Model Drawing strategy

8/10/2019 Model Drawing strategy

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Model-Drawing Strategyto Solve Word Problemsfor 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 theNational History Museum for a field trip.

20% of students went to the zoo. 50%of the remaining students went to afarm. Only 60 students didnt have a

field trip and stayed at school. Howmany students are there in this school?


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Abstract

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

The 30-week intervention used asingle-subject design to teach an 8-step model-drawing approach for

solving problems with fractions andpercentages.

The results showed improvement insolution accuracy.

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Word-problem Solving and LD

difficult and frustrating cognitive processes involved in successfulproblem completion.


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Purpose of the Study

An 8-step model-drawing technique isintended

to enhance the conceptual understandingof the problem at task

to reduce the amount of information tobe held in working memory

No prior studies done with students withlearning disabilities

Primary purpose of this study-to assess theusefulness of Singapore model drawingtechnique 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 sentence

6. 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 theNational History Museum for a field trip.

20% of students went to the zoo. 50%of the remaining students went to afarm. 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 remainingFarm 60

school

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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?


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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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?

Rosie baked 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 - girls1)

5 units - boys

21 3 4 5

1/5 boys with black hair Or 4/5 without black hair1 3 42

403)

2)

40 / 4 = 10 (one unit bar) =>

10 x 8 = 80 (students in the class)Frostig CenterThere were 80 students in the class.


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Method

5 students (2 control)2 girls & 3 boys (mean age 16-1) 10 th 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

R____

0

10

20

30

40

50

60

70

80

90

100

110

1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 a

2 4 b 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3

Weeks

S c o r e s

Accuracy Points Accuracy Percentage

Baseline No InterventionIntervention 1Fractions Intervention 2Fractions ntervent onPercentiles

N o

I n t e r v e n

t i o n

F o

l l o w - u p

F r a c

t i o n s

F o

l l o w - u p

P e r c e n

t i l e s

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 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 a

2 4 b 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3

Weeks

S c o r e s


Baseline No InterventionIntervention 1

FractionsIntervention 2


Percentiles

M=21.33

N o

I n t e r v e n

t i o n

F o

l l o w - u p

F r a c

t i o n s

F o

l l o w - u p

P e r c e n

t i l e s

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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 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 a

2 4 b 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3

Weeks

S c o r e s




Fractionsntervent onPercentiles

M=1.25

N o

I n t e r v e n

t i o n

F o

l l o w - u p

F r a c

t i o n s

F o

l l o w - u p

P e r c e n t

i l e s

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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 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 a

2 4 b 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3

Weeks

S c o r e s





N o

I n t e r v e n

t i o n

F o

l l o w - u p

F r a c

t i o n s

F o

l l o w - u p

P e r c e n t

i l e s

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 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 a

2 4 b 2 5 2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3

Weeks

S c o r e s



Fractionsntervent on


N o

I n t e r v e n

t i o n

F o

l l o w - u p

F r a c

t i o n s

F o

l l o w - u p

M=2


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Conclusion

Model-drawing strategy can be an effectivealternative method of teaching fraction andpercent problems to students with LD;

Although the training yielded improvement,it took longer for the students to learn thetechnique than initially planned;

Students performance remained higher thantheir pre-intervention scores, though itslightly declined at the 4-week follow-up;


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ImplicationsTheoretical and Practical Considerations

Due to their abstract nature, word problems withpercent and fractions are especially hard to tacklefor students with LD.

The model-drawing approach gives students amore concrete method in comprehending andsolving word problems in order to get past theirlanguage difficulties.By drawing out what they are reading, thestudents are creating a concrete visual applicationof the problem. This helps them to manipulate thenumbers more easily.

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Implications (cont.)The word problem instruction could also beapplied in different ways: either in the large-group format or as part of differentiatedinstruction.The model drawing gives students a clearprocedure for comprehending and executingproblems.As students understand each level of aproblem, the problem of the day or of thelesson can eventually be taught at gradelevel.


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Model Drawing strategy

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