The Effects of Calculator and Technology Use on Mathematical Academic Performance

Abstract

The purpose of this paper is to address calculator and other technology use in the secondary and college classrooms, mostly in the US, and how it affects academic performance. Some calculator use can enhance learning for students with disabilities and those who traditionally struggle with math. Some calculator use, specifically over reliance, in secondary school can adversely affect performance in college calculus. And some technology use can allow the students to find solutions without learning basic concepts. This paper does not advocate removing technology from the classroom. It will define the problems and concerns associated with calculator and other technology use and address all the viewpoints for the purpose of informing decisions of the uses of technology in secondary math classes. While the main focus of this paper is on secondary education, the unintended consequences of technology use may also apply to lower grades, and thus may carry additional implications for teaching and learning in these settings.

Keywords: calculator, technology, math class, academic performance, secondary education, college calculus, cheating

The Effects of Calculator and Technology Use on Mathematical Academic Performance

Introduction

For years, high school students have been using the latest calculators in mathematics class to solve problems. Recently students have been bringing more than calculators to class such as smart watches, tablets, phones, and similar technology that allow the student to do much more than calculate (Bain, 2015; Migicovsky, et al., 2014). There is an ongoing debate concerning whether the use of this new technology has been beneficial to the learning process (Boyle, & Farreras, 2015). When considering calculator and other technology use in the high school classroom, some say that students are just using their resources to solve problems (Crawford et al., 2016; Orellana & Barkatsas, 2017; Salani, 2016; Thomas & Muñoz, 2016). Others say that the students’ use of technology in their math classes enhances their understanding of underlying concepts (Crawford et al., 2016; NCTM, 2000; Orellana & Barkatsas, 2017). Additionally, some say that, for those entering STEM careers, overreliance on calculators and other technology in high school adversely affects college academic performance (Boyle & Farreras, 2015, Mao et al., 2017; Nagle, 2017); while others say that students are using the latest technology to inconspicuously collaborate on exams, thus thwarting the assessment process in high school (Bain, 2015; Migicovsky, et al., 2014). This paper will define the problems and concerns associated with calculator and other technology use and address all the viewpoints for the purpose of informing decisions of the uses of technology in secondary math classes. While the focus of this paper is on secondary education, the unintended consequences of technology use may also apply to lower grades, and thus may carry additional implications for teaching and learning in these settings (Nworie & Haughton, 2008).

The Debate

In the analysis of the literature concerning the use of technology in secondary math classes, the discourse reveals two opposing views. The first view is that technology is essential for the learning process (Chamblee, et al., 2014; Crawford, et al., 2016; Desoete, 2017; Farmer, 2016; Heller, 2015). The second view is that the use technology is used to circumvent the learning process, thus having devices to do the work so that the student does not need to learn math concepts (Bain, 2015; Boyle & Farreras, 2015; Brown, et al., 2007; Mao, et al., 2017; Mead, 2014; Migicovsky, et al., 2014; Nworie & Haughton, 2008). The National Council of Teachers of Mathematics (NCTM, 2000) published standards for mathematical instruction which reflects this debate. Whereas they stated that technology use “is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances student learning” (p. 24). However, in the same publication, they also caution that “calculators do not replace fluency with basic number combinations, conceptual understanding, or the ability to formulate and use efficient and accurate methods for computing” (p. 145). And they stated 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. 25). They further admonished that “all students [must] have opportunities to use technology in appropriate ways so that they have access to interesting and important mathematical ideas” (p. 14), which implies that there are inappropriate ways to use technology. Also they advised “when teachers are working with students on developing computational algorithms, the calculator should be set aside to allow this focus” (p. 32). These statements define both sides of the debate. Thus, both sides have valid points; therefore neither side should be ignored.

Educators have varied opinions based on which side of the debate they are on. On one side, many believe that technology can help a student learn concepts by allowing the student to check their work and point them in the right direction to solve problems (Farmer, 2016). They noted that technology use can especially enhance the learning of students who traditionally struggle with mathematics, students who have limited prior knowledge of mathematical concepts, and students with disabilities (Desoete, 2017).

However, on the other side of the debate, researchers are not saying that technology use is bad; rather they are saying that the overuse of it handicaps those students who pursue a STEM career. There is a growing concern among college professors that technology is being used to allow students to submit work they cannot do apart from technology, thus they do not understand the underlying mathematical concepts (Bain, 2015). They also believe that technology is allowing students to collaborate during exams, thus submitting others’ works as their own. Therefore, in many college settings such as the Graduate Record Examination test, technology is generally banned or severely limited due to the temptation to cheat (Bain, 2015; Brown, et al., 2007).

Technology Use Benefits Students with Disabilities and Students who Struggle with Math

Some say that one benefit to technology use in high school is that it will help those students with disabilities who struggle in math (Desoete, 2017). Desoete (2017) studied adolescents and adults with mathematical disabilities and adults with combined mathematical and reading disabilities. These students were asked to take tests on procedural calculation and number knowledge, numerical facility and visuospatial skills. Metacognitive skillfulness was assessed. He claimed that students with disabilities who are trying to learn math do so more effectively with the use of technology. His study revealed that a lot of adults with mathematical disabilities still have problems solving mathematical tasks in dual-task or limited-time conditions. The authors concluded that technology can be used to overcome deficiencies.

Just as technology can help students with disabilities, other students who struggle with math can benefit as well. Hellar et al. (2015) studied the relationship between the use of graphing calculators and student achievement in secondary education algebra classes. 674 students were assessed in Oregon and Hong Kong. The authors stated that it appears that some gains in student learning of mathematics with handheld graphing technology are a function of how the technology is used in instruction, even in classes that all use the same textbook. The authors found significantly higher student test performance for students who had access to graphing calculators during algebra instruction. The authors also concluded that scores were significantly higher where teachers reported receiving professional development on how to use a graphing calculator in math instruction (Hellar et al., 2015).

Calculator and Other Technology Use in the Classroom

Moreover, not every school incorporates calculator use in their classrooms. Keckler (2015) examined the equitable use of calculators to see if students from different schools had equal access to calculators. The authors surveyed high school students about how often they use calculators in math class and what kind of calculator they used for tests, with the options of no calculator use, scientific non-graphing calculator, online calculator, or graphing calculator. The authors concluded that graphing calculators are very useful in the classroom. However, The findings suggested that not every school district has equal access to technology creating a gap in achievement. The authors also concluded that there are inequities between classes in the same school due to such problems as teacher preference (Keckler, 2015).

The schools that do include technology in the classroom have seen an increase in academic achievement. Crawford et al. (2016) conducted a study to assess students’ use of technology and compared that with academic performance. They studied a sample of 73 students in grades 4–6. This study examined schools in north central Texas. Students completed online lessons over the course of 6 weeks. Lessons were chosen to supplement the instruction students’ received in their mathematics classes. The authors concluded that there was a correlation between students’ use of technology and their academic skill level (r = .31, p < .001). Correlations were also found between students’ use of specific electronic support tools and their basic academic skill fluency which were found between the pre and post mathematics testing (t(72) = 6.463, p<.001), The implication is that students who are struggling with mathematics can use electronic support tools to supplement their prior knowledge and have more success.

The Other Side of the Debate

While calculator and other technology use in the secondary education classroom can enhance a student’s effectiveness in learning content, they can also be used in ways to undermine the learning process. This is not to say that technology is not to be used, but rather that it should not take the place of basic understandings and intuitions (NCTM, 2000). The view that technology should not be used in today’s world is ubiquitous. This side of the debate states that students use technology incorrectly. Students can use devices to do all of the work so that they do not need to learn concepts (Bain, 2015). While it may seem fortuitous for students to use resources to solve problems, according to this view, the need for basic understanding is being ignored. Additionally, those on this side of the debate state that schools are not teaching mental math skills which are essential in college math classes (Mao, et al., 2017).

How Technology Use in High School Affects College Performance

On this side of the debate, there are concerns that there is an achievement gap between high school math and first year college calculus. Mao et al. (2017) studied 7087 students enrolled in college calculus at 134 colleges and universities in the US. He examined the data and conducted a study to assess the performance of students in introductory calculus courses in the US and compares that with calculator use in high school. The study raised doubts about the long-term effects on college mathematics performance of calculator use in high school. The findings revealed that the more extensive the uses of calculators in high school, the lower the scores were in college calculus. The implication was stated that calculator use should be discouraged for those high school students on a path to curriculums requiring college calculus (Mao et al., 2017).

Mead (2014) also spoke of how calculator dependence affects college academic performance. Many first year college students have weaknesses in mathematics which cause errors, not in higher level mathematics, but in basic mathematical procedures (Mead, 2014). Students also have trouble understanding that the answers a calculator provides might be wrong and why it might be wrong (Graff & Leiffer as cited by Mead, 2014). As students are more dependent on calculators and other technology, they lose the ability to perform simple tasks and mathematical problems without such technology (Mead, 2014). Being able to make change without a calculator or computerized cash register is becoming a lost art, which is worrisome as it is a simple enough task, yet society is choosing to let the technology do the work and not understand the basic concept and procedure (Mead, 2014).

Technology Use and Student Collaboration and Plagiarism

In addition to poor college performance, calculator use and the use of more modern technology allows students to collaborate on exams, plagiarize others’ works, and present solutions to problems that they do not have the skills and prior knowledge to do, thus thwarting the assessment process. Bain (2015) wrote an opinion article discussing technology use and what types are being used. He suggested that students are able to use technology to inappropriately find solutions to problems without understanding the basic concepts. Thus, the only way these students can solve a problem is if someone else or something else did the work for them. Bain (2015) concluded that e-cheating should be dealt with using low-tech methods of pedagogy.

In addition to e-cheating, technology can be used for inappropriate collaboration during exams (Migicovski et al., 2014). Migicovsky et al. (2014) wrote an opinion article about how useful smartwatches are for students who wish to collaborate during exams. He warned that technology could be used to allow students to answer questions without understanding how they got the answer and to communicate that with other students during examinations (Migicovski et al., 2014). The authors suggested that there are new technological devices on the market such as glasses, bracelets, and watches that do so much computing that they pose a risk when it comes to security and privacy. Thus, they suggested that a teacher can have a situation where students are collaborating on tests, which can lead to a false conclusion about what the students have learned (Migicovski et al., 2014). The authors concluded that, since devices such as digital watches are banned during tests such as the Graduate Record Examination, teachers should also ban such items during tests in their secondary mathematics classes (Migicovski et al., 2014).

Using Technology to Do the Understanding for the Student

In addition to cheating and plagiarism, those on this side of the debate noted that students also use technology to do the work for them instead of understanding the concepts behind the exercise (Brown, et al., 2007). The calculator may provide the students with the correct answer, but the student may not have learned the basic concepts that would help solve the problem (Mead, 2014). McCauliff (2003) discussed in her opinion paper teachers’ attitudes toward calculator use, and pointed out a way to make calculators a useful tool instead of a crutch. She stated that students can spend more time working on solving problems more abstractly and conceptually. Next, calculators do not have an adverse effect to the student. Also, students will have increased confidence and a better attitude about mathematics when using a calculator, which can be a positive motivator. She also stated that the proper use of calculators will also enhance number sense and help to develop the conceptual understandings and abilities. She also stated negative effects of relying on calculator use. She said that most teachers do not know how to implement the calculator properly, and hence, students are often at a disadvantage. She further stated that students do not understand the basic concepts and will not have success in future classes. There is an advantage to students when they are taught how to do mental math when they get to higher grades (McCauliff, 2003).

Teacher Perspectives on Technology Use

Just as there are differences of opinion among writers and researchers regarding appropriate use of technology, there are differences among teachers as well. Brown et al. (2007) conducted a survey of more than 800 elementary, middle school, and high school teachers in a large city in the US in which the participating teachers were asked about their beliefs and practices of mathematics teachers regarding calculator use. The results were analyzed across grade bands for differences. Brown et al. (2007) found that some teachers see technology as a way to solve problems without understanding underlying mathematical processes. Further, they found that teachers of higher grade bands more consistently saw calculator use as a way to get answers without doing the work than did elementary teachers (Brown et al., 2007). The findings revealed that high school teachers generally acknowledged calculator use as an enhancement of student performance, motivates students and encourages them to higher-level thinking, and stimulates their interest. However, they also stated that technology use did not displace seeing their students explain via pencil and paper how they got the answer to assess understanding (Brown, et al., 2007).

Conclusion

Technology can enhance the learning of students with disabilities (Desoete, 2017) and students who struggle with math (Hellar et al., 2015). Conversely, technology can help some students cheat (Bain, 2015). High schools that include technology in the classroom affect academic achievement in a positive way (Crawford et al., 2016). However, overreliance on technology can affect college academic performance among first year college students (Boyle & Farreras, 2015; Mao, 2017). Those who defend the use of technology often say that it absolutely enhances the learning process. At no time did the proponents consider that there were wrong uses of technology, only that teachers were ill equipped to use the technology in their classroom.

In conclusion, technology use in the modern high school classroom can benefit students by encouraging them to work forward, allowing them to concentrate on abstract thinking, and to have more academic achievement. However, students can also use technology to do the work for them so that they need not understand the basic concepts, giving the students a disadvantage in college and in the workforce. NCTM (2000) recommends the use of technology in the classroom as long as it does not replace basic understandings and intuitions. And teachers need to know how to be smart in their use of smart technology by expecting paper and pencil explanations of students’ work to assess understanding.

However, the overreliance on calculators and other technology can have negative consequences. If the goal of education is to teach students what they need to know in the real world, we as educators need to find a balance between the use of technology and assessing students’ knowledge of how to solve problems and perform tasks without it (Mead, 2014).

Thus, the debate should not be about whether or not to use technology such as calculators in the secondary education classroom, as is often the case in various articles. It should be about whether or not students are learning basic concepts in mathematics and whether or not they can perform necessary tasks through mental calculations when the technology does not provide the answers. Educators cannot ignore the need to spend more time teaching concepts such as mathematical order of operations so that students can understand how the calculator will perform their calculations and avoid errors. Educators need to teach those who work in the retail business need to understand counting change without relying on their cash register which will not tell the worker what coins to give to the customer. The technology can still be used. But the user of the technology should have a basic understanding of how it works and how it solves problems and to make sense of solutions.

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