Mathematics Strategy Instruction (SI) for Middle School Students with Learning Disabilities
By: Paula Maccini and Joseph Gagnon (2006)
One of the greatest challenges teachers currently face with students who are struggling academically is how to provide access to the general education curriculum.
The No Child Left Behind Act of 2001 and the Individuals with Disabilities Education Act of 2004 support the assertion that all children, including those with disabilities, should have access to the same curriculum. Furthermore, the National Council of Teachers of Mathematics (2000) supports providing all youth equal access to mathematical concepts.
However, students with disabilities in general, and those with learning disabilities (LD) at the middle school level, often have difficulty meeting academic content standards and passing state assessments (Thurlow, Albus, Spicuzza, & Thompson, 1998; Thurlow, Moen, & Wiley, 2005). Specifically, students with LD often have difficulties with:
- mathematics, including basic skills (Algozzine, O'Shea, Crews, & Stoddard, 1987; Cawley, Baker-Kroczynski, & Urban, 1992)
- algebraic reasoning (Maccini, McNaughton, & Ruhl, 1999)
- and problem-solving skills (Hutchinson, 1993; Montague, Bos, & Doucette, 1991).
Many of these students struggle with how to:
- approach math problems
- make effective decisions
- carry out the chosen plan (Maccini & Hughes, 2000; Maccini & Ruhl, 2000)
One effective approach to assisting middle school youth with LD in accessing challenging mathematical concepts is to provide strategy instruction (SI). This brief defines strategy instruction, identifies key features of effective strategies, and identifies key components necessary for instructing youth in the use of a strategy.
In addition, we provide a practical example for the use of a math instructional strategy that can be applied to a variety of concepts and settings, and provide some key considerations when using strategy instruction in mathematics classes.
What is a strategy and what are the key features?
- Memory devices to help students remember the strategy (e.g., a First Letter Mnemonic, which is created by forming a word from the beginning letters of other words);
- Strategy steps that use familiar words stated simply and concisely and begin with action verbs to facilitate student involvement (e.g., read the problem carefully);
- Strategy steps that are sequenced appropriately (i.e., students are cued to read the word problem carefully prior to solving the problem) and lead to the desired outcome (i.e., successfully solving a math problem);
- Strategy steps that use prompts to get students to use cognitive abilities (i.e., the critical steps needed in solving a problem); and
- Metacognitive strategies that use prompts for monitoring problem solving performance ("Did I check my answer?") (Lenz, Ellis, & Scanlon, 1996).
Some strategies combine several of these features.
STAR is an example of an empirically validated (Maccini & Hughes, 2000; Maccini & Ruhl, 2000) first-letter mnemonic that can help students recall the sequential steps from familiar words used to help solve word problems involving integer numbers.
- Search the word problem;
- Translate the problem;
- Answer the problem; and
- Review the solution (see Figure 1).
Teachers can use self-monitoring forms or structured worksheets to help students remember and organize important steps and substeps. For example, students can keep track of their problem solving performance by checking off (√) the steps they completed (e.g., "Did I check the reasonableness of my answer?" √ ).
What is strategy instruction and what are the key components in math?
Strategy instruction involves teaching strategies that are both effective (assisting students with acquiring and generalizing information) and efficient (helping students acquire the information in the least amount of time) (Lenz et al., 1996, p. 6).
Student retention and learning is enhanced through the systematic use of effective teaching variables (Rosenshine & Stevens, 1986). That is, certain teaching variables (i.e., review, teacher presentation/modeling, guided practice, independent practice, feedback, and cumulative review) are both effective and efficient for teaching math to secondary students with LD (see Gagnon & Maccini, in press, for a complete description).
Example of strategy instruction in secondary math
The example below demonstrates a classroom lesson incorporating the first-letter mnemonic strategy, STAR (Maccini, 1998). This strategy incorporates the previously noted strategy features and effective teaching components to help teach the information efficiently and effectively.
In addition, the strategy incorporates the concrete-semiconcrete-abstract (CSA) instructional sequence, which gradually advances to abstract ideas using the following progression:
- concrete stage (i.e., three-dimensional representation in which students manipulate objects to represent math problems)
- semiconcrete (i.e., two-dimensional representation in which students draw pictures of the math problem)
- abstract (i.e., students represent the problem using numerical symbols)
Prior to the lesson, the teacher should pretest students to make sure they have the prerequisite skills and vocabulary relevant to the appropriate math concept(s) and to make sure the strategy is needed.
The teacher then introduces the strategy and describes what a strategy is, including the rationale for learning the specific instructional strategy and where and when to apply it. After an explanation, the teacher asks students to explain the purpose of the strategy, how it will help them solve word problems, and how to use the strategy.
Students should memorize the steps of the mnemonic strategy and related substeps for ease of recall by using a rapid-fire rehearsal. This rehearsal technique involves first calling on individual students (or throwing a ball to students) and having them state a strategy step, then repeating the process with other students in the class. The rehearsal becomes faster as students become more fluent with the steps and rely less on teacher prompts or written prompts.
What are some considerations to keep in mind when using strategy instruction in math classes?
There are a few recommendations to keep in mind when using strategy instruction in your math class (Miller, 1996; Montague, 1988):
- Recognize student characteristics (cognitive and behavioral) and preferences.
When teaching strategy instruction, be aware of student characteristics and preferences. For example, some students may prefer highlighting relevant words while reading a word problem aloud, while others may prefer underlining and silently reading the problem.
Equally important is the need to recognize student behavioral characteristics, including their self-esteem in math and motivation. For instance, students with low motivation may need additional supports to promote active engagement. Examples include creating individual student math contracts with the targeted math objectives and the goal/criterion and promoting active student involvement by having students lead discussions while using a strategy (e.g., "How did you arrive at your solution?").
- Promote individualization of strategy instruction (SI).
Students should be encouraged to individualize use of SI in math class via adapting a strategy learned in class. For example, as processes involved in the STAR strategy becomes more automatic for students, recalling the first step, "Search the word problem," may prompt students to read the problem carefully and to initiate translation into mathematical form (i.e., translating words into an equation).
- Program for generalization.
It is imperative that both special and general education math teachers program for both near (i.e., maintaining the same structure but using different story lines) and far generalization (i.e., incorporating more complex problems than the problems in the instructional set) of the SI math strategies in order to promote retention and application of strategy use.
For example, for near generalization, different story lines can be incorporated for generalization (i.e., use of integer numbers with problems involving time zone changes, sea level, and age) in addition to the problems used in the instructional set.
For far generalization, more complex problems are introduced than the problems initially taught in the instructional set (e.g., In a certain city, if the difference between the highest and lowest altitude is 155 m and the altitude of the highest point is 900 m above sea level, what is the altitude of the lowest point?).
In addition to its application to problem solving involving integer numbers, the STAR strategy can be generalized across math topics (see Figure 3 for an example involving area).
Students with learning disabilities in mathematics often have difficulties deciding how to approach math word problems, making effective procedural decisions, and carrying out specific plans (Maccini & Hughes, 2000; Maccini & Ruhl, 2000).
Strategy instruction is an effective method for assisting middle school students with learning disabilities as they complete challenging mathematical problems. To support teacher use of math strategies, this brief defined strategy instruction, and provided key features of effective strategies and instructing youth in the use of a strategy.
The practical examples presented illustrate how strategies such as STAR can be applied to a variety of math concepts and can provide the support necessary to ensure student success.
This article is also available as a downloadable PDF.
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Algozzine, B., O’Shea, D. J., Crews, W. B., & Stoddard, K. (1987). Analysis of mathematics competence of learning disabled adolescents. Journal of Special Education, 21, 97-107.
Cawley, J. F., Baker-Kroczynski, S., & Urban, A. (1992). Seeking excellence in mathematics education for students with mild disabilities. Teaching Exceptional Children, 24, 40-43.
Ellis, E. S., & Lenz, B. K. (1996). Perspectives on instruction in learning strategies. In D. D. Deshler, E. S. Ellis, & B. K. Lenz (Eds.), Teaching adolescents with leaning disabilities (2 nd ed., pp. 9-60). Denver, CO: Love Publishing Co.
Gagnon, J. C., & Maccini, P. (in press). Teacher use of empirically-validated and standards-based instructional approaches in secondary mathematics. Remedial & Special Education.
Hutchinson, N.L. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. Learning Disabilities Quarterly, 16, 64-63.
Individuals with Disabilities Education Act of 2004, Pub. L. No. 108-446.
Lenz, B. K., Ellis, E. S., & Scanlon, D. (1996). Teaching learning strategies to adolescents and adults with learning disabilities. Austin, TX: Pro-Ed, Inc.
Maccini, P. (1998). Effects of an instructional strategy incorporating concrete problem representation on the introductory algebra performance of secondary students with learning disabilities. Unpublished doctoral dissertation, The Pennsylvania State University, University Park.
Maccini, P., & Hughes, C. A. (2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research & Practice, 15, 10-21.
Maccini, P., McNaughton, D., & Ruhl, K. (1999). Algebra instruction for students with learning disabilities: Implications from a research review. Learning Disability Quarterly, 22, 113-126.
Maccini, P., & Ruhl, K. L. (2000).Effects of a graduated instructional sequence on the algebraic subtraction of integers by secondary students with learning disabilities. Education and Treatment of Children, 23, 465-489.
Miller, S. P. (1996). Perspectives on math instruction. In D. D. Deshler, E. S. Ellis, & B. K. Lenz (Eds.), Teaching adolescents with leaning disabilities (2 nd ed., pp. 313-367). Denver, CO: Love Publishing Co.
Montague, M. (1988). Strategy instruction and mathematical problem solving. Reading, Writing, and Learning Disabilities, 4, 275-290.
Montague, M., Bos, C. S., & Doucette, M. (1991). Affective, cognitive, and metacognitive attributes of eighth-grade mathematical problem solvers. Learning Disabilities Research & Practice, 6, 145-151.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
No Child Left Behind Act. Reauthorization of the Elementary and Secondary Education Act. Pub. L. 107-110, § 2102(4) (2001).
Rosenshine, B., & Stevens, R. (1986). Teaching functions. In M. C. Witrock (Ed.), Handbook of research on teaching (3 rd ed., pp. 376-391). New York: Macmillan.
Thurlow, M., Albus, D., Spicuzza, R., & Thompson, S. (1998). Participation and performance of students with disabilities: Minnesota’s 1996 Basic Standards Tests in reading and math (Minnesota Report 16). Minneapolis, MN: University of Minnesota, National Center on Educational Outcomes.
Thurlow, M. L., Moen, R. E., & Wiley, H. I. (2005). Annual performance reports: 2002-2003: State assessment data. Minneapolis, MN: National Center on Educational Outcomes. Retrieved August 17, 2005, from http://education.umn.edu/nceo/OnlinePubs/APRsummary2005.pdf
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About the Authors
Dr. Paula Maccini, Associate Professor of Special Education, University of Maryland College Park, is currently investigating special education teachers' use of effective instructional practices in mathematics for secondary students with mild disabilities.
Dr. Joseph Gagnon, Assistant Professor, George Mason University, College of Education and Human Development, is currently investigating interventions that positively impact the performance of students with learning disabilities in secondary general education classrooms.
For additional information on this or other topics, please contact The Access Center at email@example.com. The Access Center: Improving Outcomes for All Students K-8 The Access Center is a cooperative agreement (H326K020003) funded by the U.S. Department of Education, Office of Special Education Programs, awarded to the American Institutes for Research 1000 Thomas Jefferson St. NW, Washington, DC 20007 Ph: 202-403-5000 | TTY: 877-334-3499 | Fax: 202-403-5001 | e-mail: firstname.lastname@example.org website: www.k8accesscenter.org
This report was produced under U.S. Department of Education Grant # H326K020003 with the American Institutes for Research. Jane Hauser served as the project officer. The views expressed herein do not necessarily represent the positions or policies of the Department of Education. No official endorsement by the U.S. Department of Education of any product, commodity, service or enterprise mentioned in this publication is intended or should be inferred.
Maccini, P., Gagnon, J. (2006). Mathematics Strategy Instruction (SI) for Middle School Students with Learning Disabilities. Access Center