1. Model-Drawing Strategy to Solve Word Problems for Students with LD
Olga Jerman and Jacqueline Knight
The Frostig Center
DISCES CEC
Riga, Latvia
July , 2010
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2. Example: Word 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 didn’t have a field trip and stayed at school. How many students are there in this school?
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3. 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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4. Word-problem Solving and LD
difficult and frustrating
cognitive processes involved in successful problem completion.
US defines Learning Disabilities (LD) as average IQ with significant discrepancies in achievement
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5. Different ways to minimize demands:
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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6. 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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7. 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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8. Example: Word 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 didn’t have a field trip and stayed at school. How many students are there in this school?
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9. Step 1: Draw a unit bar and divide it into 10 equal parts
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 = ?
60 / 2 = 30
30 x 10 = 300
Answer: There are 300 students in the school.
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10. 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? 1 2 3 4 5 6 7 63 ?
63 / 7 = 9 (one unit bar equals 9)
9 x 4 = 36 (sugar cookies)
63 / 7 = 9 (one unit bar equals 9)
3 x 9 = 27 (chocolate chip cookies)
63 – 27 = 36 (sugar cookies)
Rosie baked 36 sugar cookies.
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11. Example: Fraction Problems
5/8 of the students in my class are boys. 1/5 of the boys have black hair. If 40 boys don’t have black hair, how many students are in my class in all? 1 2 3 4 5 6 7 8
5/8 - boys
3/8 - girls 1)
5 units - boys
1/5 – boys with black hair Or 4/5 without black hair 40 3) 2)
40 / 4 = 10 (one unit bar) =>
10 x 8 = 80 (students in the class)
There were 80 students in the class.
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12. Method 5 students (2 control) 30 weeks intervention
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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13. Scores and Progress of a Control Student #1
Accuracy percentage means how many problems were correctly solved;
Accuracy points were accrued by getting points for using the 8 steps.
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14. Scores and Progress of a Control Student #2
Almost always 100% correct, but low point accuracy because she did not use the model
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15. Scores and Progress of a Tx student #1
T stands for Treatment Subject
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16. Scores and Progress of a Tx student #2
T stands for Treatment Subject
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17. Scores and Progress of a Tx student #3
T stands for Treatment Subject
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18. 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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19. 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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20. 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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21. 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,
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 ).
Newcombe, N. S., Ambady, N., Eccles, J., et al (2009). Psychology’s Role in mathematics and Science Education. American Psychologist, 64, 6,
Powell, S. R., Fuchs, L. S., Fuchs, D., Cirino, P. T., & Fletcher, J. M. (2009). Do word-problem features affect problem difficulty as a function of students’ mathematics difficulty with and without reading difficulty? Journal of Learning Disabilities, 42,
Swanson, H. L. & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 96,
Xin, Y. P., Wiles, B., & Lin, Y. (2008). Teaching conceptual model-based word problem story grammar to enhance mathematics problem solving. The Journal of Special Education, 42,