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Calculators in the Mathematics ClassroomSince calculators have become more main stream in mathematics classrooms, it has become a pressing issue to identify the proper uses and appropriate assessments for calculators. Much research is shown in support of using technology in the classroom, though much focus still remains on the ability of teachers to use them properly and finding assessment methods (Bobis, 1996). Many individuals preach to the disadvantages of calculator use, pointing towards the differences between the ways they were taught mathematical concepts versus the ways these same concepts are being taught today. To show the extreme difference in views in the United States, look at the following comparison: the state of California has proposed legislation banning the use of calculators before sixth grade while Virginia recently purchased 200,000 calculators for middle and high school students “to put every student on an equal footing…” (Bracey, 1998). To help with this dispute and try to find a way to deal with calculator use, this paper is to give a descriptive and informative synopsis of the benefits and draw backs of technology (mainly calculators) in math classes.The majority of research points to the abundance of perks that come with the use of calculators in the classroom. By allowing students to explore mathematical concepts while using technologies allows them to develop problem-solving skills that can better fit their type of thinking (Forster, 2006). Forster also sees that by utilizing these skills, students tend to stray away from strictly procedural computation and are forced to use their judgment on the best way to approach the problem and if calculators are even necessary (2006). Ozel, Yetkiner, and Capraro also touch on this finding, stating that using calculators enhances students’ higher-thinking skills (2008). In turn, students can calculate formerly tedious calculations in an extremely efficient manner which allows the students focus on properties and relationships rather than the result (Forster, 2006). This, of course, cannot happen by just using calculators and makes selecting appropriate types of problems a huge part in ensuring that students start to think critically about mathematics. By using calculators properly, students can “amplify… cognitive abilities and help reorganize… current mathematical understanding and thought patterns” (Grassl, 2002). Overall achievement has also been found to increase from the use of technology, this according to a study of the National Educational Longitudinal data (Ozel, 2008). This increase in achievement can be partially linked to student motivation when using technology. Studies have found that motivation increases when students are allowed to use calculators in their work (Ozel, 2008). Then yet another link can be found between the increased motivations that students feel and their improved enthusiasm and confidence in mathematics when they are allowed to use calculators (Bobis, 1996). Bracey backs these findings by saying that when students get to use calculators they have a better attitude towards their assessments and gain a larger feeling of empowerment (1998). Ozel also touches on this, stating that children are more engaged in mathematics when they can use technology (2008). Teachers who take advantage of calculators in their classroom can present real-life problems to students that, without calculators, would be impossible (Bracey, 1998). In turn, by using more realistic problems, students will remain more engaged. All together, this shows that when calculators are allowed to be used in the classroom, students find mathematics more “user-friendly” in all respects. This makes sense considering today’s youth has grown up in an era of technology and being allowed to use calculators will make them feel more comfortable and more engaged in the concepts being taught. Studies are not the only way of seeing the increased importance of calculators in the mathematics curriculum, though. If a person is to analyze the most influential math education documents, such as the Virginia SOLs and the National Council of Mathematics Teachers’ (NCTM) policy statement, it is prevalent that calculators are pertinent in the classroom. Numerous Virginia SOLs express the need for calculators, for example, recognizing numerical patterns using calculators (K.4) as well as adding and subtracting numbers less than 10,000 using calculators (3.8) (Commonwealth, 2002). The NCTM also states its advocacy of calculators, calling on teachers to use calculators in all grade-levels, as long as it is intertwined with the curriculum appropriately (Cavanagh, 2005). It is also seen that curriculums across the nation are starting to incorporate calculators more and recognizing their importance (Ozel, 2008).So far, in this paper, only positives to calculator use have been presented. Though the majority of research does have a positive outlook on technology in general, there are definite concerns over its use. The most common of these concerns among the public is that the focus on technology comes with a lesser focus on mental computation. In everyday life, about 75% of all calculations that are needed to be performed are done mentally (Bobis, 1996). By allowing students free access to calculators on problems that require only basic computational skills, the student becomes reliant on the technology and becomes less efficient. Though a somewhat logical argument, this falls short if calculators are implemented correctly into the classroom (implementation is explained below). Bobis argues that if calculators are used in substitution for thinking, then of course this is true, but the same can be said about pencil and paper techniques, hence why assessment methods are so important (1996).This may be the biggest concern to most Americans, but the real concern with technology use in the classroom is its accessibility and being equitable. Depending on student backgrounds, they may have a lesser understanding of how to use calculators and thus, may be at a huge disadvantage if they do not learn the proper background information for the technology (Forster, 2006). Forster goes on to say that even if students learn the knowledge necessary to use the technology, they may still adopt inefficient methods in solving the problem or be overly concerned with properly entering the equations that they forget the real focus of the activity (2006). Even if students are on a level playing field when it comes to an understanding of the technology, there can still be huge equity issues with students’ access to calculators. Unless classroom sets are provided, students may have no access to a graphing calculator in upper-level classes or to simpler calculators in elementary and middle school. On top of this, not all calculators are the same and, unless there is some sort of standard calculator in the classroom, there can be a wide range of how each individual student’s calculator can be used for an assignment (Bracey, 1998). This is the biggest issue because, unlike the other factors, there is no real control over these equity issues.The last concern in calculator use is teacher understanding. Many teachers lack the conceptual understanding needed to try new approaches to problems and to effectively use calculators (Bobis, 1996). When teachers do not have a deep enough understanding to explore mathematical topics, many of their lessons, whether they are calculator-based or not, become procedural and do not help students gain conceptual knowledge (Ozel, 2008). Not only do teachers lack mathematical understanding, but there are many teachers who have technological issues when trying to incorporate calculators, so they avoid using them (Ozel, 2008). Ways to assist in these matters can also be found below.All of these concerns come back to the idea of how to properly incorporate calculators into the math classroom. To fully benefit from calculators, teachers need to use the technology well (Ozel, 2008; Cavanagh, 2005; Bobis, 1996). This is done by challenging students with more project-like problems and using a variety of assessment methods that require students to use all sorts of techniques to solve. Teachers need to check the worth of using calculators in activities and assess if using calculators for these benefits is worth the additional time and resources needed to use them (Ozel, 2008). By thinking this through, it ensures that teachers are using technology to better instruction and not to just use calculators.As calculators become more complex, students will be able to do more computation with them, so teachers need to create (or find) open-ended problems that truly engage students in higher-level thinking (Grassl, 2002). These problems need to have multiple approaches for their solution, more than one possible answer, and do not easily follow traditional algorithms (Grassl, 2002). The types of problems that are asked must also force students to decide if calculators are necessary to solve the question effectively. There can be three types of these questions and they can be calculator-active, -passive, or –neutral (Bracey, 1998). In an active problem, calculators are necessary to efficiently arrive at a solution; in a passive problem, the use of a calculator is unnecessary; and in a neutral problem, calculators neither help nor hinder the problem (Bracey, 1998). Using a variety of these problems helps students differentiate when calculators are necessary and when they are not. As Derringer (2007) quoted Steve Wahl saying: A calculator is simply a tool and nothing more. A screwdriver is good to have but it isn’t going to help you pound nails. A calculator can be a valuable tool for a student to have but they have to realize that it won’t do everything for them, they’ll still have to use their head (no page).To help teachers feel comfortable using calculators in their classroom, school districts need to provide professional training to teach educators the proper use of technology (Ozel, 2008). Also, on top of being taught how to use the technology, teachers need to have access to support in case they do have issues with their resources so that they can be solved in a timely fashion (Ozel, 2008). If these two items are in place, teachers will feel more comfortable in exploring the use of calculators in their classroom. Depending on the grade level, calculators can be used for a variety of things, such as in kindergarten, children can type numbers on the calculator and arrange themselves in numeric order or in fifth grade having students develop estimation skills of multiple digit multiplication (Bracey, 1998). Notice in these activities, the focus is not on the result, but really on the thought process to arrive at the solutions, and that is why calculator use is appropriate.Throughout this paper, the main concerns always come back to the teacher’s ability to use calculators effectively. Rightfully so, this is a huge reason why technology is not more widespread in classrooms. By training pre-service teachers while in college and having professional development for educators already in schools, calculators can be used more appropriately and help students explore mathematics in a deeper sense. The advantages to using calculators in a classroom are so a beneficial to the students it is unjust not to find useful ways to incorporate them. As time continues, technology will continue to become more main stream and educators will need to adapt to this by engaging their students in relevant mathematics that calls on technology, but more specifically, calculators. ReferencesBobis, J. (1996). Mathematics education: Of primary concern. Primary Educator, 2(1), 5.Retrieved from Education Research Complete database.Bracey, G. (1998). Calculations about calculators. Phi Delta Kappa, 79(6), 473. Retrieved fromEducation Research Complete database. Cavanagh, S. (2005). NCTM to revise position on calculator use. Education Week, 24(33), 10.Retrieved from Academic Search Complete monwealth of Virginia Board of Education. (2002). Mathematics Standards of LearningCurriculum Framework: Kindergarten – 8th. Richmond, VA. Derringer, J. (2007). Classroom calculator use has its pros, cons. The Crescent News. Retrievedfrom , P. (2006). Assessing technology-based approaches for teaching and learningmathematics. International Journal of Mathematical Education in Science & Technology, 37(2), 145-164, Retrieved from Teacher Reference Center database.Grassl, R., & Mingus, T. (2002). On the shoulders of technology: Calculators as cognitiveamplifiers. International Journal of Mathematical Education in Science & Technology,33(5), 715-723. Retrieved from Education Research Complete database.Ozel, S., Ebrar Yetkiner, Z., & Capraro, R. (2008). Technology in K-12 MathematicsClassrooms. School Science & Mathematics, 108(2), 80-85. Retrieved from TeacherReference Center database ................
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