November 9, 2007
Teaching Calculator Skills to Elementary Students Who Have Learning Problems
By Steele, Marcee M
ABSTRACT: The most recent amendments to the Individuals With Disabilities Education Act (IDEA; 2004) and the regulations of the No Child Left Behind Act (2002) emphasize teaching general education curriculum to students with disabilities whenever possible. As a result, the majority of students with mild disabilities are educated in the general classroom, and elementary teachers are responsible for helping them succeed in the grade-level curriculum. The National Council of Teachers of Mathematics standards stress the use of technology for mathematics instruction at all grade levels, and middle and high school mathematics teachers use graphing calculators extensively. In this article, the author discusses why it is important for elementary education teachers to introduce early calculators with modifications for students with mild disabilities. KEYWORDS: calculators, elementary education, mathematics instruction, modifications, students with learning problems, technology
THE MOST RECENT AMENDMENTS to the Individuals With Disabilities Education Act (IDEA; 2004) and the regulations of the No Child Left Behind Act (2002) emphasize teaching general education curriculum to students with disabilities whenever possible. As a result, the majority of students with mild disabilities are educated in the general classroom, and elementary teachers are responsible for helping them succeed in the grade level curriculum. Some state standards and the National Council of Teachers of Mathematics (NCTM) standards stress the use of calculators and technology for all levels of mathematics instruction, including the primary grades. In addition, middle school and high school mathematics teachers and students use graphing calculators extensively.
With the placement of students with special needs in the elementary classroom, a focus on calculators in mathematics curriculum, and the future emphasis on the use of graphing calculators, it is important for elementary teachers to introduce technology early and prepare students with the technology skills that they will need in later years. Students can use calculators to compensate for their deficits in learning. However, students with mild disabilities may experience frustration and difficulties in using the calculators. Several strategies and modifications may help teachers and children have success with calculators for elementary mathematics lessons. The purposes of this article are to review characteristics of students with learning problems that can interfere with the use of calculators and then to describe some modifications and strategies that elementary mathematics teachers can use to ensure success for all students.
Students With Learning Problems
The students with mild disabilities whom administrators typically place in a general education elementary classroom have labels such as learning disabilities (LD), intellectual disabilities (ID), behavior disorders (BD), attention deficits/ hyperactivity disorders (ADHD), and communication disorders (CD; Smith, Polloway, Patton, & Dowdy, 2004). Although the labels and definitions vary, many of the students exhibit similar characteristics that can interfere with calculator use.
Many students with mild disabilities have below-average skills in reading and writing (Bos & Vaughn, 2006). On the one hand, low- level reading skills can make it difficult for students to follow textbook directions involving calculators. On the other hand, writing problems can make it difficult for students to record accurately the numbers that are in the text, on an assignment sheet, or on the calculator screen, and that difficulty will result in errors in the calculations.
Problems in processing, which are typical of students with LD and sometimes those with ID and CD (Wood, 2006), also can interfere with the use of the calculator in a mathematics lesson. If students have trouble interpreting what they see, they may misunderstand the answer on the calculator screen or in an example problem that a teacher works on the board. Auditory processing problems could lead to a student's not understanding the oral explanation for calculator use or specific procedures. Motor-processing problems make it difficult for students to copy work and show all of their work when completing problems by using the calculator. There may be number transpositions (e.g., "17" for "71"), omissions (e.g., "3548" for "35498"), and additions (e.g., ".333379" for ".33379"). Of course, when these errors occur, the answers will be incorrect, and the students will lose points, especially when partial credit is not given.
Language problems are also typical characteristics of students with communication, learning, and intellectual disorders (Wood, 2006). Receptive language problems can make it difficult for a student to interpret a teacher's oral clarification and to follow directions for a problem or assignment. An expressive language problem can make it difficult for a student to give a response aloud. These language problems can also interfere when students are working in cooperative groups and playing mathematics and calculator games for practice.
Behavior problems are present in students with labels of BD and often those of ADHD and LD as well (Smith et al., 2004). Examples that may interfere with calculator use include (a) social skills deficits, (b) problems in focusing, (c) excessive movement, and (d) disruptive behaviors. Consequently, students may have trouble with group work in mathematics, in using the calculator appropriately instead of playing with the keys and functions, and in working on mathematics problems with several steps that are typical for calculator use.
Problems with cognitive skills such as abstract reasoning and memory are characteristics of people with learning and intellectual disabilities (Wood, 2006) and also can make mathematics and calculator use a problem. For example, students who have difficulty with abstract reasoning may not understand word problems that often involve the calculator. They may not be able to generalize and relate answers on the screen to problems in the book. Memory problems will interfere with the ability to associate the keys with the various functions and also the ability to remember all of the steps in using a calculator for a particular type of problem. All of these characteristics can make calculator use a challenge for students and teachers. However, there are strategies that can make the work easier.
Modifications for Using Calculators
Teachers can try some basic strategies to help students with learning problems use calculators more effectively and efficiently. Specific lessons on the use of the calculator can help students that have memory, cognitive, and processing problems. Teachers can teach the calculator skills initially and then review them prior to each lesson. Students and teachers can review and practice the purposes of each button before the actual mathematics lesson (Cox, 2001). With money and decimal problems, it would be helpful for teachers to instruct students to add a zero to an answer to indicate- for example-that .9 = .90 = $.90 (Bley & Thornton, 2001). Students or teachers can create individual reminder charts or booklets with pictures of the keys and brief descriptions of their uses to help students remember the function of each key as they work problems on the calculator for new procedures. For practice with the keys and steps, teachers could have students work a few drills as games.
Another suggestion for using calculators in the elementary classroom is for teachers to teach students to make appropriate decisions about when to use the calculator (Charles, 1999). Teachers can emphasize mental mathematics, paper-and-pencil calculations, and the calculator as alternatives for students to choose according to the situation. The use of these methods will vary at each grade level according to its objectives and purposes (Reys & Reys, 1998). Because of students' possible conceptual and memory deficits, for teachers to be sure that they select the appropriate method, it would be helpful for the students to practice making these decisions explicitly before actually performing the calculations. Freund and Rich (2005) suggested that teachers give students a page of computations and have them select the examples that they can perform faster mentally than with either paper and pencil or a calculator. Another possibility is to have small groups of students make up their own problems that could be solved more efficiently on the calculator, with paper and pencil, and by using mental calculations (Freund & Rich).
Teaching students to check their work is a strategy that is important to teachers for all levels of mathematics assignments, homework, and tests. It is also an important strategy to teach for work on the calculator. One way to check their calculator work is to have them match frequently the numbers and symbols that they think they are keying in with the actual display on the calculator (Bley & Thornton, 2001). This extra check is particularly important for students who have motor processing, visual processing, and memory deficits. The students can easily key in the wrong number and obtain incorrect answers for their problems even if they mastered the mathematics skills involved. Even in kindergarten, when students are using their calculators for counting, they can learn to check their work to be sure that the numbers that they say aloud match the numbers that they see on the display. Students with learning problems also benefit from real-life examples so that they can relate and generalize. If the examples that teachers present on calculators resemble problems that they can relate to, students with language and processing difficulties will be able to understand better the connections between their class work and the real-world applications. Realistic examples provide motivation. Also, teachers can use them easily because the calculator enables children to work with larger numbers than possible with paper-and-pencil calculations (Charles, 1999). Students could use realistic examples by making class charts of pets or brothers and sisters and then calculating totals for the rows and columns of tally marks. Students in the early grades can practice entering realistic numbers in the calculators such as their ages, number of people in their families, and number of books in their book bags.
Working in groups for mathematics activities can also be valuable and enjoyable for the students when using calculators. These activities foster active learning (Krach, 2000), which mathematics and special educators highly recommend as critical for the success of students with mild disabilities. The math lessons can be less stressful when a cooperative group is involved if students understand the rules and if teachers select the group members carefully. Students can help each other and experiment with the technology in a nonthreatening way. In primary grades, children can work with partners to explore calculators and make numbers for their partners to read on the display. They can work in groups of three to determine answers to large number problems with each student using a different method-mental mathematics, paper and pencil, and calculator. Then, they can compare their answers and check for accuracy.
Relating mathematics to other subjects is also helpful for teachers when teaching children to use calculators (Cox, 2001; Krach, 2000). It is beneficial for students with learning problems because it teaches them to generalize and gives additional practice that is necessary if the students have conceptual or memory problems. Students can use the calculator to compute large numbers such as planet masses and numbers of species of various animals in science and to compute populations of cities and flying distances between locations in social studies. These examples can help students to see applications and practice calculator use in subjects other than mathematics during the day. These strategies can help students with mild disabilities to succeed in their class work, homework, classroom tests, and high-stakes mathematics tests.
Summary of Strategies
The following list provides a summary of the aforementioned strategies for teaching calculator skills:
1. Plan specific lessons on calculator keys, functions, and procedures.
2. Review calculator skills that are necessary for specific problems prior to each lesson.
3. Have students keep review charts or booklets with specific functions and keys.
4. Have students play games to practice and review calculator use.
5. Teach students to match the method (paper and pencil, calculator, or mental mathematics) with the type of problem and purpose.
6. Provide practice activities and games for students to select method of calculation without the extra stress of actually solving the problems.
7. Have students check their display frequently to be sure it matches what they think they are entering.
8. When using the calculator, use realistic examples so that students can relate to the problems and make connections to their lives, to help them to understand the value of the calculator.
9. For calculator games and practice, try cooperative groups, selecting the members carefully and reviewing rules and procedures for working in groups prior to the activity so that everyone has a chance to participate and benefit.
10. Use the calculators for other subjects such as social studies and science so that students can better retain and transfer the procedures and see the everyday value of calculator use.
These strategies are important for students who have learning problems to succeed in using calculators for mathematics. In addition, the strategies will help students prepare for future and more complex use of calculators in middle school mathematics and high school algebra and geometry classes. Further, the strategies will help students succeed on the high-stakes mathematics tests that federal, state, and local mandates require. Some of these strategies would be helpful to students with disabilities for work in other elementary subjects and to students without disabilities.
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Bos, C. S., & Vaughn, S. (2006). Strategies for teaching students with learning and behavior problems. Boston: Allyn & Bacon.
Charles, R. I. (1999). Calculators at the elementary school level? Yes it just makes sense! Mathematics Education Dialogues, 2, 11.
Cox, S. (2001). Using the TI-73 at Ringwood Junior School. Micromath, 17, 17-20.
Freund, L., & Rich, R. (2005). Teaching students with learning problems in the inclusive classroom. Upper Saddle River, NJ: Pearson.
Individuals With Disabilities Education Act of 2004, 20 U.S.C. [section] 401 et seq. (2004).
Krach, R. M. (2000). Using hand-held technology with fourth grade mathematics students. Ohio Journal of School Mathematics, 41, 30- 33.
No Child Left Behind Act of 2002, 20 U.S.C. [section] 301 et seq. (2002).
Reys, B. J., & Reys, R. E. (1998). Computation in the elementary curriculum: Shifting the emphasis. Teaching Children Mathematics, 5, 236-241.
Smith, T. E. C., Polloway, E., Patton, J. R., & Dowdy, C. A. (2004). Teaching students with special needs in inclusive settings. Boston: Pearson Allyn & Bacon.
Wood, J. W. (2006). Teaching students in inclusive settings. Upper Saddle River, NJ: Pearson.
Marcee M. Steele is a professor of special education in the Watson School of Education, University of North Carolina, Wilmington. She teaches undergraduate and graduate courses in learning disabilities, assessment, program development, exceptionalities, and methods for special education. She has also taught individuals with learning problems from preschool to graduate school in public and private settings for 35 years. Copyright (c) 2007 Heldref Publications
Copyright Heldref Publications Fall 2007
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