____________________

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

 

††††††† Dr. Virginia Horak

††††††† 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 Foundationís VIGRE program.

 

7.†††† Student Achievement

This study will provide insight into studentsí 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 studentís inherent knowledge when algebra is taught in middle school.These techniques may assist teachers in increasing studentsí 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 Studentsí Intuitive Techniques for Solving Algebraic Word Problems

 

 

 

10.Purpose of Study

The purpose of this study is to explore middle school studentsí methods for solving word problems and their utilization of algebra for problem solving.This research will provide insights into middle school studentsí 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 6th and 8th 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?

 

  1. 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 studentís inherent approaches to problem solving and algebra.

 

††††††† In a study of 6th gradersí pre-instructional use of equations, Swafford and Langrall discovered that ďsixth-grade students in this study showed a remarkable ability to generalize problem situations by describing relationships and writing appropriate equations using variablesĒ (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 studentís informal methods for solutions and the studentís 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 studentsí 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

 

  1. Research Design/Data Collection

ResearchDesign and Methodology

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 studentsí 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 studentsí work then will be analyzed for trends in the data that could suggest the consistent use of certain techniques by 6th and/or 8th 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 6th grade students (11-12 years old) and another with five 8th 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 6th grade and one 8th 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.

 

  1. Investigators - number, names and qualifications

 

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 researchersí works and the XXXXX School District texts for 6th and 8th 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 Roehlerís 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 studentsí 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 studentsí 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 studentís inherent knowledge when algebra is taught in middle school.These techniques may assist teachers in increasing studentsí 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 Studentsí Intuitive Techniques for Solving Algebraic Word Problems

 

Purpose of Research:

 

In this study, we will explore middle school studentsí methods for solving word problems and their utilization of algebra for problem solving.This study will provide insights into middle school studentsí 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 6th and 8th 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:

 

Research Methodology

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.

 

Treatment

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.

 

Instruments

We will be using three word problems for the problem-solving session.These problems were developed using examples of past researchersí works and the XXXX School District texts for 6th and 8th grade mathematics.See attached problems.

 

 

Number of Students/ Teachers:

The study requires one group composed of five 6th grade students (11-12 years old) and another with five 8th 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 6th grade teacher and one 8th 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.