Problem Solving

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Problem Solving

Joseph D. Williams

MEDO87

Indiana Wesleyan University

EDU 550

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

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.

Information

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.

Solutions

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

Choice

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.

Operation

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

lesson planning.

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

efforts.

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

world.
Problem Solving    8

References

Indiana department of education (2006). School Snapshot, Clark Pleasant Middle School, 3427.

Retrieved February 15, 2007, from

http://mustang.doe.state.in.us/SEARCH/snapshot.cfm?schl=3427

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

http://www.ed.gov/inits/Math/glenn/report.pdf

Northwest evaluation association (2006). NWEA results. Retrieved February 15, 2007, from

https://reports.nwea.org/TeacherReport/teacherReport.asp

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.

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