After attending the GED Mathematics Training Institute, I collaborated with a colleague from Iowa Lakes to determine how we could use the information that we received. We plan to share the information with other GED instructors to help them recognize areas of math with which GED math students have the most difficulty and help them adapt instruction practices to help students perform better on the GED math test. The presenter, Nancy Coursen, gave us information presented at a conference in Washington, D.C. in August 2006 by the U.S. Department of Education Office of Vocation and Adult education Division of Adult Education and Literacy. The GEDTS Study found that there were three areas that had the most missed questions on the GED math test. These were: Geometry and Measurement, Applying Basic Math Principles to Calculation, and Reading and Interpreting Graphs and Tables. Several helpful tips were given to help students in each area of difficulty.

Another topic that was discussed was Problem Solving Strategies. This is the area that I plan to implement with my GED math students and also in my developmental math classes. One strategy that was suggested was a Warm Up Sheet to begin a class which would contain 3 problems of different difficulty levels: one easy, one medium and one hard. I plan to use this idea along with Math Puzzlers each day to teach different problem solving strategies. After the class has worked on the problems we will discuss what approached they used to work on the problem and what the various strategies are.
Problem solving strategies used in math are the same problem solving strategies used in life, so it is possible to bring in a wide variety of problems. I also think this is a good time to try and get to know the students in a fun and relaxed atmosphere. I hope to change the attitude that so many of my students have, ie. “I hate math”, and also try to alleviate some of the math anxiety which is so common with my students. The problem solving strategies that I plan to each include:

• Problem Solving Strategies:
  • Elimination
  • Draw a picture
  • Guess and check
  • Solve a simpler problem
  • Substitution
  • Work backwards
  • Make a table, chart or list
  • Find a pattern
• Problem Solving Skills:
  • Solve problems out loud
  • Explain your thinking process
  • Allow students to explain their thinking process
  • Use the language of math and require students to do so as well
  • Model strategy selection
  • Make time for discussion of strategies
  • Build time for communication
  • Ask open-ended questions
  • Create lessons that actively engage learners

Journal
The first day of class for Math Strategies, I wanted to spend some time for students to get to know each other and for me to get to know them. I had the students complete a worksheet asking for their goals, strengths, weaknesses and strategies for success. One student refused to respond to the questions and proceeded to say that he hated math, etc. We proceeded discussing the questions, and talked about math anxiety and the affect it has on your ability to do math. In the first day activities, I included some puzzlers, which were fun and seemed to create a relaxed and comfortable atmosphere.

I began the next class with the suggested Warm-up sheet. It seems to get the kids thinking and talking and laughing right away. The first question was a review of material covered on the first day. By using a fun math problem where they pick a number and need to perform several operations, and all end up with the same number, I found out that students didn’t know the basic operations by name (ie. what operation to perform when it says, find the sum, product, difference or quotient).
The next class, I used a group activity to review the importance of using parenthesis in mathematical expressions. It is a good opportunity for the students to work together and see how using different sets of parenthesis change the answers. This lead to a discussion of the problem solving strategy used to solve these problems. The strategy was guess and test and we discussed when this strategy might be affective.

The next class, I used a couple puzzlers, not related to math. The problem solving strategy was thinking outside the box. The questions concerned situations where you have to be a detective to solve a mystery and the victims who are dead are actually fish and not people. The other situation involves determining a person’s occupation from some clues that are provided. Both problems created some lively discussion and fun attempts to answer the question. Thinking outside the box encourages students to look at things differently and not just make the same old assumptions they have always made. This is also true of starting college and math class.
As we progress in the math book, there are more and more puzzler problems related to the lessons we are covering. During the chapter on fractions, I used several puzzlers which related to fractions. One had to do with dividing up a cake, which lead to a discussion on many shapes of cake and how to divide them into pieces.

The next puzzler had to do with taking a trip and going a fraction of the distance each day. Several problem solving strategies could be used including drawing a picture with required no calculations with fractions. This was a surprise to some who thought that you would have to do many fraction calculations to get an answer.

Outcome of the implementation of the strategy
I have found that the puzzlers encourage the students to interact more than they do during the rest of the class time. They seem to be making friends and be more willing to ask questions and discuss ideas with each other. The atmosphere of the class always starts out on a fun note and I think the students are more relaxed than when walking into a class and just thinking about the fact that they hate math, etc.

These problem solving strategies are also helpful to my GED students who I work with on a one-to-one basis. I always say there is more than one way to do a problem and it makes them feel more open to talking about what they were doing, and talking through how I would do it.

One challenge is to make the puzzlers hard enough to be challenging but not so difficult that no one can solve it. I sometimes give clues to lead them the direction they need to go, and usually someone can come up with a solution and have the opportunity to share it with everyone. I feel that using puzzlers to discuss problem solving strategies has been very successful with my math classes. I believe it serves many purposes in that it also relieves math anxiety by creating a more relaxed and fun atmosphere to do math in and gives all of us a chance to get to know each other on a more personal level and create a learning community.