Meridian Middle School Computer Technologies Journal
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Abstract
Since high school science and mathematics teachers use calculators extensively, the incorporation of calculators in middle school classes can better prepare students for their high school experience. In addition, national and professional standards stress the use of technology—including calculators—for all grade levels. Generally, calculators and other forms of technology enhance teaching and learning in the classroom; however, for many students with learning problems, certain modifications may be needed to help them benefit from calculator use. This article reviews the characteristics of students with learning problems that may interfere with successful use of graphing calculators and presents ideas to prepare these students for future success in their high school classes.
Introduction
High school algebra, geometry, and science teachers use graphing calculators extensively to enhance their instruction and student performance. Furthermore, national standards recommend the use of calculators for all grade levels. Because of recent legislation including No Child Left Behind and amendments to the Individuals with Disabilities Act, most students with mild disabilities are educated in general education mathematics and science classes. Conceivably, students with learning problems may have difficulty using calculators even though the technology could potentially improve instruction and performance. Several teaching modifications can help students benefit from the use of calculators during instruction. The purposes of this article are to review student characteristics that interfere with successful use of calculators and present suggestions to help students with learning problems succeed in middle school mathematics classes and prepare for their high school courses.
Characteristics
Students with mild disabilities who are placed in general education middle school mathematics classes are typically those with learning disabilities (LD), attention deficit hyperactivity disorder (ADHD), behavioral disorders (BD), and communication disorders (CD). Many of the characteristics manifested by students with these disabilities can make the use of graphing calculators complex and challenging. For example, students with LD and often BD and ADHD havebasic skills that are significantly below grade level in reading and writing(Vaughn, Bos, & Schumm, 2006). If there are reading problems, it will likely be difficult for students to comprehend the textbook description of how to use calculators for specific types of problems. For instance, an explanation for generating a box-and-whisker plot could take up an entire page and include challenging, technical vocabulary that is difficult to comprehend. Writing problems can also cause errors when students are transferring information from the calculators to their papers.
In addition to low level academic skills, memory deficits are common characteristics of students with learning disabilities (Friend & Bursuck, 2006) and can make it difficult for students to remember the sequence of steps needed for using the graphing calculator, the functions associated with each key, and the symbols on the keys that represent various functions. Other processing problems of students with LD and CD may include visual, auditory, and motor skills deficits, and these challenges can render the graphing calculator difficult to use (Lewis & Doorlag, 2006). First, visual processing deficits can make the graphs students create appear confusing. For instance, graphs of three parallel lines may be difficult for a student with visual processing deficits to interpret because of the sheer amount of information presented on the screen at one time. These visual problems can also make it difficult for students to understand the display of numbers when entering them, for example, to create a histogram. Since the numbers in a histogram appear in one place while entering them and then appear later as part of a list, the steps may be especially confusing for some students. In addition, students with visual deficits may easily confuse the negative key and the minus key. Second, auditory deficits can make the teacher’s explanation for calculator use puzzling. For example, even when a teacher describes the two functions associated with each key and the use of the labels above the keys as second functions, it can be confusing for a student with auditory difficulties. Additionally, motor processing problems can make the graphing calculator difficult to use because of the fine motor skills required to manipulate the keys. These processing and memory problems are very common among students with mild disabilities and make graphing calculators challenging, frustrating, and perhaps intimidating.
Students with CD and sometimes students with LD have language problems (Vaughn, Bos, & Schumm, 2006), and these problems can make using the graphing calculator difficult. When a teacher explains the graphing of ordered pairs, for example, involving L1, L2, STAT, LIST, PLOT, and ZOOM, the students with receptive language problems could get lost easily. On the other hand, students with expressive language disorders may have problems explaining their results from an exercise such as coin flipping probability simulation using the random number generator. Both receptive and expressive language problems can then create frustration for teachers and students as they try to communicate information related to graphing calculator problems.
Attention difficulties associated with ADHD and sometimes BD and LD may make graphing calculator work particularly difficult (Friend & Bursuck, 2006). For many problems, such as graphing functions, sustained attention is required to comprehend and progress through all of the steps (Y=, WINDOW, GRAPH, TRACE functions) accurately. Students with attention problems often have a difficult time staying on task and working through the steps necessary for success.
Notably, many students with mild disabilities also exhibit problems in organization and study skills (Friend & Bursuck, 2006). For example, students with learning and behavioral disabilities frequently struggle to keep their class notes and assignments organized for use on homework and in preparation for test problems. When they set aside time to study, they may not have the notes they need to remind them how to use the calculator for specific problems. In addition, a student may have difficulty matching his calculator notes to the appropriate problems. Many of these deficits manifested by students with mild disabilities can be addressed with modifications for instruction in mathematics.
Suggestions for Teaching with Calculators
Some instructional interventions can help teachers and students have success with middle school mathematics lessons involving graphing calculators. Additional instructional time for clarifying graphing calculator steps for a particular type of problem may be useful in assisting with specific assignments. In addition, this emphasis on calculator use will prepare students for algebra I, geometry, and other high school classes. The directions can be presented orally by the teacher as well as visually on the board, on the overhead, or in handouts so that students with reading, processing, and language problems will have multiple chances to comprehend the material. Davis (1997) recommends the use of exact pictures of the graphing calculator as well as clear communication about the steps as a valuable strategy for initial learning experiences. This precise representation of the visual image and the step-by-step explanation help students who have processing, memory, and organizational difficulties.
Specific lessons that incorporate demonstration, modeling, and practice are beneficial, especially for students with attention, reading, and processing deficits (Mastropieri & Scruggs, 2004). For example, the teacher could demonstrate systematically how to graph three equations. Much practice could be used just for one equation until the students have mastered that step. Then the addition of the second equation can be incorporated again—with teacher demonstration and then additional practice—until mastered. Finally, the third equation can be added once the students are comfortable with the steps and procedures. This sequential instruction and mastery learning can be valuable strategies for students with mild disabilities.
Another important strategy for students learning to use the graphing calculator for the first time is to present a specific lesson on the calculator buttons and functions including comparisons to the keys on a regular calculator (Cox, 2000). In this way, the students can relate the new information to previous knowledge, a beneficial approach if processing and organizational problems exist. A great deal of practice and repetition in understanding, finding, and using the keys will provide the fluent use of the calculators necessary for subsequent, more advanced work with difficult problems. Because of the typical memory, attention, and processing problems of students with mild disabilities, it is also helpful to have students make a list of the new functions and keys as they learn them so they have a reference when working problems and assignments.
Another way to help students use graphing calculators is to incorporate a multi-sensory approach to instruction, often recommended for students with reading and writing problems. O’Neal (2001) recommends instruction incorporating both visual and auditory methods when using technology in teaching mathematics. She describes activities that include oral explanation and discussion to clarify the problems as well as the use of visual representations comparing the slope and intercepts of graphs that students create. By presenting the lessons using many senses, the students with learning problems will have a greater chance for success by receiving the new information in a variety of stimulating ways.
Finally, it is valuable and reinforcing to illustrate the use of graphing calculators for other subjects. Students with learning problems will benefit from the additional practice and repetition involved when they use the calculators in more than one class and from learning to generalize their skills to other subjects. Many science and social studies themes can incorporate the use of graphing calculators. For example, students can generate scatter plots, to illustrate the correlation of cars in a household and the amount of gasoline used; histograms, to show distances for geography concepts; and box-and-whisker plots, to compare temperatures of various cities. Students can also use the technology for science experiments (Cox, 2000). Lessons on tide schedules, the timing of sun rises, and space travel distances are just a few examples of topics in science that can easily be incorporated into a math lesson with a graphing calculator. All of these opportunities for practice will reinforce the newly learned calculator skills and bolster overall learning and student confidence.
Conclusions
The strategies described in this paper can enhance success for students with mild disabilities. They encourage individualized instruction based on the specific learning needs of students and make it more likely for students with learning problems to comprehend the mathematics lessons using graphing calculators. It is also likely that many of these ideas will be useful for other students struggling in middle school mathematics. Many students may have difficulty in mathematics and with calculators because of problems not related to a disability. For example, students who have missed a great deal of school and have gaps in their skills and students who have family difficulties may also fall behind in their mathematics classes. If students are underachieving for any reason, they may benefit from the more individual and systematic instruction. Moreover, the suggestions can aid teachers when they use calculators and other technology in science courses as well. Clearly, technological advances provide remarkable resources for students and teachers; however, some students need and deserve the additional modifications to fully benefit from these learning tools.
References
Cox, S. (2000). Using the TI-73 at Ringwood Junior School. Ti-Time, 1,12-14.
Davis, S. J. H. (1997). How mastering technology can transform math class. Educational Leadership, 55, 49-51.
Friend, M., & Bursuck, W. D. (2006). Including students with special needs: A practical guide for classroom teachers. Boston: Allyn and Bacon.
Lewis, R. B., & Doorlag, D. H. (2006). Teaching special students in general education classrooms. Upper Saddle River, NJ: Pearson-Merill Prentice Hall.
Mastropieri, M. A., & Scruggs, T. E. (2004). The inclusive classroom: Strategies for effective instruction. Upper Saddle River, NJ: Pearson- Merrill-Prentice Hall.
O’Neal, J. (2001). Y = mx+b really is found in real-life situations. Ohio Journal of School Mathematics, 43, 18-20.
Vaughn, S., Bos, C. S., & Schumm, J. S. (2006). Teaching exceptional, diverse, and at-risk students in the general education classroom. Boston: Allyn and Bacon.
About the Author
Marcee M. Stelle, PhD, University of South Florida, is a professor of
special education at the 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 pre-school to graduate school level in public and private
settings for 35 years.
Email: steelem@uncw.edu
Send correspondence to:
Marcee M. Steele, Professor
University of North Carolina Wilmington
Watson School of Education
Wilmington, NC 28403