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Butkowski, Jean; And Others
AUTHOR
Improving Student Higher-Order Thinking Skills in
TITLE
Mathematics.
27 Apr 94
PUB DATE
331p.; Action Research Project, Saint Xavier
NOTE
University-IRI.
Research/Technical (143)
Reports
PUB TYPE
Undetermined (040)
Dissertations /Theses
MFO1 /PC14 Plus Postage.
EDRS PRICE
Affective Behavior; *Cognitive Ability; Elementary
DESCRIPTORS
Education; *Elementary School Students; Grade 3;
Grade 5; Grade 6; *Mathematics Achievement;
Mathematics Education; *Problem Solving; *Thinking
Skills
Illinois; Mathematics Education Research
IDENTIFIERS
ABSTRACT
This report describes a program for improving
(n=27)
higher-order thinking skills in mathematics of (n=17) third,
community.
fifth-, and (n=27) sixth-grade students in a middle class
(1) cooperative learning to develop
Three interventions were chosen:
(2) the
student self-confidence and to improve student achievement,
strategies,
instruction of students in mathematical problem-solving
supplementary
and (3) curriculum revision with the addition of a
solving. All strategic solutions were
program on mathematical problem
related to improving student cognition and advancing student
.
achievement on higher-order thinking skills. All of the components
projected:
that contributed to the original problem were reduced as
strategies became
student acquisition of mathematical problem-solving
evident, student confidence levels in mathematics increased, and
requiring higher order
student achievement on non-routine problems
thinking skills improved. Appendices include: problem-solving pre-
teacher
and post-test results, sample problems, student survey,
questions,
questionnaire, teacher observation checklist, sample test
reflection sheet,
attitude survey, student evaluation form, student
(Author/MKR)
and sample activities. (Contains 55 references.)
***********************************************************************
Reproductions supplied by EDRS are the best that can be made
from the original document.
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IMPROVING STUDENT HIGHER-ORDER THINKING SKILLS IN
MATHEMATICS
by
Jean Butkowski
Colleen Corrigan
Terri Nemeth
Leslie Spencer
Submitted in partial fulfillment for the
requirements for the degree of Master's
of Arts in Education
Saint Xavier University-IRE
Field-Based Master's Program
Action Research Project
Teachers
Site: Wheeling
Joyce Kilmer School
Submitted: April 27, 1994
Buffalo Grove, IL
U.S. DEPARTMENT OF EDUCATION
"PERMISSION TO REPRODUCE THIS
Office of Educabalal Rematch lino imr.govement
MATERIAL HAS BEEN GRANTED BY
EDUCATIONAL RESOURCES INFORMATION
(ERIC)
P
his document has Peen reproduced at
.e,veci from the parson or organization
originating it
BEST COPY AVAILABLE
0 Minor changes have been made to improve
reproduction quality
Points of view or opinions slated in thrO docu-
TO THE EDUCATIONAL RESOURCES
merit do not necessarily represent ofhcial
OERI position or policy
INFORMATION CENTER (ERIC)...
This Action Research was approved by
SXU Facilitator
,
IRI/Skylight Facilitator
,
Dean, Schoo of Education
:3
Table of Contents
Page
Abstract
vi
Chapter
Problem Statement and Community Background
I 1
General Statement of Problem
1
Immediate Problem Context
1
The Surrounding Community
5
Regional and National Context of Problem
7
. .
.
Problem Definition and Evidence
10
II
Problem Background
10
Problem Evidence
12
Probable Causes of Problem
23
The Solution Strategy
89
III
Review of the Literature
89
Project Outcomes
131
134
Project Solution Components
Action Plan for Implementing the Solution
IV
i
4
136
Strategy
Description of Problem Resolution Activities.
136
142
Methods of Assessment
VA Third Grade Group A Evaluation of Results
144
and Processes
144
Implementation History
Presentation and Analysis of Project Results
151
.
157
Reflections and Conclusions
VB Third Grade Group B Evaluation of Results
159
and Processes
159
Implementation History
Presentation and Analysis of Project Results .
165
168
Reflections and Conclusions
170
VC Fifth Grade Evaluation of Results and Processes.
170
Implementation History
Presentation and Analysis of Project Results.
176
179
Reflections and Conclusions
VD Sixth Grade Evaluation of Results and Processes.
181
Impelentation History
181
5
197
Presentation and Analysis of Project Results
.
207
Relections and Conclusions
215
Third and Fifth Grade Decisions On the Future
VIA
.
215
The Solution Strategy
217
Additional Applications
217
Dissemination of Data and Recommendations
219
Sixth Grade Decisions On the Future
VIB
219
The Solution Strategy
220
Additional Applications
224
Dissemination of Data and Recommendations
.
235
References Cited
241
Appendices
Appendix A
Third Grade Group A Problem
Solving Second Grade Level Pre
242
and Posttest Results
245
Student Survey
Appendix B
247
Teacher Questionaire
Appendix C
Second Grade Level Pretest and
Appendix D
250
Posttest
6
260
Third Grade Level Posttest
Appendix E
270
Teacher Observation Checklist .
Appendix F
. .
Third Grade Group A Scores on
Appendix G
Third Grade level Practice Sheets
271
and Posttest
Appendix H Number of Third grade Group B
Correct Responses on Pretest and
274
Posttest
275
Fifth Grade Pretest and Posttest .
Appendix I
.
Fifth Grade Problem Solving Test
Appendix J
280
Results Pretest and Posttest
Criterion Reference Test (CRT)
Appendix K
281
Sample Questions
285
Sample Sixth Grade Problems
Appendix L
288
Appendix M Sixth Grade Attitude Survey
294
Appendix N Sixth Grade Pretest
Appendix 0 Sixth Grade Student Pretest
297
Evaluation Form
298
Appendix P Student Reflection Sheet
iv
7
300
Appendix Q Candy Bar Math Activity
Appendix R M &M Math Activity Sheet
301
Balloon Math Activity and
Appendix S
302
Reflection Sheets
Appendix T Mean, Mode, Median, and Range
306
Activity and Reflection Sheets.
.
.
Basketball Mean, Median, Mode, and
Appendix U
Range Activity and Reflection
310
Sheets
Appendix V Gummi Worm Math Activity and
314
Reflection Sheets
317
Appendix W Sixth Grade Posttest
Sixth Grade Posttest Reflection
Appendix X
320
Sheet
Sixth Grade Pretest and Posttest
Appendix Y
Data
321
v
Abstract
AUTHORS: Jean Butkowski
SITE: Wheeling
DATE: April 1994
Colleen Corrigan
Terri Nemeth
Leslie Spencer
Improving Student Higher-Order Thinking Skills in
TITLE:
Mathematics
This report describes a program for improving higher-
ABSTRACT:
order thinking skills in mathematics of third, fifth, and sixth grade
students, in a middle class community located in
a suburb of
The problem was noted by the teaching staff, the
Chicago, Illinois.
prin,-Ipal, and the district administrators, who found students
unable to solve non-routine problems in which higher-order thinking
skills were necessary to find the solutions.
Teacher anecdotal
records, standardized test scores, district problem solving c; iterion
reference tests (CRT), and the Illinois Goal Assessment Program
(IGAP) test in mathematics confirmed the problem and described its
extent.
Analysis of the probable cause data revealed that students were
primarily exposed to a curriculum that was historically based in
computational skills.
Non-routine problems were rarely addressed
by the textbooks presently in
conjunction with the
use.
In
inadequate textbooks, teaching methods were limited to direct
instruction that emphasized the product rather than the processing
of the problems.
Three interventions were chosen:
cooperative learning to develop
student self-confidence and to improve student achievement; the
instruction of students in mathematical problem solving strategies;
and curriculum revision with the addition of a supplementary
program on mathematical problem solving.
All strategic solutions
were related to improving student cognition and advancing student
achievement on the higher-order thinking skills.
vi
C
All of the components that contributed to the original problem were
reduced as projected:
student acquisition of mathematical problem-
solving strategies became evident, student confidence levels
in
mathematics increased, and student achievement on non-routine
problems with higher order thinking skills improved.
v i
i
