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
Email: steelem@uncw.edu
Send correspondence to:
Marcee M. Steele, Professor
University of North Carolina Wilmington
Watson School of Education
Wilmington, NC 28403
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, 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.
