Transcript Using UDL to Reduce Barriers to Math Word Problems

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
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 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.
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
ANALYSIS
SINGLE-CASE DATA COLLECTION AND
CROSS-CASE ANALYSIS
Select Cases
Develop
Theory
 Relate
this study
to
previous
theory
 Provide
rationale
for the
study
 Identify
districts
 Nominations
from teachers
(Level 2
score on
NYSTP-M)
 Administer 5
problem
solving
questions
 Gain consent
Design Data
Collection
Protocol
 Define
procedures
 Define
procedural
outcomes
 Use formal
data
collection
techniques
Figure 3. Multiple Case Study Method
Begin 1 st
Case Study
 Condition One
 Session 2
 Session 3
 Session 4
 Final
Begin 2 nd
Case Study
 Condition One
 Session 2
 Session 3
 Session 4
 Final
Conduct
Remaining Three
Case Studies
 Condition One
 Session 2
 Session 3
 Session 4
 Final
Complete Contact
Summary Forms
after each session
to inform final
Individual
Case Report
Draw CrossCase
Conclusions
Modify Theory
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
Develop
Suggestions for
Future
Implementation
and Research
Write CrossCase Report
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
After Brian Robeson landed the Cessna airplane
in the Canadian
at $12.95 each and 3 model cars at $8.50
each. How much will he spend?










wilderness
he had to survive on his own.
Hint:[m1]
Hint: [m2]
Hint:[m3]
Hint:[m4]
Hint:[m5]
plane he had 43 jellybeans in his pocket.
[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.
before they were gone?
everyday until they were gone.
Hint:
Hint:
Hint:
Hint:
When he landed the
He decided to eat 4 jellybeans
How many days did Brian eat the jellybeans
How many did he eat on the last day?
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:
Student
Problems completed
accurately and
independently/Number
of problems completed
Base. Cond. Post
Pret. One Interv.
Andrew
3/10 1/7
2/6
Brittany
3/10 1/9
2/9
Casey
1/10 1/7
4/9
Dominique 3/10 2/7
4/9
Edward
1/10 1/9
3/6
Percentage completed Average time spent
accurately and
on independent and
independently
accurate problems
Base.
Pret.
30%
30%
20%
30%
10%
Cond.
One
14%
11%
14%
29%
11%
Post
Interv.
33%
25%
44%
44%
50%
Cond.
One
1:00
1:43
1:57
1:08
1:20
Post
Interv.
2:39
2:12
3:30
2:29
2:41
General Findings
Student
Reduced
Print
Barriers
Andrew
X
Brittany
X
Casey
X
Dominique
X
Edward
X
Increased
Increased Decreased Increased
Engagement Accuracy Level of Confidence
Time
Support
X
X
X
X
X
X
X
X
X
X
X
X
X
X
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.