Mathematics Strategy Instruction (SI) for Middle School Students with Learning Disabilities

What is a strategy and what are the key features?

A strategy refers to, "a plan that not only specifies the sequence of needed actions but also consists of critical guidelines and rules related to making effective decisions during a problem solving process" (Ellis & Lenz, 1996, p.24). Some features that make strategies effective for students with LD are:

1. 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);
2. 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);
3. 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);
4. Strategy steps that use prompts to get students to use cognitive abilities (i.e., the critical steps needed in solving a problem); and
5. 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.

The steps for STAR include:

• 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?" √ ).

Figure 2: Structured worksheet of the STAR strategy

Problem: On a certain morning in College Park, Maryland, the low temperature was -8°F, and the temperature increased by 17°F by the afternoon. What was the temperature in the afternoon that day?

Strategy Questions

S earch the word problem

1. Read the problem carefully
2. Ask yourself questions: "What do I know? What do I need to find?"
3. Write down the facts

• In the morning it was -8° F.
• During the day, the temperature rose by +17° F.
• One positive and one negative cancel each other out.
• I need to find what the temperature was in the afternoon.

T ranslate the words into an equation in picture form

A nswer the problem

I can cancel -8 and +8, which leaves me with +9 tiles remaining, therefore:

(-8°F) + (+17°F) = +9°F

R eview the Solution

1. Reread the problem
2. Ask yourself questions: "Does the answer make sense? Why?"
3. Check the answer

I checked my answer.

+9 remains when I cancel -8 and +8 and I keep my units of 9°F.

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:

1. concrete stage (i.e., three-dimensional representation in which students manipulate objects to represent math problems)
2. semiconcrete (i.e., two-dimensional representation in which students draw pictures of the math problem)
3. 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).

Figure 3: Area Example

Problem: Matt is buying wall-to-wall carpeting for his bedroom, which measures 12 feet by 16 feet. If he has $40 to spend, will he have enough money to buy the carpet that costs $2 per square yard?

Strategy Questions

Search the word problem

1. Read the problem carefully
2. Ask yourself questions: "What do I know? What do I need to find?"
3. Write down the facts

• The bedroom is 12 feet by 16 feet.
• Matt has $40.
• Carpet costs $2 per yard.
• First, I need to find out the area of the room in yards.
  • Area is calculated by multipying the width by length.
  • There are three feet in a yard.
• Then I need to find out how much the carpet will cost, and compare that number with the amount of money that Matt has.

Translate the words into an equation in picture form

Answer the problem

Area of the room: 12 ft x 16 ft = 192ft²

I know that 3 ft = 1 yd, and (3ft)² = (1yd)² so 9 ft² = 1 yd². I will divide 192 ft² by 9 to get yd²: 192 ÷ 9 = 21.3 yd²

The carpet costs $2/yd², so I will need to multipy the square yardage of the room by $2: $2 x 21.3 yd² = $42.60.

$42.60 is more than $40. Matt does not have enough money.

Review the Solution

1. Reread the problem
2. Ask yourself questions: "Does the answer make sense? Why?"
3. Check the answer

I checked my answer and it makes sense – Matt needs $2.60 more in order to buy the carpet for his room.

Conclusions

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.

References

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

Endnotes

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.

Maccini, P., Gagnon, J. (2006). Mathematics Strategy Instruction (SI) for Middle School Students with Learning Disabilities. Access Center