THE FREQUENCY OF CALCULATOR-USE IN

Running Head: The Frequency and Effects of Calculator-Use in Elementary Schools

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THE FREQUENCY OF CALCULATOR-USE IN ELEMENTARY SCHOOLS: EFFECTS ON STUDENTS’ MATHEMATICAL ACHIEVEMENT BY FIHAYYA PLAIR

An Honors Thesis Submitted to the Department of Education and the Honors College

Southern Connecticut State University New Haven, Connecticut December 2014

The Frequency and Effects of Calculator-Use in Elementary Schools

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THE FREQUENCY OF CALCULATOR-USE IN ELEMENTARY SCHOOLS: EFFECTS ON STUDENTS’ MATHEMATICAL ACHIEVEMENT BY FIHAYYA PLAIR This honors thesis was prepared under the direction of the candidate's thesis advisor, Dr. Adam Goldberg, Department of Education and it has been approved by the members of the candidate's thesis committee. It was successfully defended and accepted by the University Honors Thesis Committee.

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Dr. Adam Goldberg Thesis Advisor ___________________________ Dr. Laura Bower-Phipps University Reader ___________________________ Dr. Susan Cusato Second Reader ___________________________ Dr. Steven Greengross Department Chairperson ___________________________ Date


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Table of Contents Abstract ............................................................................................................................... 5 Introduction ......................................................................................................................... 6 Background/Review of Relevant Literature ....................................................................... 9 What is Numeracy Fluency and Mental Arithmetic Skills? ............................................ 9 The Controversy over Calculator Use in the Classroom ............................................... 10 The Use of Calculators in Elementary School Classrooms .......................................... 11 Relevant Research on the Effects of Calculator Technologies on Achievement .......... 12 Change is Coming ......................................................................................................... 18 Methods and Materials ...................................................................................................... 21 Results ............................................................................................................................... 24 Discussion ......................................................................................................................... 31 References ......................................................................................................................... 38 Appendix A ....................................................................................................................... 42 Appendix B ....................................................................................................................... 44 Appendix C ....................................................................................................................... 50 Appendix D ....................................................................................................................... 55 Appendix E ....................................................................................................................... 57


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Table of Figures Figure 1) Teaching Experience ................................................................................................. 22 Figure 2) Grade Levels .............................................................................................................. 23 Figure 3) Calculator use ............................................................................................................. 25 Figure 4) The Frequency of Calculator-use ............................................................................ 26 Figure 5) Situations Where Calculators are allowed.............................................................. 26 Figure 6) Comparison of calculator-use to other classrooms ............................................... 27 Figure 7) Grade levels teacher’s believed calculators should be introduced ...................... 27


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ABSTRACT Author:

Fihayya Plair

Title:

THE FREQUENCY OF CALCULATOR-USE IN ELEMENTARY SCHOOLS: EFFECTS ON STUDENTS’ MATHEMATICAL ACHIEVEMENT

Thesis Advisor:

Dr. Adam Goldberg

Department:

Department of Education

Year:

2014

For the purpose of investigating the current and changing policies in public elementary education concerning calculator use in the primary grades, a literature review on the effects of calculator-use on students’ mathematical understanding and achievement was conducted. The question of whether mathematic technology is benefiting or hindering students was also considered. A study was then conducted to survey the frequency of calculator use in the classroom and teachers’ opinions about the effects of calculators in elementary school. Three research questions were used to guide the study: (1) Are calculators used in New Haven/Hamden CT elementary schools (K-6)? (2) How frequently are they used and to what extent? (3) What are teachers’ perceptions of the effects calculator may have on student performance/achievement? The study included a quantitative and a qualitative component. Results of the quantitative and qualitative analysis indicate that (1) calculators are used in elementary school, (2) calculators are not used very frequently, (3) teachers’ opinions about the effects calculators have on their students vary widely, but a large majority believe calculators should not be used if math facts are not mastered, and (4) further research is required to pursue more accurate conclusions about the current role that calculators play in the primary grades of American education, which might influence educational policy for the future. Keywords: Mathematical achievement, arithmetic skills, numeracy fluency, calculator-use, primary grades.


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Introduction Mathematics is a cornerstone to civilized societies both ancient and modern (Hom, 2013). It incorporates the knowledge of logic, shape, quantity and problem solving abilities. The language of mathematics is unique and serves as the foundation for much of our everyday lives, from money, to technology, science, architecture, and even art. The roots of mathematics can be traced back to even the most primitive of cultures. When societies grew so did the need for mathematics. The complexity of society thus seems to correlate with the complexity of the mathematical needs and advances (Hom, 2013). The National Academy of Sciences and Engineering (2000) stated that to be prepared for today's workforce, informed about important issues, and able to understand the complex world in which we live, all Americans must have a solid education in science, mathematics, and technology. Mathematical concepts and problem-solving abilities are some of the most important skills we need in order to get through our daily lives. If data from the National Assessment of Educational Progress (NAEP) are any indication, “Elementary school mathematics programs have had some success in helping students perform calculations but have been largely unsuccessful in developing students’ problem-solving abilities” (Reys & Arbaugh as cited by Silver and Kenney 2000, 2001, p. 3). In April 1970, Tokyo, Canon Business Machines produced the “world's first electronic handheld calculator” (Green, n.d., p. 1). Controversy arose soon afterwards concerning the role of calculators in primary schools. How would the incorporation of this technological advance influence the development of students’ basic reasoning skills, specifically in the elementary classroom? Would the use of the calculator take away from students’ ability to think and reason through problems? (Reys, 2001) With all the controversy that has plagued this topic, it is time to review how and when to best use calculators to encourage greater numeracy skills in young


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children and rethink when such a tool is to be introduced to them to maximize successful mathematical understanding and achievement. Current day public elementary schools pride themselves on preparing their 21st Century students for the technological advances around which their future lives will revolve (National Academy of Sciences, 2000). As a result, students as early as third grade are allowed to use and are taught calculator skills in elementary schools. The literature reports some concerns over the possible negative influence of calculator use in elementary grades (Rittle-Johnson, 2008) (Walcott & Stickles, 2007) and (Brown, 2007). Recent Common Core and Partnership for Assessment of College and Career Readiness (PARCC) policies have resulted in the ban of calculator use in standardized exams in grades three through five (SBAC, 2013). Specifically, the new Smarter Balanced Assessment Consortium, which replaced the CMT assessments in 2014, stated that the Smarter Balanced summative mathematics assessments at grades 3-5 do not allow for calculator usage. There seems to be conflicting policies regarding calculator use and the ways that the use of calculators might impact students’ skills. This topic remains controversial within math education. This research paper investigated current trends in calculator use in elementary schools. A literature review was conducted to explore of the effects of calculators on students’ mathematical understanding and achievement and consider whether calculator use is benefiting or hindering students. This literature review informed my understanding of how to help elementary students effectively improve their mental arithmetic skills and successfully develop numeracy fluency. As part of this research, teachers were surveyed concerning the frequency of calculator use in the classroom and their opinions about the use of calculators in elementary school. The results of this project as a whole have inspired me to further consider the current role that calculators play in the


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primary grades, as well as consider how further investigation might influence educational policy for the future. The debate about calculators is not new. According to the National Council of Teachers of Mathematics (NCTM, 2011) there are nearly 200 research studies, dating from 1976 to 2009, on calculator use in the classroom. This research is designed to provide current information regarding the influence of calculators in elementary classrooms. The results will be useful in helping educators make their own decision about the matter. Does the calculator help free students to spend more time problem solving, or is it merely an excuse for a student not to utilize the mental computation skills they were taught? This matter may always be open for opinion; only now people can better know how this pertains to elementary school students. As an aspiring teacher, this research will definitely have an impact on my professional practices in the classroom. Based on what I have discovered, I have a choice to make. I can either decide to embrace calculators as a handy tool for furthering my mathematical agendas in the classroom or restrain their use unless absolutely necessary.


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Background/Review of Relevant Literature In order to properly investigate the topic of calculators use in elementary schools, it is important to consider the body of research that defines the role of calculators in mathematics instruction and assessment in our nation. This study first considered numeracy fluency and the role of mental arithmetic skills in the classroom, the development of the controversy of calculator use in the classroom, past relevant research, and the recent policy changes that will affect future mathematics standardized assessment. What is Numeracy Fluency and Mental Arithmetic Skills? When thinking of an early reader in elementary school, the concept of literacy is analogous to the concept of numeracy. Based on my education courses, a student works on their literacy skills as they learn to read and comprehend what they are reading. Once a child can read fluently, meaning accurately, quickly, and with expression, and can understand what they read, they are considered literate. The same goes for mathematics. Students work on their numeracy skills as they learn to perform operations and solve problems. They develop the capacity to be numerate by using mathematical ideas effectively to participate in daily life. This involves “developing their use of numerical, spatial and graphical concepts and skills in a variety of contexts” (Fischer, 2006, p. 1). The National Council of Teachers of Mathematics (2009) suggests that instructional programs from pre-kindergarten through grade 12 should enable all students to understand numbers, ways of representing numbers, relationships among numbers, and number systems; understand meanings of operations and how they relate to each other; and compute fluently and make reasonable estimates. They noted that, “Technology should not be used as a replacement for basic understandings and intuitions; rather, it can and should be used to foster those understandings and intuitions.” (p.2)


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It has been shown that numeracy skills plays an important role in effective decision making and problem solving, (Peters, 2005) but this is also true for mental arithmetic. Mental arithmetic skills comprise arithmetical calculations that are done in a student's head without the guidance of pencil and paper, calculators or other aids (Morin, 2014). Mental math is often seen as an avenue to calculate and estimate quickly, using the math facts that a student has memorized, such as multiplication, division or doubles facts. Like everything else, learning mental math at an early age can help boost a child’s confidence when it comes to mathematics, develop mental calculation abilities, and provide a sense of achievement as their aptitude improves (Morin, 2014). According to Morin (2014), it can also lead to greater mental capacity, enhance problem-solving capability, enrich creativity and last but not least, improve concentration and mental endurance. Mental arithmetic skills may not enable a person to calculate quantities as quickly and accurately as the calculator can, however it can help students make estimations and double check their calculations accuracy.

The Controversy over Calculator Use in the Classroom There are many contrasting views concerning the correct and continually effective use of calculators as an academic tool. The common stance, however is that there needs to be a balance in the use and non-use of calculators in elementary school. One might assume that having a calculator guarantees the ability to perform any common calculation; this assumption is wrong. “Effective use of a calculator requires an understanding of numbers” (McIntosh, 1990). McIntosh (1990) indicated that parents and educators alike often agree that using calculators causes children to become idle and dependent on calculators to do their work for them. The National Institute of Economic and Social Research conducted research in 1996 involving international comparisons and suggested that “calculators should be blamed for poor standards in mathematics and that they


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should be banned from tests with more emphasis being placed on arithmetic” (Green, n.d., pp. 13). Acknowledging the lack of fluency in mental and written calculations alike, the Cockroft Report (1982) advised that “availability of a calculator in no way reduces the need for mathematical understanding on the part of the person who is using it” and that “the weight of evidence is strong that the use of calculators has not produced any adverse effect on basic computational ability” (Green, n.d., p. 3).

The Use of Calculators in Elementary School Classrooms The real question that needs to be addressed first is just how early and how often are calculators used in classroom instruction and standard assessment during elementary school, today? The 1989 "Curriculum and Education Standards," a publication of the National Council of Teachers of Mathematics NCTM says calculators "must be accepted at the K-4 level," (p. 3) and that calculators will help the children in kindergarten through fourth grade have "valuable conceptdevelopment experiences" (Klutch, 1991). According to the NCTM (2011), calculators have an important role in supporting and advancing elementary mathematics learning. In a review of 127 research studies on calculator use in K–12 classrooms, Ellington (2003) noted, “Students received the most benefit when calculators had a pedagogical role in the classroom and were not just available for drill and practice or checking work” (p. 456). The key here is that their use was deliberate, tied to specific learning activities and outcomes (NCTM, 2011). Despite such trends, there are some states including Arizona, California, Nevada, New York, and Ohio, who forbid calculators in elementary school (Robelen, 2013). Every other state in America allows the use of a calculator in elementary school classrooms; this includes Connecticut.


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Relevant Research on the Effects of Calculator Technologies on Achievement NCTM (2000) Principles and Standards for School Mathematics supports the advancement of technology, such as the calculator, in the classroom, and asserts that the use of technology often allows for problem solving to occur in greater depth. It also recognizes that the essential principle of learning necessitates students to actively learn with comprehension and form new knowledge from experience and prior knowledge (NCTM, 2000). New knowledge is, after all, built upon the foundation of pre-existing information. To further investigate the role that calculators play in the classroom several research studies were reviewed. In the research study conducted by Thom and Pirie in 2002, several students at the third grade level were required to complete a set of mathematical problems. This study was unique in the sense that although it tested the student’s knowledge of the concept of the volume of a box to solve the problems, it was not done directly. The types of questions that were presented in the competition required the students to do much more than identify the mathematical idea (volume) or operation and then apply it. The questions required the students to problem solve; this means monitoring themselves, questioning whether one method was the best way to go about the problem, and realizing when it is time to try a different method or to integrate several different methods together, formulate their own methods and identify the operations that they feel would best bring them to the correct solution. In this, the computations themselves were an important part in arriving at the correct answer, however it would not be the most critical piece in solving the problem. The authors did note that when the students started getting frustrated with their failed attempts to repeatedly add and even multiply two-digit numbers, a calculator would have come in handy to help move the problem solving along. A calculator was then allowed from then on out because it was not seen to have much of an impact on the true purpose of the study. This in a way confronts


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a common question concerning calculators and their impact when it comes to problem solving as opposed to their impact concerning basic computations. Why these third grade students could not solve a two digit multiplication problem without the help of a calculator wasn’t in any way expanded upon in the study, nor was any information on how frequently these students used the calculator on a regular basis disclosed throughout the discussions and conclusions. The results of this study, however do show that when it comes to learning and grasping a new mathematic concept such as volume, it helps for the student to initially engage in a group problem solving activity which introduces them to and allows them to explore the concepts. For this, a calculator would be greatly encouraged. In an earlier study done in 1995, Bridgeman, Harvey, and Braswell conducted a survey to determine whether using a calculator on a standardized test affected mathematical reasoning. They randomly selected a sample of 11,457 high school juniors, all whom had decided to attend college upon graduation, from two hundred and seventy-five high schools. These students took a test containing 70 SAT math questions and with half of the students given permission to use calculators, while the other half were forbidden. Before the testing actually took place, the students were given a questionnaire concerning their previous use of calculators in general. Did they use calculators on a regular day-to-day basis, and if so what kind, basic, scientific, or graphing? Also, did they normally use calculators on their classroom math tests? It turns out that about 90% of the students used calculators at the very least several times a week, but when it came to taking tests in their math classes, about 17% were always prohibited from utilizing the calculator. This posed a problem to the researchers. They wanted to make sure that the students who never used calculators on math tests before, were not put at a disadvantage to those students who reported to have used a calculator on every or almost every math test they took in class. Interestingly, it turns out that the


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students who used calculators on classroom tests did significantly better on the test in this study if they were part of the group who were allowed the calculator. However, students who never used calculators in classroom tests performed only slightly better on this study’s test if they were allowed to use the calculator. This shows that students who were used to using the calculator performed worse without the calculator than students who were used to not using the calculator for testing. In the end, however, the study concluded that the use of calculators on a test containing mathematical reasoning question types, such as those found on the SAT, resulted in a significant score increase, regardless of whether the calculator had positive, neutral, or negative effects on individual testing items. In a pilot study done in 1980 with twenty-five fifth grade students, Charlotte L. Wheatley conducted an investigation in order to see what effect calculators would have on the students’ abilities to problem solve. Wheatley wanted to know whether the permission to use a calculator on a regular basis would cause that student be more focused on the strategy needed to solve a problem. After the study, Wheatley concluded that students who are permitted to use calculators spend about the same amount of time to complete a task as those who are not. The calculator group had fewer errors in computation, of course, and spent more time problem solving as opposed to doing computations. In this sense, Wheatley’s findings seem to accurately support NCTM’s belief that technology supports problem solving. However, Huntley, Rasmussen, Villarubi, Sangtong, and Fey (2000) conducted a study that compared the growth of problem solving skills in students, as well as the understanding of algebra, and basic math skills, in regards to the Core-Plus Mathematics Project curriculum and a more conventional curriculum. In the article, they claimed that even though the use of a calculator may offer a student a diversity of influential new learning and problem solving tactics, it still diminishes the necessity for the student to attain a high degree


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of skill in symbol manipulation (Villarubi, 2000). The next question therefore is, if the time spent to complete a given task on average with or without a calculator is around the same, and if using a calculator really does lessen the need for students to acquire higher degrees of computations skills, is it really benefiting elementary students as a whole? Although these studies have provided a great deal of information to consider, only two studies touched on calculator use in the elementary grades, one in Wheatley (1980) and Huntley, Rasmussen, Villarubi, Sangtong, and Fey (2002). Many other studies were conducted concerning the effects of calculator technology on the achievement of students in middle school, high school, or college. However, elementary school students are unique and therefore are the focal point of this study. The question of repercussions of giving such a powerful tool like a calculator to these students should be given deeper consideration. How are schools and teachers intervening to minimize the costs and maximize the benefits of calculators and is it working? In a more recent study done in 2007, with 800 elementary, middle and high school teachers, Brown, Karp, and Petrosko conducted an investigation in order to gain insight on K-12 teacher’s beliefs and teaching practices concerning calculator use in their mathematics classrooms. The study was designed around two questions: what are the beliefs and practices of the teachers regarding calculator use, and how those beliefs and practices differ among the three grade groups, elementary, middle, and high school. Three different surveys were distributed specific to each grade group. 327 of the 816 surveys that came back were elementary teachers. It was reported that elementary school teachers used the 4-function calculator more often than middle school teachers used the scientific calculator and high school teachers used graphing calculators. However, a significantly larger percentage of high school teachers believed that calculators were a positive force in mathematic instruction when compared to elementary teachers. At the same time there


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was a positive correlation between the grade level of the teacher and teachers’ perception that calculator use may be a way of getting answers without students understanding mathematical processes. Meaning, compared to elementary school teachers, middle and high school teachers were more likely to believe that their students were using the calculator as a crutch. Teachers’ beliefs therefore reflected in their practices. Teachers who believed that calculators were a “catalyst” used the calculator freely and diversely, while teachers who believed that calculators were a “crutch” limited the use of calculators in their practices (Brown, 2007, p.112). In the research study conducted by Walcott and Stickles in 2007, the calculator section of fourth and eighth grade National Assessment of Educational Progress Main Mathematics were examined and compared. A total of 189,800 fourth graders from 7,310 different schools and 147,300 eighth graders from 6,400 different schools were sampled to take the NAEP Main mathematics assessment. It was found that the groups of fourth grade students who did not use the calculator on their problem-solving items had considerably higher composite scale scores when compared to the groups of fourth grade students who reported using the calculators. However, for the groups of eight graders who reported using the calculator on problem-solving items, the average composite scale scores were considerably higher than those reported not using their calculators. As a result of these findings, Walcott and Stickles concluded that when it comes to mathematic problems in which calculators can be used as a tool, it is suggested that students must have efficient amount of knowledge that allows them to discern when they should and should not use the calculator and how to use it in the most efficient way. Such a filter will help influence their decisions and positively affect their mathematical achievement. This conclusion is also supported by previous research conducted by Campbell and Stewart in 1993, Hembree and Dessart in 1986, and by Suydam in 1987. They all agreed that once students are ready and mature enough to use


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calculators as a tool for problem solving, student achievement is improved. This is because, by that time their thinking skills are also more mature along with their abstract understanding of ideas. This allows for a certain level of efficiency concerning calculator use and problem solving. To investigate the effects of calculators on first grade students’ mathematics achievement, Drew Polly conducted a study in 2007, utilizing date from the Early Childhood Longitudinal Study-Kindergarten Cohort (ECLS-K). The data was collected during the fall and spring of 13,812 students’ Kindergarten and First Grade years. Study’s main focus was to investigate how calculator use as well as other instructional practices influence first grade mathematics students. A significant basis for this study, supported both by studies conducted by Braswell (2001) and Gonzalez (2004), was that results of international and national assessments “indicate that students are struggling with basic computational skills as well as basic problem solving skills” (Polly, 2007, p.245). Besides calculator use, other significant influences that were investigated were writing algebraic expressions, explaining approach to solving problems. Solving real-life problems, solving problems with multiple solutions and solving problems with partners. Polly (2007) concluded that the use of calculators alongside effective instructional practices can have a significant influence on the mathematics achievement of first graders. However, while calculators alone accounted for less than 20% of the improvements found in this study, other instructional practices, such as writing algebraic expressions and explaining their mathematical strategies, accounted for 80% of the improvement. These two instructional practices alone would improve student learning, but when coupled with calculator use, as recommended by NCTM (2000), student learning is taken to the next level. The final study that was examined was conducted by Rittle-Johnson and Kimickewycz in 2008 to explore two questions: Should children use calculators to learn arithmetic facts, or should


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they generate them on their own? Does the impact of generating answers depend on prior knowledge of arithmetic facts? They compared problem solving accuracy by generating the answers to reading the answers from a calculator from a sample of 55 third graders from two private Catholic schools. The children completed a pretest, a study session, a posttest, and a retention test. It was during the study session that students were randomly assigned to the generate group or the calculator group. In the end, the study concluded that the effect of generating answers and reading them from calculator, relied heavily on children’s prior knowledge. So calculators' effectiveness in mathematics classes, depends in large measure on students' pre-existing knowledge of basic math. The researchers found that for students who had a solid understanding of multiplication, calculator use did not have an impact on their performance. But among students who struggled with multiplication, calculators had a negative effect. This study also found that students using calculators were able to practice more problems and had fewer errors. The findings suggested that it is important for students to learn how to calculate on their own, but after that, calculator use is acceptable (Rittle-Johnson, 2008).

Change is Coming Recent changes to the Common Core State Standards in 2013 state that “students taking Common Core State Standards math exams in grades 3 to 5 will not be permitted to use calculators, but students in middle and high schools will have some access to the devices, according to policies by the two consortia developing the exams” (Robelen, 2013, p. 1). The Standards, however, do not take a position concerning the calculator for any specific grade level. Instead they only stressed that they be used appropriately and strategically in the classroom. Prior to this declaration, the Partnership for Assessment of College and Career Readiness (PARCC) in July 2012 issued a


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policy statement stating that PARCC mathematics assessments for grades 3 – 5 will not allow calculator usage (Robelen, 2013). Educators and math experts alike have had diverse reactions to the PARCC policy. The National Council of Teachers of Mathematics in 2011, a longtime advocate for the importance of using calculators over a wide range of grade levels, issued a policy statement overtly highlighting the fact that only "selective and strategic use of calculators” will produce the desired results when it comes to supporting elementary math learning (Robelen, 2013, p. 1). On the one hand, a 2012 teacher survey by Banilower, Smith, Weiss, Malzahn, Campbell, and Weis suggested that calculators are not often used at the third through fifth grade level. This survey reported that the four-function calculators, whose only functions are addition, subtraction, multiplication, and division, have 58 percent availability in elementary classrooms, but are used at least once a week in only 13 percent (Robelen, 2013). Linda Gojak, the past president of the NCTM, voiced her opinion stating that she was not troubled much by the third through fifth grade calculator ban on exams. However, a math-curriculum consultant for the 14,500-student Kenton County district in Kentucky, Jennifer Barrett, welcomed the restriction. She felt that it would give teachers a reason to spend more time on the grade-level fluencies enforced in the common core, which had been de-emphasized in the past few years. "If calculators are used, how is computational fluency and number sense being supported?" Ms. Barrett questioned (Robelen, 2013). On the other hand, this new policy was not intended to send a no-calculator message to teachers. Teachers were still expected to use them in classroom instruction. Having confidence with the methods of addition, subtraction, time tables and division long before utilizing the calculator to assist them when working with more complex problems is something that all young children should have. Banning calculators in the math test is sure to reduce the dependency students are having on to


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compute the most basic sums and encourage student confidence and mastery of their math facts, namely, “number sense skills, number sense, and fluency”, supported Ms. Piper, a senior adviser for mathematics at Achieve, a Washington-based organization working on the PARCC assessments (Robelen, 2013). With that, children will have a more solid foundation upon which they will later build the math skills they will need in their adult lives. The Issue Spans Outside of America This is not an issue that America is facing alone. Worldwide, countries are debating the best methods for teaching their 21st-century elementary students the mathematics to properly prepare them for their future lives. Another country has come to the same solution; namely to limit or ban the calculator and re-emphasize the mastery of mental arithmetic and written mathematical methods. Currently, the London primary school math curriculum advocates introducing calculators at the age of seven, about second grade (Burns, 2012). However, the British government believes that banning calculators from fifth grade math tests for the 2014 school year in England and limiting the use of calculators in primary schools will decrease student dependency on them (Burns, 2012). This remains consistent with a draft primary school curriculum publication recommending the delay of calculator use as part of math lessons. Elizabeth Truss, the Education Minister in London, argued that an “over-reliance” on calculators revealed that students failed to obtain a strong foundation in mental and written arithmetic needed to progress onto middle and high school. Truss also stated that students should not be allowed to utilize such a learning tool until they have mastered their times tables and fully understand the methods required to add, subtract, multiply and divide (Burns, 2012). It was Ms. Truss that later stated the unfortunate reality that “while math is now more important in our societies than ever before, it appears that for one to be bad with numbers has become acceptable” (Burns, 2012).


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According to a recent McKinsey Global Institute report, it is projected that America needs 140,000 to 190,000 more workers that have good mathematical and analytical skills and 1.5 million more data literate managers. Analyzing today’s deluge of data is an ability that has become increasingly important in our societies (NCTM, 2004). At the same time, when it comes to international math comparisons, America finds itself rather mediocre. According to a comparison study conducted primarily by Kelly and Xie (2013) from the National Center for Educational Statistics, China ranks number one in the Program for International Student Assessment (PISA) for 2012 and China is one of the few nations that has completely banned the use of calculators from their entire educational system (Yang, 2012). On the other hand, the United States of America, while they did rank number twenty-five in 2010, ranked number thirty-one as of 2012. If America wants the next generation of young minds to aspire towards careers as data scientists and mathematicians, something must change. “Today's students must master advanced skills in mathematics, science, and technology to stay on track for college and for promising careers” (NCTM, 2004). There are significantly fewer studies of calculator use in elementary schools compared to those in middle and high school. This study will contribute to the limited literature available on calculator use in elementary schools.

Methods and Materials Methods The subjects for this study were teachers in the local New Haven and Hamden area, ranging from kindergarten through to eighth grade teachers. This study was approved by the IRB, giving me permission to conduct human research. A questionnaire was created and sent


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electronically to all elementary and middle schools in the Hamden and New Haven districts. Survey links were initially sent to teachers and principals with whom I had previously done field work placements. This worked well with the Hamden Schools, but for the New Haven schools permission was required from the NHPS math supervisor before teachers and principals could participate. Participants The link to the survey was then sent to the New Haven District central office, where it was distributed to K-8 teachers of all New Haven Public Schools. New Haven and Hamden schools were chosen primarily because of their localness and the fact that I’ve worked with both districts before. Seventy-two teachers filled out the survey and returned it. According to figure 1, 15% of the 72 teachers surveyed were 1st year teachers, 6% were 2nd year teachers, none were 3rd year teachers, and 79% of the remaining teachers taught for 4 years plus.

Teaching Experience 15% 6% 0%

1 Year 2 Years 3 Years 4+ Years

79% Figure 1) Teaching Experience

Surprisingly, the current grades taught by the candidates were quite evenly distributed among the seven grade levels of elementary school. 14% of the candidates taught Kindergarten, as well as


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2nd, 3rd, 5th, and multi-grades. 15% of the candidates taught 1st grade, 8% taught 4th grade, and 7% taught 6th grade.

Grade Level 8%

16%

16% 18% 10% 16%

Kindergarten 1st Grade 2nd Grade 3rd Grade 4th Grade 5th Grade 6th Grade Multi.Grde

16%

Figure 2) Grade Levels

See table 1 in Appendix D for the table of grades taught by the candidates and their corresponding years of teaching experience. Data Analysis The data collected consisted of responses from seventy-two teachers who completed the online survey. The survey collected two types of data, quantitative and qualitative. To analyze the quantitative data, graphs and chart were created using a Microsoft Excel spreadsheet, with each question as a variable. Correlations were then ran. To do this, the data was converted into numerical answers. For example, the frequency questions were converted from never, hardly ever, often, and very often to 0, 1, 3 and 4. With these numerical answers, using the Correlation function in Excel, I selected two variables (questions) and calculated their correlation. A correlation of 1 means the variables are positively correlated to each other, and -1 means the variables are negatively correlated. A correlation of 0 means that the two variables selected are not related at all.


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To analyze the qualitative data, I reviewed all of the short responses that the candidates provided for the last two questions of the survey (see Appendix B and C). The responses were then categorized into three groups. Concerning the first qualitative question, teachers’ rationales for why they choose whatever grade level they believed students should be introduced to the calculator, responses were broken down into three categories: student readiness, technological enrichment of learning, and grade appropriateness. Concerning the second qualitative question, teachers’ opinions about the effects that the presence/absence of calculators may have on their students’ mathematic performance/achievement, responses were categorized into five main groups: no effect, benefits of calculator presence, and benefits of calculator absence, detriments of calculator presence, and detriments of calculator absence. Materials Because a review of the literature did not yield many specific answers concerning how frequently calculators are used in elementary school classroom or teachers quoted opinions, a survey was designed to obtain such answers. The survey, The Frequency of Calculator-use in Elementary Schools and Their Effects on the Students’ Mathematical Achievement, consisted of 9 questions (see Appendix A). Questions #1 and #3 gathered specific information about the teachers themselves, such as how long they have been teaching and what grade they teach. Questions #2, #4, #5, and #6 gather information pertaining to the use of calculators in the classroom. Questions #7, #8, and #9 gathered qualitative data that were related to teacher attitudes and opinions regarding calculator use and their possible effects on student achievement.

Results This study set out to investigate the frequency of calculator use in public elementary/middle school classrooms and as well as teachers’ perspective on the effects calculators may have on


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student mathematical achievement. The primary interest was to determine whether calculators are used in elementary school classrooms and if so, how often and to what extent. The secondary interest was to determine teachers’ attitudes and opinions about calculators in the public elementary/middle school classroom setting. In addition, possible correlations between the frequency of calculator use and teachers’ attitudes and opinions about calculators were explored. This section presents the results of the data collected via online surveys, a statistical analysis of the results. One of the most pressing questions of this entire research project was to discover whether calculators are really used in elementary school. As supported by the literature review, the NCTM have permitted and encouraged the use of calculators in all grade levels. According to the data gathered and presented in figure 3, 28% of teachers use calculators in their elementary school classrooms and 69% do not. So even though it is encouraged, the majority of teachers do not use calculators in their elementary school classrooms. CALCULATORS AS A RESOURCE Yes 29%

No

71% Figure 3) Calculator use

The second most pressing question that this research project set out to investigate was just how frequently calculators are used as a resource in elementary school classrooms. According to this study, not often at all (see figure 4). Fifty-seven percent of the teachers surveyed never use


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calculators, while 28% claimed to hardly ever use them. 10% of the teachers say they use them once or twice a week, while only 6% claim they use them often.

The Frequency of Calculator Use Rarely

65%

Once or twice a week

22%

Often

10 13 0

5

10

15

20

25

The Frequency of Calculator Use

Figure 4) The Frequency of Calculator-use

The figure below represents when the candidates allowed calculators to be used in their classrooms: during instruction, drills, independent practice, or assessment.

Situations Where Calculators are Allowed 0

2

4

Instruction

6

8

10

12

14

16

18

20

26%

Drills2% 2% Independent Practice Assessment

Figure 5) Situations Where Calculators are allowed

44% 30%

Situations Where Calculators are Allowed

Among all the candidates, excluding those who don’t have calculators in their classrooms, 43% allow calculators for independent practice, 25% use them for instruction, 30% allow them during assessment, and only 1 claimed to use them during morning drills. For the next question, represented by the graph below, I took a more subtle approach to the subject by asking teachers how they feel their classroom’s use of calculators compare to others.


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COMPARISION OF CALCULATOR USE TO OTHER CLASSROOMS

More

15%

Less 23% 62%

About the Same

Figure 6) Comparison of calculator-use to other classrooms

According to the data collected, the majority of teachers, whose classrooms use calculators, feel that the calculator-use in their classroom is about the same as the calculator-use in other classrooms of the same grade level. Last but not least, candidates were asked to select the grade level they found most appropriate for calculators to be given to students for ordinary use. 28% of the teachers surveyed chose 3rd grade as the grade level most appropriate for calculator-use, while 15% chose 2nd grade and 4th grade alike. GRADE LEVELS TEACHERS BELIEVED CALCULATORS SHOULD BE INTRODUCED

7%

3%

15%

13% 28%

19%

2nd Grade

3rd Grade

4th Grade

5th Grade

6th Grade

7th Grade

8th Grade

High School

15% Figure 7) Grade levels teachers believed calculators should be introduced

So from the graph above, it can be concluded that the majority of the teachers surveyed preferred calculators be given to students in the real early years of their education, such as 2nd and 3rd grade, rather than later such as 7th or 8th grade.


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For further analysis, I calculated the correlation between how frequently teachers use calculators in the classroom and what grade they would introduce the calculator, but there was no noticeable correlation [-0.240]. I also calculated the correlation between what grade the teachers taught and the grade they would introduce the calculator, and again there turned out to be no correlation [-0.108]. However, after subtracting the grade the teachers taught from the grade they would introduce the calculator to their students, and taking the average of those differences, I got 1.43. This means that on average, the teachers thought calculators should be first introduced a grade and a half higher than the grade level they themselves taught. The very next question in the survey asked teachers to reveal the rationale as to why they preferred the grade level they chose over others. Twenty-three responses fell into the first category, student readiness. The following responses were given by teachers in this group: “I believe students need to have a firm grasp on addition, subtraction, multiplication, and division before using a calculator. By 4th grade students have learned basic math and can use a calculator to complete more challenging problems.” “I think it’s important for students to get the math basics and not depend on a calculator for what they can do using other strategies. By 5th grade, they should be mature enough to use the calculator along with other strategies they have learned.” Fourteen responses fell into the second category, technological enrichment of learning. The following response were given by teachers in this group: “It is an important "life" resource and with the importance of technology in the world today coupled with how well students can use technology, it's important to start early.” “Calculators are helpful at any level and do not lead to less number sense...”


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Twenty responses fell into the third category, grade appropriateness. The following responses were given by teachers in this group: “I believe that sixth grade is a good grade level to introduce the use of a calculator into the classroom because the mathematics becomes more complex in the upper middle school years. Also, if by that time students are still struggling to solve basic math equations, they need a calculator as a tool so that they can move forward.” “I chose 4th grade to start implementing calculators into the classroom because in this grade the math curriculum or particular math problems would start to require the use of calculators to solve problems.” Fourteen responses were returned blank. The last question in the survey asked teachers to give their opinions concerning the effects that the presence or absence of calculators may have on their students’ performance/achievement. There were five categories established to group the responses that were given: no effect, the benefits of the presence of calculators, the benefits of their absence, the detriments of their presence, and the detriments of their absence. Thirteen responses fell into the first category, they believed that calculators have no effect on their students’ mathematical achievement. Eleven responses fell into the second category, they believed that the presence of calculators had a positive impact on their students’ mathematical achievement. The teachers who fell into this category commonly spoke of the advantages of being able to check their answers, have independence, focus on more advanced problem solving, and the necessity of calculators for students with IEPs. The following response were given by teachers who held this view: “In my low class the calculators have helped them because they don't know their facts as well as they should. In my higher class it did not make a difference other than that they finish sooner.


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“I think that comparing estimates to actual answers is a good skill to have before they reach me. I would use them more IF I HAD A SET! If students haven't memorized their facts by this point... they need the help to do the computations more quickly!” “6th grade seems to be a good time in a child's academic journey where they are moving from basic level math in elementary school to higher level problem solving and abstract math in middle school and later in high school. Also by 6th grade our students should have a firm hold on their basic math facts. Only once that is mastered can a child move forward and advance to high levels of learning.” Sixteen responses fell into the third category, they believed that the absence of calculators had a positive impact on their students’ mathematical achievement. Those who argued the benefits of the absence of calculators commonly spoke of the development of mental math, applying foundational skills, using their brains and achieving mastery without a crutch. The following statements are several of the responses given by this group. “My students do very well without calculators. Most, if not all of them, perform at the proficient or goal level. They are using their brains and applying the skills taught without the crutch of a computer/calculator doing it for them. In first grade, the mathematical principles are simpler, therefore they need to be mastered without a calculator in order for students to succeed. We are teaching them the foundational skills they need and will use throughout their lives.” “I teach second grade and the absence of calculators in the classroom allow students in this grade/age to learn how to use their rote memory for basic addition and subtraction facts rather than rely solely on a calculator to solve it for them. By being dependent on a calculator this early students will never be able to recall basic facts.”


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Four responses fell into the fourth category, they believed that the presence of calculators had a negative impact on their students’ mathematical achievement. They often focused on the concept of overreliance. The following responses were given by several teachers in this group. “Students can rely on the calculator too much which is why they are not often used in my classroom. Many of my students do not know their basic math facts so I try to avoid using calculators unless the math process is not the focus.” “The younger students who are not yet fact fluent become too dependent on a calculator and see no need for memorization.” Two responses fell into the fifth category, they believed that the absence of calculators had a negative impact on their students’ mathematical achievement. The following responses were given by two teachers in this group. ” I wish I had a full set but I don't which prevents me from doing more challenge logic problems.” “I wish I had a set but they are given to the math teacher and I borrow them periodically for Science. There are children who have "able to use a calculator" in their IEP's, so I take them when we are computing means for our investigations. Otherwise, there just aren't enough to go around! They get broken, batteries die or solar cells crack, and sometimes they just "disappear". It is a huge expense for the District!” Twenty-six responses returned blank.

Discussion The current study addressed three primary research questions. These questions asked whether calculators are used in elementary school classrooms, how frequently are they used, and what are teachers’ perspectives on possible effects that the calculator’s presence/absence might have on students’ mathematical achievement. First and Second Research Questions


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Results of the study showed that calculators are used in elementary school; however, they are not used very frequently. As expected, no kindergarten or first grade teachers used calculators in their classroom (see Table 2 in Appendix E). The grade range of true interest for this study was 3rd-5th grade classrooms. The data showed that 1% of the 3rd grade classrooms, 0% of the 4th grade classrooms and 70% of the 5th grade classrooms used calculators. Therefore, it can be concluded that calculators are indeed used in elementary school, but more so at the end to help prepare students for middle school, where they will most likely need them. The data also suggest that the majority of teachers who use calculators as a resource in their classrooms do not use them often and believe that the majority of other same level classrooms also use them sparsely. If they could chose the grade level at which calculators are introduced to students, the majority of teachers said they would chose 3rd grade. Keeping in mind the limitations of this study, no correlations were found concerning teaching experience, teaching grade level, calculator frequency, or preferred grade level for calculator introduction. However, it was found that in this study that teachers on average preferred calculators to be introduced a full grade and a half above what they themselves taught. One of the many reasons teachers gave for choosing the grade level they did, was because they felt that by then students should have mastered their math facts and would be using the calculator to further their understanding of more advanced topics. A possible reason that teachers chose a grade and half higher than what they taught might be because they felt their students have not yet achieved such mastery and thus should not be given a calculator. If this were the case, then the mastery of basic math facts may be a common deficient among the different bands of elementary school. However, we must also keep in mind that a fair amount of the participants


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were kindergarten and first grade teachers, who definitely choose grades higher than their own. This may have well effected the average score. An important observation that can be taken away from this study is the apparent difference between what is true of calculator use in New Haven and Hamden schools today, and what teachers would prefer things to be. On the one hand, the majority of teachers in this study claimed not to use calculators in their classroom, and those who did, claimed that they did not use it often. Fifth grade, sixth grade and teachers who taught multiple grades were most common to claim that calculators were used as a resource in their classrooms. On the other hand, third grade, second grade, and fifth grade were the most common grades teachers preferred calculators to be introduced. Considering the fact that the majority of teachers fell into the first category, student readiness, as they revealed their rationale for picking their preferred grade levels, it can be assumed that a good percentage of teachers truly felt that students in second, third, and fifth grade have adequate mastery of the basics and are ready to move on to more advanced skills with the help of a calculator. Another common response, especially among the teachers who preferred calculators to be introduced in the lower elementary grades, was that calculators enrich the learning experience and are important technological tools in today’s world; thus students should know how to use them. One sixth grade teacher who believed that the calculator should be introduce in third grade made the following statement: “Typically, this is the grade that students would begin CMT testing, and now they begin SBAC testing. The computer provides calculators on the assessment therefore that is a good grade to introduce it.” The SBAC this teacher refers to is the new computerized assessment, Smarter Balanced Assessment Consortium that is replacing CMTs in Connecticut. This teacher however, is mistaken. The SBAC does not permit students from grades


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3-5 to use calculators during testing. I do not know how many of the teachers surveyed were aware of this fact, but it is of great interest to this study. It was this ban that motivated this study as a whole. Therefore, it is interesting that other than the teacher just mentioned, none of the teachers mentioned anything about standard testing in their rationale for calculator introduction. This raises questions. How relevant are changes in testing when it comes to practices in the classroom? How informed are teachers on the features of the new SBAC testing?

Third Research Question The third Research question asked “How does the presence or absence of a calculator effect the student performance/achievement in your classroom?” Out of the five categories that were developed to analyze the data provided, the majority of responses fell into the third category, the benefits of the absence of calculators on student mathematical achievement. The minority of responses fell into the last category, the detriments of the absence of calculators on student mathematical achievement. All in all, more teachers spoke of the benefits of the absence of a calculator in the classroom than they did of the benefits of the presence of a calculator, when it comes to student mathematical achievement. Thus, according to this data, it can be concluded that, when it comes to mathematical achievement in elementary school, the development of mental math, acquiring numeracy skills, applying foundational skills, and achieving mastery of basic math facts is more prevalent than being able to quickly check answers and devote more time to advanced problem solving skills than to computational skills. In conclusion, many teachers agreed that students must know their math facts before using the calculator, at the same time they also argued that if they don’t know their math facts by a certain time, they should be given the calculator to keep up. This seems reasonable and


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counterproductive at the same time. One teacher stated: “I think students need to have a solid foundation of basic math skills. Many students today do not know their basic facts because technology has made it so easy. Students should understand the math behind the problem and only use the calculator when problems become more complex and are testing the skill of how to compute formulas correctly.” Limitations Various limitations existed in this study. 1) The time at which I completed the survey form and received IRB approval effected my ability of obtaining a large enough sample size for the study. The survey was completed at the end of a spring semester, early May. By the time they were distributed across the district, teachers and principals were busy wrapping up their school years and I received hardly any responses. Returning in the fall semester, I had another wave of emails dispatched across the district schools. However, this time, returning teachers and principals were busy setting up for the new school year and in the end only 72 surveys were returned to me. 2) The level of clarity and conciseness of the survey’s questions had an impact on the accuracy of the data that was gathered. For example, question #1 asked for the years of teaching experience of the participants and the options given were 1, 2, 3, or 4+. It turned out that the majority of the teachers had been teacher for more than four years. This data would have been more revealing if the teaches were allowed to specify exactly how many years they have been teaching. There is a huge difference between a teacher who had been teaching for 4 years and a teacher who had been teaching for 10 or even 15 years. However, with the way that the questions was formulated, these teachers were all grouped into the same category, which makes it very hard to seen patterns or compare this variable to another as far as correlations go. 3) Time and resources were also major limitations to this study. I originally planned to make an


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additional investigation of student mathematical achievement using pre and post assessments of elementary classrooms who used calculators and those who did not use calculators at all. A project such as this would take the entire school year, for me two full semesters, to complete data gathering. I did not have such time on my hands, nor the resources to properly analyze the different classrooms and receive permission from all parents and teachers involved. A study such as this, however, would have been a perfect addition to the study that I instead settled for. 4) My lack of experience with statistical analysis definitely limited the range of tests I was capable of running on the data that was collected. Recommendations for Further Research Given the opportunity to further this research project, the tools for gathering data need to be improved to produce more accurate and informing results. For example, the questions in the survey would need to be modified to better gather the desired results. To avoid skewing the data, kindergarten and first grade teachers need to be excluded from the study. Two different surveys should be given to teachers who use calculators and those who do not, seeing how the interests in both groups would be considerably different. To make more accurate conclusions, a much larger sample must be surveyed and analyzed. The correlations that were tested during this study might not have all come back negative had the sample size been larger thus more representative of the population. Also, the additional study of student achievement should definitely be included. The topic of this study is very important and definitely demands greater investigation. A more advanced analysis of the effects of calculators on student achievement as well as the effects that the SBAC testing might have on classroom practices is required. Is it wise to continue using the calculator in the classroom just as much as before they were banned from elementary standard testing? What kind of effects will it have on students? Why was this ban made? What


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was the policy makers really trying to bring about? Will it work if classroom practices remain the same? What can we do to maximize the mathematic achievement of our elementary school students?


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References Brown, E. T. (2007). Crutch or Catalyst: Teachers' Beliefs and Practices Regarding Calculator Use in Mathematics Instruction. School Science and Mathematics, 102-117. Burns, J. (2012, November 8). Government bans calculators from primary maths tests. Retrieved from BBC News: Education and Family : http://www.bbc.co.uk/news/education20259382 Fischer, D. P. (2006). Nimble Numeracy; Fluency in Counting and Basic Arithmetic. Retrieved from Oxton House Publishers, LLC: http://www.oxtonhouse.com/nimble_numeracy.html Hom, E. J. (2013). What is Mathematics. Retrieved from LiveScience: http://www.livescience.com/38936-mathematics.html Green, C. (n.d.). Calculating the Difference: A Discussion of the Use of Calculators in the English Primary Classroom. Retrieved from NRICH Enriching Mathematics: http://nrich.maths.org/2553 Klutch, R. J. (1991, September 29). The Calculator Crutch. The New York Times, p. 1. Morin, A. (2014). What is Mental Math? Retrieved from Parenting School Age Children: http://childparenting.about.com/od/schoollearning/a/mental_math_def.htm NCTM. (2009). Number & Operations Standard. Retrieved from National Council of Teachers of Mathematics: http://nottingham.k12.nh.us/curriculum/math.pdf NCTM. (2011). Calculator Use in Elementary Grades. Retrieved from National Council of Teachers of Mathematics: http://www.nctm.org/tcm009/ NCTM. (2004). Mathematics in Today’s World. Retrieved from National Council of Teachers of Mathematics: http://www.nctm.org/resources/content.aspx?id=9344 Peters, K. (2005). Numeracy and Decision Making. Psychological Science, 407-413.


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Polly, D. (2008). Modeling the Influence of Calculator Use and Teacher Effects on First Grade Students' Mathematics Achievement . School Science and Mathematics, 245-263. Preparing for the 21st Century: The Education Imperative. (2000). Retrieved from The National Academy of Sciences: http://www.nas.edu/21st/education/ Reys, B. J., & Arbaugh, F. (2001). Clearing Up The Confusion Over Calculator Use In Grades K-5. Academic Search Premier. Rittle-Johnson, B. (2008). When Generating Answers Benefits Arithmetic Skill: The Importance of Prior Knowledge. Journal of Experimental Child Psychology, 75-81. Robelen, E. W. (2013, August 28). Calculator use on exams to shift with Common Core. Education Week, pp. 1-3. Retrieved from Education Week. Ruthven, K. (1998). The use of Mental, Written and Calculator Strategies of Numerical Computation By Upper-Primary Pupils within a 'Calculator-aware' Number Curriculum. British Educational Research Journal, 21-42. Sheets, C. L. (2007). Calculators in the Classroom: Help or Hindrance? Wallace, NE: Department of Mathematics; University of Nebraska-Lincoln.

Reference(s) Consulted Admin, C. (2012, April 7). International Comparison of Math, Reading, and Science Skills Among 15-Year-Olds. Retrieved October 13, 2013, from Woodstock CT Café: http://www.woodstockctcafe.com/2012/04/07/international-comparison-of-math-readingand-science-skills-among-15-year-olds/ Bell, A. B. (1978). A Calculator Experiment in a Primary School. Retrieved from Shell Centre for Mathematical Education, Nottingham, UK.


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Braswell, B. B. (1995). Effects of Calculator Use on Scores on a Test of Mathematical Reasoning. Journal of Educational Measurement, 32, 323-340. Bridgenman, B. (1995). Effects of Calculator Use on Scores on a Test of Mathematical Reasoning. National Council on Measurment in Education, 323-340. Golden, D. (2000, December 15). From Inner-City Schools, Calculators May Be The Wrong Answer. Wall Street Journal. Retrieved from Academic Search Premier: September 11, 2013. Huntley, M. A. (2000). Effects of Standards-Based Mathematics Education: A Study of the Core-plus Mathematics Project: Algebra and Functions Strand. National Council of Teachers of Mathematics, 328-361. Pirie, J. S. (2002). Problems, Perseverance, and Mathematical Residue. Educational Studies in Mathematics, 50, 1-28. Ruthven, K.. (1998). "The use of Mental, Written and Calculator Strategies of Numerical Computation By Upper-Primary Pupils within a 'Calculator-aware' Number Curriculum." British Educational Research Journal: 21-42. Taylor, Bob L. & Robert C. McKean. (1979). "News Notes." Educational Leadership 37.1: 94. Retrieved from Education Research Complete: September 11, 2013. Thom, J. S. (2002). Problems, Perseverance, and Mathematical Residue. Educational Studies in Mathematics, 1-28. Walcott, C. (2007). Calculator Use on NAEP: A Look at Fourth- and Eighth-Grade Mathematics Achievement. School Science and Mathematics, 240-254.


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Wai, J. (2013, Feburary 14). Why We Need The Math Police. Retrieved from Education Week: http://blogs.edweek.org/edweek/on_innovation/2013/02/why_we_need_the_math_police. html Walter, Janet G., & Hope Gerson. (2004). "Lyn’s Representation Of Slope As An Iterative Process. “Conference Papers -- Psychology Of Mathematics & Education Of North America: 1. Retrieved from Education Research Complete: September 11, 2013. Wheatley, C. L. (1980). Calculator Use and Problem-Solving Performance. Journal for Research in Mathematics Education, 11, 323-334. Yang, R. Y. (2012, October 14). Should Calculators Be Allowed in Elementary Math? Retrieved from Enchanted Collar® Teach Kids Math: http://enchantedcollar.com/calculator/


Appendix A The Online Survey (part 1)

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The Frequency and Effects of Calculator-Use in Elementary Schools The Online Survey (part 2)

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Appendix B Data collected from Short Response question #8 In your personal opinion, at what grade do you feel it most appropriate to introduce the calculator into the classroom?

Give a brief explanation as to why you choose that grade level.

2nd Grade

this is when math problems become more complicated

2nd Grade

While I think it is important to learn the problem solving strategies, I think it is important for children to have the strategies to check their work in a quick fashion.

2nd Grade 2nd Grade

Calculators are helpful at any level and do not lead to less number sense...

2nd Grade

Sometimes the proces to solve a problem is more important then the computation

2nd Grade

They're already using computers-the skill should be transferable

2nd Grade

I feel at this age the students should have a good foundation and number sense and can use the calculator to work faster when solving more advanced problems with multiple steps.

2nd Grade

This is when students start adding and subtracting larger quantities.

2nd Grade

Grade 2 students need to know their facts. They can use a calculator to check their answers.

2nd Grade 2nd Grade

Kids can use calculators as tools to check their work. It also gets them to ready to use certain computer applications.

3rd Grade

Typically, this is the grade that students would begin CMT testing, and now they begins SBAC testing. The computer provides calculators on the assessment, therefore that is a good grade to intorduce it.


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3rd Grade

3rd Grade

In third grade the children are transitioning from learning strategies in how to solve addition and subtraction problems into more complex problems where the use of a calculator can sometimes be beneficial. Calculators are real world tools that students need to know how to operate.

3rd Grade

3rd Grade

It is an important "life" resource and with the importance of technology in the world today coupled with how well students can use technology, it's important to start early.

3rd Grade

Students should know basic math facts by this grade level

3rd Grade

Because children have had a chance to try to learn facts automatically & can now use the calculator as a resource.

3rd Grade

They have a better understanding of the various functions that are very basic. I also feel that sometimes people get too dependent on them for basics.

3rd Grade

checking work

3rd Grade

3rd Grade

I think 3rd graders have a grasp of the algorithms behind the calculations and are moving on to higher level thinking and can benefit from calculators.

3rd Grade

I was given grade 4

3rd Grade

Students should be able to do basic math facts before resorting to a calculator.

3rd Grade

The students need to be able to do mental math fluently before introducing calculators so they do not use them as a crutch. By third grade. they should know their math facts and be ready to use a calculator as a reference.


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I feel that the children are mature enough at that age to handle the responsibility. In addition, they have learned to understand and perform the basic math functions by that grade level so the calculator can serve as an additional resource rather than a crutch for them to lean on.

3rd Grade

3rd Grade

Resource students would get confused possibly and not utilize approriately before a certain maturity level.

3rd Grade

3rd Grade

I think it is a great tool for checking your work in third grade. I do not like kids to use otherwise as i Enrichment groups tend to use them when working on performance tasks where the focus is not on calculations. My students in need of math help use them when the task is not focused on adding and subtracting, etc. With this said, exposure at an early grade level is important so the students are calculator literate as they reach the upper grades and the use is necessary.find it impedes on learning their facts.

3rd Grade 3rd Grade

4th Grade

I chose 4th grade to start implementing calculators into the classroom because in this grade the math curriculum or particular math problems would start to require the use of calculators to solve problems.

4th Grade

Students need to be able to use a calculator in order to do more complex math problems. In my opinion, by fourth grade students should have mastered basic addition, subtractions, multiplication, and division and should be able to work a calculator appropriately in order to begin more complex, multi-step math problems.

4th Grade

Prior to 4th grade students need to be automatic in their fact fluency to adeptly and quickly solve basic mathematical problems.

4th Grade

I believe students need to have a firm grasp on addition, subtraction, multiplication, and division before using a calculator. By 4th grade students have learned basic math and can use a calculator to complete more challenging problems.

4th Grade

I chose 4th grade because of the math curriculum, which requires multi-digit computation in addition, subtraction, multiplication and division. My students have learning disabilities, which often has to do with a difficulty memorizing facts.


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I think that comparing estimates to actual answers is a good skill to have before they reach me. I would use them more IF I HAD A SET!

4th Grade

If students haven't memorized their facts by this point... they need the help to do the computations more quickly!

4th Grade

They have begun to mature at 4th grade

4th Grade

They have been doing multiplication for a few years and are starting long division. I think it would be helpful for them to be able to check their division and make sure their skills are correct.

4th Grade

I feel that students have developed enough automaticity in subtraction, addition, multiplication, and division to introduce calculators without effecting math automaticity.

4th Grade 4th Grade

5th Grade

I chose 5th grade as an appropriate grade level to incorporate calculators because the students should know the basic skills such as adding, subtracting, multiplying and dividing before they get a calculator. Many students use calculators as a crutch therefore they lose the ability to do math mentally.

5th Grade

I think its important for students to get the math basics and not depend on a calculator for what they can do using other strategies. By 5th grade, they should be mature enough to use the calculator along with other strategies they have learned.

5th Grade

I believe that the basic math skills should be taught before allowing kids to use calculators. If students feel like they can always rely on a calculator then they are less likely to learn the basic math skills needed. Plus, calculators are not permitted on tests until 6th grade, so there is no reason to introduce them sooner.

5th Grade

In math lessons up to fifth grade, the emphasis should be on understanding "how" math equations are solved and exploring various ways to arrive at an answer. Because of this, I feel there should be ample years of exploration and limitation for using a calculator.

5th Grade

calculations get more difficult and as long as students understand concepts they should be able to do work or check work

5th Grade

You can allow students to work on multi-step problems that may require multi- digit operations. The students can persevere through the problem rather than get caught up in the calculations.

5th Grade

I think any grade level under 5th grade should learn math without a calculator.


5th Grade

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Exponents

5th Grade

5th Grade

Some work at this grade level requires the use of calculators

5th Grade

They should know the math facts (=,-,X,/) fast in thier own before they use the caculators at aid in the speed of more complex math concepts.

5th Grade

It is part of our technological world. Once students have an understanding of basic multiplication and division calculators help them get answers quicker. Students are then able to focus on other math concepts that are being taught. EX: Finding out if a number is prime or composite and what are it's prime factors.

5th Grade

I think students need to learn basic math skills themselves (such as multiplication facts) before relying on calculators

5th Grade

I think by 5th grade students have been exposed to the algorithms enough and they start doing more complicated problems where it is necessary to use a calculator.

6th Grade

6th grade seems to be a good time in a child's academic journey where they are moving from basic level math in elementary school to more higher level problem solving and abstract math in middle school and later in high school. Also by 6th grade our students should have a firm hold on their basic math facts. Only once that is mastered can a child move forward and advance to high levels of learning.

6th Grade

The Math is more complex and it is a great recourse for children with Math goals in an IEP.

6th Grade

Children need to learn strategies for solving problems before it's made that easy for them.

6th Grade

I chose 6th grade because at that grade level, most math practices regarding adding, subtracting, multiplying, and dividing have been mastered.

6th Grade

They get into more difficult computations.

6th Grade

Elementary school students need to learn to calculate mentally and using algorithms and various others strategies before they rely on calculators.


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6th Grade

I believe that sixth grade is a good grade level to introduce the use of a calculator into the classroom because the mathematics becomes more complex in the upper middle school years. Also, if by that time students are still struggling to solve basic math equations, they need a calculator as a tool so that they can move forward.

6th Grade

Math becomes more complex with graphing, etc and students can benefit from calculators.

6th Grade

7th Grade

I think students need to have a solid foundation of basic math skills. Many students today do not know their basic facts because technology has made it so easy. Students should understand the math behind the problem and only use the calculator when problems become more complex and are testing the skill of how to compute formulas correctly.

7th Grade

I think students need to have a solid foundation of basic math skills. Many students today do not know their basic facts because technology has made it so easy. Students should understand the math behind the problem and only use the calculator when problems become more complex and are testing the skill of how to compute formulas correctly.

7th Grade

By that level they should have basic skills and can use calculators to make things quicker.

7th Grade

7th Grade

I think students should have a firm grasp of most everyday uses of math, and use calculators for theoretical, advanced courses or in science when the math is not the learning focus.

High School

students need to master mental computation

High School

I believe students should be using their brains and mathematic knowledge to do computations in their heads or on paper. I believe that calculators are used for more complicated operations and are associated with classes such as Advanced Algebra and Probability and Statistics.


Plair 50

Appendix C Data collected for Short Response Question #9

What grade level do you currently teach?

How does the presence or absence of a calculator affect the student achievement/performance in your classroom?

1st Grade

1st Grade

In first grade the students are learning strategies to solve addition and subtraction story problems with sums less than 20. It is not yet appropriate to introduce the calculator while group

1st Grade

1st Grade

Has no affect

1st Grade

We do not use calculators. My students do very well without calculators. Most, if not all of them perform at the proficient or goal level. They are using their brains and applying the skills taught without the crutch of a computer/calculator doing it for them. In first grade, the mathematical principles are simpler, therefore they need to be mastered without a calculator in order for students to succeed. We are teaching them the foundational skills they need and will use throughout their lives.

1st Grade 1st Grade 1st Grade

Students may seek the easy way out.

1st Grade

Doesn't

1st Grade 1st Grade

2nd Grade

I teach second grade and the absence of calculators in the classroom allow students in this grade/age to learn how to use their rote memory for basic addition and subtraction facts rather than rely solely on a calculator to solve it for them. By being dependent on a calculator this early students will never be able to recall basic facts.

2nd Grade 2nd Grade

I feel the students need to master mental computation before they use a calculator. a calculator should only be used to check work at my level.


Plair 51

2nd Grade

2nd Grade

Doesn't really affect student achievement or performance as my students are just beginning to add and subtract using two digit numbers with regrouping.

2nd Grade

It doesn't

2nd Grade

It enhance studen performance because they rely on their own minds

2nd Grade 2nd Grade 2nd Grade

I don't know if it does.

3rd Grade

The absence of a calculator seems to really force my students to learn and retain their basic math facts that they learned back in their previous grades and build on these skills.

3rd Grade

They really never use one so I don't really think they miss them.

3rd Grade

The absence of a calculator forces students to memorize and learn their math facts. This is important for all students to accomplish in order to succeed in math. The only way that calculator should be used at the lower grade level is if the student had an IEP.

3rd Grade

The absence of a calculator forces students to memorize and learn their math facts. This is important for all students to accomplish in order to succeed in math. The only way that calculator should be used at the lower grade level is if the student had an IEP.

3rd Grade

Without calculators being used in my room at all, students must depend on checking their work using alternative strategies. They also must depend on their growing mental math. I feel my students greatly benefit from gaining self confidence as a result.

3rd Grade

Students to not rely on calculators to solve problems. They have to learn skills themselves and practice.

3rd Grade

unsure

3rd Grade

Students are just learning how to multiply and for me it is more important that they learn the strategies and the facts in order to be able to do the multiplication instead of relying on a calculator.

3rd Grade 3rd Grade 4th Grade

I'm not sure if the absence of calculators actually affects my students.


4th Grade

n/a

4th Grade

Checking and higher level calculation.

Plair 52

4th Grade

4th Grade

I am sure not resorting to the use of a calculator makes solving equations more time consuming, but the students must understand the process of solving an equation. If they rely too heavily upon a calculator for an immediate answer, they will bypass the thinking part of the entire process (they will get an answer, but not understand why it is correct or incorrect). I must also note here (since it was not explicitly asked in the survey), that if a child needs a calculator as an accommodation to succeed, then they should be provided one regardless of grade level.

4th Grade

5th Grade

The presence of a calculator would hinder the sucess and achievement of my students because they would begin to rely on the technology to solve simple math problems. Math concepts should be mastered before administering calculators. Calculators should be used to enhance instuction and skills later on ina child's education, only after they understand how to solve the problems without the use of a calculator. I teach students with moderate to severe disabilities that achieve far below grade level. Most are learning to use the calculator as a life skill because memorizing facts is not possible. I wish I had a set but they are given to the math teacher and I borrow them periodically for Science. There are children who have "able to use a calculator" in their IEP's, so I take them when we are computing means for our investigations. Otherwise, there just aren't enough to go around! They get broken, batteries die or solar cells crack, and sometimes they just "disappear". It is a huge expense for the District!

5th Grade

I use calculators mostly as a resource for students with IEPs. It allows for students to stay focused without worrying about the basic facts they made not know.

5th Grade 5th Grade

5th Grade 5th Grade

I wish i had a full set but I don't which prevents me from doing more challenge logic problems.

5th Grade

it does not, i rarely use. i only use to let kids check work or when computation isnt my focus

5th Grade

We are using it more as a way to double-check our computations. We find it increases engagement, but needs to be monitored carefully. We often will have one or two "experts" checking the class's answers.

5th Grade 5th Grade


Plair 53

6th Grade

Students can rely on the calculator too much which is why they are not often used in my classroom. Many of my students do not know their basic math facts so I try to avoid using calculators unless the math process is not the focus. I do not currently teach math, but I think if I did, calculators would be used much more often in my classroom to help students focus on the skill we are working on rather than the basic computations. I always try to teach students how to calculate with paper and pencil first. Once students know the process and how to calculate, I like to have students use a calculator to double check their work. In addition, I allow them to use calculators when it is a problem that requires a larger amount of work. I would prefer students to know what a calculator is doing instead of doing it for them. That way, they can decifer whether their answer is accurate or not.

6th Grade

I use calculates as a resource to teach higher level skills so I can assess my students better. For example if students are struggling with basic math facts and I'm trying teach how to add mixed fractions, the use of calculators eliminate the "basic"'fact portion of the skill where I can focus on the process of add mixed fractions.

6th Grade

Students can focus on the process in longer tasks.

6th Grade

In my low class the calculators have helped them because they don't know their facts as well as they should. In my higher class it did not make a difference other than that they finish sooner.

Kindergarten

n/a

Kindergarten

I teach kindergarten, and children at this grade level are learning to identify numbers and what numbers represent. At this age, there is no reason for calculators.

Kindergarten

NA

Kindergarten

My students, as Kindergartners, have yet to learn many of their basic addition and subtraction facts. Therefore, if they were to use calculators, it would be much harder for me to figure out whether they knew the material or just pressing buttons.

Kindergarten

N/A

Kindergarten

We do not add/subtract quantities that would validate using a calculator. Students might in enjoy being exposed to calculator use if it was a part of the curriuclum.

6th Grade

Kindergarten

Kindergarten

As kindergarteners they are just learning what numbers are and developing a number sense. I do not feel that it is appropriate for 4-6 year olds to use them as part of the learning process.


Plair 54

Kindergarten Kindergarten Multiple grades

The younger students who are not yet fact fluent become too dependent on a calculator and see no need for memorization.

Multiple grades

We use it to check the accuracy of their calculations, which goes along with our objective of self-assessment and independence.

Multiple grades

I teach music so it really doesn't affect it.

Multiple grades

my room is just language arts

Multiple grades

Students should be able to perform the four arithmetic operations without a calculator. Also, the calculator will only assist the student if the student knows what to enter into the device.

Multiple grades Multiple grades

It is a tool and thus should be thought of as a tool not a replacement for calculations.

Multiple grades

n/a However it would be helpful for particular assessments.

Multiple grades

I teach Music and do not use calculators.

Multiple grades

It helps kids determine if their calculations are correct. If their answer doesn't match the calculator answer, they can look for a mistake and correct themselves before handing in their work. Some students have memory issues and will never be able to memorize facts. The calculator will help them move forward in their understanding of concepts and algorithms. Unless you are doing a fact assessment, I see no reason not to allow calculator use.


Appendix D Table 1: Teaching experience and grade levels of the participants

Grade Level 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 4th Grade 4th Grade 4th Grade 4th Grade

Teaching Experience 4 Years or more 4 Years or more 1 Year 4 Years or more 2 Years 4 Years or more 1 Year 2 Years 4 Years or more 1 Year 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 1 Year 4 Years or more 4 Years or more 4 Years or more 2 Years 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more

Plair 55


4th Grade 4th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 6th Grade 6th Grade 6th Grade 6th Grade 6th Grade Kindergarten Kindergarten Kindergarten Kindergarten Kindergarten Kindergarten Kindergarten Kindergarten Kindergarten Kindergarten Multiple grades Multiple grades Multiple grades Multiple grades Multiple grades Multiple grades Multiple grades Multiple grades Multiple grades Multiple grades

4 Years or more 4 Years or more 1 Year 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 1 Year 1 Year 1 Year 2 Years 4 Years or more 4 Years or more 4 Years or more 1 Year 4 Years or more 4 Years or more 4 Years or more 1 Year 4 Years or more 4 Years or more 1 Year 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more 4 Years or more

Plair 56


Plair 57

Appendix E Table 2: Grade levels of the participants and calculator use.

Grade Level 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 1st Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 2nd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 3rd Grade 4th Grade 4th Grade

Do you use calculators as a resource in you classroom? No No No No No No No No No No No No No No No No No No No No Yes No No No No No No No No Yes No No


Plair 58

4th Grade 4th Grade 4th Grade 4th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 5th Grade 6th Grade 6th Grade 6th Grade 6th Grade 6th Grade

No No No No Yes Yes No Yes Yes No Yes Yes No Yes Yes Yes Yes Yes Yes

Kindergarten

No

Kindergarten Kindergarten

No No


No No


No No


No No

Kindergarten

No

Multiple grades

Yes

Multiple grades

Yes

Multiple grades

Yes


Yes

Multiple grades

Yes


Plair 59


No No

Multiple grades

No

Multiple grades

Yes

THE FREQUENCY OF CALCULATOR-USE IN

THE FREQUENCY OF CALCULATOR-USE IN

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