alternative education

Teaching Techniques for 5th to 9th Grade Students with Learning
Disabilities in Algebra and Geometry


Cognitive and Metacognitive Strategies

F. D. Rivera, Ph.D.
Assistant Professor
Department of Mathematics
San Jose State University

~ Module 15, Session 8~
Lecture Notes

Three strategies are discussed below.

Strategy 1. Seven Steps Rule

Students with learning disabilities in math should learn and eventually memorize the following cognitive steps necessary for solving word problems:

  1. Read (what it says)
  2. Paraphrase (how you want to say it)
  3. Visualize (picture, table, or equation?)
  4. Plan (what’s the best way to solve it?)
  5. Solve (apply the rules)
  6. Check (are the steps correct?)
  7. Reflect (did you follow the six steps above?)

First, the teacher models the steps using problems on an overhead projector.

Second, students with learning disabilities in math model the steps in class, taking turns to elicit more interaction and repetition.

Third, students with learning disabilities in math can work either individually or in pairs to increase retention.

Step 7, Reflect, is a metacognitive strategy. It forces students with learning disabilities in math to stand back and check to see if they have carefully thought through a problem using the six steps. At the start, it might help to provide students with a sheet consisting of the strategies listed either in row or in column. Students can then mark off each step by a check mark as they solve a problem to indicate that they have gone through the steps.

  1. Personalized Error Checklist Strategy

 

First, the teacher should begin by handing out a worksheet of ten to fifteen problems for students with learning disabilities in math to do. The problems should be similar and should focus on a particular mathematical concept or process.

Second, the teacher explicitly models how such problems are solved. Students are then asked to accomplish the worksheet within a given time frame. Correct answers are assigned two points and the points could be used in exchange for prizes.

Third, the teacher then collects the worksheets and grades them. The teacher then generates a list of errors for each student. When the worksheets are returned, each student gets two sheets each. The first sheet is the corrected worksheet and the second sheet is a list of errors.

Fourth, the teacher gives the class another worksheet that is very similar to the ones they did earlier. Then, they are requested to accomplish the worksheet. Using the checklist of errors that each student has, the student goes over each problem solved, putting a plus mark (with a plus 2) on correct items and a minus mark on incorrect items. They are then asked to redo wrong problems, putting the correct solution next to the incorrect one.

When each student has achieved the target success rate, the error checklist is removed.

3. Self-Instruction Prompts Strategy

Students will be asked to generate self-instruction statements whenever they are solving problems. The statements are broken down into two types:

  • Work habits
  • Task-specific habits

Work habits pertain to general behavior and action that positively contributes to successfully accomplishing a problem. For instance: “I need to focus all the time.”

Task-specific habits pertain to mathematical behavior and action or personalized steps that are needed to successfully solve a problem. For instance: If the problems involve combining polynomials, one self-instruction could be, “Are the two terms that I am combining similar?” or “Need to make sure I only combine terms whose variables look exactly the same.” Or it could be a series of steps such as: “First I need to …. Second, I have to … .”

This strategy can be institutionalized slowly and usually at the start of each new lesson. Teachers model this strategy first for students for a particular problem. Students are then given problems that will allow them to develop self-instruction statements. The teacher can then have a whole-class discussion on each type so that everybody in the class gets to benefit as well. Students can keep the prompts until such a time when they can make the statements on their own without assistance.

 

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