By signing below the Principal Investigator assures to the IRB that all other investigators (co‑ investigators, collaborating

investigators, involved statisticians, consultants, or advisors) are fully aware of, and concur with, the project submission and that all Human Subjects training verification information provided in this form is accurate.



†††††† Michelle Roehler†††††††††† †††††††______________________________________††††††††††††††† †††† ____________________________

Principal Investigator (typed)††††††††††††††††††††††††††† Signature/Date†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Department


Title of Project:†† Middle School Studentsí Intuitive Techniques for Solving Algebraic Word Problems




I certify that (1) facilities are available to the investigator for assuring the safety and well‑being of human subjects involved; (2) I assume responsibility for ensuring the competence, integrity, and ethical conduct of the investigator(s); (3) no procedural changes relating to the human subjects involved will be allowed without prior review by the Human Subjects Committee; (4) I am satisfied that the procedures to be used for obtaining informed consent comply with the spirit and intent of DHHS regulations; (5) I certify that the investigator(s) is/are fully competent to accomplish the goals and techniques stated in the attached proposal; (6) the signed consent forms will be filed in the Departmental file and retained for a period of six years.



_____________________________________________________††† __________________________________________________

Head of Department, Dean of the College or comparable authority††††††††††† Signature


_____________________________________________________††† __________________________________________________

Title††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Date



We/I have examined the proposal cited above, and find that the information contained therein is complete; that the scientific aspects of the project include appropriate provision for protecting the rights and welfare of the human subjects involved; and that the required forms have been filled out properly in accordance with the Institutional Assurance filed by the University of Arizona with the U.S. Department of Health and Human Services.


____†††††† Exempt from Human Subjects Committee review.

____†††††† Minimal risk to human subjects (this category includes projects which require full committee review as well as those that may meet criteria for expedited review).

____†††††† Subjects at risk: full Human Subjects Committee review required.



_____________________________________________________††† __________________________________________________

Chairman of Departmental Review Committee (signature)††††††††††††††††††††††††††† Date






Verification of Human Subjects Training


All individuals conducting research involving human subjects (with or without financial support of any sponsoring organization or agency) must complete Human Subjects training. Those individuals include principal investigators, co-investigators and all other individuals involved in the conduct of research. Students and their advisors must meet the same standard as faculty and staff.


Please list all individuals involved in the above-cited research study



Research Role

(PI, Co-PI, Collaborator, Sub-I, Data Manager, Research Assistant, etc.)

Will this person be involved in the consenting process? *

Date Human Subjects training



Michelle Roehler


(YES)†††††† NO


Virginia Horak


(YES)†††††† NO




YES†††† †††††† NO




YES†††† †††††† NO




YES†††† †††††† NO




YES†††† †††††† NO




YES†††† †††††† NO



*Consent forms are to be signed and dated by the subject (or their legal representative) and by the Principal Investigator or Co-Principal Investigator (no other study personnel may sign as Investigator without prior approval of the IRB). Other study personnel involved in the consenting process may sign as Presenter, but not as Investigator.







Project Title:†††† Middle School Studentsí Intuitive Techniques for Solving Algebraic Word Problems


Principal Investigator(s) and Degree(s):Michelle Roehler, Undergraduate Mathematics Senior


Advisor (if applicable):Professor Virginia Horak, PhD


Status or Rank:Undergraduate, Associate Professor†††††††† Office Phone:(520) 626-5987


Department:Mathematics††††††††††††††††††† College:Science


Building and Room:Mathematics Building, Room 522


Campus PO BOX:210089



Sponsoring Agency:National Science Foundation, Department of Math and Science: VIGRE

Annual Budget (either total or per case amount):†† $1250


Project Period: September 2003 Ė May 2004 Budget Period:Fall Semester 2003



Will grant funds be deposited and administered by UA? Yes††††††††††††††††† (No)


or BRFSA (VAMC)?†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Yes††††††††††††††††† (No)



Please provide answers to all of the following questions. All projects submitted for review must be typed (no handwritten proposals accepted). If appropriate, after review by the Departmental Review Committee, please forward their opinions and comments along with the signatures on the Project Approval Form to the Human Subjects Committee, University of Arizona, 1350 N. Vine Avenue, PO BOX 245137, Tucson, Arizona 85724‑5137. Only one copy is required and will be retained for the Human Subjects Committee files and eventually microfilmed for a permanent record.





How do students approach word problems?Are students intuitively drawn to algebraic methods, or do their approaches differ from these commonly emphasized techniques?In this study, I 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.




In many classrooms, students are taught to tackle 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.





1.†† Number of subjects to be involved:10 students



2.†† Description of population to be recruited and rationale for their participation (indicate age range):

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.These students will be recruited because the focus of the study is possible changes in middle school studentsí solutions of algebraic word problems.Sixth and eighth graders would allow for studying this transition.



3.†† How are the subjects being recruited (submit a copy of advertisement for approval):

We will first contact the principal at the middle school for his/her approval.Once the principal has granted approval, we will then work directly with the teachers.We will ask each teacher to select the students and locate a quiet location for the problem-solving sessions.The teachers will also be responsible for setting up a meeting time for us to talk to the students about the project, and helping us establish contact with the parents.After the recruitment meeting, if the student would like to be part of the study, the studentís parent or guardian, as well as the student, must give consent.



4.†† What are the criteria for their selection:

The 6th grade students must have little or no formal algebraic experience.The 8th grade group must have some formal algebraic exposure.



5.†† What (if anything) is planned to encourage the recruitment of minorities and women:N/A





6.†† Summary:

††††††††††† I 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.I 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.I 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.I 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, I will have the student explain their problem solving strategies, elaborating on what they are doing at each step and why they chose each method.I 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.



7.†† Where will the project be conducted (room number or area; if not U of A location, site authorization allowing this research must be provided):

The study will be conducted at XXXXX Middle School.The problem-solving sessions will be held at the school, possibly in the studentsí own classroom(s).I will work with the studentsí teacher(s) to secure a quiet area for doing the research.A letter of authorization from the principal at XXXXX Middle School is attached.



8.†† How will the project be explained to the subjects:

After the teacher recommends the students, I will meet with them individually or in a group.I will give them a brief oral description of what I am doing and what would be asked of them (See enclosed script).If they are interested in being involved, I will give them a consent form for their parent/guardian to sign (See enclosed parental consent form).These forms will go into further detail about the project.If parent/guardian consent is obtained, I will then provide a separate assent form for the student to sign (See enclosed student assent form).When I am working on the study with the individual student, I will restate what I am doing and what is being asked of them.



9.†† If the subjects are minors, how will assent be secured:

††††† I will provide written assent and consent forms for the students and parent to sign and return (See enclosed).



10. How will you make it clear to the subjects that their participation is voluntary and that they may withdraw from the study at any time they wish to discontinue participation:

††††† I will make it clear in the assent and consent forms that the students are under no obligation to participate and may withdraw at any time.I will restate this prior to and during the one-on-one session with the student, as well.



11. Will your project utilize (check):††††††††††††††††††††††††††††† Questionnaires (submit a copy)

÷††††††††† Interviews (submit sample of questions)

÷††††††††† Observations (submit a brief description, stating your role in the activities observed)

††††††††††† Medical records review




12. Who will have access to the gathered data:

††††††††††† Professor Virginia Horak and Michelle Roehler will be the only people with access to the data.



13. How will confidentiality of the data be maintained:

No students will be identified by name.In addition, the school and district will also remain confidential.Each student and the school will be assigned a false name that will be used as identification throughout the documentation.Only the investigators, Michelle Roehler and Dr. Virginia Horak, will have access to any data collected.



14. Will a Certificate of Confidentiality (through Federal agency) be utilized:NO



15. How will the data be recorded (instruments, notes, etc.):

The study will utilize an audio tape recorder to tape the interviews, and parts of the interview will be transcribed for analysis.The studentsí written work will be used as artifacts for the study.The observer may take notes throughout the interview and observation.


16. What are the plans for retention of data:

The interview transcripts will be saved on 3 ĹĒ diskettes or written by hand.The tapes, artifacts, written and electronic transcriptions, and notes will be retained for five years in the University of Arizona Mathematics Building, Room 522, the office of Dr. Virginia Horak.



17. What are the plans for future use of data as part of this study or use beyond this study:

A VIGRE research report will be written based on the data, with the possibility of presentations or publications to follow.



18. How will the data be destroyed and at what point in time:

After five years, the tapes, artifacts, written transcripts, and notes will all be destroyed.The tapes will be cleared and paperwork will be shredded.The disks containing the transcripts in electronic form will be erased.



19. Where will the signed consent forms be stored (list administrative office and room number):

††††† The consent forms will be stored in the University of Arizona Mathematics Building, Room 522.Copies will be stored in the XXXXX School District Office of Accountability and Research (per XXXX School District requirements).†††




20. What are the potential benefits to the subjects:

††††††††††† There are no benefits to the subjects.



21. What may be revealed that is not currently known:

The study may provide additional insight into how adolescent students utilize algebraic and non-algebraic methods in solving word problems.



22. Will monetary or other compensation be offered to the subjects:NO



23. What are the costs to the subjects (monetary, time):

The only cost will be the subjectsí time.We will work with the teachers to find times that will not take away from important classroom time, i.e. during recess, down time in the classroom, etc.



24. What risks to the subject are most likely to be encountered (physical, psychological, sociological):

††††††††††† There is minimal risk due to the possibility that the student may feel nervous or uneasy around math.



25. What approach will you make to minimize the risks:

††††† It will be clear to the students that they are not obligated to participate or complete the problems, and they will not be graded.The interviewer/observer will have time to work and observe in the classroom prior to the study to make the students more at ease.Thus, the students will know the interviewer/observer, having interacted with her several times before the interview.This will prevent any uneasiness on the part of the students and make them comfortable and open during the interview session.



††††† See attached written consent forms for parent/guardian and student.



††††† See attached possible interview questions.




††††† I will be working with each student individually.To understand the studentsí approaches and problem-solving methods, I will need to interact with him or her throughout the session.I will encourage the student to explain each step of the problem-solving process.As they solve each word problem, I will observe which strategies or ideas they present, which tools they utilize, and pose questions based upon my observations at each step that will reveal the studentís reasoning.I will take notes on the studentís confidence, hesitations, use of tools, and other important observations during the session that would not be recorded on the audiotape.After the session, the audiotape and studentís work will be used for further analysis after the problem-solving session.I will compare and analyze each studentís approach to obtain a clear understanding of the use of algebra or non-algebra skills in solving word problems.