Thursday, November 29, 2012

Prblem Solving Top Ten List #2

A good process problem uses no set algorithm to find the solution.  It requires a variety of processes (problem solving strategies) to find the solution.  It is a problem that is easy to understand, is interesting, perhaps even whimsical, and has numbers sufficiently small enough so that lengthy computation is unnecessary.

Standard Word Problem:  Jack's family plans to rent a camping trailer for vacation.  The rent is $22.50 a day.  What will it cost to rent the camping trailer for one week? 

A Problem that Requires Problem Solving:  Drew and Addie are playing a game.  At the end of each game, the loser gives the winner a chip.  When they are done playing several games, Drew has won three games, but Addie has three more chips than she had when the game began.  How many games did Drew and Addie play?

So what happens when your students try to do the process problem above and they have no idea what to do?  In my last posting, I listed ten reasons why students get stuck when problem solving.  Now let's consider why students get stuck in the first place.

Top Ten Reasons for Getting Stuck in the First Place:

  1. You tried to rush through the problem without thinking.
  2. You did not read the problem carefully.
  3. You don't know what the problem is asking for.
  4. You don't have enough information.
  5. You are looking for an answer that the problem isn't asking for.
  6. The strategy you are using doesn't work for this particular problem.
  7. You are not applying or using your strategy correctly.
  8. You failed to combine your strategy with another strategy.
  9. The problem has more than one answer.
  10. The problem cannot be solved.

Next time, we will look at the final Top Ten List entitled The Top Ten Worst Problem Solving Habits.

Since students today tend to be more visual than anything else, a graphic organizer becomes a valuable math tool.  The Triangular Graphic Organizer is generic so that it can be used to solve all kinds of formula problems such as d = rt, A = lw, or c2 = a2 + b2.  This five page handout explains in detail how to use the graphic organizer.  It also contains several examples as well as a page of blank triangular graphic organizers to copy and use in your classroom.
Want the answer to the process problem? 
Check out the page above entitled: Answers to Problems.

Wednesday, November 14, 2012

Problem Solving Top Ten List #1

The study of mathematics should emphasize problem solving so that students can use and apply a wide variety of strategies to investigate and understand mathematical content. In this way, they will acquire confidence in using mathematics meaningfully. 

What is a real problem that requires problem solving?  It presents a challenge which cannot be resolved by some routine procedure known to the student and where the student accepts the challenge!  But what happens when students become frustrated and say they are stuck? Let's look at ten ways to get them unstuck.

The Top Ten Ways to Get Unstuck:
    1. Re-read the problem.
    2. Modify your strategy.
    3. Change your strategy.
    4. Combine your strategy with another strategy.
    5. Look at the problem from a new perspective.
    6. Look at the answer.
    7. Look at other similar problems.
    8. Ask for help.
    9. Wait awhile and then try again.
    10. All of the above.
Next week we will review the Top Ten Reasons for Getting Stuck in the First Place!


Wednesday, November 7, 2012

Putting the Pieces Together

What does it mean to think mathematically?  It means using math vocabulary, language and symbols to describe or interpret mathematical concepts, procedures and to discover relationships among ideas.  Therefore when a student problem solves, they use previous knowledge, skills, and understanding of concepts to solve a problem.  This process might include formulating problems, applying a variety of strategies, or interpreting results.

What can we do to help our students become better mathematical thinkers?  We can teach and model problem solving strategies such as the nine listed in the October 25th posting.  We can remember and plan our lessons to involve the three stages of conceptual development: concrete, pictorial, and abstract.  (Refer back to December 23, 2011 posting entitled Lesson Plans and Research.)   We can have the students talk or write about how they got an answer either with the class or with a partner.  We can use writing in the mathematics classroom (such as math journals) to allow the students to practice expository writing and show their understanding.  We can exhibit math word walls and have the students use the glossary in their book to write and define terms. 

We can also create a positive and safe classroom atmosphere for problem solving by being enthusiastic and allowing the students to take risks without consequences.  By emphasizing the process as well as the answer, the students may be willing to try unconventional or different ways to solve the problem.  I always tell my students that there isn't just one right way to get an answer which surprises many of them.  In fact, this is one of the posters that hangs in my classroom.

As math teachers, let's continue to emphasize problem solving so that all students will acquire confidence in using mathematics meaningfully. But most of all, let's have fun while we are doing it!


If you are interested in having a math dictionary for your students, check out A Simple Math Dictionary.  It is a 30 page dictionary which uses easy and clear definitions as well as formulas and examples so that students can learn and understand new math words without difficulty or cumbersome language.  Most definitions include diagrams and/or illustrations for the visual learner.  Over 300 common math terms are organized alphabetically for quick reference.