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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. Frostig Center. Example: Word Problems with Percentage.
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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. FrostigCenter
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
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) 3 x 9 = 27 (chocolate chip cookies) 63 – 27 = 36 (sugar cookies) 63 / 7 = 9 (one unit bar equals 9) 9 x 4 = 36 (sugar cookies) Rosie baked 36 sugar cookies. FrostigCenter
1 2 3 4 5 6 7 8 1) 5/8 - boys 3/8 - girls 1 2 3 4 5 5 units - boys 2) 1/5 – boys with black hair Or 4/5 without black hair 1 2 3 4 40 3) 40 / 4 = 10 (one unit bar) => 10 x 8 = 80 (students in the class) 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? There were 80 students in the class. 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% FrostigCenter
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; 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.