Model-Drawing Strategy to Solve Word Problems for Students with LD Olga Jerman and Jacqueline Knight...

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

Olga Jerman and Jacqueline KnightThe Frostig Centerwww.frostig.org

DISCES CECRiga, LatviaJuly 11- 14, 2010

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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?

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.

• 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

1. Read the problem2. Decide who is involved3. Decide what is involved4. Draw unit bars5. Read each sentence6. Put the question mark7. Work computation8. Answer the question

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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?

Solution

40%Museum

20%Zoo

50% of remaining

Farm 60school

Total students = ?

1) 60 / 2 = 302) 30 x 10 = 300

Answer: There are 300 students in the school.

Step 1: Draw a unit bar and divide it into 10 equal parts

One unit bar = ?

100% remaining students

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?

Example: Fraction Problems

a) 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)

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?

Rosie baked 36 sugar cookies.

Example: Fraction Problems

b) 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

21 3 4 5

1/5 – boys with black hair Or 4/5 without black hair

1 3 42

403)

2)

40 / 4 = 10 (one unit bar) => 10 x 8 = 80 (students in the class)

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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%

Scores and Progress of a Control Student #1

R____

0

10

20

30

40

50

60

70

80

90

100

110

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24a

24b 25 26 27 28 29 30 31 32 33

Weeks

Sc

ore

s

Accuracy Points Accuracy Percentage

Baseline No InterventionIntervention 1

Fractions

Intervention 2Fractions

Intervention 3Percentiles

No

Inte

rven

tion

Fol

low

-up

Fra

ctio

ns

Fol

low

-up

Per

cent

iles

M=20

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Scores and Progress of a Control Student #2

E____

0

10

20

30

40

50

60

70

80

90

100

110

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24a

24b 25 26 27 28 29 30 31 32 33

Weeks

Sc

ore

s



Fractions



M=21.33

No

Inte

rven

tion

Fol

low

-up

Fra

ctio

ns

Fol

low

-up

Per

cent

iles

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Scores and Progress of a Tx student #1

C______

0

10

20

30

40

50

60

70

80

90

100

110

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24a

24b 25 26 27 28 29 30 31 32 33

Weeks

Sc

ore

s



Fractions



M=1.25

No

Inte

rven

tion

Fol

low

-up

Fra

ctio

ns

Fol

low

-up

Per

cent

iles

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J____

0

10

20

30

40

50

60

70

80

90

100

110

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24a

24b 25 26 27 28 29 30 31 32 33

Weeks

Sc

ore

s



Fractions



No

Inte

rven

tion

Fol

low

-up

Fra

ctio

ns

Fol

low

-up

Per

cent

iles

M=1


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O____

0

10

20

30

40

50

60

70

80

90

100

110

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24a

24b 25 26 27 28 29 30 31 32 33

Weeks

Sco

res



Fractions



No

Inte

rven

tion

Fol

low

-up

Fra

ctio

ns

Fol

low

-up

M=2


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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;

ImplicationsTheoretical 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.

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). Psychology’s Role in mathematics

and Science Education. American Psychologist, 64, 6, 538-551.

• 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, 99-111.

• 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, 471-491.

• 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, 163-178.

Model-Drawing Strategy to Solve Word Problems for Students with LD Olga Jerman and Jacqueline Knight...

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