Top Ten Reasons for Getting Stuck when Problem Solving

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.

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.

Problem Solving - Getting Unstuck!

Math courses are not like other courses. To pass most other subjects, a student must read, understand, and recall the subject matter. However, to pass math, an extra step is required: a student must use the information they have learned to solve math problems correctly. Special math study skills are needed to help the student learn more and to get better grades.

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 acquire confidence in using mathematics meaningfully and the assurance that they can be successful in math.

But what is a real problem that requires problem solving? A real problem solving problem presents a challenge that cannot be resolved by some routine procedure known to the student and where the student accepts the challenge! Now, there's the dilemma, students who actually accept the challenge and are persistent enough to solve the problem.

What can we, as math instructors, do when students become frustrated, exasperated and discouraged and say they are stuck? Let's look at ten ways to help them get "unstuck".

Top Ten Ways to Get Unstuck

Free Resource

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.

Would you like a free resource about study tips? Check out Study Tips You Won't Forget. This resource lists 20 math study tips or guidelines intended to help students succeed in math.

Problem Solving Strategies

My math classes have been looking at different problem solving strategies, trying them out, and discovering what works best individually.  We've tried:

Poster that Hangs in My Classroom

1. Using Models or Manipulatives
2. Drawing a Picture
3. Acting it Out or Role Playing
4. Making a Chart or Table
5. Making a List or a Graph
6. Looking for Patterns (All math is based on patterns.)
7. Working Backwards
8. Guessing and Checking
9. Making the Problem Simpler

I believe problem solving should be the central focus of any mathematics curriculum.  It is the major reason for studying math and provides a context in which concepts and skills can be learned.  It is the major vehicle for developing higher order thinking skills.  However, there is one problem solving strategy that will not work, although many students try it. It is called staring!  That is why the non-strategy poster seen above always hangs in my classroom.

Need some problem solving activities that are enjoyable, offer variety, and increase interest? Think Tank Questions is a 14 page handout that contains 46 various questions. Most subject areas are included in the questions which are appropriate for grades 2-6.

Give Reading A Helping Hand!

I believe the Conceptual Development Model should be constantly used when creating lessons for students, no matter what their age or grade level. (I even use it on the college level.) This particular model helps to bring structure and order to concepts found in almost any discipline. Here is an example of how I used the model in reading.

When I taught third grade, I noticed that my students often had difficulty identifying the different components of a story. I knew I needed a concrete/pictorial example that would help them to remember. Since we always had our hands with us, I decided to make something that would be worn on the hands. By associating the abstract story concepts with this concrete object, I hoped my third graders would make connections to help them visually organize a story's elements. I also suspected it would increase their ability to retell, summarize, and comprehend the story.

I purchased a pair of garden gloves and used fabric paint to write the five elements of a story on the fingers...**characters, setting, problem, events, and solution. In the middle of the glove I drew a heart and around it wrote, "The heart of the story." (theme) Towards the wrist was written "Author's Message." (What was the author saying?)

After we read a story, I would place the glove on my hand, and we would go through the parts of the story starting with the thumb or characters. (a person, animal, or imaginary creature in the story). We then proceeded to setting (where the story took place.) We did not progress through all the story elements every day, but would often focus on the specific part that was causing the most difficulty. The fun came when one of the children wore the glove (Yes, it was a little big, but they didn’t seem to mind) and became the "teacher” as the group discussed the story. As the student/teacher talked about each of the fingers, we would all use our bare hands without the glove.

I also made and copied smaller hands as story reminders. This hand would appear on worksheets, homework, bookmarks, desks, etc. Sometimes the hand contained all the elements; sometimes it was completely blank, and at other times only a few things would be missing. The hand became known as our famous and notorious Helping Hand.

Why would I allocate so much time to this part of the curriculum? Because…

1) If a student learned the elements of a story, then they understood and knew what was happening throughout the story.

2) If a child is aware of who the character(s) were, then they cab identify the character’s traits during the story.

3) If the child knows the setting of the story, then they recognize where an event was taking place.

4) If they know the problems that are taking place, then they can be a part of the story and feel like they are helping to solve it.

Such visual tools allow a teacher the flexibility to focus on one single story element or present a more complex or intricate view of all parts of a story. By knowing the components of a story, students are more engaged and connected to their reading. It’s as if they assimilate the story and become a part it. So, are you ready to Give Reading a Helping Hand in your classroom?

**The five parts of a story may be identified as introduction, rising action, climax, falling action, and resolution or other similar categories.