Model-Drawing Strategy to Solve Word Problems for Students with LD Olga Jerman and Jacqueline Knight The Frostig Center www.frostig.org DISCES CEC Riga, Latvia July 11- 14, 2010 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? 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

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 FrostigCenter

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 FrostigCenter

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 FrostigCenter

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 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? FrostigCenter

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. FrostigCenter

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. FrostigCenter

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. FrostigCenter

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% FrostigCenter

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. FrostigCenter

Scores and Progress of a Control Student #2 Almost always 100% correct, but low point accuracy because she did not use the model FrostigCenter

Scores and Progress of a Tx student #1 T stands for Treatment Subject FrostigCenter

Scores and Progress of a Tx student #2 T stands for Treatment Subject FrostigCenter

Scores and Progress of a Tx student #3 T stands for Treatment Subject 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; FrostigCenter

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. 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. FrostigCenter

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.