Cognitive and Metacognitive Strategies

1
Cognitive and Metacognitive Strategies

• F. D. Rivera, Ph.D.
• Department of Mathematics
• San Jose State University
• Module 15, Session 8

2
Seven Steps Rule

• students with learning disabilities in math
  should learn and eventually memorize the
  following cognitive steps necessary for solving
  word problems
•  
• Read (what it says)
• Paraphrase (how you want to say it)
• Visualize (picture, table, or equation?)
• Plan (whats the best way to solve it?)
• Solve (apply the rules)
• Check (are the steps correct?)
• Reflect (did you follow the six steps above?)

3
Seven Steps Rule How to Do It

• 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.

4
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.
•  

5
Personalized Error Checklist Strategy

• 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.

6
Personalized Error Checklist Strategy

• 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.

7
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
• 1.      Work habits
• 2.      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.

8
Self-Instruction Prompts Strategy

• 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 .

9
Self-Instruction Prompts Strategy

• 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.