1. HESC Initiative 9B Faculty Fellowship: A Universal Design for Learning Mathematics: Reducing Barriers to Solving Word Problems Dr. Merry L. Staulters Dr. Deborah C. May State University of New York at Albany School of Education Department of Educational and Counseling Psychology 2006

2. Abstract A multiple-case study design was employed to investigate how Universal Design for Learning procedures (CAST, 2002; Rose & Meyer, 2002) could be applied to word problems in mathematics for:  assisting decoding and comprehension  fact retrieval  strategy application  process application

3. Rationale  Limitations in word problem solving ability reduce confidence for mathematics and affect learner performance on informal classroom evaluations as well as on standardized state assessments ( Jordan, Hanich, & Kaplan, 2002).  Students need to be competent problem solvers to meet the regimen of educational standards and most importantly to demonstrate proficiency in using mathematics to solve real life problems (Wilson & Sindelar, 1991).

4. Barriers to Solving Mathematical Word Problems Educators and their students will benefit from practical suggestions for helping students to improve:  working memory deficits  reading comprehension  decoding and word recognition  process recognition and application

5. Universal Design for Learning Technology can be used to support learner recognition, planning and execution of strategies, and motivation for the problem solving task. In this study: Digitized word problems were modified to contain hidden comments accessible by the learner if s/he experienced problems with decoding or comprehending the text. Some comments contained hints to prompt the learner to use strategies for: fact retrieval, selecting an approach, visualizing the problem, or finding relevant information to determine the appropriate operation. Pictures and relevant context were embedded in the problems to encourage learners to engage with the problem and to visualize the situation and conditions. Learners were encouraged to modify print size and spacing and to highlight and underline relevant information in the text.

6. Research Questions 1A: How did the digitized presentation reduce print related barriers to affect decoding and comprehension of the language in the word problems? 1B: How did students use the digitized presentation to aid fact retrieval, process application and strategy identification? 1C: How did the word problems formulated to incorporate students’ interests and influence engagement with the problem solving process? 2: In what way did the digitized presentation of the problems affect performance on informal measures of problem solving? 3: Did the application of the digitized presentation improve learners’ confidence in and self-efficacy for solving math word problems?

8. Subjects: Profile Information and Teacher Reports -Barrier Analysis Andrew Bio: Ten-year old, Caucasian male. Level 2 on NYS Grade 4 Math Assessment. Academic intervention services (AIS) daily for 45 minutes. Brittany Bio: Ten-year old, Caucasian female. LD in ELA. Resource room instruction 3x wkly for 45 minutes, AIS daily for 45 minutes, & speech & language 3x wkly for 30 minutes. Level 2 on NYS Grade 4 Math Assessment. Casey Bio: Ten-year old, Caucasian female. LD in ELA. Resource room instruction 3x wkly for 45 minutes, AIS daily for 45 minutes. Level 2 on NYS Grade 4 Math Assessment. Dominique Bio: Ten-year old, Bi-racial female. Not identified as disabled. Receives AIS daily for 45 minutes. Scored level 2 on NYS Grade 4 Math Assessment. Edward Bio: Ten-year old, Caucasian male. Not identified as having a disability. Scored level 2 on NYS Grade 4 Math Assessment. Receives academic intervention services (AIS) daily for 45 minutes.

9. Types of Prompts and Hints Applied  Simplified vocabulary hints.  Pictures to support word recognition.  Pictures to support context and conditions  recognition  General application hints  Problem specific hints  Computation and fact retrieval hints

10. Sample Word Problems Kevin buys 7 action figures at $12.95 each and 3 model cars at $8.50 each. How much will he spend? Hint:[m1][m1] Hint: [m2][m2] Hint:[m3][m3] Hint:[m4][m4] Hint:[m5][m5] [m1] Underline what you know. Highlight what you need to find out. [m1] [m2] Read the problem carefully. How many action figures did he buy? What was the cost of them? (+, -, x, d)[m2] [m3] What was the cost of the model cars? (+, -, x, d)[m3] [m4] What was the total cost for all the items? (+, -, x, d) Check your work and label.[m4] [m5] Was your answer $116.15? If not, try another way.[m5]

11. Results: Question One 1A)  visual prompts cued two students to stop and reflect  Pictures cued context  Familiar context encouraged discussion and facilitated transformation 1B)  fact retrieval prompts were ineffective.  Hints provided scaffolds that guided procedures.  Students responded best to general hints  Process application improved when the problem related to the most current topic of study (fractions) 1C)  All students engaged longer with the digitized problems with prompts and hints

12. Results: Question Two 4/5 students performed better on informal assessments All students completed more complex problems All students reported that they used strategies or procedures applied to the digitized problems on classroom tasks Results: Question Three All students reported higher levels of self-efficacy for word problem solving One student reported he was only better at problem solving when the hints were available Four students specifically described positive changes in their problem solving skills Students persevered longer on word problem tasks

13. Students’ Independent Performance on Problems for Sessions

14. Performance Across Assessments:

15. General Findings

16. References CAST, inc. (1999-2005). CAST [Online]. URL: http://www.cast.orghttp://www.cast.org Jordan, N.C., Kaplan, D., & Hanich, L.B. (2002). Achievement growth in children with learning difficulties in mathematics: Findings of a two-year longitudinal study. Journal of Educational Psychology, 94, 586-597. Microsoft Windows. (2000). Microsoft Word. Microsoft Corporation Rose, D. H. & Meyer, A. (2002). Teaching every student in the digital age: Universal design for learning. Alexandria, VA: Association for Supervision and Curriculum Development. Wilson, C.L. & Sindelar, P.T. (1991). Direct instruction in math work problems: Students with learning disabilities. Exceptional Children, 57(6), 512-520.