Hi all,
I need some help, if you have a few minutes. I am looking for some quality blog posts and/or websites which offer the following:
Stories from the Front: On the ground experiences of teachers teaching problem solving in the math… the good, the bad, the ugly
War Strategies: Different ways teachers actually do problem solving in the classroom, and maybe some hints/tips/technqiues (e.g. whiteboarding, Moore Method, Harkness Table, problem sets, grouping ideas, hint tokens, etc.)
Weapons: Good websites (or books) which contain good math problem solving problems (e.g. Exeter problem sets, AMC questions, etc.). My personal thought on questions is that they don’t need to be hard to be problem solving… In fact, the harder the problems are, the less accessible and fun the problem solving will be, and the more my kids will be turned off.
What I’m not really looking for is Polya’s How To Solve It, which is great reading but lacks in the day-to-day practicality and concreteness I’m looking for. I don’t need to know what problem solving is (like Potter Stewart, I know it when I see it), or read philosophical exhortations about how important it is in promoting meaningful and deep learning. I want practicality. Stories, resources, tips, etc.
If I get some responses in the comments, I will compile them into either a comprehensive post, or if there are a lot, I’ll make a new page (a la the Virtual Filing Cabinet) for it.
The reason behind this is selfish, but I’m hoping the output could be collectively useful. My department is thinking seriously about how to integrate problem solving into our curricula… and I wanted to show them: “hey, there are a ton of good ideas from teachers who do it!”
So if you could help a teacher out…
PS. Not to make you jealous, but yesterday I designed and ordered these buttons! (You have to recognize I don’t know what I’m doing with Photoshop, so the pictures aren’t all that great. And these buttons have a large bleed area, so the text will actually be just near the outer rim of the button instead of with all that blank space between the text and the outside of the pin.)
Continuous Everywhere but Differentiable Nowhere 
I have a colleague here at Stanford who has a blog which has gotten quite a bit of attention. http://blog.mrmeyer.com/ I don’t know too much about his blog, but I do know that his research interests are mostly related to student problem solving, so the blog might be of interest to you.
Last year, I adapted some of these activities for my 9th grade algebra class: http://fcit.usf.edu/fcat8m/resource/default.htm
Here’s a geometry problem-solving activity that we discussed recently in one of my classes: http://nrich.maths.org/4973. We extended the problem more than what is on this site, but this should give you an idea.
I come across all sorts of great problems in the research that I read, and I’m hoping to start including some of these on my own blog. But that hasn’t happened yet. Right now, it’s mostly about shoes. ;-) If you’re interested in some of the literature, I’d be happy to send some your way. Just let me know.
Sam,
Not sure if this is what you’re looking for but here are all my posts marked problem solving. http://deltascape.blogspot.com/search/label/Problem%20Solving
Let me know if there’s anything else I can do to help.
risps are good: http://www.risps.co.uk
I’ll look forward to seeing if anything new to me shows up in your collection.
My new blog (http://uncoverafew.wordpress.com) aims to be a supply of problems at a wide range of difficulty levels but all of which are more suitable for investigation/problem solving. For instance, my latest post relates to the multiplication table and fits well for a class that’s involved in distributing multiplication over addition.
Maybe my favorite source, especially for more straightforward problems, problems for younger kids, and problems with clearer ties to curriculum, would be NRICH: http://nrich.maths.org/public/
The ancient but still excellent Math Forum has its problem of the week, which is sometimes more like an exercise but often has some good ideas: http://mathforum.org/pows/ . They also have a lot of good advice on how to teach from a problem-solving perspective, and particularly on how to give feedback on student work.
There’s also some material at http://mathcircles.org but it’s hard to pick and choose the right kind of problem for your needs.
You might find something of interest at http://jrmathfestival.org (click on the “Festival Activities” link)
Perhaps you want the collection all the AMC problems:
http://209.222.159.179/a-activities/a7-problems/problem81012archive.shtml
The Art of Problem Solving books are good for what you want to do:
http://www.artofproblemsolving.com/Store/contests.php
I’m going to recommend my colleague’s blog post on “Problem Solving stations”. See http://mssphillips.wordpress.com/2011/09/21/problem-solving-stations/
Someone just this week recommended St. Ann’s problem of the week site: https://sites.google.com/a/saintannsny.org/problem-of-the-week/Home/november-15-2011
You’re doing important work, here, Mr. Shah. Important work. I would really appreciate a repository of these, like your virtual filing cabinet. Here’s a list of my posts that fit your headings above.
WAR STRATEGIES
My series of posts on the process of “learning through problem solving.
http://thescamdog.wordpress.com/2011/04/29/learning-through-problem-solving-ltps-defined/
http://thescamdog.wordpress.com/2011/04/30/learning-through-problem-solving-is-not/
http://thescamdog.wordpress.com/2011/05/02/3-of-6-ltps-examples/
http://thescamdog.wordpress.com/2011/05/03/4-of-6-ltps-what-students-learn/
http://thescamdog.wordpress.com/2011/05/05/ltps-how-to/
STORIES FROM THE FRONT
A description about how some of these went in real life classrooms.
http://thescamdog.wordpress.com/2011/05/08/ltps-a-day-of-morning/
http://thescamdog.wordpress.com/2011/06/06/ltps-a-day-of/
WEAPONS
My collection of problem solving websites
http://thescamdog.wordpress.com/useful-weblinks/problemspuzzlesgames/
I can’t wait to see what you collect from other bloggers.
Sorry that all those links aren’t links. That’s going to be a pain in the butt for you.
Have you been following Avery’s blog, Without Geometry Life is Pointless? He writes often about problem-solving, and is working on a list of habits of mind he hopes will help students learn math. He mentions lots of good problems on his blog.
There are also lots of good problems on Henri Picciotto’s MathEd Page, though you’ll have to wade through lots of other (good) stuff to find them.
There was a recent discussion on the NSTA Physics mailing list about problem-solving strategies.
To summarize, Dick Heckathorn has a generalized process called GUESS, which is summarized in a PowerPoint (second link here: http://web.cvcaroyals.org/~rheckathorn/HONORS/web%20pages/HonorsChapter1.htm). Some people add a Graphic Organizer at the front, making the delightful acronym GO GUESS, and use it across subject areas. However, without a structured understanding of the underlying concepts, any method can end up reduced to randomly picking an equation and hoping for the best. There were a number of interesting stories from teachers at various secondary and post-secondary levels about their own students and problem-solving.
Bill Robertson (author of the Stop Faking It! series [http://www.nsta.org/publications/press/stopfakingit.aspx]) also weighed in.
Sorry that last link didn’t come through as a link. Here it is again: http://www.nsta.org/publications/press/stopfakingit.aspx
I’m new to the blogging scene, but I try to focus on problem solving in my new blog: Algebra, Essentially.
I also have been posting my resources at Teachers Pay Teachers, which is a quickly expanding venue for teacher sharing. My primary free resource there is an excellent problem solving tool that I have used so very effectively in my algebra classes.
I’ve been having a lot of success with small groups of 4-5 this year. I’ll make up a small problem set (such that everyone has at least 1 to do) and have them compile the results on a small poster. For systems of equations the groups were given 5 systems and had to choose the best method for solving them (substitution, elimination, or graphing). It generates a ton of discussion amongst the kids as they teach one another. I wrote up the whole experience here:
http://infinitesums.com/commentary/2011/11/8/dividedebatediscuss.html
I did a mirror activity when I showed the magic of solving systems with matrices.
I think you’re overlooking the times when you’re already doing problem solving. Sure, you can approach problem solving as something different from just teaching your curriculum well, but there’s also problem solving embedded in a lot of good lessons. What comes to mind first for me is Kate Nowak’s logarithm lessons
http://function-of-time.blogspot.com/2009/12/introducing-logs.html
http://function-of-time.blogspot.com/2010/12/log-laws.html
That way of teaching content by having students figure out questions, make conjectures and reason their way to learning is one of the classic examples of what problem solving is and should be.
You didn’t mention pcmi. I know you already know about those, but others following this comment thread might be excited to learn about them.
Sam – You should check out http://parkmath.org/. They are doing some really good stuff with problem solving.
I can offer my own humble list of problems that I’ve taught…
http://brainopennow.wordpress.com/category/problems-2/
I would recommend the book: Problem Solving Strategies: Crossing the River with Dogs from Key Curriculum. The caveat is that it’s more of an integrated curriculum and less of a resource to pick and choose problems.
hahahahah love the logarithms button!!!!
me too for the log button. I might steal that idea. What a coveted prize that could become.
If you are looking for some good problem solving question you might want to try Professor Stewarts Hoard of Mathematical Treasures. There are alot interesting and though provoking questions in there. I have some questions from the book up on my blog.
http://derivativediary.blogspot.com/2011/10/mathematical-puzzles.html
I blog about all of things I am learning about during my senior year in college while studying to be a math teacher. I am trying to keep track of everything that will be helpful once I start teaching. Take a look if you get a chance.
Sam
The Emma Willard School – a girls school in or near Albany NY – has gone to a problem based learning approach in the not too distant past. One of their math faculty members Carmel Schettino (her website is http://www.carmelschettino.com/) helped develop this program. She may not be there anymore but you can reach her through her website. I had the pleasure of meeting her at an Exeter summer conference, she is a great resource. At my last school I had my room set up in groups of three or four students all facing each other in little desk pods. I got constant positive responses from this approach. My room in my new school does not work this way due to layout, so instead I went more Harkness style with long tables. Again, I get good feedback about the feeling of responsibility to each other and I get the sense that real communication is happening with my kids. I tried a problem set approach for a few years in my Calculus class but was having real trouble with academic honesty issues on those kind of challenge problems outside the class. When I confine them to class discussions I get good results.
Can’t wait to see how this looks when it is compiled. You’re doing us all a great favor here.