Graphing Calculators in High School Classrooms

7/30/2019 Graphing Calculators in High School Classrooms

1/31

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


2/31


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.


3/31


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.


4/31


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


5/31


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.


6/31


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.


7/31

No

Yes

Have you

evertaught

Algebra I?Selectone.

Higher thanBachelor's

Bachelor's

RHighestDegree


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%).


8/31


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


9/31


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


10/31


(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)


RIntroAfterAlgI

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Percent

NoYes


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


11/31


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


12/31


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


to Higher Grades (by age)


RHigherGrades

70.0%

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Percent

41+

21-40

RAgeat40


to Higher Grades (by graphing calculator background)


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


13/31


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


RCheatPlay

80.0%

60.0%

40.0%

20.0%

0.0%

Percent

Female

Male

1=Male,2=Female


RCheatPlay

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Percent

No

Yes



14/31


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


15/31


RHigherScores

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Percent

Female

Male

1=Male,2=Female


RHigherScores

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Percent

41+

21-40

RAgeat40


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)


to Higher Scores (by graphing calculator background)


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


16/31


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


17/31


Figure 23: Ban Graphing Calculators on

State Tests (by gender)


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)


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.


18/31


Figure 25: Graphing Calculator Usage Leads to Deeper

Levels of Understanding (Overall)

AgreeNeutral

DisagreeRDeeperUnderstanding


Levels of Understanding (by age)


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


Levels of Understanding (by graphing calculatorbackground)



70.0%

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Percent

Less than50%

50% orMore

RGCFrequency


Levels of Understanding (by teaching experience)



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.


19/31


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.


with Student Engagement (Overall)

Agree

NeutralDisagree

RStudentEngagement


20/31



with Student Engagement (by age)


RStudentEngagement

80.0%

60.0%

40.0%

20.0%

0.0%

Percent

41+

21-40

RAgeat40


with Student Engagement (by graphing calculator

background)


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)


RNotOnTest

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Percen

tFemale

Male

1=Male,2=Female


21/31


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


Offer Enough Training (by age)


RGCTraining

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Per

cent 41+

21-40

RAgeat40


Offer Enough Training (by graphing calculator

background)


RGCTraining

60.0%

50.0%

40.0%

30.0%

20.0%

10.0%

0.0%

Perce

nt Less than

50%

50% orMore

RGCFrequency


22/31


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


23/31


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.


24/31


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.


25/31


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


26/31


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


27/31


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


28/31


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.


29/31


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


30/31


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


31/31


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:

Graphing Calculators in High School Classrooms

Documents

Transcript of Graphing Calculators in High School Classrooms