—its isolation from life. When the child gets into the schoolroom he has to put out of his mind a large part of the ideas, interests and activities that predominate in his home and neighborhood. So the school being unable to utilize this everyday experience, sets painfully to work on another tack and by a variety of [artificial] means, to arouse in the child an interest in school studies …. [Thus there remains a] gap existing between the everyday experiences of the child and the isolated material supplied in such large measure in the school.” – John Dewey, The School and Society

Or, IOW, The WKYDWT problems are in the very top strata of the top layer of the top level of bloom’s taxonomy, not just for the subject matter, but for pedagogy as well. You’re not going to get a kid with little to no teaching experience beyond tutoring the kids next to them to be able to deliver something worthwhile.

I can give my kids an assignment like the one you outline and they’ll do it. From the outside, it may look like there is some authentic learning taking place, but in reality, many of these kids will simply be jumping through another hoop (albeit a high one) whereas Dan’s kids may say, “screw your hoop, I’m tired of jumping.” Which kid really “get’s it?”

It’s one thing to ask a kid to find an example of erosion in the real world but another to ask a kid to find an example of linear relationships, rates of change, etc. because of the working knowledge a kid may need in order to even recognize it. Heck, there are times Dan throws up a WCYDWT and I even scratch my head at what the actual objective may be. But in order for a teacher to do this kind of teaching, the concept has to be understood inside and out. Otherwise what is intended to be an inquiry based lesson turns out to be a half baked investigation where no one really knows where it’s going to end up.

Two, if your curriculum defies real-world exploration, to what extent can you realistically expect real-world exploration from your students.

[Sidebar: to what extent should all curricula apply to a student’s daily life?]

Three, were I to somehow summon up enough faith and courage and high expectations and all that so that my remedial students brought in digital artifacts expressing their understanding of the real-world applications of, let’s say, “factoring quadratic equations with leading coefficients greater than one,” I imagine the process of presenting and collectively winnowing those presentations down to a working definition (again, for the real-world application of factoring quadratic equations with leading coefficients greater than one) would take hours longer than the alternate route through direct instruction. Just guessing. And, for the record, I would prefer it to direct instruction. But that long-term strategy would have us through 50% of California’s Algebra I standards at the end of the year, courageously kicking the can down the hall to their next teacher.

I mean, four, case in point: everyone guessed at the number of jelly beans in a jar yesterday. I gave them laptops, a spreadsheet with everyone’s answer, and the exact answer of jelly beans. I asked the students what they wanted to know. They wanted to know who was the best guesser, who was the worst guesser, and a ranking of the people in between.

I knew we needed to get through absolute value, percent error, and average percent error. I had some amazing, truly satisfying conversations with pairs of remedial students who strained for a definition of “correctness” and strained to operationalize it in Excel. I had to chomp off my tongue repeatedly to allow them to come up with the definition unassisted. We needed more time. In a two-hour block half of the groups made it through half of the day’s content standards. Half hit absolute value. Nobody hit percent error.

[Sidebar: does anyone yet have a fix on where these kinds of impediments fit into Joe’s framework of faith, high expectations, and courage? I’m at a loss here.]

Five, I’m not looking for someone to spell out what, by Joe’s definition, can only be spelled out by teachers according to the needs of their students. But it would be helpful to see a few case studies of teachers making that happen within California’s Algebra 1 curriculum. Shouldn’t be that hard to find a few courageous teachers among thousands. Right?

I can definitely understand where you’re coming from. And especially now that you have a structure outlined, the ideas that you have been spouting are starting to come full circle. I can see your reasoning.

Although I resent being summed up to having no faith in the abilities of my students, I can understand where that one quotation of mine you chose to focus on could be interpreted as such. My main point was along the same lines that josh g is taking.

You may have a handful of students that could be really good at finding real-life situations, stories, or stills that would apply to the concept being taught, but it wouldn’t come naturally, nor would it come consistently enough to build a class around the theory, mainly because you would be assigning them a task to perform. So the motivation is not truly intrinsic, because it is assigned, even if they find something in which they are interested. My ending paragraph had that summed up in fewer words, along with the idea that it would not be sustainable or consistent enough to have students not only bring in a WCYDWT, but make it enough to build a lesson or driving question around every day, or even once a week.

I can imagine right now a student bringing in a very true example of slope found in real life: two planks going from the ground up to the tail-bed of a truck to get their four-wheelers up into the truck. They would take a picture of it, assuming correctly that this could be interpreted as slope and feel like they completed the homework assignment. That would be the minimalist student, doing only the little he needs to get by.

Then you have another similar student that would see the purpose of WCYDWT, not only taking a picture of the planks, but also measure the horizontal and vertical distances needed to measure slope. I can imagine this student asking “what is the slope?” to the class, leading the class on the hunt to find the slope in, umm, a minute?

This example is a fairly true example of slope in real-life (kind of), but the driving question is boring. And most of all, who cares what the slope of it is. They just want their four-wheelers in. As a teacher, you may come back with “Well what would happen if the planks were shorter/longer?” or “How short can the planks get, yet still get the four-wheeler into the truck?”, but at this point, you have nothing concrete to show, demonstrate, or test with the students. It’s reduced down to the boredom found in a textbook problem with a picture of a truck and planks next to it.

Maybe the students I am imagining are sub-par to the ones you are imagining or wishing for or actually have, but these personalities and the amount of investment put into homework are real to me at this point. To the other teachers out there, am I crazy or faithless to assume that there would be many well-intending students that would fall into this category, and not just be in the 80% of students not doing the homework as stated in other comments?

Another hole that I see in your theory (or application) is that these students would be finding real-life applications of how the concept at hand really applies to the world around them, or even better, something they are actually interested in. I have to ask, when would a student ever come up with a “Stacking Cups” activity to model linear relationships without ever knowing what linear relationships are? When would they come up with an activity to discuss the concepts of slope and y-intercept without even knowing the words? The purpose of these activities are to pose questions that are structured and designed to get you from point a to point f or g or x through scaffolding in a way that can be talked about in escalating amounts of math terminology. The point is to get them to think of the situation first, then think about a way to solve it, and then “oh crap! We’ve been talking about math this whole time without realizing it”.

If your point is to make the student-led applications at the end of a unit or concept as a project of how to apply it, then I can definitely see it working pretty well for some. I cannot, however, imagine a whole year centered around this student-led pedagogy.

I could see myself giving this a try. However, I can also see the need to have a backup plan in case students don’t bring you much of anything. (I hope for the best in my students, but blind faith in other mere mortals is dangerous business.)

I would be seriously surprised if students frequently came up with examples that went from “Good” to “Best” in Dan’s curriculum rubric. Not because I don’t have faith in students, but because I’m respecting just how big a design challenge that last step can be. Heck, we’re here as educators trying to master this for a living and still struggling with it. I’d have a hard time placing that expectation (ie. assessment) on students; which means that teacher-originated WCYDWT’s fill a role that this student-created media approach doesn’t.

I can also see this working a lot better with some areas of mathematics than others. Sending students out to find examples where you need to figure out the surface area of something could work; asking students to take videos of factoring quadratics or logarithmic functions would be nuts. (Maybe not impossible, but not worth gambling on unless your kids have a long track record of success at this.)

In that sense, this is something where science fits this approach much easier than math. Science is all about observing the world; math is all about abstractions we can use to understand … the world, or whatever, or just math itself. There’s an extra degree of separation in there.

On the other hand, you can do advance exploration in more abstract realms with software or calculators. I’ve seen this approach tossed around a lot; heck, even in textbooks. I tend to swing between hating and loving these kinds of approaches depending on how they construct meaning (and/or my snarkiness levels for the day).

All that said:

Joe: Do you have your kids develop WCYDWTs? Does the authority ever flow the other way?

Assigning students to finding their own examples of math in action gets bonus points for building connections between math and reality, for sure. And students get empowered as media creators rather than media consumers, so the digital media side of me is happy about that. But you’re still assigning homework. You’re still fundamentally the one asking the question, and you’re probably losing some of the value of well-crafted WCYDWT lessons. This seems to me like a trade-off rather than a moral-high-ground improvement when I look at my student-centered-pedagogy checklist.

I still like the idea of empowering students to ask their own WCYDWT questions, but I think structuring it as an assignment is missing what goes on when Dan and others hit on something like this. You can’t assign someone to get inspired by the WCYDWT fairy. At best, you can ask them to produce results that are superficially similar to what happens when the WCYDWT fairy drops by. But my hyper-idealist side tells me that’s no substitute for the real thing. If I want my students inspired to see math in things, they need real inspiration. I can’t just assign authentic inspiration experiences to students and expect them to appear. I need to model what they look like and try to be ready to help when they show up. As far as that goes, Dan’s WCYDWT lessons have got the modeling-inspiration part in spades.