Model-Drawing Strategy to Solve Word Problems for Students with LD

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Model-Drawing Strategy to Solve Word Problems for
Students with LD

• Olga Jerman and Jacqueline Knight
• The Frostig Center
• www.frostig.org
• DISCES CEC
• Riga, Latvia
• July 11- 14, 2010

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ExampleWord Problems with Percentage

• 40 of the school students went to the National
  History Museum for a field trip. 20 of students
  went to the zoo. 50 of the remaining students
  went to a farm. Only 60 students didnt have a
  field trip and stayed at school. How many
  students are there in this school?

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Abstract

• The study examined the effectiveness of using
  model-drawing methodology to solve problems for a
  group of high school students.
• The 30-week intervention used a single-subject
  design to teach an 8-step model-drawing approach
  for solving problems with fractions and
  percentages.
• The results showed improvement in solution
  accuracy.

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Word-problem Solving and LD

• difficult and frustrating
• cognitive processes involved in successful
  problem completion.

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• Research findings indicate that the reduction of
  demands on the working memory system (WM) seems
  to be highly beneficial.
• Different ways to minimize demands
• use of visual support via pictures, diagrams
  schemas
• use of cognitive strategies

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Purpose of the Study

• An 8-step model-drawing technique is intended
• to enhance the conceptual understanding of the
  problem at task
• to reduce the amount of information to be held in
  working memory
• No prior studies done with students with learning
  disabilities
• Primary purpose of this study-to assess the
  usefulness of Singapore model drawing technique
  for students with LD

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Model Drawing Strategy

• 8 Steps of Model drawing
• Read the problem
• Decide who is involved
• Decide what is involved
• Draw unit bars
• Read each sentence
• Put the question mark
• Work computation
• Answer the question

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ExampleWord Problems with Percentage

• 40 of the school students went to the National
  History Museum for a field trip. 20 of students
  went to the zoo. 50 of the remaining students
  went to a farm. Only 60 students didnt have a
  field trip and stayed at school. How many
  students are there in this school?

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Solution
Step 1 Draw a unit bar and divide it into 10
equal parts
50 of remaining Farm
40 Museum
20 Zoo
60 school
?
Total students ?
100 remaining students
One unit bar ?

1. 60 / 2 30
2. 30 x 10 300

Answer There are 300 students in the school.
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Example Fraction Problems

• Rosie baked 63 cookies. 3/7 of them were
  chocolate chip cookies and the rest were sugar
  cookies. How many sugar cookies did Rosie bake?

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2
3
4
5
6
7
63
?
63 / 7 9 (one unit bar equals 9) 3 x 9 27
(chocolate chip cookies) 63 27 36 (sugar
cookies)
63 / 7 9 (one unit bar equals 9) 9 x 4 36
(sugar cookies)
Rosie baked 36 sugar cookies.
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Example Fraction Problems

• 5/8 of the students in my class are boys. 1/5 of
  the boys have black hair. If 40 boys dont have
  black hair, how many students are in my class in
  all?

There were 80 students in the class.
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Method

• 5 students (2 control)
• 2 girls 3 boys (mean age 16-1)
• 10th grade
• 30 weeks intervention
• 20 weeks for fraction problems, 10 weeks percent
  problems
• Treatment fidelity 73

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Scores and Progress of a Control Student 1
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Scores and Progress of a Control Student 2
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Scores and Progress of a Tx student 1
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Scores and Progress of a Tx student 2
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Scores and Progress of a Tx student 3
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Conclusion

• Model-drawing strategy can be an effective
  alternative method of teaching fraction and
  percent problems to students with LD
• Although the training yielded improvement, it
  took longer for the students to learn the
  technique than initially planned
• Students performance remained higher than their
  pre-intervention scores, though it slightly
  declined at the 4-week follow-up

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Implications

• Theoretical and Practical Considerations
• Due to their abstract nature, word problems with
  percent and fractions are especially hard to
  tackle for students with LD.
• The model-drawing approach gives students a more
  concrete method in comprehending and solving word
  problems in order to get past their language
  difficulties.
• By drawing out what they are reading, the
  students are creating a concrete visual
  application of the problem. This helps them to
  manipulate the numbers more easily.

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Implications (cont.)

• The word problem instruction could also be
  applied in different ways either in the
  large-group format or as part of differentiated
  instruction.
• The model drawing gives students a clear
  procedure for comprehending and executing
  problems.
• As students understand each level of a problem,
  the problem of the day or of the lesson can
  eventually be taught at grade level.

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References

• Jitendra, A. K., Griffin, C. C., McGoey, K.,
  Gardill, M. C., Bhat, P., Riley, T. (1998).
  Effects of mathematical word problem-solving by
  students at risk or with mild disabilities.
  Journal of Educational Research, 91, 345-355.
• Marshall, S. P. (1995). Schemas in problem
  solving, Cambridge University Press.
• Montague, M. Self-Regulation strategies for
  better math performance in middle school. (In M
  Montague and A Jitendra 2006, pp. 86-106).
• Newcombe, N. S., Ambady, N., Eccles, J., et al
  (2009). Psychologys Role in mathematics and
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• Powell, S. R., Fuchs, L. S., Fuchs, D., Cirino,
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• Swanson, H. L. Beebe-Frankenberger, M. (2004).
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  and not at risk for serious math difficulties.
  Journal of Educational Psychology, 96, 471-491.
• Xin, Y. P., Wiles, B., Lin, Y. (2008). Teaching
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