HESC Initiative 9B Faculty Fellowship: A Universal Design for Learning

Mathematics: Reducing Barriers to Solving Word Problems

Dr. Merry L. StaultersDr. Deborah C. May

State University of New York at AlbanySchool of Education

Department of Educational and Counseling Psychology2006

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

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).

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

Universal Design for LearningTechnology can be used to support learner recognition,planning and execution of strategies, and motivation for theproblem 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.

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?

DESIGN SINGLE-CASE DATA COLLECTION AND ANALYSIS CROSS-CASE ANALYSIS

Figure 3. Multiple Case Study Method

Design Data Collection Protocol

Define procedures

Define procedural outcomes

Use formal data collection techniques

Develop Theory

Relate this study to previous theory

Provide rationale for the study

Select Cases Identify

districts Nominations

from teachers (Level 2 score on NYSTP-M)

Administer 5 problem solving questions

Gain consent

Conduct Remaining Three Case Studies

Condition One Session 2 Session 3 Session 4 Final

Begin 2nd Case Study

Condition One Session 2 Session 3 Session 4 Final

Begin 1st Case Study

Condition One Session 2 Session 3 Session 4 Final

Complete Contact Summary Forms after each session to inform final Individual Case Report

Complete Contact Summary Forms after each session to inform final Individual Case Report

Complete Contact Summary Forms after each session to inform final Remaining Individual Case Reports

Write Cross-Case Report

Develop Suggestions for Future Implementation and Research

Draw Cross-Case Conclusions

Modify Theory

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.

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

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] Hint: [m2] Hint:[m3] Hint:[m4] Hint:[m5]

[m1] Underline what you know. Highlight what you need to find out.

 [m2] Read the problem carefully. How many action figures did he buy? What was the cost of them? (+, -, x, d)

 [m3] What was the cost of the model cars? (+, -, x, d)  [m4] What was the total cost for all the items? (+, -, x, d)

Check your work and label.  [m5] Was your answer $116.15? If not, try another way.

After Brian Robeson landed the Cessna airplane in the Canadian

wilderness he had to survive on his own. When he landed the

plane he had 43 jellybeans in his pocket. He decided to eat 4 jellybeans

everyday until they were gone. How many days did Brian eat the jellybeans

before they were gone? How many did he eat on the last day? Hint: Hint: Hint: Hint:

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

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

Students’ Independent Performance on Problems for Sessions

Table 13 Students’ Independent Performance on Problems for Sessions Two-Five

Student Session Two Session Three Session Four Session Five

Andrew 0% 20% 12.5% 33%

Brittany 0% 20% 22% 25%

Casey 0% 0% 37.5% 44%

Dominique 0% 43% 33% 44%

Edward 0% 11% 50% 50%

Performance Across Assessments:

Problems completed accurately and independently/Number of problems completed

Percentage completed accurately and independently

Average time spent on independent and accurate problems

Student

Base. Pret.

Cond. One

Post Interv.

Base. Pret.

Cond. One

Post Interv.

Cond. One

Post Interv.

Andrew 3/10 1/7 2/6 30% 14% 33% 1:00 2:39 Brittany 3/10 1/9 2/9 30% 11% 25% 1:43 2:12 Casey 1/10 1/7 4/9 20% 14% 44% 1:57 3:30 Dominique 3/10 2/7 4/9 30% 29% 44% 1:08 2:29 Edward 1/10 1/9 3/6 10% 11% 50% 1:20 2:41

General Findings

Student Reduced Print Barriers

Increased Engagement Time

Increased Accuracy

Decreased Level of Support

Increased Confidence

Andrew X X X X X Brittany X X X X Casey X X X X X Dominique X X X X X Edward X X X X

References

CAST, inc. (1999-2005). CAST [Online]. URL: http://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.