Trying to make it matter.
One (90 minute period) day in my honors class I gave a picture (with a prominent shadow) and asked "what time of day is it?"I handed out three hint tokens and left the rest to them.They could use any resource, including the Internet, doing experiments with flashlights, and going outside to do measurements (although for the last the whole class had to go at once).It was both a.) playing with math b.) differentiated (due to the hint tokens; the stronger students tried to avoid using them more) and c.) led them to take ownership of their learning (since they were driving what physical / mathematical experiments to do).Allowing playing with math in a time-crunched California classroom? I have no idea. The hint tokens work with anything, though.
I think schooling takes away the ownership of learning. So K12 teachers are in a difficult situation. As a college teacher, I can pretend my students came because they wanted to learn, but they didn't really. They take math because it's a requirement for something else they want. So I'm stuck too.I'm going to keep doing things outside the classroom to remind me that math can be pure fun, and I hope that will keep helping me to share that perspective in the classroom.And I keep looking for ways to help them see how to make it their own. It is a dilemma. Sorry I'm not offering anything concrete here. Have you been reading Shawn Cornally? He's definitely playing, in a classroom, and writing it up with specific details. I'm looking forward to seeing other people's comments on this.
When I was a grad student at Vandy, we had a lecture-with-pizza series thing on random evenings for the undergrads. We'd present interesting/fun math concepts that don't fit into the usual curriculum. I took some of those ideas and maybe once a month add them to my lecture rotation.Topics like: infinity, golden ratio, what abstract algebra really is, counting in binary/other base systems, etc. The students enjoy taking a day "off" to "have their minds blown." I encourage them that, if they slog through all the mess of algebra and calculus and whatnot, they may be able to study interesting things like topology or abstract algebra or create models for "real life" situations.I don't know how to get them to take as much ownership of their learning as I think other teachers may be getting (at least, the impression I get reading other blogs, tweets, etc.). Once in a while, with our somewhat-random-Algebra2-standards, I'll let them decide something like, "Do you want to do probabilities or conics next? One is stats and numbers, the other is geometry and shapes." It's not much in the way of choosing, but some of them like the idea of it.Anyways, I don't know that I'm much help here either. Like Sue, I hope someone comes along who has some great ideas and I'll look forward to reading them.
I'm pretty sure no one really knows, but consultants pretend like they do so they can charge your school district a lot of money to come wave their hands and make teachers feel incompetent.Not that I'm bitter or anything.
jbdyer,I dig the "what time of day is it" prompt. May have to steal that one. Sue,Good point re: schooling getting in the way of learning. So you find that the college kids have just become more effecient hoop jumpers, huh? I like the idea of introducing the random things that make math cool like Dave suggests, but I wonder why we can't do the same thing with our mandated curriculum. So let's go into business, Kate. I can wave my hands like the rest of them. Maybe make a few bucks and not have to depend on my state retirement system which is gonna be bankrupt before too long. We can be bitter all the way to the bank.
>So you find that the college kids have just become more efficient hoop jumpers, huh? Not more efficient, just more determined. In high school, they weren't feeling it, now they know they need to get through those hoops, and maybe learn something, in order to get a job that's better than flipping burgers. Although it's not clear to me that the economy will support enough of those 'better' jobs to satisfy everyone who does get through the hoops of college. (This article is unsettling...)I hate to end on such a dismal note. I want schools that give kids enough freedom to keep the learning joyous. I want schools that help every student. I want a lot.
the first part of the problem is we all have a picture in our head of what an idealized classroom/school looks like. Differentiating in my ideal classroom might look a lot different than in yours. We know the buzz words but can't agree on a clear definition. For example in science, we always talk about "inquiry-based" everything. Every science teacher I know defines it differently. I'm not a big believer in pure open discovery but there are people that swear by it. The one that always kills me is "scaffolding." I don't know how many staff PD or workshops I've been to where they'll say something like "you just need to scaffold (insert crazy complex thing) and that will get them there." Oh..that clears things up. All these years of kids not getting whatever and all I needed to do was scaffold. BTW - I think your assessment cycle hits at least a couple of those things you mentioned. Each kid can know their own strengths and can work on their own weaknesses.
When giving kids an open-ended activity that's supposed to be fun, it's important to remember that they need to be able to work with the tools they have in order to actually have fun. I took a stab at playing with math by setting the students loose on a preconfigured geogebra file. They did not yet have the skills to transform functions, but they definitely had the skills to drag functions around in geogebra. I wrote it up at http://larkolicio.us/blog/?p=50.
SueIt's ok to want a lot, isn't it?jybCouldn't agree more. The buzz words get thrown around a lot. The scaffolding thing has been a conversation that has come up recently here as well. I think that my assesment cycle does help. My students know where they are weak better than they ever have. They know why they have the grade they do and they know what they can do about it. RileyI've become a big fan of GeoGebra this past year and a half and create applets for them as often as I can. Good point re: making sure they have the skills necessary to play. A good GGB applet really evens the playing field for many kids.
>It's ok to want a lot, isn't it?He** yes! But that makes it hard to figure out how to get from here to there.I need to learn how to use geogebra. (I'm a bit of a technophobe, actually. Each new techno-skill takes me some courage to get started on.)
I can't recommend GeoGebra highly enough. I had a trial of Sketchpad once, but for whatever reason, it didn't stick with me. I've picked up GGB fairly quickly. There are also a lot of great people out there eager to help.
>> "I think that my assessment cycle does help. My students know where they are weak better than they ever have. They know why they have the grade they do and they know what they can do about it."David, in which post do you discuss your assessment cycle? I am interested to see what this is and how you use it.
Here you go
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