Comments on: Best Of 101questions [4/14/12]

By: Nick

Nick — Thu, 06 Jun 2013 18:01:40 +0000

Thanks, for that Dan,

I wasn’t being critical – I really brought into your way of teaching Math.
I am a primary teacher for the UK and Maths is not my degree subject, not finding a solution at first really brought insecurities out.
However, I still persisted at it and so did the class and I must say I have been so impressed with the way the children have responded to it.
We cover only basic algebra at my level, but on the follow up activity of working out the circumference of the circles, I actually saw two amazing formulas created for working out the 22 inch circle. Considering that these children have not really had major working with algebra, the two, different, formulas were extremely impressive.
I am a big convert mate, but the removal of the structure is also challenging me. Which I am loving!
Thanks – I might come asking for more pointers in the future.

By: Dan Meyer

Dan Meyer — Thu, 06 Jun 2013 03:05:01 +0000

Hi Nick, I don't hate seeing people look for a formula. I don't find it productive to give people a formula for which they don't have any intuition. Here's what I'd do. Load those values into a table and graph them. Notice that the graph doesn't look linear at all. Try a quadratic. Drag the slider for "a" around until you see a good fit. Then go out to x = 22.

By: Nick

Nick — Mon, 03 Jun 2013 19:25:40 +0000

I know that you hate people looking for the formula.

But I am trying to solve the Penny Circle problem and I have the following coins for each circle diameter:

Diameter (inches) Pennies needed to fill
1 1
2 5
3 12
4 21
5 35
6 52

22 ?

Even when I insert the correct answer for the 22 inch circle, I can’t see how.

By: Dan Meyer

Dan Meyer — Tue, 17 Apr 2012 15:06:52 +0000

As far as assessment goes, I grade all classwork and homework for completion only. Completion, in this case, will include all the first act elements (guess, high / low, if applicable, etc.), then also the work in act two. Sometimes a calculation of margins of error in act three. Sequels are at the discretion of the teacher.

By: a different eric

a different eric — Mon, 16 Apr 2012 23:15:32 +0000

@Dan… that makes a lot of sense. I’ve been trying to do these without much lecture… or we’ll do some of the nuts and bolts (like how to find the area of a circle investigation) followed by a cool problem the next day.

Did you ever assess the work from 3-Act math? I made up a very loose worksheet for the kids to fill out while we do them so I don’t have a page full of numbers to look at (the overall question, too high – too low – guess, questions we need answered, work and calculations, and overall answer) but I’m having trouble giving grades for it. I don’t want to punish kids for not coming up with something valid… at the same time I don’t want kids that just sit around and copy all the groups calculations to get the same credit as the ones busting their rears the whole time. I also want the kids to develop the ability to make good arguments that I can “read” as opposed to “interpreting”… so maybe that’s how I start?

Or maybe I don’t collect anything at all? The reward is in the work and being able to be a part of the discussions… I’ll know if they understand it during the Concept Quizzes?

By: Dan Meyer

Dan Meyer — Mon, 16 Apr 2012 18:09:48 +0000

@Nathan @Eric, the second act of these problems is where students get the tools, information, and resources for answering their question from act one. A brief explanation is a valid response to students who ask you, "How do I get an answer to my question?" Lecture is problematic when its use is unmotivated, unsolicited, or the students aren't familiar enough with the context to make use of it. The advantage of the three-act structure isn't that it eschews lecture in act two. It's that the first act gives students a reason to want a lecture.

By: Nathan Kraft

Nathan Kraft — Mon, 16 Apr 2012 16:24:33 +0000

Eric, I have the same problem (that 10%). And I find that they are less of a problem depending on how much information I give prior to having them work on it. But then I worry that I’ve given away too much, especially to those who would have figured it out on their own.
I know that there’s another discussion on this (“They Really Get Motivation, Don’t They”) and from my own experience, I find that students typically feel more confident solving a problem if they have already solved something similar to it. And so I find myself asking, should I show how a similar problem is done before we do one of these activities? And I guess that it really depends on the makeup of your class. If they are strong for the most part, don’t give them anything. If there is a mix, and you have a number of students who struggle to do anything, maybe it’s best to put those particular students in the same group, and then, most of your coaching could be with that one group.
As I experiment with this, I’m sure I’ll have more to say on the subject. I’d love to know how others use these videos/pictures with those 10%.

By: a different eric

a different eric — Mon, 16 Apr 2012 12:51:33 +0000

I was looking at a few of these… and thought, “I wanna know the answer! Where’s Dan’s part 2 and part 3?”

Wait a minute… you mean I might have to figure these out without a Teacher’s Edition???

There’s nothing like having kids run up to me in class asking me, “Is this RIGHT?” and I get to reply, “I have no idea… explain to me what you did.” Their reasoning becomes more important to them and not their answers.

I would love to hear how some of you how the kids accountable for 3-Act Math work. 90% of the kids are engaged and rockin’ class… but it’s that 10% I’m struggling with.

By: Dani

Dani — Sun, 15 Apr 2012 22:31:44 +0000

Loved these – the phone comparison made me laugh:)

By: Nathan Kraft

Nathan Kraft — Sun, 15 Apr 2012 12:40:15 +0000

When I first saw the penny problem, I wasn’t that interested. But now that you’ve posed the value to area question, I really want to solve it. I think it shows that it’s probably worth your time to see what others have asked when you can’t think of anything.
I’ve also had a lot of issues with Vimeo.com videos not loading. Not sure if I’m the only one.