Problem Solving 1
Joseph D. Williams
Indiana Wesleyan University
February 2, 2007
Statement of Academic Honesty. I have read and understand the sections in the Student
Bulletin and / or course syllabus relating to IWU’s Honesty / Cheating Policy. By affixing this
statement to the title page of my paper, I am certifying that I have not cheated or plagiarized in
the process of completing this assignment. If it is found that cheating and / or plagiarism did
take place in the writing of this paper, I understand the possible consequences of the act which
could include expulsion from Indiana Wesleyan University.
Problem Solving 2
Problem solving is a major key for students to be successful on Indiana Statewide Testing
for Educational Progress (ISTEP). The problem begins with the mastery of basic math skills. In
addition to these skills students must be able to read and comprehend what the problem is about
and asking for. There is no specific rule or strategy for teachers to teach problem solving.
Problem solving can range from a plethora of ideas or topics and be presented in a variety of
forms. It takes patience and understanding for students to become good problems solvers.
Patience is one thing that educators do not have a lot of time for, especially in a standard
curriculum driven education. Problems solving is a very important tool for society. In the real
world a person must be able to think on their toes and solve problems that are not expected.
More and more jobs are being outsourced and competition for jobs is at an all time high.
Problem solving is an area that has been showing statistically weak for Clark Pleasant
Middle School (CPMS). There has been a trend going on over the last few years in which
problem solving is falling farther and farther behind the state average on ISTEP. Only four years
ago CPMS scored 1.6 higher than state average, the following year it was .2 higher, last year
CPMS scored -.5 lower and this year problem solving scored -1.7 below state average (Indiana
department, 2006). This trend represents CPMS’s 7th and 8th grade students. Another source of
statistical data comes from Northwest Evaluation Association (NWEA) results. In mathematics
NWEA tests seven categories: problem solving, stats/ data/ probability, measurement, geometry,
algebra and functions, computation, and number sense. Out of all seven, problem solving scores
the lowest mean for 7th and 8th grade (Northwest, 2006).
Problem Solving 3
Not only is problem solving a critical issue for CPMS but according to the Program for
International Student Assessment (National center, 2004) the U.S. student population is falling
behind other countries. The U.S. students are scoring lower in problem solving than their peers
in 25 of 38 other countries and even the U.S. highest achievers were outperformed by other
countries (National center, 2004). Problem solving is a critical issue for all educators across the
nation and new strategies to teach problem solving need to be implemented.
To help students become successful in problems solving, research has been performed on
personalizing problems for students. Personalizing problems for students have generated better
performances on problem solving (Wiest, 2002). Students are more apt to become interested in
the problems and not just see the problem as a bunch of words or non-meaningful information.
According to this study, gender also played a role in interest to problems. Females were more
interested in problems dealing with younger children and males were more interested in
problems dealing with family businesses (Wiest, 2002).
“The use of different tools offers students the possibility of examining situations from
perspectives that involve the use of various concepts and resources” (Trigo, 2004, p. 2).
Students need to be able to model a problem. Technology is a tool that students are very
interested in and is a vital tool for success in the real world. A majority of students are visual
learners and if students can find a way to represent their problem other than just data, more
students can become successful. “It is well recognized that an important component in
mathematical instruction is to provide students with an opportunity to develop and use diverse
representational systems in order to solve a variety of mathematical tasks” (NCTM, 2000, as
cited from Trigo, 2004, p. 1).
Problem Solving 4
Teachers will also need to change their style of teaching to meet the growing needs of
students in problem solving. Japan has a higher percentage of students performing on problem
solving and also uses a different approach in teaching. Students are presented problems with
principals they have not learned and are allowed to work alone or collaboratively for a period of
time and then present their answers. The class then works together to uncover the math concepts
and reasoning behind the problem (Before it’s too late, 2000, p. 20). Students use the discovery
method regularly to solve problems and are forced to use problem solving skills that are often not
used in U.S. math courses. Students are required to problem solve, and this practice creates
better problem solving.
The statistical data and evidence provided in research details the need to help students
succeed in problem solving. The following solutions could be implemented to help students
reach this success.
Personalize Problems (Maybe)
Students could relate to problems that are personalized and make a connection to their own
lives. By creating a connection students would become more motivated to work on solving
problems. An opportunity could exist by students working together on similar problems they
are interested on, such as gender theme problems. A few downfalls are it would take time for
a teacher to get to know all of the students and it would be time consuming for a teacher to
create individual problems.
Incorporate Technology and Other Models (Maybe)
Representing problems in several forms only create avenues that help students solve
problems. A student who can model a problem is expressing that problem in a form that the
Problem Solving 5
student can understand. Technology is a tool that is becoming more incorporated into our
daily lives and students are growing up using technology. This is a great tool for students to
use to model a problem and a tool most students know more about than teachers. This leads
to a predicament for teachers because most teachers are not trained on how to use technology
in their classroom. Not only are teachers not trained but several school corporations do not
have technology widely available for students or teachers on a daily use. Also, with a
standardized curriculum teachers do not have a vast amount of time to teach a variety of
methods to represent problems. Teachers do not always know what works best for students
until everything is attempted and this takes a great amount of time in the classroom.
Discovery Method (Outstanding)
There is a saying the “practice makes perfect” and without practicing problem solving
students are not going to master problem solving. Students need to practice problem solving
on a daily or frequent basis. A great way to practice problem solving is through the
discovery method. Start out each day or as often as possible with a problem that students are
not familiar with. It is the job of the students to use trial and error to solve that problem.
Students can work by themselves or in a team and then present their solutions to the class.
Not only does this give students plenty of practice but the classroom then becomes student
lead. This will take practice by both the teacher and students until it becomes normal for the
class. There may be times when the students do not solve the problem and the teacher may
have to give suggestions to lead the class to the solution. A teacher will also need to
encourage students to attempt the problems and express that any attempt is a good attempt
when solving. This method will take a large amount of time and patience but a class where
students are doing all the thinking can only benefit students.
Problem Solving 6
In order for middle school students to become successful in problem solving, the choice
that would benefit the students the most would be the discovery method. This method would
give students practice on a frequent basis. It would be up to the teacher to decide how involved
the problem could be, but problem solving would become an integral part of class. Along with
the discovery method, the choice of teaching different forms of representation could be
incorporated at given moments. These moments would only provide more gateways to help
students become better problem solvers.
Students practicing and learning how to problem solve is the main goal for this solution.
Teachers could intertwine their own problems and create problems that lead into topics being
instructed. The following are action steps that could reach this goal.
1) Structure Planning: Time should be considered when planning to use the discovery
method. In order for students to practice, time for problem solving must be a factor in
2) Creating Problems: Teachers need to become creative and form problems that will spark
student’s interest. These problems can be either very involved or basic problems,
depending on time allotted in class. Great resources to use could be any math text book,
problems created by the teacher, or websites such as
http://www.nyiteez.org/MarcoPoloNY/index.php which is aligned to New York
standards but very informational or http://www.mathstories.com which requires a fee but
deals with specific story problems.
Problem Solving 7
3) Individual Time: Each student needs at least a few minutes to gather their thoughts about
the problem. This will allow each student to at least think about how they would solve a
problem before getting help.
4) Team Time: A classroom can be arranged in student teams. After there is a chance for
individual time, students would then work as a team to discover a solution. Students
would be collaborating and working with each other.
5) Review Class Time: Each team would present their solution. The review should include
the different approaches or representations that were presented. If the solution was not
discovered, suggestions could be provided or the problem could be set aside for the next
day. The teacher should point out important aspects presented and appraise student
Problem solving is a critical area that needs to be addressed. The action steps described
will enable students to practice problem solving. Through this practice students will learn a
better understanding of how to problem solve and be better equipped to function in the real
Problem Solving 8
Indiana department of education (2006). School Snapshot, Clark Pleasant Middle School, 3427.
Retrieved February 15, 2007, from
National Center for Education Statistics. (2004). International outcomes of learning in
mathematics literacy and problem solving: PISA 2003 results from U.S. perspective.
Retrieved February 15, 2007, from http://nces.ed.gov/pubs2005/2005003.pdf
National Commission on Mathematics and Science Teaching for the 21st Century. (2000). Before
it’s too late. Retrieved February 15, 2007, from
Northwest evaluation association (2006). NWEA results. Retrieved February 15, 2007, from
Trigo, M. (2004, Spring). The role of technology in students' conceptual constructions in a
sample case of problem solving. Focus on learning problems in mathematics. Retrieved
February 15, 2007, from Find Articles database.
Wiest, L. (2002, Spring). Aspects of word-problem context that influence children's problem-
solving performance - Statistical Data Included. Focus on learning problems in
mathematics. Retrieved February 15, 2007, from Find Articles database.