Challenging problems in math education and "Problems of the Week"

This post kind of follows the earlier line of thought about "Life without answer keys"... Also I want to tell you I'm going to have a blog contest with giveaways real soon! Stay tuned...

I've mentioned the importance of challenging problems before. You know, just learning concepts and practicing procedures all the time is not going to make your child a good problem solver in math.

Have you ever wondered how a tailor or a car mechanic or a hairdresser got so skillful at what he/she is doing? Some of it may be talent and natural abilities, but a lot of it is due to EXPERIENCE or we could call it PRACTICE.

And, have you ever wondered how some people get to be good problem solvers in math? I will tell you the same thing: some of it may be natural talent, but a lot of it is due to PRACTICE. Those folks have solved many problems!

And I don't mean just simple calculation problems, but true problems that require the student to think a little

All math curricula supposedly "emphasize problem solving". They have charts about problem solving strategies. They have lessons which concentrate on a certain strategy. But, does that sort of thing really help the students a lot? If you know what strategy you're supposed to use on a problem, then the problems are easy. Sure, it helps to see examples of problem situations. But that is just "mild exercise" - it won't yet get your student to be a proficient problem solver in math.

And kids' minds NEED 'exercise' to grow, to develop. You need to feed the mind, and you need to provide good exercise. Most of the problems in a typical math book are to help the student learn concepts and procedures. Then some are 'applications' or word problems of some sort.

Often, lamentably, the word problems are in the end of a lesson and are solved using the same operation that is studied in the lesson. This just about leaves word problems with the status "last and least".

If you're like me, you wish something more for your students.

One way to add challenging problems to math education is using a Problem of the Week activity.

Those problems are more challenging, sometimes open-ended. The student can't just check an answer key but has to use that brain, struggle a little.

→ And this is where the soon upcoming BLOG CONTEST will come in! The Math Forum is going to donate some free memberships to their Problem of the Week service. I will post the details of this contest later (hopefully this coming Sunday), so stay tuned!

The Math Forum PoW service is truly of a professional quality. Some of the main features of the Math Forum PoWs are:

  • The Math Forum PoWs come in four different flavors: Math Fundamentals (grades 3-5), Pre-algebra (grades 6-8), Algebra, and (high school) Geometry. Also available are special problem libraries for Discrete Math and Trig/Calculus.

  • A student can revise his solution unlimited number of times (a fantastic feature!)

  • Mentoring is available.
    (There are two kinds of mentoring offered: you can either pay an extra fee for it, or receive free mentoring which is subject to availability.)

As Suzanne Alejandre, Educational Resource & Service Developer from The Math Forum, says,

"Our research has shown that a student's mathematical thinking and their communication skills really improve if they are encouraged to revise. ... It's really a mindset -- it's that idea that you treat problem solving as you would the writing process.
You have a draft, you reflect, you talk with peers or someone (like the teacher) who has read your first draft, you write a second draft, you reflect, etc.

I've written more about this topic so please continue reading: Challenging problems and how to use a "Problem of the Week" activity in homeschooling.

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