EDET J780 Group Project Graphing Calculators and High Stakes Testing

7/31/2019 EDET J780 Group Project Graphing Calculators and High Stakes Testing

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THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 1

The Effect of Calculator Use on High Stakes Testing in Math Students

Michelle New, Jennifer Guest, Devin Biggers, and Sylvia Hodge

University of South Carolina Aiken

EDET 780 Group Research Project


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Abstract

This study will assess the effectiveness of 10th grade students using calculators in

conjunction with a high stakes test, specifically the South Carolina High School Exit Exam, HSAP

(High School Assessment Program). According to Hembree and Dessart, calculators can prove

beneficial to overall problem solving when used in correlation with mathematics instruction.

Similarly, Clark and Dion charge that prior to integration, both teachers and students should

become trained in calculator technology. The presence and absence of various calculators

(scientific and graphing) are analyzed within this study. We hope to see a correlation between

calculator use and student scores. An extended question is to be answered as well: Does lack of

familiarity with a specific calculator negate its ability to enhance student performance?

Conclusions may be used to direct future classroom instruction and make appropriate

accommodations to state assessments.


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Introduction

The fact that students tend to have higher failure rates in mathematics than in other

academic disciplines, provides the impetus for research into methods to improve skills in

mathematics calculations as well as confidence in the study of mathematics. While extensive

research is available concerning methods of improvement, including the utilization of graphing

calculators in higher level mathematics, further research is warranted. Since the 1980s, with the

publication ofA Nation at Risk, continuing through the era ofNo Child Left Behind, and still

today, standardized testing in the area of mathematics, is a high-stakes reality in American schools.

As a result of testing such as the PASS and the HSAP in South Carolina, as well as the looming

Common Core testing that will be national in scope, the need for improvements in mathematical

skills and abilities of American students has never been more pronounced. Many technological

tools exist for assistance with computational skills, but none is more affordable and accessible than

the graphing calculator.

Literature Review

The notion that K-12 and university students struggle with mathematics has long been

understood. The fact that students tend to have higher failure rates in mathematics than in other

disciplines explains the need for research into ways of helping students be more successful in

upper level mathematics. Significant research has been conducted concerning the usefulness of

graphing calculators in mathematics education throughout the past three decades. The possibility

that a simple tool such as a graphing calculator might improve understanding and successful


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computation on the part of the students provides the reasoning behind the need for research in this

area.

It may well be the case that technology does not help or hinder students in the

memorization of facts, but technology does help students to develop conceptual understanding and

problem-solving abilities, Tan cites Griffith (p. 76) (Tan, 2012, p. 1117). Similar to Griffith,

Hembree & Dessart agree that the use of calculators in concert with traditional mathematics

instruction apparently improves the average students basic skills with paper and pencil, both in

working exercises and in problem solving. Brown also indicates this in his paper when he refers

to the findings of another study that state, ...the use of calculators facilitated skill development

and students had a more positive attitude toward mathematics than students who did not use

calculators. (T. Brown; 2007; p. 109-10) Tans research involved 65 pre-university students in

Malaysia which were divided into a control and a treatment group for twelve weeks of instruction

concerning probability. At the end of the study, the experimental (treatment) group, who had been

taught utilizing graphing calculators, scored significantly higher than the control group on a

posttest of the mathematics covered throughout the course of the experiment. In a study similar to

Tans, Merriweather also used control and experimental groups. Merriweathers study, however,

focused on changes in attitude of the students about math when they were given calculators to use.

Merriweathers results found that the students...were able to solve problems with the graphing

calculator that they were not able to solve before. Her results also showed that ..76% of the

control group thought that using the graphing calculator would make math fun... (Merriweather;

1999; p. 11). Most studies have found that when given the chance to use calculators in everyday

math instruction, students seem to inherit not only a better attitude about math but also seem to

improve their level of achievement.


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According to both Clark and Dion, it is crucial that calculators be integrated into math

classrooms. Clark refers to calculators as valuable instructional tools. Clark states, however, that

students need to develop an understanding of the mathematical calculations of a topic before they

are allowed to use a calculator. Clarks idea is supported by (T. Brown 2007; p. 103) when he

states, ...teachers must first, acknowledge the significance of calculator use in students

conceptual understanding of mathematics and second, actually employ the appropriate use of

calculators in mathematics instruction. Before calculators can be integrated fully into everyday

math instruction, both teachers and students need to have both training and experience with these

technologies. One study revealed higher test scores for students of teachers who received training

about how to use calculators when delivering mathematics content to students. (Wolfe; 2010; p4)

Brown offers a fitting solution when he states, Therefore, teachers at all grade bands need to be

informed of the latest research through meaningful professional development. (T. Brown, 2007; p.

111)

In his research of the introduction of graphing calculators into three centralized

examination systems in Denmark, Australia, and the International Baccalaureate, R. Brown found

that only two out of the six mathematics examinations considered demonstrated any significant

change in the types of skills assessed in conjunction with the introduction of the graphics

calculator (R. Brown; 2010, p. 181). According to R. Brown, the graphing calculator is a

revolutionary tool in mathematics education, but its introduction will not by itself lead to a change

in the mathematics skills assessed in high stakes examinations (p. 200). Clearly further study is

necessary which delves into the changes, or lack thereof, that widespread graphing calculator usage

has brought about in terms of standardized testing.


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Currie, in a dissertation study conducted in Tennessee, found that students taught algebra

with the use of graphing calculators achieved at higher levels than students taught without the use

of graphing calculators (Currie, 2006, p. 7). An interesting finding of Curries work was that

teachers attitude about when graphing calculators should be used did not determine whether they

used the technology (p.8, citing NCLB study of 2002). This research involved Algebra 1 and

Algebra 1B students in a large urban high school in west Tennessee, and the results from the

study showed that students of average ability, as determined by their placement of Algebra 1 in

grade 9 or Algebra 1B in grade 10, who used graphing calculators in Algebra 1 did show a

significant positive difference in level of achievement when compared to students who did not use

graphing calculators , and the effect of teachers mastery orientation on their use of graphing

calculators was found to be non-significant ( p. 74).

The National Council of Teachers of Mathematics (NCTM), in 2000, stated that

technology is an essential component in teaching mathematics; it influences the way mathematics

is taught and learned (Ye, 2009, p. 134). Since mathematics is such an important academic field

of study throughout the world, and since it is seen as a universal language, it is significant to

realize that these issues are the focus of research worldwide. Ye argued that Chinese mathematics

educators have struggled with whether to use graphing calculators in mathematics classrooms and

wondered what the vital roles of graphing calculators are in student learning and teaching

mathematics (p. 134). This study involved a collaborative project between Texas Instruments and

Chinese teachers in secondary schools in Zhejiang Province, and the participants were 400 high

school students. The Chinese teachers were hesitant to use the graphing calculators (TI 92+ for

Algebra and Geometry). Yes conclusions included that the use of graphing calculators in


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secondary mathematics teaching is conducive to the reform of evaluation systems; especially in the

way exams are constructed (p. 137).

In a meta-analysis of the effects of calculators on student attitude and achievement,

Ellington concluded that when calculators were included in instruction but not testing, the

operational skills and the ability to select the appropriate problem-solving strategies improved for

the participating students and when calculators were part of both testing and instruction, the

operational skills, computational skills, skills necessary to understand mathematical concepts, and

problem-solving skills improved for participating students (Ellington, 2003, p. 455). Clark states

in his articles that several studies have documented higher test scores for students who use

calculators regularly during mathematics instruction. Merriweather also discusses the topic of test

scores in her study. She states that, it has been shown that calculator use in the classroom

increases test scores for low and average students. (Merriweather; 1999; p. 7) Ellington found no

significant difference between scores of students who used scientific, compared with graphing

calculators, when calculators were not allowed during testing. But when calculators were an

integral part of the testing process, the results based on graphing calculator use were significantly

better than the results of basic or scientific calculators in two areas: conceptual skills and problem-

solving skills (Ellington, 2003, p. 457). Dions study included several references to SAT testing

as well. According to her study, the Educational Testing Service conducted a survey on calculator

use to discover how calculators were being used in the classroom. The results of this study showed

that allowing calculators on the SAT Mathematics tests is a reflection of what is occurring in

classrooms. (Dion; 2001; p.433 ) These results refer directly back to the discussions, studies, and

findings on implementing calculators in classroom instruction. These prove what her statement on

calculators being an integral part of the mathematics curriculum. Most standardized tests given


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today now include opportunities for the use of calculators. Calculator use on standardized tests,

according to Brown, prompted teachers to provide opportunities for students to use calculators in

classroom activities. (T. Brown 2007 p. 110) This would then give the students an advantage

when it came time to take the test.

In his review ofThe Didactical Challenge of Symbolic Calculators: Turning a

Computational Device into a Mathematical Instrument, Fey stated that there has been a

substantial amount of empirical research exploring the benefits and risks of encouraging/allowing

students to use scientific and graphing calculators, with the consistent finding that thoughtful use

of such tools tends to enhance student understanding and problem-solving ability, with no

significant diminution of learning traditional computational skills (Fey, 2006, p. 350). This

review emphasized that with the significance of technology, both graphing calculators and

computers, in contemporary mathematics classrooms, teacher training institutions must adapt their

programs to ensure that future K-12 mathematics educators are competent and comfortable in

teaching with such technologies.

Less research is available concerning the inequities among access to technology in

mathematics, both in schools and in homes. Students from certain minority populations; both in

terms of ethnicity and socioeconomic status, have less consistent access to graphing calculators

and computer technology, and the achievement gap continues to be an issue as a result. Nzukis

dissertation, which investigated African American students identity and agency in a mathematics

and graphing calculator environment stated that the major gap in the research that attempted to

examine equity issues with graphing calculators is that rather than being the fundamental problem

for investigation, the equity issues were often included as incidental and/or as an afterthought (p.

90). Nzukis study attempted to fill in this void by exploring African American students


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identities and agencies that emerge in action as they participate in social practices of learning

mathematics mediated by graphing calculators (p. 90). The case study involved both quantitative

and qualitative data collection, with study participants comprised of two high-achievers and three-

low achievers from an intermediate Algebra III classroom at a low-SES high school. According to

Nzuki, the highest level of using technology is in the role of technology as an extension of self.

Here the technology provides an extension of students mathematical abilities and becomes an

integral part of their mathematical repertoire (p. 144). Very few of the participants in the case

study felt that they had achieved the level of technology as an extension of self.

In conclusion, Nzuki argued that although there is a great deal of equity research in

mathematics education that has been conducted to highlight disparities and limited persistence

along racial lines, there has been a general lack of theorizing about race and racism and their

relationships to mathematics learning and participation (p. 221-222).

Clearly technologies such as graphing calculators are of significance in assisting students

mastery of problem solving in mathematics. Graphing calculators simplify tedious calculations,

and they allow students to contemplate higher level topics at earlier ages than in years past.

Significant research has been conducted concerning the utility of the graphing calculator to

mathematics students across the globe, yet further research is warranted. Where inequities exist

concerning access to technologies such as the graphing calculator, students are placed at a

disadvantage to their counterparts who use the technology every day. Although much data

supporting the use of graphing calculators in mathematics education exists, more extensive and

specific research is needed on this extremely important topic.


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Hypotheses

Hypotheses for Part 1:

Null Hypothesis The presence of calculators will have no impact in general on student HSAP

scores.

Research Hypothesis The presence of calculators will have an impact in general on student

HSAP scores.


Null Hypothesis The presence of calculators will have no impact on the HSAP scores of

students with a GPA of 4.0 or higher.

Research Hypothesis The presence of calculators will have an impact on the HSAP scores of

students with a GPA of 4.0 or higher.



students with a GPA of 3.0-3.9.


students with a GPA of 3.0-3.9.



students with a GPA of 2.9 or below.


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students with a GPA of 2.9 or below.

Research Problems

Graphing and scientific calculators have been the subjects of much discussion for many

years. Although criticized, calculators are one of the most recognized technologies for mathematics

or science based classrooms. The ubiquitous nature of these tools present many important

questions about their effectiveness and roles in the classroom. Therefore, three research questions

are posed:

1. Do calculators inhibit student performance in mathematics courses?

2. Are students dependent on calculators to perform mathematical assessments?

3. Which type of calculator (scientific or graphing) serves as the greatest asset to students on

a high stakes test?

To answer these questions, we will implement different approaches to collect essential data. We

will conduct a survey for teachers, an assessment for students, and a pre- and post-assessment

survey for the students in order to learn more about how the students are using the calculators.

The aim of this study is to determine whether the presence of calculators during the math

portion of the HSAP will impact student scores, and if so, which type proves the most beneficial.

Method

A mixed methods approach is appropriate for this research. On the qualitative side, we will

use a survey of students confidence and attitudes toward using graphing calculators with


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mathematics. As to quantitative, we will conduct a randomized comparative experiment involving

treatment and control methods for each participant, within each part.

Setting and Participants

Participants will be selected from eight high schools in the Columbia area and include 10th

grade students in their second semester. The study will include four parts. A total of 240 students

will take part in this study. Part 1 involves 120 students of varying ability levels. For parts 2,

3,and 4 students are selected based on their cumulative GPAs. A roster of all students will be

compiled. The initial group will be selected using a simple random sample design. The names

will be alphabetized and the 120 individuals will be randomly selected using a random number

generator from a TI-84+ calculator with a seed of 26. The remaining students will be categorized

based on their GPAs, creating a stratified sample. The strata (the students GPAs) will be

categorized as 4.0 and above, 3.0 - 3.9, and 2.9 and below. There will be 40 students selected to

participate in each of the remaining three parts. Again, the names will be alphabetized. Once the

remaining students are divided among the three parts, they will be selected for participation, again

using a random number generator, but this time a seed of 77 will be chosen. We will change the

seed after the first selection to ensure that the students placement on the alphabetic list is not the

automatic means of selection. When all members of each group have been selected, the

individuals within each part: 1, 2, 3, and 4, will be divided among three sub-groups.


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Design

Each group will begin the study with a pre-test survey. This survey will consist of

questions regarding students use and familiarity with calculators prior to the testing experience.

Upon completion of the pre-test survey, a practice HSAP math test will be administered with no

calculator offered. The results of the first HSAP practice test will be used to analyze the results

and discuss implications of later practice HSAP scores. Within each part (1, 2, 3, and 4) the

participants will be divided into one of three sub-groups. The sub-groups will distinguish between

the type of calculator (or lack thereof) each student is allowed to use during the given trials. Sub-

group membership will be randomly assigned. Each individual, regardless of part or sub-group,

will take three HSAP practice math tests during the experiment: one with no calculator offered,

one with a scientific calculator offered, and one with a graphing calculator offered (TI-84+). The

first sub-group will not be allowed to use a calculator during the first trial, be given a scientific

calculator during the second trial, and a graphing calculator during the third. Participants selected

for the second sub-group will use the graphing calculator during the first trial, a scientific during

the second, and no calculator will be offered during the third trial. Individuals in chosen to be in

the third sub-group will be given a scientific calculator during the first trial, the calculator will be

taken away and no calculator will be permitted during the second trial, and a graphing calculator

will be given during the third trial. The order in which the calculators are presented will vary to

ensure better assessment of the enhancements the calculator provides for student scores. If all

students progressed through the same patterns of use with the calculators, then the number of times

the student had taken the test may be a lurking variable. To eliminate this possibility, order will be

altered as stated above.


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The study will take place over the course of three days. We want to keep the trials together

to better eliminate the possibility of outside factors impacting and skewing our data. This study

will be conducted in various classrooms of the Swearingen building on the University of South

Carolinas campus. Transportation to and from the study will be provided to participants as

needed. The pre-test will be administered on the first day of the study; the practice tests will be

graded and the results recorded. The three trials will take place on the second day of the study.

Students will be allowed a fifteen minute break between the administration of the three practice

HSAP tests. It should be noted that though the technology tools allowed will vary among

members of the sub-groups, the test being taken during each trial will be consistent. By

administering the same test to each participant during a given trial we will eliminate the possibility

of a more difficult practice HSAP math test skewing our results. Additionally, students will not be

informed of their scores on the pretests or any of the three trial tests during the study. This

stipulation is put in place to ensure students enter into each test with the same base knowledge as

they did the previous test. The three practice math HSAP tests will be graded and the scores will

be recorded at the end of the second day. On the third day of the study, students will answer

questions to a written survey describing their experiences and thoughts while taking each of the

three tests. The students teachers will also be asked to participate in this portion of the study.

Teachers will take part in a similar survey discussing the use of calculators in their respective

classrooms during instruction

Data Analysis Procedures

Using an analysis of variance test (ANOVA), we should compare individuals within each

sub-group on a pretest to ensure homogeneity and academic ability.


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Results of this study will be analyzed using a matched t-test. A matched pairs study will

allow researchers to analyze a students results under various conditions. The results will be

discussed with respect to part in the study (1, 2, 3, or 4) and sub-group within the part. Aspects of

an ANOVA test will be used for the sub-groups. Sub-group results will be calculated by

determining the measures of central tendency, central variance, and the five number summary for

the statistics of each sub-group. We will use mean and median for the measures of central

tendency, standard deviation for the measure of central variance, and the minimum, maximum, and

quartile values for the five number summary (the median will have previously been established

within the measures of center). The Null and Research hypotheses for each of the parts are as

follows: Null Hypothesis The presence of calculators will have no impact on student HSAP

scores. Research hypothesis The presence of calculators will have an impact on student HSAP

scores. The stated null and research hypotheses are the basis for each part and will be tested in this

manner within the study. If the null hypothesis is rejected, we will use results from the sub-group

analysis to determine which calculator serves as the greater asset to students while taking the

HSAP. Rejection or failure to reject the null hypothesis in any part of the study will not affect the

results of another part. Each of the parts of this study is independent from the others. Therefore,

assumptions can be drawn as to the effectiveness of calculator use in high stakes testing within

specific strata, for this study - cumulative GPA.

Recommendations

Limitations to this study may exist, including length of study, calculator knowledge, geographic

constraints, and prior mathematics instruction. This study is designed to take place over the course

of three days, with all practice HSAP math tests taken on the second day. The design is in place to


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eliminate outside factors from affecting student scores; however, taking three tests in one day may

have effects as well. Students could become tired and disengaged by the end of the testing period.

A second possible limitation would be a students familiarity with calculators prior to the study.

To address this concern, we are including a pre-test survey to gather related information. Close

proximity of subjects can make performing a study much simpler. When participants are located

within a close area, they are more easily contacted and tested, but they may share certain

demographic characteristics that affect the results. Finally, a students math background will play

a huge part in his/her performance on a high stakes test. While a pre-test will be administered to

determine homogeneity among individuals taking part in the study, various techniques, instructors,

and methods of mathematics instruction may impact student scores.

Conclusion

Null and research hypotheses were established for each part of this study. Rejection of the

null hypothesis will imply that calculators do enhance student performance on high-stakes tests,

specifically the South Carolina Exit Exam, HSAP. Upon rejection of the null hypothesis students

scores can be further analyzed to determine whether more advanced calculator technology serves

as an asset or hindrance. Failure to reject the null hypothesis at any part of the study will support

the belief that calculators do not impact student scores on the test.

The use of calculators in math classrooms and on various high stakes tests is an issue of

great contention. Prior studies have addressed this topic approaching it from differing sides.

Dissenting thoughts center on the loss of basic calculation skills, the lack of training with the tool,

and the ultimate creation of a crutch. Those in favor of calculator use support thoughts of more

efficient process, creation of more integrated curriculums, and elimination of basic computational


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mistakes which can nullify any success in process. It is the author's belief that calculators do

enhance student learning when used in the correct manner. With pre-developed understanding of

fundamental math concepts and proper instruction on the use of the tool, calculators may be able to

grow student success.

The data gathered from the surveys and assessments will definitely have significant

implications about the use of calculators to increase learning outcomes. These surveys will help to

determine teachers attitudes about calculators within the classroom. Analysis of the data should

reveal if students are using calculators as a crutch to complete assignments, or if utilizing these

technologies is actually beneficial for learning outcomes. This data is essential to allow instructors

within mathematics realms to develop the most effective curriculum possible.


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References

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lead to change in the types of mathematical skills tested?Educational Studies in

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fromhttps :// www .pearsonassessments .com /NR /rdonlyres /8612144 A - D 4 A 5-4823- B 643-

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EDET J780 Group Project Graphing Calculators and High Stakes Testing

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