The evolution of a study on the role students perceive the graphing calculator plays in their mathem

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The evolution of a study on the role students
perceive the graphing calculator plays in their
mathematical experiences
Tool or Teddy Bear?
Allison McCulloch Rutgers University MetroMath
Fellow
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Development of my dissertation idea
?
small literature synthesis for class
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Development of my dissertation idea
?
small literature synthesis for class
Research Course.. 2 student study
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Development of my dissertation idea
?
small literature synthesis for class
Research Course.. 2 student study
Test ideas 14 student study
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Development of my dissertation idea
?
small literature synthesis for class
Research Course.. 2 student study
Test ideas 14 student study
Further test ideas and
methods 4 students
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Development of my dissertation idea
?
small literature synthesis for class
Research Course.. 2 student study
Test ideas 14 student study
Further test ideas and
methods 4 students
Now the BIG study!
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What I learned from reading
There have been a lot of studies that address how
students that use the graphing calculator perform
on course or standardized assessments. (ex
Ellington, 2003 Quesada Maxwell, 1994
Scheuneman, et. al., 2002 Smith Shotsberger,
1997). There have been studies on how graphing
calculators are used as a learning tool in a
classroom situation or for a specific topic.
(ex Choi-Koh, 2003 Doerr Zangor, 2000
Ruthven, 1990)
Quantitative
Qualitative
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Initial questions
How do students use the graphing calculator when
they are working on problems independently? Why
do they choose to use the graphing calculator as
a tool to facilitate the problem solving process?
How?
Why?
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What I learned from the first and second study

• 2 students 14 students
• AP Calculus AB students
• Classroom observations
• Homework journals
• Task-based interviews
• Categories for calculator use as a tool
• Triggers for calculator use
• Data collection and analysis methods that work
  (and dont work).

Participants
Methods
Findings
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Categories for calculator use as a tool
Role of Graphing Calculator as a Tool
Description of Student Actions
Numeric Computational Symbolic Computational
Data Collection and Analysis Visualizing
Evaluating numerical expressions and
rounding Using the CAS capabilities Gathering
data, controlling phenomena, finding
patterns Finding symbolic functions, displaying
data, interpreting data, solving equations
(adapted from Doerr Zangor, 2000)
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Triggers for calculator use
Trigger
Description of Student Actions
Skipping a Step Getting Oriented Saving
Time New Approach Checking
The student does not know how to approach the
task by hand, but uses the calculator effectively
to meet a goal. The student uses the calculator
as a starting point with the purpose of getting a
feel for the problem. The student know how to
complete the task, but chose to use the
calculator to save time. The student was having
difficulty with the task and chose to use the
calculator to try another approach. The student
is using the calculator to confirm results or
conjectures, understanding multiple symbolic
forms.
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What I learned from the third study

• 4 Calculus Students
• 2 boys 2 girls

Participants

• Task based interview (w/o)
• Task based interview (w)
• Follow up interview
• Audio video taped
• Calculator screen video taped

Data
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What I learned from the third study (cont.)

• The calculator plays a key role in the students
  feelings of security especially when working
  independently.
• How students report using the graphing calculator
  often differs from the way they actually use it.
  
• Perfected methods and analysis

Findings
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Examples Olivia Sarin
Im not that great at the calculatora lot of
calculus I dont even know how to use the
calculator for.
The calculator gave you more opportunities to
learnit increased the learning experience.
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Attitudes toward calculator use
comfortable
I think it is more pressure when you dont have
the calculator available.
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Attitudes toward calculator use
comfortable
I think it is more pressure when you dont have
the calculator available. I was sure I was right
when I could check my answer, and that always
feels good!
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Attitudes toward calculator use
comfortable
I think it is more pressure when you dont have
the calculator available. I was sure I was right
when I could check my answer, and that always
feels good! Like, I think it is more of a
security net kind of thing, I feel more
comfortable with the calculator next to me
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Attitudes toward calculator use
comfortable
stressful
I think it is more pressure when you dont have
the calculator available. I was sure I was right
when I could check my answer, and that always
feels good! Like, I think it is more of a
security net kind of thing, I feel more
comfortable with the calculator next to me
Using a calculator is kind of like
stressfulusing a calculator becomes more
difficult when solving a problem.
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Attitudes toward calculator use
comfortable
stressful
I think it is more pressure when you dont have
the calculator available. I was sure I was right
when I could check my answer, and that always
feels good! Like, I think it is more of a
security net kind of thing, I feel more
comfortable with the calculator next to me
Using a calculator is kind of like
stressfulusing a calculator becomes more
difficult when solving a problem. If I dont
remember where everything is on the
calculatorthat causes stress!
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Problem Solving Behavior
I do a lot of basic computation and a lot of
graphsa lot, a lot of graphs!
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Problem Solving Behavior
I do a lot of basic computation and a lot of
graphsa lot, a lot of graphs!
Im definitely more comfortable with the
calculator only because I know that if I really
didnt know the problem at least I can plug
things in.
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Problem Solving Behavior
I do a lot of basic computation and a lot of
graphsa lot, a lot of graphs!
Im definitely more comfortable with the
calculator only because I know that if I really
didnt know the problem at least I can plug
things in. If I dont know how to do something I
can like fiddle around with it on my calculator,
try to figure something out
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Problem Solving Behavior
I do a lot of basic computation and a lot of
graphsa lot, a lot of graphs!
I got caught up in trying to use the calculator
and lost track of what I was doing
Im definitely more comfortable with the
calculator only because I know that if I really
didnt know the problem at least I can plug
things in. If I dont know how to do something I
can like fiddle around with it on my calculator,
try to figure something out
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Problem Solving Behavior
I do a lot of basic computation and a lot of
graphsa lot, a lot of graphs!
I got caught up in trying to use the calculator
and lost track of what I was doing
Im definitely more comfortable with the
calculator only because I know that if I really
didnt know the problem at least I can plug
things in. If I dont know how to do something I
can like fiddle around with it on my calculator,
try to figure something out
I like solving and writing down each and every
step I dont know what the calculator is doing
with every stepit doesnt like list itwhen Im
solving I put down every step in case I make a
mistake I can go back to that step and correct
it
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Data Collection Methods
For what values of x is -2 lt k x lt 5?
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Now what?
I have taken what I have learned from the
previous studies and have formulated meaningful
and practical research questions.
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Now what?
I have taken what I have learned from the
previous studies and have formulated meaningful
and practical research questions.
I have taken what I have learned from doing these
studies and planned my data collection and
analysis methods accordingly.
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Research questions
How do students use the graphing calculator when
they work independently?

• What tools on the graphing calculator do students
  regularly use?
• In what context do they use these tools?
• What aspects of the calculator output do they
  attend to?

Why do students use the calculator when they do?

• What reasons do students give for choosing to use
  the calculator in a particular way?
• Is there a difference between what students say
  they do and what they actually do?

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Methods

• AP Calculus AB students from four different New
  Jersey high schools
• Survey data (111 students)
• Qualitative data (6 students)
• Background interview
• Task based interview
• Reflection interview
• All interviews will be video and audio taped and
  video will be collected from the graphing
  calculator when it is used.

Participants
Data
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Survey data (so far)

• Demographics
• Teacher rated ability
• Calculator most often used
• How often use each tool (likert scale)
• How comfortable with each tool (likert scale)
• Reason for using each tool
• Preference on assessments working with others
  /or using a graphing calculator (free response)

Data
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Survey data (so far)

• 111 students
• 4 schools
• 51 female / 59 male
• 8 African American or Black
• 44 Asian, Asian American, Pacific Islander
• 3 Latin American, South American, Central
  American, Hispanic
• 54 White
• 11 have attended school outside of the U.S.
• 108 have graphing calculators to use outside of
  school

Participants
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Survey data (so far)
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Survey data (so far) If you were given the choice
to a) take a test with another student or b)
use a graphing calculator on the test, which
situation would you choose and why?
Calculator
Student

• I trust the calculator more than I trust another
  student.
• With the calculator Im guaranteed to get some
  help.
• The calculator is a reliable way to check your
  work.
• I generally to fine on my own and with the
  calculator I can find many ways to solve
  problems.
• The calculator it helps me visualize problems
  better with graphs.

• Hopefully the other student will know how to do
  maththe calculator doesnt know anything.
• The calculator only knows as much as you do.
• I prefer talking with students and hearing their
  opinions.
• Sometimes you enter the wrong information on the
  calculator
• I would pick someone smarter than me!

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Case Studies
Based on survey data I decided on the
characteristics of students that I wanted to
interview
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Case Studies
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Conclusion
Every course Ive taken and every article Ive
read has influenced this study in some way.
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Conclusion
Every course Ive taken and every article Ive
read has influenced this study in some way.
From presenting and conferences and discussions
with others in the area, I know that Im doing
something that is interesting to others and not
just me!
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Conclusion
Every course Ive taken and every article Ive
read has influenced this study in some way.
From presenting and conferences and discussions
with others in the area, I know that Im doing
something that is interesting to others and not
just me!
It has been a long journey that isnt done yet!