Problem solving

[roberto]

Dear group,

If you had to suggest some resources about mathematical problem solving skills and processes, based on your experience, what would you choose ?

I'd like to shift problem solving reasoning to a much central place in my courses (age 14 - 18).

Thank you very much.

--
Roberto

[John Mason]

Have a look at Dan Meyer's TED video on utube

"It is not the task that is rich, but whether the task is used richly"

JohnM

[Joshua Zucker]

Start with Polya!  _How to Solve It_ is good for the kids, and that and some of his other writing will be good for you.

There's also a growing body of math circle curriculum (beginning with an import from Russia, _Mathematical Circles: Russian Experience_) that has a lot of good problems to get you going, organized around a lot of the key strategies that kids might not be familiar with.

A huge part of building that problem solving culture is naming the problem solving skills you (and they) already use and keeping a list in a prominent place where you refer to it frequently.

There are a ton of bloggers on the topic, too.  I'd particularly recommend the "Habits of mind" conversation and in particular Avery Pickford's take on it: http://www.withoutgeometry.com/2010/09/habits-of-mind.html

--Joshua

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[Linda Fahlberg-Stojanovska]

Because of today’s technology, I think it is very important to consider how to integrate the critical thinking skills of problem solving (such as Polya), but include at every step the use/non-use of technology.

Very briefly (from a slide show for an ISTE-Verizon webinar I just did),

---

Learning to do math with computing devices

 teaches us important problem solving skills.

•       How to think about problems and to organize.

•       What computing devices can and cannot do.

§  What is the human role in problem solving?

§  What is the computational part of each problem?

§  How do answer the problem?

---

Example: We paid $30 for 15 tickets. How much does each student need to pay for his/her ticket?

Solution:

       Can you put this problem directly into a computing device? 

        What if you tell the computer to solve:  30x=15?

                Will the computer know you have the wrong equation?

        Now assume we put in the correct equation:  15x=30

          The device gives the “solution” x=2.

                  Is “2” the answer?  No.  What is the answer?

         Answer: Each student needs to pay $2.

---

Why use computing devices?

What computing devices can and cannot do.

• What is the human role in problem solving? How do we turn that word problem into math language? How can we check this since no computing device can do this part?
• What is the computational part of each problem? How can we get this into our computing device? How can we check that we have input this correctly and used our device correctly?
  Did we add parentheses to guarantee the order of operations?
• How do answer the problem? Our device gave us a number – how do we make this number into an answer?

 

Warm regards, Linda

[Phillip Kent]

I recently enjoyed working on problems by:

A. Posamentier & C. Salkind, "Challenging Problems in Geometry" (Dover
Publications)

The style of this is quite "maths olympiad" so not aiming for a typical
classroom. However this led me to a teacher guide by the same author:

"Teaching Secondary Mathematics: Techniques and Enrichment Units"
A. Posamentier et al
(still in print, I bought an old 4th edition used and cheap)

which does aim for problem-solving in a regular classroom. I just got
the book so can't comment in detail, but it has a lot of good stuff,
whilst being perhaps a little old-fashioned geometry in emphasis.

I also believe that not everything to be done in learning maths is
seeing everything as a "problem", so the "habits of mind" ideas
originated by Cuoco, Goldenberg and Mark are definitely important:

http://ltd.edc.org/sites/ltd.edc.org/files/HabitsOfMind.pdf

- Phillip

++++++
Dr Phillip Kent, London, UK
mathematics education technology research
philli...@gmail.com mobile: 07950 952034
www.phillipkent.net
++++++
"A picture had better be worth a thousand words,
it takes more bandwidth"

[Christian Baune]

Hi,

I wrote these 5 pages times ago : https://docs.google.com/file/d/0B-_hh3IZyMrJYWMxODJhMDUtMmMxNi00ODk3LWJhNGMtNDFjMWRmMjY4NjY5/edit?usp=sharing

Christian

[Maria Droujkova]

I would suggest focusing on problem-POSING. 

Also, a great resource is the site Art of Problem Solving, including their active forums: http://www.artofproblemsolving.com/Forum/index.php?

Math Future event with their leader Richard Rusczyk: http://mathfuture.wikispaces.com/Art+of+Problem+Solving

Cheers,
Dr. Maria Droujkova
919-388-1721

 

[Sue VanHattum]

A book on problem posing that I love is The Art of Problem Posing, by Stephen Brown

I would also recommend The Art and Craft of Problem Solving, by Paul Zeitz, and Out of the Labyrinth: Setting Mathematics Free, by Robert and Ellen Kaplan.

I am looking forward to discussion on the "f-word" (fun)!

I agree with Josh that we should expect our math to be fun, but the word I would use is engaging. I expect to sweat (like with calisthenics), and I expect to enjoy it, because I love seeing what emerges. I wouldn't do it if I didn't enjoy it. I get my calisthenics from swimming, yoga, and biking, all of which give me pleasure.

Warmly,
Sue

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From: drou...@gmail.com
Date: Mon, 4 Mar 2013 06:18:28 -0500

Subject: Re: [Math 2.0] Problem solving

To: mathf...@googlegroups.com

[John Sharp]

Correction The Art of Problem Posing, is also by Marion Walter

John S

[roberto]

Does anybody know if the authors of http://ltd.edc.org/sites/ltd.edc.org/files/HabitsOfMind.pdf (or someone else) has realized a set of mathematics problems around the Habits of Mind suggested in that paper ?

Thank you.

Roberto

Roberto

[Maria Droujkova]

On Wed, May 1, 2013 at 4:01 AM, roberto <robe...@gmail.com> wrote:

Does anybody know if the authors of http://ltd.edc.org/sites/ltd.edc.org/files/HabitsOfMind.pdf (or someone else) has realized a set of mathematics problems around the Habits of Mind suggested in that paper ?

Thank you.

Roberto

James Tanton, Yelena McManaman and I are about to release "kiddie versions" of some problems that illustrate some of these practices. The list is different (it's made by James for MAA originally), but it will help. I will let you know when we publish it.

Cheers,
Dr. Maria Droujkova

moebiusnoodles.com
919-388-1721

[Sue VanHattum]

Check out Avery Pickford's blog, with a search on Habits of Mind (http://www.withoutgeometry.com/search?q=habits+of+mind). He's got lots of good stuff.

Warmly,
Sue

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Date: Wed, 1 May 2013 10:01:20 +0200

Subject: Re: [Math 2.0] Problem solving

From: robe...@gmail.com
To: mathf...@googlegroups.com

[Zor Shekhtman]

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