January 4, 2007
Graphing Calculators: Teaching Suggestions for Students With Learning Problems
By Steele, Marcee M
IntroductionHigh school algebra and geometry teachers use graphing calculators extensively in their classes today. National and state mathematics curriculum standards recommend their use for class work, tests and assignments (Dion, Jackson, Klag, Liu, & Wright, 2001). Because of recent legislation, including IDEA 2004 and No Child Left Behind, most students with mild disabilities are placed in general education classes. Although graphing calculators are clearly useful resources for both teachers and students, the calculators frequently present challenges for students with learning problems. The purposes of this article are to describe the characteristics of students with learning problems that interfere with the use of graphing calculators and then to make recommendations that will help students and teachers have successful experiences in algebra and geometry classes.
Characteristics of students with learning problems
Students with learning problems
The students with learning problems that will most likely be taking general education algebra I, algebra II and geometry classes have labels such as learning disabilities (LD), behavior disorders (BD), communication disorders (CD) and attention defkits/ hyperactivity (ADHD). Although the labels are different, many of the characteristics that the students exhibit are similar and can create obstacles to using graphing calculators. The sections that follow describe typical characteristics of students with mild disabilities and the related problems they might have using graphing calculators.
Many students with LD, CD and ADHD exhibit processing disorders (Mercer and Mercer, 2005). Students who have visual processing problems, for example, may have difficulty remembering the functions of the graphing calculator keys; the negative and subtraction keys look similar and the various keys with "X" might get confused in terms of purposes. They may also have trouble pressing the keys in the correct order for problems that have several steps. In graphing a piecewise function, students might have difficulty remembering all of the steps in order including setting the mode, entering each piece including the truth functions and the values, adding, choosing the viewing window, graphing and using the trace feature. Students with visual processing problems may also have trouble interpreting the graphs they produce such as graphs of inequalities with shading or graphs of linear systems with several lines included.
Auditory processing deficits, on the other hand, can interfere with a students ability to understand the oral presentation or lecture when the teacher explains how to use the calculator for various problems. An explanation of graphing a circle using the center and radius by selecting the window, using the zoom and drawing features, and entering the center coordinates and radius could be confusing when presented orally.
In addition, motor processing problems could make it difficult to press the correct keys even if the students know the order and steps required. The fine motor coordination required could make it difficult to use the calculator accurately. For example, the keys are small and close together, with many opportunities to hit the wrong key or two keys together.
Below average academic skills such as reading and writing can also interfere with mathematics performance and are typical characteristics of students with LD, BD and ADHD (Mastropieri & Scruggs, 2004). Students who have reading problems may have trouble comprehending the manuals and textbook explanations that clarify the steps and procedures for using graphing calculators. For example, the long and detailed explanations that are in the manuals often include complex vocabulary and sentence structure that make them difficult to understand. Poor writing skills make it difficult for students to keep appropriate notes in class; therefore, they may be unable to follow the steps and directions they have recorded in their notebooks leading to poor performance on homework and tests. If students have steps written in the wrong order or steps omitted, they will not be able to use their work accurately for practice and review.
Some of the social, emotional and behavioral issues associated with BD and ADHD (Mercer & Mercer, 2005) can interfere with successful mathematics performance. Students who have attention deficits will often lose concentration on graphing problems with multiple steps. Even if a student knows how to graph polynomial equations to find solutions, he may get frustrated and give up before entering both equations, changing the viewing window, using the intersect feature and then determining the solutions. Students with social skills deficits may have trouble with the group activities that teachers often use for class work and projects. Students could get in trouble by playing with the calculators instead of attending to the lessons and learning how to use them accurately.
Language deficits are characteristics of students with LD and CD (Mastropieri & Scruggs, 2004) and can make mathematics instruction challenging. Receptive language problems can make the class presentation confusing when teachers try to explain the steps or directions for using graphing calculators; expressive language problems, on the other hand, make it difficult for some students to ask for the assistance that they need without embarrassment.
Below average cognitive skills such as conceptualizing, abstract reasoning and generalizing (Mercer & Mercer, 2005) will make it difficult for some students to apply their knowledge and skills to problems for homework when the situations are slightly different from those covered during class. They could have difficulty applying new information to word problems that are critical for mathematics instruction in algebra and geometry. Although word problems help students see the applications of math in the real world, long problems with numerous equations, numbers, variables and numerous steps for entering the data on the calculators for tables and graphs can be too complex.
These typical characteristics of students with learning problems, summarized in Table 1 on the following page, can interfere with success when teachers and students are using graphing calculators. However, algebra I, algebra II and geometry teachers can use strategies to enhance the possibility of success for all students.
Suggestions for using graphing calculators in algebra and geometry for students with learning problems
Several modifications and interventions will enable teachers and students with learning problems to have success in lessons involving graphing calculators. The following discussion includes a description of well-researched and recommended practices for students with learning problems with related examples and applications for graphing calculator use.
If students have memory problems, teachers can use mnemonic strategies to help them memorize the steps and procedures (Mercer & Mercer, 2005) they need. Teachers and students can create first letter mnemonics to learn a set of procedures involving the calculator. To graph equations such as 2X+6Y=24, "SEW" can be used to remember the steps. "Solve" will remind students to solve for Y, "Enter equation" to remind students to type the equation into the calculator and "Window" to remind students to set the window for appropriate viewing.
Multisensory instruction could also help students with learning problems understand the lesson by presenting the information in a variety of ways (Salend, 2005). Reading the textbook and handouts about the graphing calculator (visual input) combined with discussion and lecture (auditory input) can reinforce the steps and procedures required for a particular problem. Emulator software, available through a variety of companies, is another example of technology that teachers can use to incorporate a multisensory lesson for students with learning problems. The software provides an accurate model of a graphing calculator using the computer screen (visual input) and provides options for teachers to record or use prerecorded scripts with instruction (auditory input) on their use and applications to problems (TI-SmartView, 2005).
Modeling can provide the additional examples that are needed for students with processing problems. Teachers can use several examples and models to clarify procedures, thereby helping students generalize the steps to other problems (Salend, 2005). The teachers' examples can help clarify if the directions and explanations in the book for using the graphing calculator are confusing. In addition, scaffolding is a procedure involving modeling in which teachers talk through the procedures for students and then the students eventually learn to talk through the steps themselves or with minimal prompting (Polloway, Patton, & Serna, 2005). In an individual, small group or whole class setting, the teacher could provide this support to students by demonstrating sequentially the steps for a problem using the graphing calculator. Then the students can work through the steps with guidance as needed, and finally when they are ready, the students can practice the steps independently.
Sometimes the p\rocedures in a long problem need to be broken down into very small steps and practiced with additional repetition and review for students to have success (Mastropieri & Scruggs, 2004). For example, using sinusoidal modeling, students could practice scatter plot graphing until mastery and then add on the sinusoidal regression graph before finally checking whether the model is a good fit.
Students with memory deficits would also benefit from steps, procedures and sample problems written in a section of their notes or notebooks so they have something to refer to each time they have difficulty remembering (Salend, 2005). Perhaps these reminders could even be used for tests initially until students are able to remember on their own with much practice and review. The directions for using the calculators for various problems could be clarified by explaining in very easy vocabulary and simple sentences. Students should be able to repeat back the instructions in their own words to be sure they understand prior to using the rules for homework and tests.
Encouraging students to ask questions can be very beneficial in teaching mathematics to students with learning problems (Polloway, Patton, & Serna, 2005). Questions about the calculators and steps for using the calculators to solve problems should be encouraged. In addition, notes should be checked to ensure students have correct information before doing homework or studying for tests.
Real life examples are also beneficial to ensure that students understand the purpose of various procedures and uses of the graphing calculators. Cyrus and Flora, for example, recommend teaching technology with realistic examples to clarify learning of concepts and applications (2000). Osawa provides a real life example he used with a graphing calculator in which the high school students participated in a relay race in order to generate the data needed to solve the problem. The students reported a high interest level and motivation to succeed with the mathematics lesson, an overall better attitude toward learning mathematics and an interest in working additional problems. Furthermore, according to the teacher, the students gained more insight into the specific concepts and procedures in the lesson using real life examples and the graphing calculator.
Practice, practice, practice
Students would benefit from sufficient time to practice the problems and use of graphing calculators independently and in small groups. In this way, they can get feedback and prompts as needed. The practice in groups can be used to improve mathematics and social skills (Goos, Galbraith, Renshaw, & Geiger, 2000).
The suggestions presented in this paper are summarized in the table that follows. These modifications would be helpful for students with learning problems but also useful for many students in the classroom who are having trouble with calculators for a variety of reasons. Many of the suggestions could be used for other aspects of mathematics instruction besides graphing calculator use, and used for other subjects like science and social studies whenever graphs are involved in the instruction.
'Although graphing calculators are clearly useful resources for both teachers and students, the calculators frequently present challenges for students with learning problems.
Cyrus, V. F., & Flora, B. V. (2000). Don't teach technology, teach with technology. Mathematics Teacher, 93(7), 564-567.
Dion, G., Jackson, C., Klag, P., Liu, J., & Wright, C. (2001). A survey of calculator usage in high schools. School Science and Mathematics, 101(8), 427-438.
Goos, M., Galbraith, P., Renshaw, P., & Geiger, V. (2000). Reshaping teacher and student roles in technology-enriched classrooms. Mathematics Education Research Journal, 12(3), 303-320.
Mastropieri, M. A., & Scruggs, T. E. (2004). The inclusive classroom: Strategies for effective instruction. Upper Saddle River, NJ: Pearson Merrill Prentice Hall.
Mercer, C. D., & Mercer, A. R. (2005). Teaching students with learning problems. Upper Saddle River, NJ: Pearson Merrill Prentice Hall.
Osawa, H. (2002). Mathematics of a relay-problem solving in the real world. Teaching Mathematics and its Applications 21(2), 85-93.
Polloway, E. A., Patton, J. R., & Serna, L. (2005). Strategies for teaching learners with special needs. Upper Saddle River, NJ: Pearson Merrill Prentice Hall.
Salend, S. J. (2005). Creating inclusive classrooms. Upper Saddle River, NJ: Pearson Merrill Prentice Hall.
Texas Instruments. (2005). TI-SmartView(TM) emulator software from Texas Instruments helps teachers enhance lessons using graphing calculator technology. Retrieved September 8, 2006, from http:// education. ti.com/educationportal/sites/US/ nonProductSingle/ about_press_release_news62.html
Marcee M. Steele, 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 techniques and special education methods. She has also taught individuals with learning disabilities from pre-school to graduate school level in public and private settings for over 30 years.
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