It’s not technology that affects learning positively – in fact indiscriminate use can affect it negatively. It’s the creative use of technology. And that’s what you showed there. :-)

Dan,

I share your concerns about Joe’s response. It is very difficult to teach things that the students find intrinsically motivating. I would argue that if we only taught math that the students found interesting, then we wouldn’t teach them much of anything at all. A major criticism of a wholly-student driven curriculum is that the students don’t know (and can’t know) what is interesting in a subject because they don’t know the subject! It is incumbent on the teacher to show students about the interesting parts of their chosen discipline (perhaps with interesting questions) and gradually increase their involvement in the choice of question and/or topics to pursue.

However, Joe is right that we tend to talk at kids instead of with kids. There are constraints built into the education system that force some teacher-directed content where some of us would rather have intelligent dialogue. The challenge (and I think Dan is attempting to meet it head-on) is to engage students in as much interesting content as possible given a not-perfect world.

I mean, seriously, where else would these elaborate math problems originate if not in the head of the teacher? Especially if the students do not have a background in looking for math in their surroundings? If Dan had these kids for 10 years and was still creating the problems for them, then there would be an issue to address. But since that’s not the case, then why not have a talented teacher show students where math could be applicable?

(Sorry, just to make really clear, they knew the answer, but now really really wanted to know why. That turned out to be much more gripping than just “B or C?”)

These problems and subsequent discussion remind me of a few of George Polya’s Ten Commandments for Teachers

1. Be interested in your subject.

4. Try to read the faces of your students, try to see their expectations and difficulties, put yourself in their place.

6. Let them learn guessing.

9. Do not give away your whole secret at once — let the students guess before you tell it — let them find out for themselves as much as feasible.

10. Suggest it; do not force it down their throats.

Then I am reminded of a research study on problem solving that found if students can’t solve a problem in something like two minutes, they think it can’t be solved.

I think these problems address these five commandments, as well as the result of the study.

By the way, I think your style is incredibly engaging (and not just for students). Thank you for these really organic examples of critical thinking and ‘problem’ solving!

@Joe – sure the real world is plenty compelling…especially for physics. I do auto-accident deconstruction problems, golf, basketball, pretty much anything with physics – which is pretty much anything.

But there are times when using something completely comical (and outrageous) will pull the group together.

I find the variety important. When trying to help students find patterns and understand relationships in the world around them it is sometimes useful to do ‘what if’ scenarios.

…what if g=-4.5 m/s2 instead of -9.8 m/s2.
…what if the electrostatic force were weaker?
…what if the force of friction were independent of weight?

@Steve – I tend to be wary of lists. This is interesting but is there anything on there that is surprising to any of us?

Oh and I forgot to mention.

Dan (and those in the commenting on here), I appreciate the dialogue and recurring shot in the arm! Keep it up!

@Josh: I think you bring a set of important points into the discourse at this point. And yes, they are philosophical, which is intimately related to practice. Both are important and cannot be separated into disparate parts, as Friere himself articulated. And it is for this reason that we need to unpack all this stuff, I think…

Let me step back for a minute and introduce the time factor. In my own science classroom I had to scaffold activities that moved generally from less ownership over learning towards more ownership as the year progressed. My students were trained in the ways of learned helplessness and correct-answer-grubbing over their many preceding years of schooling that by the time they got to me, it wasn’t enough to just think that I could throw inquiry science at them and that they would pick it up without careful scaffolds on my end. Having said that, the more I challenged them by “being less helpful”, the more intrinsically they were able to learn. This is where Dan, and you, are correct. I think that Dan could throw the WCYDWT to the students and allow them to organically create the experience. But that’s a HUGE leap of faith that isn’t generally rewarded given the intensely controlled nature of schools under the accountability movement.

For me, it’s the interplay between the teacher-centeredness and the student-centeredness that is really interesting. Dan’s Oliver Wendell-Holmes quotes get right to the heart of that point. I think this needs to change over time towards autonomy. Sadly, I think schools do the exact opposite as the students ages.

@Dan: Perhaps here’s a different challenge. Ask your students to come up with a WCYDWT. You know the standards in CA. Pick some that are coming up and see if your students can find it somewhere in their world. I bet they can, and I would love to read about that experience here.

PS – In the interest of full disclosure, I should note that I just had a class the other night with some parents that homeschool their children for exactly the reasons that we’re talking about here. But that’s a huge rabbit-hole that we probably shouldn’t go too much further into. Still, it’s dominating my thinking, especially since I have a lot invested in the model of public schooling.

In order to encourage students to care about what they are learning, why not ask them to accomplish something with their new knowledge?

In the last few years, I’ve begun to adopt a modeling approach to teaching my physics classes. (Full disclosure: The following is not my idea, but one I saw in a modeling workshop.) A lesson starts out in much the same way as Dan described the water tank activity. Show them a pendulum, ask the students what is relevant about it’s motion and what they could change which might in turn change that motion. Once a number of reasonable ideas have been suggested (length, mass, angle, etc.), turn them lose in the lab to determine how these variables relate to how quickly the pendulum swings. After numerous stumbles, they develop a model for the period of the pendulum vs. length that they feel confident in. And then I challenge that confidence.

I ask them to build a pendulum that will keep time with the beat of their favorite song. Everyone brings in iPods, selects a song and uses the model that they developed to construct their pendulum. They’re nervous and unsure of themselves as the moment comes to test it, but when it works (and it always does) they begin to see the usefulness and power of learning about the world around them.

For constant velocity, they predict where a collision between carts occurs ala the classic two trains problem. For accelerated motion, they determine the get away time for a constant velocity cart vs. a rolling cart on a ramp. Each time, they are asked to use their knowledge to accomplish something. In my experience, this extra step starts to answer the “Who cares?” question.

But that’s the thing Dan, when I say “faith”, I mean faith in the students, not the system or your abilities as an educator. I think all your readers, myself included, have faith in your abilities as an educator. And well, the system is…the system. I’m not sure I have much faith in that…but I digress.

I still feel like you’re dodging my original point though. I was critiquing the locus of the constructivist activity you presented in the WCYDWT. The content locus still rests with you in that activity, and ultimately not with the students. I think you know this, but you still seem unwilling to give up some control here. Am I wrong on this?

I definitely sympathize with your situation, as I’ve been there myself, including the students with the criminal backgrounds. I worry though that we (and I include myself here) get stuck thinking that “the kids aren’t ready” for this type of learning, which can then be used to justify the self-fulfilling prophecy of not experimenting with a true student-centered pedagogy. This is the reason I wrote so much about having to scaffold these experiences into the school-year. You cannot just throw linear equations at them without any scaffolds. But I bet they will surprise you. Why not give them some bare-bones, high-expectation instructions and then see what they come up with? Do this enough and it will become your classroom culture. I know this from personal experience.

And let’s definitely not kid ourselves, not all kids are going to be able to do this. It’s a spectrum like anything else. Have faith in them, and provide lots of scaffolds along the way.

Give it a shot man. Then write about it here.

PS – Freire – Pedagogy of the Oppressed, Chapters 2 and 3 are money on this topic.

As I see it, there are two routes you can go here. They already know about linear equations, so what you describe would be them just going out and finding something they already know. You could do that, but that’s a simple application activity. Might be useful.

Instead, I would have them take their knowledge of linear relationships and use it to explore something they find in the world that requires the use of their prior knowledge to get at some larger unknown (and a higher level curriculum standard). Math isn’t my bag (I’m a science teacher), but I’m sure you can think of some high-level process thing that is coming up in your curriculum that would require the use of linear relationship knowledge. They already have the scaffold of understanding linear relationships. Now have them use it to learning something much more complex. You’ll have to figure out what that expectation is (and yes a scored rubric is probably a good idea here so that everything is transparent).

The point is that student exploration of whatever your next concept is should precede the formal instruction of that concept. Then use what they produce to teach whatever that next concept is. Scaffold along the way as needed. You’ll have to gauge the kids as you go along. Does that make sense?

On a related note, you might be interested in this in terms of teacher development/training. We use a modified version of this protocol with our science student teachers:

http://physicsed.buffalostate.edu/AZTEC/RTOP/RTOP_full/

The actual observation form can be found here:

http://physicsed.buffalostate.edu/AZTEC/rtop/RTOP_full/PDF/RTOPform_IN001.pdf

I can email you a more concise version if you are interested. That might be helpful for evaluating practice.

Jason: I can say it likely there will be very few students who actually do what is described above.

Sounds like a lack of faith to me.

Just “experience with a very similar thing knowing that this is going to have trouble working as a take-home”. That one educational structure will not work and another might be needed has nothing to do with faith or lack theoreof in students.

While I haven’t done the exact assignment before, I have done a similar one with 2 takers out of a class of 32.

I’m sure it’s possible to structure things different for a different result. I’m just not sure yet what that different would be.

Best I can think of is to be pretty light and forgiving on what consitutes a mathematical artifact; make it low-risk, make it personal. Let students bring in pictures of their dogs and figure out what the WCYDWT might be in class. Maybe there won’t be one for a particular artifact, but in the process students will have a better idea what a artifact to bring in is.

Maybe after a low-risk run, students will get a better idea of what actually works as a WCYDWT, and the difficulty could be bumped up a bit.

@Joe – You beat me to the punch. Must be someone lunch time for someone else.

It is hard to expect great results and be disappointed but I think that too is important. Show disappointment. I’ve had students respond quite positively to me just acting surprised/disappointed that they did not complete an assignment.

Avoid the message of “…it doesn’t matter to me one way or another whether you do work, I’m just punching a time clock. Plus the less work you do, the less grading I have to do.”

This is essentially a quote from a past colleague (has since retired).

What sort of results to suppose he got in return?

Dan, before I respond more fully, I’m wondering if you can say more about “it’s mostly an external confrontation between man and nature.”

So, if I’m hearing you correctly, there are all sorts of barriers that stand in the way of the implementation of more student-centered pedagogy and the creation of their own WCYDWT. Everything from student demotivation and apathy to increased class size and budgetary violence. I will completely agree with you here. Those dilemmas are very real.

But I can’t sit here and say that I have easy answers or silver bullets that claim to know “what works” in generalizable situations. I don’t know your kids or the unique situation that you are in. But that’s the whole point of the constructivist pedagogy. It’s going to look different for your classroom and with your kids. And that pretty much goes against the official line being sold to us about standardization and cuts right to the heart of mass-production schooling.

All that I am asking is that you try. Those limiting factors aren’t going away anytime soon, barring some sort of major change in policy/funding or the construction of different models of schooling.

So really, I guess it is up to us then, isn’t it? If not us, who?

This is my first time posting, although I follow this blog very closely and have followed this conversation as it’s been building. I teach high school math, so this dialogue is quite interesting

I have a hard time imagining that ideas brought in by students would be interesting enough to really maintain their curiosity, despite being applicable to the world they see around them. And, even if they did find an example of WCYDWT that would motivate them to pursue a question, I don’t know if the questions they would ask themselves or would try to think of to ask the class as a whole would be of the caliber that Dan has really pushed for in the whole structure of WCYDWT.

Think of the many posts that Dan has strongly urged the commenters to think of what question to ask, and has even complained that the questions they are asking are too simplistic or not the point or just boring.

Students can recognize the applications and bring them in, but I think the argument that Dan and Jason are making is that they would not consistently or naturally bring in material that would allow you to build a classroom built around a routine like that.

All in all, it seems like idealistic and could have a its beautiful moments, but does not seem sustainable to have a classroom centered around students ideas of WCYDWT.

Here’s a procedure that I cobbled together from the comments section of this thread:

1. Develop a safe classroom culture where kids feel okay to make mistakes and not get punished. If you don’t have this, don’t even try.
2. Determine the mandated state standard that you would like to teach/assess/worship.
3. Model a WCYDWT and the thinking that goes into planning such an activity. I’m assuming that this has already been done. Brainstorm a list of things that makes it a high-functioning and high-value activity.
4. Assign your students (probably with a rubric to maintain transparency in grading/expectations) a mission to find an example in the world of whatever standard you have chosen.
4a. There are two ways to do this, as I see it. If you are courageous, lightly scaffold the experience so that the kids are in charge of finding an example of something meaningful to them (I’m assuming that they mostly have access to some sort of digital imagery technology via cellphone and cameras). Anyway, I think you need to frame a question/problem. So, for science, find an example of erosion in your world and explain how it works. Personally, I would just ask that question straight-up. Then, have faith in the kids to actually go do it. If they don’t, be disappointed. Continue the practice. OR, for the less courageous, precede the activity with direct instruction. For me, this is less interesting and less constructivist, but I can understand the fear that some might have in turning over some of the instruction to the kids.
5. Now here is where it gets interesting. Have the kids bring whatever they have found into the classroom. Show it to everyone. Craft the meaning together. And this is tricky on the teachers end, as you have to balance both what the student is explaining to you with the “official” knowledge of the standards. This fundamentally changes your role from deliverer of knowledge to co-constructor of meaning.
5a. PS – This is how I did notes in my science room. Exploration always preceded formal instruction. Yes it takes time. You will have to balance this with the dilemmas of all the structures that are stacked against you.
6. Assess learning via your rubric or however else you decide appropriate for the given standard.

I’m probably forgetting something from this thread, but that’s roughly how I would do it. You might say we “co-constructed” the meaning here.

@Jeremy – You say this:

“I have a hard time imagining that ideas brought in by students would be interesting enough to really maintain their curiosity, despite being applicable to the world they see around them. And, even if they did find an example of WCYDWT that would motivate them to pursue a question, I don’t know if the questions they would ask themselves or would try to think of to ask the class as a whole would be of the caliber that Dan has really pushed for in the whole structure of WCYDWT.”

That’s really sad man. That’s what I mean by faith, or lack thereof.

Joe,

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.

Joe
It seems to me that you might be setting up a bit of a straw man. I am not sure this has much to do with faith, high expectations or courage because we have to consider the students in front of us. Dan and I are teaching the exact same standards to a completely different set of students. What may be high expectations for high school kids in a remedial algebra class may be the floor for a group of precocious 7th and 8th graders.

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.

Well, I think I’m basically done here. I’m not so sure there’s much more I can add beyond the process considerations that I have already put forth numerous times. I get the sense that people are looking for silver bullets, and I just don’t have any that are broadly generalizable to all of your unique situations. My original point and objection was that the WCYDWT needs to involve more student ownership. I still believe that. Dan asks:

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

I know I’m late in the game commenting, but I just came across the conversation today, and later stumbled across this book , possibly providing some requested examples of students generating their own study of mathematics. I don’t know the book at all, and if someone has read it, maybe they could comment.

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.”

I have for 8 years asked students to do this kind of “bring the math concept home” activity. And the students enjoy it, they learn how to get a project done by a deadline, they learn how to accept peer critique without feeling criticized, but in the end I wind up with a drawer of ACTIVITIES. If I can truly use 1 the following year it is rare.
Constructing “good questions” is the main focus of lesson study and many international models that the US is so hot to model. I look forward to your site with searchable lessons as a repository of something that we do well in the US imagine. And isn’t that what all your lessons are structured around Dan? Imagine this situation!!!