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Model-Drawing Strategyto Solve Word Problems

for Students with LD

Dr. Olga Jerman

The Frostig Center

IARLD Conference

Miami, Florida

January 14-16, 2010

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Abstract

The study examined the effectivenessof using model-drawing methodologyto solve problems for a group of high

school students. The 30-weekintervention used a single-subjectdesign to teach an 8-step model-drawing approach for solving problems

with fractions and percentages. Theresults showed improvement insolution accuracy.

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Word-problem Solving and LD

Word problem-solving is an area ofdifficulty and frustration for a considerablenumber of students, and this, to a greatextent, could be attributed to a largenumber of cognitive processes involved insuccessful problem completion. It is an

especially difficult area for those studentswho are identified with learning disabilities(LD).

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Recently, a considerable amount of workhas been done to examine the sources of

difficulties in problem-solving, predictorsof success, and the best practices andprograms aimed at helping strugglinglearners to better problem-solve.Research findings indicate that thereduction of demands on the workingmemory system (WM) seems to be highly

beneficial. Different ways to minimizethese demands on the WM system havebeen tested (e.g. use ofvisual support viapictures, diagrams & schemas, and use of

cognitive strategies).

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Purpose of the Study

An 8-step model-drawing technique isintended to enhance the conceptualunderstanding of the problem at task and toreduce the amount of information to be held inworking memory, which, consequently, would

lead to the increased chances of solvingproblems correctly. Although the approach wasfound to be successful for a regular studentpopulation (typically-achieving kids), nostudies, to the authors knowledge, have

examined the effectiveness of this methodologyfor students with learning disabilities.Therefore, the primary purpose of this studywas to assess the usefulness of Singaporemodel drawing technique for students with LD.

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Model Drawing Strategy 8 Steps of Model drawing

1. Read the problem

2. Decide who is involved

3. Decide what is involved

4. Draw unit bars

5. Read each sentence

6. Put the question mark7. Work computation

8. Answer the question

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Example:W

ordProblems 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. Howmany students are there in this school?

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Solution

40%

Museum

20%

Zoo

50% of remaining

Farm 60

school

Total students = ?

1) 60 : 2 = 30

2) 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 werechocolate chip cookies and the rest weresugar cookies. How many sugar cookies didRosie 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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Example: Fraction Problems

b) 5/8 of the students in my class are boys.1/5 of the boys have black hair. If 40 boysdont have black hair, how many studentsare 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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Method

5 students (2 control)

2 girls & 3 boys (mean age 16-1)

10th

grade 30 weeks intervention

20 weeks for fraction problems, 10weeks percent problems

Treatment fidelity 73%

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Scores and Progress of a ControlStudent #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

Scores

Accuracy P t Accuracy P rcentage

Baseline No Intervention

Intervention1

Fractions

Intervention2

Fractions

Intervention3

Percentiles

NoIntervention

F

ollow-upFractions

Fo

llow-upPercentiles

M=20

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Scores and Progress of a ControlStudent #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

S

es

A racy P i t Accuracy P rcentage

Baseline No Inter ention

Inter ention 1

Fractions

Inter ention 2

Fractions

Inter ention 3

Percentiles

M=21.33

NoInter

ention

Follow-upF

ractions

Follow-upPercentiles

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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

c

es

Accu acy Poin s Accu acy Pe cen age

Baseline No In e ven ion

In e ven ion 1

Fractions

Intervention 2

Fractions

Intervention 3

Percentiles

M=1.25

NoIntervention

Follow-upFractions

Follow-upPercentiles

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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

eeks

Scores

A ura Point A ura Per entage

Ba eline No Intervention

Intervention1

ra tion

Intervention2

ra tion

Intervention3

Per entile

NoIntervention

ollow-upFra

tion

Follow-upPer

entile

M 1

Scores and Progress of a Tx student #2

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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

cores

ura oin A ura er en age

ase ine No n er en ion

n er en ion 1

ra ions

n er en on

ra ions

n er en on

er en iles

No

ner

en

ion

ollo

-up

ra

ions

ollo

-up

2

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 thantheir pre-intervention scores, though it

slightly declined at the 4-week follow-up;

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Implications

The current results have important theoretical andpractical considerations. Because of the abstractnature and complex calculation processesinvolved, word problems with percent andfractions are especially hard to tackle for studentswith LD. The model-drawing approach givesstudents a more concrete method incomprehending and solving word problems inorder to get past their language difficulties. By

drawing out what they are reading, the studentsare creating a concrete visual application of theproblem. This helps them to manipulate thenumbers 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 milddisabilities. 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 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.