Model-Drawing Strategy to Solve Word Problems for Students with LD Dr. Olga Jerman The Frostig Center IARLD Conference Miami, Florida January 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

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 Study An 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 problem 2.Decide who is involved 3.Decide what is involved 4.Draw unit bars 5.Read each sentence 6.Put the question mark 7.Work computation 8.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 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 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? : 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? /8 - boys3/8 - girls 1) 5 units - boys /5 – boys with black hair Or 4/5 without black hair ) 2) 40 : 4 = 10 (one unit bar) => 10 x 8 = 80 (students in the class) FrostigCenter

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%

Scores and Progress of a Control Student #1 FrostigCenter

Scores and Progress of a Control Student #2 FrostigCenter

Scores and Progress of a Tx student #1 FrostigCenter

Scores and Progress of a Tx student #2 FrostigCenter

Scores and Progress of a Tx student #3 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;

Implications The 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

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, 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 ). Newcombe, N. S., Ambady, N., Eccles, J., et al (2009). Psychology’s Role in mathematics and Science Education. American Psychologist, 64, 6, 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, 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, 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,