DOCUMENT RESUME SE 054 687 ED 383 526 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. *********************************************************************** 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