Monday, April 25, 2011

How to incorporate WCYDWT (Rich Problems) into math class?

So, I have no idea how to bring in WCYDWT and/or Rich Problems into my math classes. I really was never taught in college how to do something like this. So I have been tweeting, asking how to start. Here are some responses I got today.

@maxmathforum @ putting up a problem scenario (video, text,...) and asking students What do you Notice? What do you Wonder? in a think-pair-share
Me (@lmhenry9) @ What if you are working with students who are unaccustomed to "wondering" about things mathematically?
@maxmathforum @ on the one hand, that slows things down. On the other, I've never had a class without a wonderer or two. In LOTS of diff. schools.
@ I love problems that generate controversy, a yes/no answer, a chance for kids to "wager" on an answer. That's a way to wonder...
Me @ Do the other students then start to join in? I'm working with lower level students who aren't real thrilled about math.
@ This is something completely new to me - do I just put out the scenario and hope they wonder abt it? Just see where it goes?
@maxmathforum @ some kids spend all yr wondering "why is the paper red?" but most start to generate questions and some start conjecturing well
@ the expectation that they write 5 noticings and wonderings on their paper, share with a buddy, and then share out seems to work.
Me @ This is the situation I want to bring to them - and I'm trying to figure out how to go with it.
@maxmathforum @ calling early on kids who rarely contribute means they say obvious/important noticings and as you solve, you refer back to theirs
Me @ That makes sense. Hadn't quite thought of it that way. That would also engage them (hopefully).
@maxmathforum @ it builds their confidence and buy-in when you say, "remember that important thing Tasha noticed..."

Me @ Part of what I am struggling with (esp since I'm very much a traditional teacher) is how the content fits in.
@ Does the problem introduce the content or have students had the content previously?
@maxmathforum @ since it's a real context, the kids' wondering might really flow. Like, "how can I get to this skill level?" or "why'd his go up?"
@ I believe that you don't learn without a question in your head. Like, "how does my score go up?" and then the content follows.
@ I'm agnostic about delivering the content after the ? is generated. If the ? is well understood, the kids will hear and make sense
Me @ When I first looked at it, I wondered whether there was an equation to determine how your score went up.
@maxmathforum So they may wonder about it & try to figure it out with what math they know. If they don't have enough math knowledge, then intro new content?

@maxmathforum @ that's what I'd do
Me @ Thanks so much for your help - I greatly appreciate it.
@maxmathforum @ happy to get to think about helping kids become problem-solvers! I'll comment on your blog too if I think of anything else
@dandersod @ you can start off pretty small with the wcydwt stuff. how many jelly beans in a jar? that brings up volume.
@ getting the students to "buy in" is important. you can do this by writing down their guesses. everyone likes to try and be right.
Me @ I primarily teach algebra - what would you suggest is a "small start?"
@dandersod @ Picture of you next to a tree/building. How tall is the tree/building? Proportions and ratios?
@maxmathforum @ cell phones... i brought in my bill and had kids figure out how much my overtime mins cost. They decided I needed a cheaper plan.
@dandersod @ maybe a doubling idea?
Me @ Am I correct in my assumption that wcydwt cannot be used with everything we are to cover in the HS math curriculum?
@ How often do you use wcydwt in your classes?
@dandersod @ 2-3 times a month maybe? it's tough work to get setup.
Me @ That's good to know. I wasn't sure whether people who did wcydwt/rich probs. did them all the time or just every so often.
@KaminskiTerry @ definitely cannot use WCYDWT with everything in curriculum. @ Only uses it about once every week or two
Me RT @ and on non wcydwt days, what does class look like? @ @ What is the answer?

@KaminskiTerry @ @ On non wcydwt days the class may look very similar to what it does right now.
@druinok @ @ can you expand on that? Do you mean traditional?
Me @ @ @ So what about those who say we should be doing prob solving daily (and w/ rich problems)?

@KaminskiTerry @ @ @ Sometimes we need to teach the kids the skills. However, we can still have them thinking.
@ @ @ Give the students the answer and have them create thequestion.
@druinok @ and how long of a process is it to get there?
@dandersod @ @ @ selfishly, it makes the classroom much more interesting for me. Kids get into it too.
@KaminskiTerry @ @ @ I agree. U have to try it and refine as u go
I should also add that @mrautomatic tweeted that I should check out Dan Meyer's blog and that's already on my "to do" list.
So... I have some answers from a couple of people.  What about others? How do you start with WCYDWT and/or rich problems in your classroom? How does it work? Do you do it every day? If not, how do the rest of the days go in your classroom? At NCTM, several people ("experts" if you will) expressed that we should be doing rich problems in our classrooms daily. Do we try to accomplish this iin our classrooms?. How do we get closer to that ideal?
Please take a few moments and respond to any and all of these questions in the comments. I'd love to see some good discussion about it - there are other teachers who have the same questions and they would benefit also. Thanks!


Dan Anderson said...

One quick point. I don't equate wcydwt problems and "rich" problems. I think that wcydwt problems are much more involved and open to different solution methods. I see rich problems as smaller and more directed. I use rich problems nearly every day in class, and wcydwt problems when I find them.

misscalcul8 said...

Just starting out, I wanted to ask you what is your ratio of lecture time to students working together without you?

I find a good way to start problem-solving is using concept attainment. Students have to guess/discover/recognize a pattern between things and figure out what makes one work and one not work. It is beautiful for vocabulary and lots of algebra concepts. It really makes students more observant and think a little harder. I think students get more comfortable with trying and guessing.

From there, I would try to teach mini lessons and then just give the students problems to solve. They work together in teams but without you. What I mean is that instead of just telling them formulas or patterns, scaffold an 'investigation' where they can figure it out themselves. Make it something they can do on their own with a little bit more thinking on each step. But remember to be less helpful! For instance, tell them they have to work for 5 minutes before you will answer any questions. Then after 5 minutes tell them that they can only ask 1 question. That helps them narrow down what information they really need.

Another method is called "three stay, one stray" where one member of the group can 'stray' to another group for 30 seconds and try to gain something that will help their group.

Most importantly, don't give up! Keep it up even if it seems pointless. The students aren't usually used to thinking or thinking hard. If they're really afraid of it, mix in some brain teasers or non-math patterns for them to figure out. Most students can't resist a good puzzle, as long as it is something they can actually do.

Lisa said...

@Dan - So I take it that means I need to really be looking at two things - the WCYDWT stuff and rich problems. So I think I have a handle on where to start with WCYDWT. How do you start with rich problems? Is there a definitive source/blog/website to begin with? I don't think I have a good idea of how to start with that.

@misscalcul8 - I appreciate you taking the time to offer your experiences. Are there any particular resources you would suggest looking into to start?

I try to give my classes time daily to work on the assigned problems in class. Many of my students don't take advantage of the time in class the way they should. They tend to do more "social" talking and not much concentrating on math. At this point in the year, it is hard to get them back, but I do want to make the most of the time I have left with them. I try to leave about 15 minutes or so in a 50 minute class period for students to be working on problems. My walking around doesn't seem to motivate them to work on the problems, although students who are working on problems will ask for help more readily if I am walking around. I guess what I am trying to say is I know what I am doing presently is not working well and I need to figure out how to restructure things so that students are working more on math and are engaged with math more.

I am very much a traditional teacher - we start each day by going over questions from the previous day's practice problems, I lecture (for lack of a better word) on the new material and students have some time to work on the problems in class. It's not working. I know that. I don't know how to fix it.

misscalcul8 said...

Mimi at has excellent resources on scaffolded investigations, she is the queen!! I got most of my inspiration to create my own based on the stuff she does. This is the first one I saw and loved and used: Then I started to create my own.

I would suggest flipping what you mentioned. Try only teaching 15 minutes and giving them 45 minutes to do the assignment. I think part of the problem with your students socializing is that with so little time left they deem it as unimportant and try to waste time until class finishes. Basically, you've done all the hard lifting of the class and just leaving them the cool down portion. Try to shift the focus to them doing all the work instead of you. With Mimi's investigation, I literally handed it to them and told them to start working. I didn't help them, I didn't teach anything beforehand, this was literally the intro into linear equations for me. It took a few minutes of them looking around waiting for me to give them the answer to realize I really wasn't going to help them. Since then, I've done more and more of that until they are very used to working without me. Here's an investigation on graphing systems of equations and one on parallel and perpendicular slope (download this one to see the fractions)

In my geometry class, I've went to doing team work almost exclusively. My most recent endeavor has been to scaffold my notes so that students work together and take notes based on patterns they find/notice on their own instead of me just giving them formulas.

As far as concept attainment, I LOVE it. Here is a link to how I introduced slope-intercept form: So I clicked through one example at a time and made them 'notice' something about each pair. What makes one a yes but the other a no? The next slide is where we recorded 4 characteristics they noticed through the examples: 1. y can't be negative 2. y has to be alone 3. x can't be on the bottom of a fraction and 4. no exponents. This is another thing where it takes students a while to realize I'm serious and adjust to a different way of thinking. I've done this four or five times and students have gotten accustomed to it. Here's a geometry example where we defined a parallelogram and my most recent that we used to define monomials

I've been trying to really shift things away from lecturing. I've posted a lot of my favorite lessons and review games on my blog if you'd like to check them out

Another thing about walking around, I noticed one day that my students relied on me less when I sat off to the side and watched. When you walk around, they become instantly more needy and you're their expert. When I sat off to the side, I was no longer a moving target but I faded into the background. They relied more on each other. It is such a great feeling to listen to students discussing math!

And here my corniness ends. But please ask anything else because this is my favorite thing to talk about!!!