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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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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 2Abstract

    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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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 3

    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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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 4computation 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. (as cited by Merriweather; p. 8)

    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. (p.11)Her results also showed that ..76% of the control group thought

    that using the graphing calculator would make math fun... (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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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 5According to both Clark and Dion, it is crucial that calculators are integrated into math

    classrooms. Clark refers to calculators as valuable instructional tools. In Dions study, he

    concludes by saying that There is strong support among mathematics educators that calculators

    should be an integral part of the mathematics curriculum. (p. 433) 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 Brown 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. (T. Brown 2007; p. 103) 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

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 6study is necessary which delves into the changes, or lack thereof, that widespread graphing

    calculator usage has brought about in terms of standardized testing.

    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

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 7graphing calculators (TI 92+ for Algebra and Geometry). Yes conclusions included that the

    use of graphing calculators in 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). Wolfe

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

    use calculators regularly during mathematics instruction. (Wolfe; 2010; p. 4) 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. (Dion; 2001; 428) 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

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 8implementing calculators in classroom instruction. These prove her statement that calculators are

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

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 9fundamental 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 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

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 10data supporting the use of graphing calculators in mathematics education exists, more extensive

    and specific research is needed on this extremely important topic.

    Hypotheses

    Hypotheses for Part 1:

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

    scores.

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

    HSAP scores.

    Hypotheses for Part 2:

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

    students with a GPA of 4.0 or higher.

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

    students with a GPA of 4.0 or higher.

    Hypotheses for Part 3:

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

    students with a GPA of 3.0-3.9.

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

    students with a GPA of 3.0-3.9.

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 11Hypotheses for Part 4:

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

    students with a GPA of 2.9 or below.

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

    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 in this study:

    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 of calculator proves most

    beneficial.

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 12Method

    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

    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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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 13

    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 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 EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 15Results 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 HypothesisThe presence of calculators will have no impact on

    student HSAP scores. Research hypothesisThe 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.

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 16Recommendations

    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 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.

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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 17The 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 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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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 18

    References

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

    Studies in Mathematics, 181-203. Retrieved on May 15, 2012 from

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    Brown, Todd E; Karp, Karen; Petrosko, Joseph M.; Jones, Jane; Beswick, Gloria; Howe, Carrie;

    Swaging, Kathy. (2007) School Science and Mathematics (107/3: 102). Retrieved on

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    _SearchValue_0=ED519032&ERICExtSearch_SearchType_0=no&accno=ED519032

    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    THE EFFECT OF CALCULATOR USE ON HIGH STAKES TESTING 21main.pdf?_tid=1a383e65bbd2bc610cc35a3963e22ec5&acdnat=1337608554_e1ffbc033d

    172a229bfc3c2173cab954

    Wolfe, Edward W. (2010) What Impact Does Calculator Use Have On Test Results? Pearson:

    Test, Measurement & Research Service Bulletin (Issue 14). Retrieved on May 17, 2012

    fromhttps://www.pearsonassessments.com/NR/rdonlyres/8612144A-D4A5-4823-B643-

    57B087B83F12/0/Bulletin_14.pdf

    Ye. (2009). Integration of Graphing Calculator in Mathematics Teaching in China.Journal of

    Mathematics Education, 134-146. Retrieved on May 15, 2012 from

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