graphing calculators in high school classrooms
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Teacher Attitudes Regarding Graphing Calculators 1
Running Head: TEACHER ATTITUDES REGARDING GRAPHING CALCULATORS
Teacher Attitudes Regarding
the Use of Graphing Calculators in High School Algebra I
Kimberly L. Carr
The University of Southern Mississippi
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Teacher Attitudes Regarding Graphing Calculators 2
Abstract
The use of graphing calculators is common practice in mathematics, but their use in Algebra I
still raises questions. This study used the survey method to gather information from teachers in
and around Hattiesburg, Mississippi, to determine their attitudes regarding the use of graphing
calculators in high school Algebra I. Fifty-four participants completed an online questionnaire
that researchers had developed for the purposes of this study. Overall, teachers appear to favor
the use of graphing calculators in the Algebra I classroom although opinions vary regarding the
advantages their use offers.
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Teacher Attitudes Regarding Graphing Calculators 3
Teacher Attitudes Regarding
the Use of Graphing Calculators in High School Algebra I
Graphing calculators are now understood to be a part of mathematics education, but the
lingering question is this: When should they first be used? More specifically, Should graphing
calculators be used in Algebra I? Many teachers embrace student exploration with this
technology and feel that students are better able to anticipate outcomes and have increased
intuitive mathematical knowledge after mathematical experiences with graphing calculators;
others fear that these handheld devices inhibit student understanding of basic algorithms and
create a desire for the answer only. As the teacher opinions are split, so are the teaching
strategies.
In a 2008 position statement, the National Council of Teachers of Mathematics (NCTM)
asserts that technology, including calculators, is critical to the teaching of mathematics. Yet the
NCTM is clear in their statement that use of technology cannot replace conceptual
understanding, computational fluency, or problem-solving skills. Thus, the issue is of concern
among mathematics teachers nation-wide. Teachers must strike a balance between helping
students use graphing calculators as resource for complex problems that saves much time and
keeping students from using them as a crutch that ultimately inhibits deeper understanding.
This is not a new issue. Since graphing calculators first hit the market in 1985,
conflicting information about their potential and problems has been available. Martha Clutter
(1999) pointed out several years ago that students using calculators make fewer arithmetic errors
and tests that simply require calculations are, thereby, made obsolete. Clutter (1999) refers to the
NCTM guideline that all mathematics should be taught from symbolic, algebraic, and graphic
approaches and emphasizes that the graphing calculator is an excellent tool for teaching from the
graphic approach.
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Teacher Attitudes Regarding Graphing Calculators 4
Eric Milou (1999) published a study entitled The graphing calculator: A survey of
classroom usage. In this report, Milou states that the use of calculators was found to have no
significant negative effect on learning mathematics, regardless of level. He did find that Algebra
I teachers were significantly less likely to use graphing calculators in their classrooms than
teachers of Algebra II or above. Ultimately, Milou reports that the use of the graphing
calculator in teaching and learning is beneficial in terms of students' level of understanding and
achievement in algebra (p1).
Students experiences with graphing calculators may be directly related to teacher
attitudes about the calculators. Kastberg and Leatham (2005) pointed out that teacher attitudes
directly influence not only how the calculators are used within the classroom but also whether
students have access to the calculators. While much of the literature about calculator use focuses
on the positive potential of increased understanding and ability to solve more complex problems,
Kastberg and Leatham (2005) make a counterpoint that some below average students may only
make superficial computational gains without any increase in depth of knowledge. They make
an additional argument that students who are not specifically instructed in the use of the graphing
calculator are not confident and may avoid its use (Kastbert & Leatham, 2005).
Heller, Curtis, Jaffe, and Verboncoeur (2005) reported research findings in The impact
of handheld graphing calculator use on student achievement in Algebra I. These researchers
concluded that, in general, students with regular experience in using graphing calculators fared
better than peers with only periodic experience. Furthermore, students whose access to
calculators was limited performed better than students who had unlimited access (Heller et al,
2005).
Today, technology is improving regularly, so educational approaches must not stagnate.
Historically, mathematics classes have been focused on student computation. Thus, it is
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Teacher Attitudes Regarding Graphing Calculators 5
inherently difficult for teachers to distance themselves from classes centered on student
computation and the means thereof. Yet as graphing calculators become the norm in classrooms,
computation is decidedly less prominent and concept-understanding more criticalbut this is
only true if teachers revise their teaching (and assessment) strategies. Understanding teacher
attitudes will help educational planners better determine whether curriculum should actively
endorse the use of graphing calculators in the Algebra I classroom and how to help teachers
reach a united position on this issue. As NCTM (2008) has stated, Teachers can capitalize on
the appropriate use of this [calculator] technology to expand students mathematical
understanding, not to replace it.
Methods
This research was conducted by the survey method. Fifty-four teachers from various
schools in South Mississippi participated in this study. Participants, 14 males and 40 females,
were teachers certified to teach high school Algebra I. Schools were selected in and around
Hattiesburg, Mississippi, for convenience sampling.
Researchers developed an online questionnaire specifically for use in this study. (See
Appendix). The questionnaire contained four demographic items in a multiple-choice format,
followed by twelve items measured with a Likert-type scale. One open-response item was
included for participants general comments. A cover letter was then developed for the
questionnaire to inform potential participants about the purpose of the study and to ensure
autonomy, anonymity, and confidentiality. The letter also assured participants the study had
approval of the University of Southern Mississippis Institutional Review Board (IRB).
Researchers contacted school principals in person and obtained written permission to conduct the
research at each school.
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Teacher Attitudes Regarding Graphing Calculators 6
The University of Southern Mississippis IRB then reviewed an application to conduct
this research. The packet included a detailed research proposal, permission forms, a copy of the
questionnaire, and the cover letter. The IRB approved this plan, and researchers began to collect
data.
Participating schools distributed a cover letter and note to eligible teachers, alerting
potential participants that another cover letter would be sent by e-mail. The electronic cover
letter contained a link to the online questionnaire. Data was collected March 07, 2008, through
April 14, 2008. Data was downloaded into an Excel spreadsheet April 14, 2008, and then
converted to an SPSS data file.
Researchers then used the SPSS program to analyze the data for a summary report.
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No
Yes
Have you
evertaught
Algebra I?Selectone.
Higher thanBachelor's
Bachelor's
RHighestDegree
Teacher Attitudes Regarding Graphing Calculators 7
Results
Data from the questionnaire included responses from fifty-five participants consisting of
14 males (25.5%) and 41 females (74.5%). One female only responded to demographic items, so
the cross tabulations involve 54 participants. Because of the small sample size, age categories
were redefined from their original format. Respondents were grouped into age ranges of 21-30
years (36.4%), 31-40 years (29.1%), and 41 years and older (34.5%).
Figure 1: Gender
Female
Male
1=Male,2=Female
Figure 2: Age
41+years
31-40years
21-30years
RAge
Most of the participants (76.4%) had taught Algebra I before and just over half of them
hold advanced degrees (56.4%).
Figure 3: Taught Algebra I Figure 4: Highest Degree Earned
Participants having used graphing calculators less than half of the time in their own
course college work (52.7%) almost balanced those indicating having used them fifty percent or
more of the time (47.3%).
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Teacher Attitudes Regarding Graphing Calculators 8
Figure 5: Personal Calculator Background
Less than50%
50% orMore
RGCFrequency
Due to the small sample size, the original five-point Likert-type scale was recoded into a
three-point scale. All responses indicating Strongly Disagree or Somewhat Disagree where
recoded as Disagree. Similarly, responses indicating Strongly Agree or Somewhat
Disagree where recoded as Agree. This change was accomplished through the SPSS system,
and all items reported here use this readjusted scale.
Researchers intended to use Pearson chi-squares to analyze the data to determine
significant trends among various demographic populations. However, due to the small sample
size, most cases contained small cells at frequencies precluding analysis by this means.
Nevertheless, many cases resulted in noteworthy trends that might prove to be significant in a
larger study.
Item 1: Students should be introduced to graphing calculators in Algebra I.
Overall, 66.7% of respondents indicated they agreed that students should be introduced to
graphing calculators in Algebra I. Female respondents were more likely to agree with this than
were males (70.0% females vs. 57.1% males). Responses to this statement were relatively
homogeneous relative to teacher age range though respondents 31-40 years of age agreed were
slightly more likely to agree. This factor indicated no notably difference in response relative to
respondents personal calculator background either. Regardless of whether participants had used
a graphing calculator in most of their own college coursework, they indicated agreement with
this statement, although those having used a graphing calculator in 50% or more were more
likely to agree. The sample indicated 60.9% of respondents holding a Bachelors degree agreed
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Teacher Attitudes Regarding Graphing Calculators 9
while 71.0% of those holding a higher degree did so. It is noteworthy that the majority (70.7%)
of respondents having taught Algebra I felt students should be introduced to the graphing
calculator as this level while those who had not taught the course were more evenly divided
(53.8% agree, 46.2% disagree).
Figure 6: Graphing Calculators Should Be
Introduced in Algebra I (Overall Response)
Agree
Neutral
Disagree
RIntroToGC
Figure 7: Graphing Calculators Should Be Introduced
in Algebra I (by Algebra I Teaching Experience)
AgreeNeutralDisagree
RIntroToGC
80.0%
60.0%
40.0%
20.0%
0.0%
Percent
No
Yes
Have youever taughtAlgebra I?Select one.
Item 2: Students should be introduced to graphing calculators afterAlgebra I.
Just over half (52.8%) of respondents indicated they agreed that students should be
introduced to graphing calculators after Algebra I. Female respondents were slightly more likely
to agree with this than were males (56.4% females vs. 42.9% males). Responses to this
statement were relatively homogeneous relative to teacher age range. Fifty-six percent (56.0%)
of teachers who used a graphing calculator in 50% or more of their own coursework disagreed
that graphing calculators should be introduced in Algebra I while a somewhat smaller portion
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Teacher Attitudes Regarding Graphing Calculators 10
(50.0%) of those who did not have the same graphing calculator background disagreed.
Similarly, 56.5% of respondents holding a Bachelors degree disagreed while 50.0% of those
holding a higher degree did so. Interestingly, more than half (57.5%) of the respondents having
taught Algebra I disagreed that students should be introduced to the graphing calculator after
Algebra I while more than half (53.8%) of those who had not taught the course agreed with the
statement.
Figure 8: Graphing Calculators Should Be
Introduced afterAlgebra I (Overall Response)
Agree
Neutral
DisagreeRIntroAfterAlgI
Figure 9: Graphing Calculators Should Be Introduced
afterAlgebra I (by Algebra I Teaching Experience)
AgreeNeutralDisagree
RIntroAfterAlgI
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
NoYes
Have youever taughtAlgebra I?Select one.
Item 3: I believe that using the graphing calculator causes students to rely on the technology
instead of fully understanding the concepts.
Overall, 50.0% of respondents agreed that using the graphing calculator causes students
to rely on the technology instead of fully understanding the concepts; 11.1% were neutral, and
37.0% disagreed. Responses to this statement were relatively homogeneous relative across
gender, age ranges, and degrees held. An apparent discrepancy in opinions exists based upon
respondents graphing calculator backgrounds: Most participants (67.9%) having used a graphing
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Teacher Attitudes Regarding Graphing Calculators 11
calculator in less than 50% of their own coursework agreed with this statement while more than
half (57.7%) of respondents who reported having used the graphing calculator in more than half
of their college coursework agreed. Participants who had taught Algebra one were more likely to
agree (56.1%) than those who had not (30.8%).
Figure 10: Graphing Calculators Cause Students
to Rely on Technology (Overall Response)
N/A
Agree
Neutral
DisagreeRRelyOnTech
Figure 11: Graphing Calculators Cause Students
to Rely on Technology (by graphing calculator background)
N/AAgreeNeutralDisagree
RRelyOnTech
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
Less than50%
50% orMore
RGCFrequency
Item 4: Students using graphing calculators have higher grades than those who do not
(assuming both groups are taught and assessed the exact same way).
Of all respondents, 48.1% agreed that students using graphing calculators have higher
scores on state mathematics tests than those who do not. Responses to this statement were
relatively homogeneous in terms of gender. Respondents 21-40 years of age were much more
likely to agree with this statement than respondents 41 years of age and older (62.9% vs. 22.2%).
Teachers who used a graphing calculator in 50% or more of their own coursework were also
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Teacher Attitudes Regarding Graphing Calculators 12
much more likely to agree than their counterparts (65.4% vs. 32.1%). Respondents with an
advanced degree were somewhat more likely to agree than those whose highest degree earned
was a Bachelors (54.8% vs. 39.1). Just over half of the respondents having taught Algebra I,
51.2% agreed while opinions of those who had not taught the course were somewhat evenly
dispersed.
Figure 12: Graphing Calculator Usage Corresponds
to Higher Grades (Overall Response)
N/A
Agree
Neutral
Disagree
RHigherGrades
Figure 13: Graphing Calculator Usage Corresponds
to Higher Grades (by age)
N/AAgreeNeutralDisagree
RHigherGrades
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
41+
21-40
RAgeat40
Figure 14: Graphing Calculator Usage Corresponds
to Higher Grades (by graphing calculator background)
N/AAgreeNeutralDisagree
RHigherGrades
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
Less than50%
50% or More
RGCFrequenc
Item 5: Students who use graphing calculators are more likely to cheat or play games than
those who do not use graphing calculators.
Overall, only 38.9% of respondents agreed that students who use graphing calculators are
more likely to cheat or play games than those who do not, but there appears to be a notable
gender difference: Chi-square analysis indicated that a significant relationship is likely to exist
between this variable and the respondents gender, 015.,427.8)54,2(2
=== pN . Male
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Teacher Attitudes Regarding Graphing Calculators 13
respondents were much likely to agree with this statement than females (71.4% vs. 27.5%).
Responses to this statement were relatively homogeneous in terms of age, calculator
backgrounds, and highest degree earned. Noticeably more participants who had taught Algebra
one were more likely to agree (43.9%) than those who had not (23.1%).
Figure 15: Students Cheat/Play Games (Overall)
Agree
Neutral
Disagree
RCheatPlay
Figure 16: Students Cheat/Play Games (by gender) Figure 17: Students Cheat/Play Games
(by teaching experience)
Item 6: Students who use graphing calculators have higher scores on state mathematics
assessments than those who do not.
Of all respondents, 48.1% agreed that students using graphing calculators have higher
scores on state mathematics tests than those who do not. Females tended to agree rather than
disagree (52.5% vs. 12.5%) while males opinions were more evenly split (35.7% agree vs. 35.7%
disagree). Sixty percent (60%) of respondents 21-40 years of age were likely to agree with this
statement while only 27.8% of respondents 41 years of age and older agreed. Teachers who used
AgreeNeutralDisagree
RCheatPlay
80.0%
60.0%
40.0%
20.0%
0.0%
Percent
Female
Male
1=Male,2=Female
AgreeNeutralDisagree
RCheatPlay
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
No
Yes
Have youever taughtAlgebra I?Select one.
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Teacher Attitudes Regarding Graphing Calculators 14
a graphing calculator in 50% or more of their own coursework were much more likely to agree
than their counterparts (61.5% vs. 35.7%). Respondents holding a Bachelors degree were
almost evenly dispersed in their agreement levels, but more than half of those holding a higher
degree (54.8%) agreed. Of the respondents having taught Algebra I, 51.2% agreed while
opinions of those who had not taught the course were almost evenly dispersed.
Figure 18: Graphing Calculator Usage
Corresponds to Higher Scores(Overall Response)
N/A
Agree
Neutral
Disagree
RHigherScores
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N/AAgreeNeutralDisagree
RHigherScores
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
Female
Male
1=Male,2=Female
N/AAgreeNeutralDisagree
RHigherScores
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
41+
21-40
RAgeat40
Teacher Attitudes Regarding Graphing Calculators 15
Figure 19: G raphing Calculator Usage Figure 20: G raphing Calculator Usage
Corresponds to Higher Scores (by gender) Corresponds to Higher Scores (by age range)
Figure 21: Graphing Calculator Usage Corresponds
to Higher Scores (by graphing calculator background)
N/AAgreeNeutralDisagree
RHigherScores
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
Less than50%
50% orMore
RGCFrequency
Item 7: State mathematics tests should ban the use of graphing calculators
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Teacher Attitudes Regarding Graphing Calculators 16
Overall, 48.1% of respondents disagreed that state mathematics test should ban the use of
the graphing calculator. However there is an interesting pattern among gender with 55.5% of
females indicating disagreement with the statement while 57.1% of males agree. Age may also
be a factor in the responses; among respondents 21-40 years of age, 57.1 % disagreed with this
statement whereas opinions of respondents 41 years of age and older were evenly distributed.
Responses to this statement were relatively homogeneous relative in relation to both degrees held
and experience in teaching Algebra I. Almost half (48.1%) of respondents who reported having
used the graphing calculator in more than half of their college coursework disagreed while their
counterparts held opinions more evenly distributed.
Figure 22: Ban Graphing Calculators
on State Tests (Overall)
Agree
Neutral
Disagree
RBanGC
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Teacher Attitudes Regarding Graphing Calculators 17
Figure 23: Ban Graphing Calculators on
State Tests (by gender)
AgreeNeutralDisagree
RBanGC
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
Female
Male
1=Male,2=Female
Figure 24: Ban Graphing Calculators on
State Tests (by age)
AgreeNeutralDisagree
RBanGC
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
41+
21-40
RAgeat40
Item 8: Students using graphing calculators have deeper levels of understanding than those who
do not.
Overall, 42.6% of respondents disagreed that students using graphing calculators have
deeper levels of understanding than those who do not, 31.5% agreed and 25.9% gave a neutral
response. Responses to this statement were relatively homogeneous relative to gender and
highest degrees earned. Responses indicate a meaningful inverse relationship may exist between
agreement and age with levels of agreement decreasing as age increases. Chi-square analysis
indicated that a significant relationship may exist between this variable and the respondents
graphing calculator background, 001.,183.15)54,2(2
=== pN . The majority (67.9%) of
those having used a graphing calculator in less than 50% of their college coursework disagreed
whereas almost half (46.2%) of their counterparts agreed with the statement. It is noteworthy
that most (61.5%) of respondents who had not taught Algebra I felt students using graphing
calculators have deeper levels of understanding than those who do not while responses of those
who had taught the course were more evenly distributed.
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Teacher Attitudes Regarding Graphing Calculators 18
Figure 25: Graphing Calculator Usage Leads to Deeper
Levels of Understanding (Overall)
AgreeNeutral
DisagreeRDeeperUnderstanding
Figure 26: Graphing Calculator Usage Leads to Deeper
Levels of Understanding (by age)
AgreeNeutralDisagree
RDeeperUnderstanding
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
41+ years
31-40 year
21-30 year
RAge
Figure 27: Graphing Calculator Usage Leads to Deeper
Levels of Understanding (by graphing calculatorbackground)
AgreeNeutralDisagree
RDeeperUnderstanding
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
Less than50%
50% orMore
RGCFrequency
Figure 28: Graphing Calculator Usage Leads to Deeper
Levels of Understanding (by teaching experience)
AgreeNeutralDisagree
RDeeperUnderstanding
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percent
No
Yes
Have you ever
taught
Algebra I?Select one.
Item 9: When using graphing calculators in the classroom, students should be still be required
to show all of their work.
Overall, 75.9% of respondents indicated they agreed that students using graphing
calculators in the classroom should still be required to show all of their work; 11.1% disagreed,
and 13.9% gave a neutral response. Responses to this statement were relatively homogeneous
across all demographic variables considered.
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Teacher Attitudes Regarding Graphing Calculators 19
Figure 29: Students Using Graphing Calculators
Should Show All Work (Overall)
Agree
Neutral
Disagree
RShowWork
Item 10: Student engagement is higher with the use of graphing calculators than without.
Overall, 63.0% of respondents indicated they agreed that student engagement is higher
with the use of graphing calculators. Responses to this statement were relatively homogeneous
across genders. Age might be connected to a respondents level of agreement: younger teachers,
those 21-40 years of age, were more likely to agree than those 41 years of age and older (74.3%
vs. 38.9%). Most respondents (76.9%) who had used a graphing calculator in most of their own
college coursework indicated agreement with this statement whereas only 50.0% of those having
used a graphing calculator in less than half of their coursework agreed. Respondents whose
highest earned degree was a Bachelors were more likely to agree than those with an advanced
degree (69.6% vs. 58.1%). It is noteworthy that the majority (70.7%) of respondents having
taught Algebra I felt graphing calculators increased student engagement while responses of those
who had not taught the course were more evenly distributed.
Figure 30: Graphing Calculator Usage Corresponds
with Student Engagement (Overall)
Agree
NeutralDisagree
RStudentEngagement
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Teacher Attitudes Regarding Graphing Calculators 20
Figure 31: Graphing Calculator Usage Corresponds
with Student Engagement (by age)
AgreeNeutralDisagree
RStudentEngagement
80.0%
60.0%
40.0%
20.0%
0.0%
Percent
41+
21-40
RAgeat40
Figure 32: Graphing Calculator Usage Corresponds
with Student Engagement (by graphing calculator
background)
AgreeNeutralDisagree
RStudentEngagement
80.0%
60.0%
40.0%
20.0%
0.0%
Percent
Less than50%
50% or
More
RGCFrequency
_
Item 11: Graphing calculators are great in classroom assignments but should not be used on
tests.
Overall, 50.0% of respondents indicated they disagreed that students should not be
allowed to use graphing calculators on tests; 31.5% agreed, and 18.5% gave a neutral response.
Interestingly, 55.5% of female respondents disagreed while 50.0% of males agreed. Responses
to this statement were relatively homogeneous across all other demographic items considered.
Figure 33: Graphing Calculators Should Not Be
Used on Tests (Overall)
Agree
Neutral
Disagree
RNotOnTest
Figure 34: Graphing Calculators Should Not Be Used
on Tests (by gender)
AgreeNeutralDisagree
RNotOnTest
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Percen
tFemale
Male
1=Male,2=Female
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Teacher Attitudes Regarding Graphing Calculators 21
Item 12: The department of education in our state does not give enough training for teachers
about using graphing calculators in Algebra I.
Overall, 46.3% of respondents indicated they agreed that the state department does not
give enough training for teachers about using graphing calculators in Algebra I while 13.0%
disagreed and 29.6% gave a neutral response. Responses to this statement were relatively
homogeneous relative to gender, highest degree earned, and Algebra I teaching experience. Age
might be a component of agreement as 57.1% of respondents 21-40 years of age indicated
agreement while only 27.8% of those 41 years of age and older agreed. Respondents who had
used a graphing calculator in most of their own college coursework were more likely to agree
than those having used a graphing calculator less frequently (57.7% vs. 35.7).
Figure 35: State Department Does Not
Offer Enough Training (Overall)
N/A
Agree
Neutral
Disagree
RGCTraining
Figure 36: State Department Does Not
Offer Enough Training (by age)
N/AAgreeNeutralDisagree
RGCTraining
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Per
cent 41+
21-40
RAgeat40
Figure 37: State Department Does Not
Offer Enough Training (by graphing calculator
background)
N/AAgreeNeutralDisagree
RGCTraining
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
Perce
nt Less than
50%
50% orMore
RGCFrequency
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Teacher Attitudes Regarding Graphing Calculators 22
Open Response Item: If you have any reason(s) why you do/do not feel graphing calculators
should be used that we have not covered, please feel free to list or discuss them below.
Twenty-two respondents entered comments (20 females, 2 males), and these were
reviewed and categorized. Two responses contained comments that fell strongly into two
categories and, thus, were separated into both categories. Thus, twenty-four comments were
reviewed. Almost a third of the respondents offering comments referred to the negative affect
graphing calculator use seems to have on students computational skills.
Table 1: Open Response Comments
Positive Negative Other
Intro Earlier 3 Intro Later 2 More Training 2
Advantages ofTechnology
3 Decreases Skills 7 Mix Methods 4
Not allowed at allcolleges
2 Depends on Use 1
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Discussion
This research project was designed to determine the attitudes of teachers in the area
surrounding Hattiesburg, Mississippi, regarding the use of graphing calculators in high school
Algebra I. This study reveals that, in general, teacher attitudes in the area favor graphing
calculator usage at the Algebra I level.
According to this study, two-thirds of the teachers qualified to teach Algebra I feel that
students should be introduced to graphing calculators at the Algebra I level. This outcome
corresponds with the position of the NCTM but indicated a surprising difference among
respondents based on their Algebra I teaching experience. Teachers who had taught the course
more strongly favored the calculator introduction at this level. This may be explained by these
respondents having increased familiarity with students typical readiness levels in Algebra I.
Another possibility is that teachers involved with the coursework are better able to discern where
the graphing calculators might be more effective than traditional teaching measures in the course.
Just over half of the respondents indicated that graphing calculators should be introduced
after Algebra I. On reflection, this item may have provided conflict for respondents. Future
studies on this matter would be improved by asking when graphing calculators should be
introduced in terms of a multiple choice item. Responses might be better interpreted if
respondents are asked to select a choice (i.e., Before Algebra I, In Algebra I, After Algebra I, or
Never) than in the two item format this study used. However, this item still generated interesting
results in that most teachers who used graphing calculators extensively in their own college
coursework felt introduction of graphing calculators after Algebra I was appropriate. A possible
explanation is that these teachers felt the primary benefits of the graphing calculator compared to
a basic scientific calculator is in its ability to solve the more complex problems encountered in
higher level mathematics courses.
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Despite the high level of support for graphing calculators, almost half of the teachers
surveyed indicated they believed using graphic calculators causes the students to rely rather than
fully understanding concepts. This is an apparent dichotomy but may have an explanation
offering consistency: Perhaps reliance on technology is not perceived by all teachers as having
negative connotations in todays technologically progressive society. However, since more than
half of the teachers who used graphing calculators extensively in their own college coursework
agreed that graphing calculators encouraged technology reliance at the expense of understanding,
it is possible that personal experience led to their response.
Almost half of the responding teachers agreed that students using graphing calculators
have higher grades than those who do not. Meaningful relationships may exist between these
respondents who indicated agreement and their age as well as personal graphing calculator
experience. While not explored in this study, it may be that younger respondents have a stronger
history with graphing calculators and, thereby, tend to agree that using graphing calculators
improves grades. While this group may have responded based on their observation of students in
their own classrooms, it must be considered that they may have transferred their own experience
as college students to this item.
While just over a third of the teachers indicated a belief that students using graphing
calculators are more likely to cheat or play games than those who do not use them, a significant
relationship is likely to exist between this belief and gender. Males were much more likely to
indicate agreement with this statement than females. There are several possible explanations for
this. Females may simply be more trusting of their students, males may transfer personal
tendencies to their students, or females may believe that the tendency to cheat or play is based
more on the students character than graphing calculator usage. This potential relationship could
be more fully explored in a larger, more in-depth study.
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Almost half the teachers participating in this study agreed that students using graphing
calculators have higher score on state tests than those who do not. As might be expected,
teachers who used graphing calculators extensively in their own college coursework were
noticeably more likely to agree with this statement than their counterparts. One explanation
might be transfer of their own experience while another explanation could be familiarity with
both graphing calculator capabilities as well as types of items included on state tests. The
correspondence to age and agreement must also be considered. Younger teachers agreed at a
much higher rate than older teachers. As mentioned above, it is likely that younger teachers
correspond to those with a strong graphing calculator background, so explanations may mirror
those just offered.
Teachers disagree over whether state mathematics tests should ban the use of graphing
calculators, and this disagreement is most clearly seen between genders. Males agreed with this
statement at the same rate females disagreed. This may be explained through this items
connection to beliefs about graphing calculators and improved scores on state tests. While this
study did not explore the possibility, the females who disagree with the ban are likely to be the
females who believe the graphing calculators improve state test scores. Males in favor of the ban
may believe that a ban would eliminate possible cheating as males tended to believe graphing
calculators increased likelihood of cheating. Younger teachers were more noticeably more likely
to disagree with this statement than older teachers, and this may be explained by a tendency
among younger people to embrace both change and technology.
Opinions differ widely as to whether students who use graphing calculators have deeper
levels of understanding than those who do not, and considerations of this variable are more
complex than some. A significant relationship is likely to exist between this item and the
respondents calculator background. Teachers who used graphing calculators in relatively little
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of their own college coursework, in general, did not agree that such usage would correspond to
deeper understanding. Respondents who have little experience using graphing calculators may
fail to acknowledge that using a graphing calculator could enhance their own depth of
understanding, and they may project this idea to beliefs about their students. Results suggest that
a meaningful inverse relationship may exist between age and the belief that graphing calculator
usage corresponds to deeper levels of understanding. A larger study may reveal this to be so, but
if this inverse relationship does exist, it could also correspond to the participants personal
graphing calculator background. If that is the case, it is likely that the strength of this
relationship will lessen over time as teachers with a strong graphing calculator background move
into an older age range. Experience teaching Algebra I seems to lead respondents to disagree
with the correspondence between deeper levels of understanding and graphing calculator usage.
Reasons for this are difficult suggest but might be of interest in further study. Perhaps
respondents who have not taught Algebra I are also younger teachers with a strong graphing
calculator background. Perhaps respondents who have taught Algebra I have done so both with
and without the graphing calculator and seen no evidence of deeper understanding among their
students.
This study found that approximately three-fourths of all respondents feel students using
graphing calculators should still be required to show all their work. This item was remarkable in
that results were within each demographic item considered. The use of the word all for this
item may have led some respondents to select an alternative response as it is difficult to
determine what all the work is. A future study could be improved by rewording the item. An
alternative statement might replace all with major steps.
The majority of teachers in the study feel that using graphing calculators does increase
the level of student engagement. Once again, the respondents age and graphing calculator
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background seem to be indicators of whether one saw the graphing calculator as a link to
increased student engagement. Furthermore, respondents whose highest degree earned was a
Bachelors were more likely to see this positive link than those having advanced degrees. While
this was not fully explored, it may be that these three demographics all correspond within the
sample. Most respondents that had taught Algebra I indicated a belief that higher student
engagement corresponds to graphing calculator usage, and this could be the result of their having
taught the course both ways and observed the connection.
Less than one-third of respondents indicated they felt graphing calculators should not be
used on tests while one-half disagreed with this statement. There may be a meaningful
relationship between gender and the respondents view in this case. Females were more likely to
disagree while males agreed more often than not. This is likely to relate to the similar results this
study found about teacher attitudes toward banning graphing calculators on state tests.
Nearly half of the respondents do not feel the state department offers adequate training
for teachers about using graphing calculators in Algebra I. Teachers 21-40 years of age were
more likely to hold this view than those 41 years of age and older, and teachers with a strong
calculator background were more likely to hold this view than those without. One possible
explanation is that younger teachers are more interested in learning to use this technology than
their older counterparts. Since older teachers did not perceive a connection between graphing
calculator use and increased depth of understanding, they may not be interested in attending
training to use this technology. A similar argument may be made about respondents graphing
calculator backgrounds.
Over a third of the respondents, almost all females, answered the open response items.
Fewer positive comments were offered than negatives, and positive comments both suggested
that the graphing calculator should be introduced before Algebra I and also lauded the
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advantages of the technology. Negative comments fell into three basic areas: Some teachers
asserted the graphing calculator should be introduced later than Algebra I; almost a third of
teachers commenting noted that students using graphing calculators exhibited decreased
computational skill levels; and a couple of teachers pointed out that not all colleges allowed
graphing calculators. Some teachers referred to the need for more training, and several
mentioned that teaching and assessment should include a mixture of both calculator and non-
calculator approaches. These comments suggest that many teachers have mixed feelings about
calculator use in general and do not necessarily target the use of graphing calculators.
Overall, teachers appear to favor the use of graphing calculators in the Algebra I
classroom although opinions vary regarding the advantages their use offers. Determining the
effects of graphing calculator use on understanding is complex and may never be fully
ascertained due to the variability among students and the homogeneity of educational policies.
This factor notwithstanding, graphing calculator use in Algebra I is likely to become more
common. It appears that younger teachers, more likely to have a strong graphing calculator
background, are stronger supporters of graphing calculators in the classroom than their older
counterparts. Thus, the support for graphing calculators in the classroom is likely to increase
over time as teachers who used the graphing calculator in their own college coursework become
a larger portion of the educational workforce.
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References
Computation, calculators, and common sense. (2008, May). Retrieved March 25, 2008, from
National Council of Teachers of Mathematics Web site:
http://www.nctm.org/about/content.aspx?id=6358
Heller, J. I., Curtis, D. A., Jaffe, R., & Verboncoeur, C. J. (2005). The impact of handheld
graphing calculator use on student achievement in Algebra I. Retrieved March 19, 2008,
from the Education Resources Information Center (ERIC) Web site:
http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/2
9/00/f9.pdf
Kastberg, S., & Leatham, K. (2005). Research on graphing calculators at the secondary level:
Implications for mathematics teacher education. Contemporary Issues in Technology and
Teacher Education. 5, 25-37.
Milou, E. (1999, March). The graphing calculator: A survey of classroom usage. School Science
and Mathematics. Retrieved March 25, 2008, from BNET Business Network Web site:
http://findarticles.com/p/articles/mi_qa3667/is_199903/ai_n8849008
The role of technology in the teaching and learning of mathematics. (March 2008). Retrieved
March 25, 2008, from National Council of Teachers of Mathematics Web site:
http://www.nctm.org/about/content.aspx?id=14233
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Appendix
Graphing Calculators in the Mathematics Classroom
SECTION I TEACHER DEMOGRAPHICS
Please select your gender:
______ Male ______ Female
Please select your current age r ange:
____21 30 years____31 40years
____41 50years____51 60years
____ 60 +years
Please select your highest degree obtained:
_________ Bachelors Degree Secondary
Education
(Emphasis: ______________)
_________ Other Bachelors Degree
(________________________)
_________ Masters degree
(Emphasis: _______________)
_________ Specialist or Higher
How often did you use graphing calculators in
your math coursework when you were a college
student? Select one.
_________ Majority of coursework (over 75%)
_________ Most of my coursework (50% to 75%)
_________ Some of my coursework (less than 50%)
_________ None of my coursework
Have you ever taught Alge bra I? Select one.
__________ Yes ___________ No
SECTION II ATTITUDES REGARDING GRAPHING CALCULATORS
Please use the degree scale above to answer the following opinions related to calculators in the classroom.
1. Students should be introduced to graphing calculators in Algebra I. 1 2 3 4 5 N/A
2. Students should be introduced to graphing calculators after Algebra I. 1 2 3 4 5 N/A
3. I believe that using the graphing calculator causes s tudents to rely on the
technology instead of fully understanding the concepts.1 2 3 4 5 N/A
1 2 3 4 5 N/A
Strongly
Disagree
Somewhat
Disagree Neutral
Somewhat
Agree
Strongly
Agree Irrelevant
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4. Students using graphing calculators have higher grades than those who do no t
(assuming both g roups are taught and assessed the exact same way)1 2 3 4 5 N/A
5. Students who use graphing calculators are more likely to cheat o r play games
than those who do not use graphing calculators.1 2 3 4 5 N/A
6. Students using graphing calculators have higher scores on s tate mathematics
assessments than those who do not.1 2 3 4 5 N/A
7. State mathe matics tests should ban the use of graphing calculators. 1 2 3 4 5 N/A
8. Students using graphing calculators have deeper levels of understanding than
those who do not.1 2 3 4 5 N/A
9. When using graphing calculators in the classroom, students should still be
required to s how all of their work.1 2 3 4 5 N/A
10. Student engagement is higher with the us e of graphing calculators than
without.1 2 3 4 5 N/A
11. Graphing calculators are great in c lassroom assignments and discussions, but
should not be used on tests.1 2 3 4 5 N/A
12. The department of education in our state does not give enough training for
teachers about using graphing calculators in Algebra I.1 2 3 4 5 N/A
If you have any reason(s) why you do/do not feel graphing calculators should be use d that we have not
covered, please feel free to lis t or discuss them below:
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