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

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?” √ ).

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.

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.