____________________ Project Number (Assigned by
Accountability & Research) |
XXXXX UNIFIED
SCHOOL DISTRICT
Office of Accountability and
Research
REQUEST TO
CONDUCT RESEARCH WITHIN THE DISTRICT
1. Today's
Date
October
29, 2003
2. Full
Names
Michelle Roehler,
Undergraduate Mathematics Student, University of Arizona
Dr.
Virginia Horak, Mathematics Education Professor, Department of Mathematics,
University of Arizona
3. Complete
Mailing Address
University
of Arizona
Department of Mathematics
617 N. Santa Rita
Campus Box #210089
Tucson, AZ 85721
4. Telephone
Number
(520) 626-5987
5. Organization
or Institution
The
research will be done through the Department of Mathematics at the University
of Arizona.
6. Purpose
This study is an undergraduate research
project done through the Department of Mathematics, funded by the National
Science Foundation’s VIGRE program.
7. Student
Achievement
This study will provide
insight into students’ intuitive approaches to algebraic word problems and
their use of algebraic methods before and after algebraic instruction. The results will hopefully suggest teaching
techniques that will build upon a student’s inherent knowledge when algebra is
taught in middle school. These techniques
may assist teachers in increasing students’ algebraic skills and understanding,
which will make them more prepared for advanced algebraic problem solving.
8. Signature
of Advisor
(if thesis or dissertation)
9. Research
Project Title
Middle School Students’
Intuitive Techniques for Solving Algebraic Word Problems
10. Purpose of
Study
The
purpose of this study is to explore middle school students’ methods for solving
word problems and their utilization of algebra for problem solving. This research will provide insights into
middle school students’ grasp of variables and their ability to develop
equations with or without previous formal algebraic experience. It will also reveal which techniques are
more intuitive to a student and might indicate ways to present algebraic
methods that build upon these skills.
The research questions to be answered
are:
1.
What techniques do 6^{th} and 8^{th}
grade students use in solving word problems that can be approached using
algebra?
2.
How do these problem-solving techniques differ
before and after students have been exposed to formal algebraic instruction in
a high school credit algebra course?
3.
Are students intuitively drawn to algebraic methods,
or do their approaches differ from these commonly emphasized techniques?
In many classrooms, students are taught to tackle
algebraic word problems with specific algorithms for each problem type, and
they often develop a reliance on cookie-cutter equations without fully
comprehending the underlying problem and the algebra used to solve it. Since many students do not understand the
concepts behind these methods, it is important to explore a student’s inherent
approaches to problem solving and algebra.
In a study of 6^{th} graders’
pre-instructional use of equations, Swafford and Langrall discovered that “sixth-grade students in this study
showed a remarkable ability to generalize problem situations by describing
relationships and writing appropriate equations using variables” (Swafford and
Langrall, 2000). On the other hand,
students in this study were more able to represent the relationships verbally
than symbolically, and few used their equations, even if correct, to obtain a
solution. This suggests there is some inherent
understanding of algebraic concepts, but the students lack the ability to tie
this intuitive understanding to formal algebraic methods that are fundamental
to higher-level algebra.
Other studies have shown that when
students build upon their own intuitive methods, they have a deeper
understanding of the underlying algebraic concepts. For example, a study by
Nathan and Koedinger suggests that contrary to many curriculums, students
develop verbal problem solving skills, i.e. the ability to work with word
problems, before they can comprehend symbolic problems. The authors recommend teaching strategies
that build more upon the student’s informal methods for solutions and the
student’s verbal skills (Nathan and Koedinger, 2000).
This study seeks to identify some of the
problem-solving techniques inherent to middle school students before and after
formal algebraic instruction. The data
obtained will provide insight into students’ intuitive grasp of specific algebraic
concepts, and we will use this information to suggest teaching techniques that
will help teachers naturally build on these methods.
12. Methods/Techniques
This
study is a qualitative study that will utilize ethnographic techniques. The researchers will employ interview
techniques while observing, taking field notes, and tape recording the work of
students as they solve word problems presented to them. The primary investigator is Michelle Roehler. She will work with each student
individually. First, the student will
be asked a few questions regarding their previous mathematical experience, favorite and least
favorite mathematical topics, etc. (see attached questions). Word problems will be typed on sheets of paper for
the student to work on, with one on each sheet (see attached questions). Tiles, rulers, graphing paper, a calculator,
and other problem solving tools will be available to the student on the table. The researcher will first let the student
know that they are not required to complete the problems if they do not want
to, and they will not be graded. They
are free to quit whenever they wish.
They may use any of the tools on the table to help them. Ms. Roehler will then give the student the
first problem to read. After going
through the problem requirements and ensuring the student understands what is
expected, the student will work on the problem alone. The investigator will observe how each student sets up and finds
the solution to the problem, paying close attention to the tools utilized. When the problem is completed or the student
decides that they are finished, she will have the student explain their
problem- solving strategies, elaborating on what they are doing at each step
and why they chose each method. She
will repeat this process for a total of three word problems for each
student. All of the students will
receive identical problems in the same order.
Each problem solving session will last approximately 20 minutes.
Data
Collection
All
problem-solving session will be recorded on audiotape and parts will later be
transcribed. The students’ written work
will be used as artifacts for the study.
The observer may take notes throughout the interview and
observation.
b. Method(s) of data analysis (2 pages or
less)
Following all of the problem-solving sessions, the
researchers will transcribe the interviews.
The interviews, field notes, and artifacts from the students’ work then
will be analyzed for trends in the data that could suggest the consistent use
of certain techniques by 6^{th} and/or 8^{th} graders in
solving problems for which algebra techniques would be useful tools. The researchers will look for consistencies
within each grade level and changes in the use of techniques across the grade
levels.
c. Number of subjects and grade levels needed
The study requires one group
composed of five 6^{th} grade students (11-12 years old) and another
with five 8^{th} grade students (13-14 years old) from a XXXXX School
District middle school. The two groups
will consist of at least two boys and two girls each. We will work with two teachers, one 6^{th} grade and one
8^{th} grade for recruiting students.
d. Number and names of school sites (or departments) you need to complete
study (be specific)
XXXXX Middle School
e. Describe
any "treatment" to be
applied to subjects (not more than 1 page)
There will be a 20-minute
problem-solving/interview session with each student. During this time, the students will work to solve three word
problems.
There will be two
investigators for this study. Dr.
Virginia Horak is an associate professor of mathematics at the University of
Arizona.
Dr. Horak has been a mathematics educator at the University of Arizona
and the Tucson Unified School District.
She has been involved in teacher preparation, professional development
of inservice teachers, and mathematics education research since 1977. Michelle Roehler is a senior
undergraduate mathematics student at the University of Arizona working on a
research project funded by the National Science Foundation. She successfully completed a research
project with the Department of Mathematics in Spring 2003. Each investigator has successfully completed
the required Human Subjects Training through the University of Arizona.
g. Resources needed
1.
Time: Each problem-solving session will take
approximately 20-30 minutes per student.
For 10 students, this is approximately 4-5 hours total. However, the sessions are not required to be
held on the same day, and we will work with each teacher to find times that
will minimize the loss of classroom time, such as utilizing before or after
school time, classroom down time, etc.
There will be very minimal time commitment from teachers and
administrators in this study.
2. Location: One small, quiet area set apart from any
distractions will be required for the problem-solving session. A separate room is preferred.
3. Materials: We will use a calculator from the classroom
that the student is familiar with. We
will provide all other materials.
13. Instruments
To Be Used
(e.g. tests, surveys, observation forms, data collection forms).
We will be using three word
problems for the problem-solving session.
These problems were developed using examples of past researchers’ works
and the XXXXX School District texts for 6^{th} and 8^{th} grade
mathematics. See attached
problems. During the problem-solving
session, the researcher will ask the students questions that probe their
thinking about the problems or the techniques they are using. See attached possible questions.
14. Use of
Results
The results of this study will be the
basis for Michelle Roehler’s undergraduate research project. The data obtained will be analyzed and used
as the foundation for a final report.
There is a possibility of future publication of this report or the use
of data as part of a poster session for undergraduate research at a regional or
national meeting. Strict
confidentiality will be maintained to protect the identities of the students,
school, and district involved. Each student and the school will be assigned a false
name that will be used as identification throughout the documentation. The information gathered from this investigation is
expected to be valuable in assessing students’ intuitive understanding of
algebra. The results will be used to
study which techniques are most inherent to middle school students and possibly
suggest alternative methods that will utilize these techniques in teaching
algebra. These insights will be shared
with the mathematics education community.
15. Benefit of
Study to District
This study will provide
insight into students’ intuitive approaches to algebraic word problems and
their use of algebraic methods before and after algebraic instruction. The results will hopefully suggest teaching
techniques that will build upon a student’s inherent knowledge when algebra is
taught in middle school. These
techniques may assist teachers in increasing students’ algebraic skills and
understanding, which will make them more prepared for advanced algebraic
problem solving.
16. Legal
Requirements
a. Terms and Conditions - sign and date the enclosed form.
b. Parent Permission Form - attach form and include:
1. that the project has "been tentatively
approved by the XXXXX School District."
2. that results will be kept
"confidential."
3. the place where parent given consent by signing name.
4. the statement as to what parent is
consenting to let research do with subject.
5. the phone number where researcher can be
contacted if questions.
c. Teacher Permission Form (if applicable) -
approval by teacher is needed if researcher is using classroom time with
his/her students.
SUMMARY OF REQUEST TO CONDUCT RESEARCH
XXXXX School District Office
of Accountability and Research
Name: Ms.
Michelle Roehler, Dr. Virginia Horak |
Date: October
29, 2003 |
Position/Title/Institution:
Undergraduate
Mathematics Senior at the University of Arizona
Associate
Professor in the Department of Mathematics at the University of Arizona
Title of Research:
Middle School Students’
Intuitive Techniques for Solving Algebraic Word Problems
Purpose of Research:
In this study, we will
explore middle school students’ methods for solving word problems and their
utilization of algebra for problem solving.
This study will provide insights into middle school students’ grasp of
variables and their ability to develop equations with or without previous
formal algebraic experience. It will also
reveal which techniques are more intuitive to a student and might indicate ways
to present algebraic methods that build upon these skills.
Hypothesis/Questions:
The
research questions to be answered are:
1.
What techniques do 6^{th} and 8^{th}
grade students use in solving word problems that can be approached using
algebra?
2.
How do these problem-solving techniques differ
before and after students have been exposed to formal algebraic instruction in
a high school credit algebra course?
3.
Are students intuitively drawn to algebraic methods,
or do their approaches differ from these commonly emphasized techniques?
Methods/Treatment/Instruments:
The primary investigator is
Michelle Roehler. She will work with
each student individually. First, the
student will be asked a few questions regarding their previous mathematical experience,
favorite and least favorite mathematical topics, etc. (See attached
problems.). Several word problems will
be typed on sheets of paper for the student to work on, with one on each sheet
(See attached questions.). Tiles,
rulers, graphing paper, a calculator, and other problem solving tools will be
available to the student on the table.
She will first let the student know that they are not required to
complete the problems if they do not want to, and they will not be graded. They are free to quit whenever they
wish. They may use any of the tools on
the table to help them. Ms. Roehler
will then give the student the first problem to read. After going through the problem requirements and ensuring the
student understands what is expected, the student will work on the problem
alone. The investigator will observe
how each student sets up and finds the solution to the problem, paying close
attention to the tools utilized. When
the problem is completed or the student decides that he/she is finished, the
researcher will have the student explain his/her problem- solving strategies,
elaborating on what was done at each step and why he/she chose each
method. Ms. Roehler will repeat this
process for a total of three word problems for each student. Each student will receive identical problems
in the same order. Each problem solving
session will last approximately 20 minutes.
There will be a 20-minute problem-solving/interview
session with each student. During this
time, the students will work to solve three word problems.
We will be using three word
problems for the problem-solving session.
These problems were developed using examples of past researchers’ works
and the XXXX School District texts for 6^{th} and 8^{th} grade
mathematics. See attached problems.
Number of Students/ Teachers:
The study requires one group composed of five 6^{th}
grade students (11-12 years old) and another with five 8^{th} grade
students (13-14 years old) from a XXXXX School District middle school. The two groups will consist of at least two
boys and two girls each. We will work
with one 6^{th} grade teacher and one 8^{th} grade teacher for
recruiting the students.
Names of schools:
XXXXX Middle School
Time/resources needed:
Each problem-solving session will take approximately
20-30 minutes. For 10 students, this is
approximately 4-5 hours total. However,
the sessions are not required to be held on the same day, and we will work with
each teacher to find times that will minimize the loss of classroom time. We will use a calculator from the classroom
that the student is familiar with. We
will provide all other materials.
Additional Comments:
You will need to obtain
ACTIVE (signed parental consent for each student) parental consent before
having contact with students.