Qualitative Research Method Assignment
Effect of a Graphing Calculator on High School Trigonometry Students
Pamela R. Hudson Bailey
The study is very interesting and absolutely worth doing. We kind of run out of gas when we get to the data analysis section. When you take the Qual methods class, you will get a good handle on how to pull the knowledge out of the transcript.
I’d add an abstract page as well after this.
Effect of a Graphing Calculator on High School Trigonometry Students
Purpose
The purpose of the
study will be to explore the relationship between students learning
mathematical concepts and graphing calculators. Sure sounds
qualitative so far! Concerns regarding graphing calculator usage
to help students make connections between multiple representations that are
enhanced by using the technology will be investigated. We would want to
develop these concerns in the introductory material before the method section. This
study is intended to replicate and extend the work of Sang Sook Choi-Koh ’s (2003)
and will involve five students at various academic levels being observed during
a trigonometric unit. Choi-Koh’s study involved only one student who did not
have a positive attitude toward mathematics but was efficient in using a
graphing calculator.
Research
Questions
Graphing calculator usage will be observed during a unit on graphing trigonometric equations, solving trigonometric equations, composite functions and inverse trigonometric functions. The researcher will be analyzing questions with regard to Bloom’s Taxonomy, mathematical thinking, and multiple representations using a graphing calculator as portrayed by Choi-Koh (2003). The research questions include:
1. What thought patterns were exhibited by students during graphing calculator based investigations?
2. What was the student’s attitude toward the learning experience while using a graphing calculator?
3. What mathematical connections did the student make between multiple representations?
4. What are some positive and negative aspects of incorporating graphing calculator technology into mathematics instruction?
Method
Design
In order to address the research questions a multiple instrumental case study will be employed. The study will involve an examination of five secondary students thinking processes while learning mathematical concepts within a technological environment.
Participants and Setting
Five
students will be chosen from two different trigonometric classes being taught
by the same teacher. Each will be chosen based on their current grade in the
classroom, one from each level A through F. The students attend an urban school
located in northeast
Data Collection Method
The research study will consist of observations and audio taping of students during classroom instruction. You might also consider and “over the shoulder” video taping so you can see what they are doing. Another wrinkle might be to use a “virtual calculator” on a computer screen and collect the students’ eye movements. The eye movements can then be played back as a stimulated recall prompt. Participants in the study will be seated together and work as a team in each of the classes. Ah the eye movement thing would have to be individual. Still, if you ever want to try it, I have the rig. Audio taping students using a think-aloud process will aid the researcher in gaining insight into their analytical thinking and reasoning. Each day the tapes will be transcribed to determine the levels of Bloom’s Taxonomy students are employing, mathematical thinking being applied, and what types and to what extent multiple representations are being incorporated into students thinking. OK. There are other taxonomies and I am not always sure that Bloom’s works for high performers. Nevertheless, it is a structure that will work. The student’s experiences, feelings, and behaviors will also be acknowledged through the observations and on the transcribed tapes.
Prior to the study beginning the participants will take a test, TYPE?, Good question. In the standardized, individually administered domain, I’d suggest the three math subtests from the Woodcock-Johnson-III standard battery. After that, it may be better to create some sort of researcher –created task to measure the skills that you hypothesize are necessary to carry out the research tasks. to determine their feelings, reactions, and competence about mathematics and using the graphing calculator. The same test will be repeated at the end of the study to determine if the use of the graphing calculator in an investigative student-centered approach changed their perceptions of what?. The pre-test and post-test are not part of the procedures incorporated by Choi-Koh (2003) however the same seven tasks will be used for the investigations. I think thsat it is a very good idea to include them. If there is a change in attitude accompanied by increased efficacy in calculator use, but no change without concurrent changes in efficiacy, you have a major clue to the riddle… One task per class period, block, of approximately 90 minutes will be facilitated by the trained teacher. The tasks described by Choi-Koh (2003) will consist of the following:
1. Investigating and creating graphs of trigonometric functions,
2. The
effects of “a” in 
,
3. The
effects of “c” and “d” in ,
4. The
effects of “b” in ,
5. Predict and test hypothesis of composite trigonometric functions,
6. Use graphical methods to solve trigonometric equations, and
7. Analyze graphs of the reciprocal and inverse trigonometric functions.
Each of the above tasks involves students analyzing graphs illustrating various applications as well as determining equations to represent real-life situations. After all the tasks have been completed, students in the study will take the post-test.
Proposed
Preliminary Data Analysis
The pre-test and post-test will probably reveal that a student’s feelings about mathematics will improve as his or her involvement in the learning process increases. Agreed but we should speak to the way that we will elicit these findings from the raw data… Student’s confidence in doing mathematics and using the graphing calculator to explore a hypothesis will increase. Progression through Bloom’s Taxonomy will be slow as student mathematical understanding improves and becomes more analytical and reflective. Perhaps. I have a little different take on this stuff since I learned how to tap expertise in the eye movement world. This cycle will begin again with a student obtaining knowledge at the new level then re-entering the analytical and application stage. A student will use the graphing calculator to explore the trigonometric functions but as confidence grows calculator usage will decrease. Connections between graphical, tabular, analytical, and verbal will be varied but all approaching higher levels of thinking and also occurring in a cyclic fashion.
Positive outcomes using graphing calculators will include the ability for a student to explore graphs that would have taken a great deal of time to create by plotting points. Visualization will enable a student to predict and make conjectures by comparing and contrasting several graphs thereby making connections between graphs, tables, words, and equations. Student interactions and motivation will increase with the implementation of real-life situations. Negative aspects may include interpreting decimal approximations of radian measures and outputs. Button pushing steps and explicit prompting to obtain the “correct” response from the class will need to be discouraged. Questions asked by the teacher need to encourage investigations but not be so challenging that they turn off student participation. Teachers unprepared or unwilling to facilitate exploratory lessons will hamper student mathematical conceptual growth and lower self-esteem and confidence.
Research Tasks to be Completed by
Participants
Adapted from Choi-Koh (2003).
Task 1: Investigating
and creating graphs of trigonometric functions
Substitute various angles into x of sin x, cos x, and tan x and compare their values.
Observe and describe the graph of y = sin x.
Observe and describe the graph of y = cos x.
Observe and describe the graph of y = tan x.
What are the difficulties in using the Texas Instrument graphing calculator?
Task 2: The effects
of “a” in
Observe and find the amplitude and periodicity of 
.
Observe and find the amplitude and periodicity of 
.
Observe and find the amplitude and periodicity of 
.
Observe and find the amplitude and periodicity of 
.
Observe the differences between the graphs and describe the role of “a”.
Repeat the above tasks for cosine and tangent functions.
Task 3: The effects
of “c” and “d” in
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe the differences between the graphs and describe the role of “c”.
Repeat the above tasks for cosine and tangent functions.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe the differences between the graphs and describe the role of “d”.
Given a graph on the calculator, determine the algebraic equation.
Repeat the above tasks for cosine and tangent functions.
Task 4: The effects
of “b” in
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
and find the amplitude and periodicity.
Observe 
, 
and find the amplitude and periodicity.
Observe 
, 
and find the amplitude and periodicity.
Observe the differences between the graphs and describe the role of “b”.
Repeat the above tasks for cosine and tangent functions.
Task 5: Predict and
test hypothesis of composite trigonometric functions
Conjecture the graph of 
and verify it with the
calculator.
Conjecture the graph of 
and verify it with the
calculator.
Conjecture the graph of 
and verify it with the
calculator.
Conjecture the graph of 
and verify it with the
calculator.
Conjecture the graph of 
and verify it with the
calculator.
Conjecture the graph of 
and verify it with the
calculator.
Task 6: Use graphical
methods to solve trigonometric equations
Solve 
at 
.
Find the general solution for 
.
Solve 
at .
Solve 
at .
Task 7: Analyze
graphs of the reciprocal and inverse trigonometric functions.
Draw the inverse functions, 
, 
, and 
by their definitions.
Compare the inverse functions with reciprocal functions.
Compare 
, 
, and 
with the basic
trigonometric functions.
What is the role of “a” in 
?
What is the role of “b” in 
?
What is the role of “c” in 
?
What is the role of “d” in 
?
Repeat the above tasks for cosine inverse and tangent inverse functions.
References
Choi-Koh, S. S. (2003). Effect of a graphing calculator on a 10th-grade student’s study of
trigonometry. The Journal of Educational Research, 96(6), 359-369.
Effect of a Graphing
Calculator on High School Trigonometry Students
INFORMED CONSENT FORM
RESEARCH PROCEDURES
This research is being conducted to explore the relationship between students
learning mathematical concepts and graphing calculators. Connections made
between multiple representations that are enhanced by using the technology will
be investigated along with attitudes and feelings regarding learning
mathematics. If you agree to participate, you will be asked to take a pretest,
participate in 7 investigative activities using a graphing calculator, each
lasting one block (90 minutes), and take a posttest.
RISKS
"There are no foreseeable risks for participating in this research."
BENEFITS
The benefits to you include the opportunity to learn, investigate, and discover
concepts related to graphing trigonometric functions and making connections to
the equations. In addition, the benefits to teachers and students will be the
self-confidence to initiate exploration, make conjectures based on the
exploration and express the results verbally and mathematically.
CONFIDENTIALITY
The data in this study will be confidential. Student’s names will be changed on
pretests and posttests with a pseudonym for researcher usage. Activities
(tasks) conducted for the investigations may have your name on them which will
be for teacher usage only to guide further instruction. All transcribed
material will use the pseudonym name. Researcher will be the only individual to
have access to participant pseudonyms.
PARTICIPATION
Your participation is voluntary and you may withdraw from the study at any time
and for any reason. If you decide not to participate or if you withdraw from
the study, there is no penalty or loss of benefits to which you are otherwise
entitled. There are no costs to you or any other party
ALTERNATIVES TO PARTICIPATION
Students not participating in the study will receive the same instruction. They
will be placed in groups and participate in the investigative activities. The
only difference will be that non-participants will not be audio recorded or
observed by the researcher. There are no costs to you or any other party
CONTACT
This research is being conducted by Pamela Bailey, department at George Mason University. She may be reached at
540-834-2500 ext. 1024 for questions or to report a research-related problem.
You may contact the George Mason University Office of Research Subject
Protections at 703-993-4121 if you have questions or comments regarding your
rights as a participant in the research.
This research has been reviewed according to George Mason University procedures
governing your participation in this research.
CONSENT
I have read this form and agree to participate in this study.
__________________________ _______
I agree to audio (video) taping.
Name
__________________________ _______
I do not agree to audio (video)
Date of Signature taping.
Version date: