Challenging / open-ended math problems

I just read a very inspirational article Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF) (html).

It tells about two teachers who frequently employ open-ended problem-solving sessions in their teaching - and the students (almost all) like it well and are very motivated.

In math education, OPEN-ENDED problem usually means it doesn't have a specific step-by-step solution. You can solve it in many different ways. Or, it may have more than one solution.

The problems these teachers use are often from real life, and not quick to solve. Instead it can take some time and struggling to get anywhere. (Hey, that's how problems in real life often are, too!)

But, struggling can be valuable. One of the teachers featured in the article, Heidi Ewer, says:

"Struggling helps them see this as an investment of their own time and energy. It makes them more willing to learn," Ewer says. "Struggling to solve problems requires students to use their intuitive skills to investigate concepts, she explains,
and, in this way, they gain a deeper and more lasting understanding of the mathematics."

There's even some value in trying impossible problems! Douglas Twitchell says in The Value of 'Impossible' Problems, "...if you have students who are interested in trying, think of the mathematics they might learn in the process of attempting these! [some very difficult problems]"

I realize dealing with open-ended problems is not easy to do if you're not an experienced math teacher - and not even then. Like the other teacher from the article, Judith Carter, says, a problem-solving activity is not something she can fit into every day, or even every week.

But, parents organize field trips in other subjects. Maybe an occasional afternoon dedicated to a challenging open-ended math problem can serve as a 'mathematical field trip'!

Find out more:
Teenager or Tyke, Students Learn Best by Tackling Challenging Math (PDF)

Teenager or Tyke, Students Learn Best by Tackling Challenging Math (html)

The article is from a publication "Northwest Teacher". Their volumes seem to have interesting titles.

If you're ready to give some challenging problems for your student(s), check out these:
Open-Ended Math Problems from The Franklin Institute Online (middle school level). Check also the links in my previous post.

And, by the way, there's nothing wrong in working together. If you as the homeschooling parent don't yet know the answer, you can work the problems together with your child.

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Anonymous said…
Thank you for posting this. I have been using this technique for Friday math for my kids for the past year or so, and it has really changed them from math avoiders to math lovers. Even a 8 year old can do a problem like, "how many kernels of popped popcorn can fit into the fireplace?" and the like. By just giving them a good, really hard, but interesting problem that they have to figure out how to solve, they've been learning loads on their own to solve them.

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