____________________ Project Number (Assigned by
Accountability & Research) |
XXXXX SCHOOL
DISTRICT
Office of Accountability and
Research
REQUEST TO
CONDUCT RESEARCH WITHIN THE DISTRICT
1. Today's
Date
October
27, 2003
2. Full
Names
Michelle Roehler,
Undergraduate Mathematics Student, University of Arizona
Dr.
Virginia Horak, Mathematics Education Professor, 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 answered 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?
11. Theoretical
Framework/Rationale (not more than 1 page)
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
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). 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 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.
Each student 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)
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 XXXX 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.
Virgina Horak is an associate professor of mathematics at the University of
Arizona. Dr. Horak has experience… 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.
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 recess, 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 TUSD texts for 6^{th} and 8^{th} grade
mathematics. See attached problems.
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. 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 teaching 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 Tucson Unified 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.
RETURN
TO: |
Dynah
Oviedo-Lim, M.A. Tucson
Unified School District Office of
Accountability and Research 442 E. 7^{th}
St. Tucson,
AZ 85705 Dynah.Oviedo@tusd.k12.az.us |
SUMMARY OF REQUEST TO CONDUCT RESEARCH
TUSD Office of
Accountability and Research
Name: Ms.
Michelle Roehler, Dr. Virginia Horak |
Date: October
27, 2003 |
Position/Title/Institution:
Associate
Professor in the Department of Mathematics at the University of Arizona
Undergraduate
Mathematics Senior 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 answered 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 questions). 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 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. Each student will
receive identical problems in the same order.
Each problem solving session will last approximately 20 minutes.
We will be using three word
problems for the problem-solving session.
These problems were developed using examples of past researchers’ works
and the TUSD 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 Tucson Unified 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:
Utterback 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, such
as recess, classroom down time, etc. 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.
RETURN
TO: |
Dynah
Oviedo-Lim, M.A. Tucson
Unified School District Office of
Accountability and Research 442 E. 7^{th}
St. Tucson,
AZ 85705 Dynah.Oviedo@tusd.k12.az.us |
In
submitting this request, the researcher agrees to adhere to the following terms
and conditions, the violation of which will be grounds for immediate
termination of the research project.
1. The researcher will obtain written permission (i.e. active consent) from
each parent or guardian and will advise each subject that
participation is voluntary.
2. For
studies involving students, no study is officially approved until all parental
consent forms are on file in the Office of Accountability and Research.
3. The
researcher will advise participant of the right to refuse to answer any
question, either written or oral. Such
a statement will appear on any written instruments, and will be made orally
before any interview.
4. Electronic recording of any information must be done with full
knowledge of the subject and with the permission of the parent or guardian.
5. Only the research project specifically approved by the District
will be conducted. The approved
methodology will be followed in detail.
Any modification of the approved methodology must have the written
approval of the Office of Accountability and Research.
6. Only the approved researchers may conduct the research. Any additional researchers must be approved
in writing by the Office of Accountability and Research.
7. While conducting the research, the researcher will act at all
times in a professional manner, and will minimize disruption of the normal
instructional process.
8. During the research, the researcher will cooperate fully with
District personnel especially as they monitor the progress of the research.
9. The researcher will not design the research to depend on District
personnel clerical support, or supplies and materials.
10. The researcher will not contact District site administrators or any
other District personnel, students, or parents until the research request has
been processed and approved.
11. The researcher will adhere to all agreed-upon deadlines, and will
contact the Office of Accountability and Research when research in the District
is completed.
12. Reports will not
refer to persons or school or the District by name.
13. One unbound copy of the results of the research will be submitted
to the Office of Accountability and Research.
I AGREE TO ALL THE ABOVE TERMS
AND CONDITIONS.
___________________________________________________________________ Signature |
____________ Date |
TUSD
Office of Accountability and Research
6/2003