MODEL DRAWING

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

Dr. Olga JermanThe Frostig Center

IARLD ConferenceMiami, FloridaJanuary 14-16, 2010

FrostigCenter

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.

FrostigCenter

FrostigCenter

Word-problem Solving and LD

Word problem-solving is an area of difficulty and frustration for a considerable number of students, and this, to a great extent, could be attributed to a large number of cognitive processes involved in successful problem completion. It is an especially difficult area for those students who are identified with learning disabilities (LD).

Recently, a considerable amount of work has been done to examine the sources of difficulties in problem-solving, predictors of success, and the best practices and programs aimed at helping struggling learners to better problem-solve. Research findings indicate that the reduction of demands on the working memory system (WM) seems to be highly beneficial. Different ways to minimize these demands on the WM system have been tested (e.g. use of visual support via pictures, diagrams & schemas, and use of cognitive strategies).

Purpose of the StudyAn 8-step model-drawing technique is

intended to enhance the conceptual understanding of the problem at task and to reduce the amount of information to be held in working memory, which, consequently, would lead to the increased chances of solving problems correctly. Although the approach was found to be successful for a regular student population (typically-achieving kids), no studies, to the author’s knowledge, have examined the effectiveness of this methodology for students with learning disabilities. Therefore, the primary purpose of this study was to assess the usefulness of Singapore model drawing technique for students with LD.

FrostigCenter

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

FrostigCenter

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

FrostigCenter

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)

FrostigCenter

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)

FrostigCenter

FrostigCenter

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

FrostigCenter

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

FrostigCenter

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

FrostigCenter

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


FrostigCenter

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


FrostigCenter

FrostigCenter

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;

ImplicationsThe current results have important theoretical and practical considerations. Because of the abstract nature and complex calculation processes involved, 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.

FrostigCenter

FrostigCenter

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

Documents

Transcript of MODEL DRAWING