FLORIDA STATE UNIVERSITY COLLEGE OF EDUCATION USING HISTORY IN THE TEACHING OF MATHEMATICS BY .AYOKUNLE AWOSANYA A Dissertation submitted to the Department of Curriculum and Instruction in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Spring Semester, 2001 The members of the Committee approve the dissertation of Ayokunle Awosanya defended on March 7,2001, lh.afth Jahbowsku Profe sor Co-Directi Dissertation JUz2LAe-d Herbert Wills III Professor Co-Directing Dissertation sa.-. Q Emanuel Shargel Outside Committee Member Akihito Kamata" Committee Member Approved: David Foulk, Chairperson, DepartAnt of Curriculum and Instruction This dissertation is dedicated to my parents and nll family members who encouraged me to realize this life's dream, but who are no longer around because they have passed to the patbeyond. This dissertation is also dedicated to all those who have encouraged me throughout my career including my wife and chiIdren. ... 111 ACKNOWLEDGMENTS I am deeply grateful to many individuals who made this stu-, possible. fin ' no words adequate to thank my major professors, Dr. Elizabeth Jakubowski and Dr. Herbert Wills El, for their valuable assistance, encouragement, and advice. They deserve the highest recognition for their contributions to my learning. So I acknowledge with pleasure my indebtedness to them. I express my appreciation to Dr.Emanuel Shargel, who served as a committee member for his time, effort, and advice in preparation of this study. Sincere appreciation is extended to Dr. Akihito Kamata, for his valuable assistance in statistics interpretations, and as a member of the committee. No acknowledgment would be completed without the appreciation of my family-my wife, Janet, who spent countless hours in supporting my effort, and my children, for their love and understanding that made my time much more enjoyable during this study. Also, I wish to thank the students who participated in this research study at Florida High School and their teachers for their cooperation throughout this research study. iv TABLE OF CONTENTS List of Tables ...................................................................................................... vi i Abstract .............................................................................................................. viii Chanter 1. THE PROBLEM .................................................................................... E Introduction ............................................................................... Uses of History .......................................................................... Benefits ofHistory .................................................................... Purpose ofthe Study ................................................................. Format of Dissertation .............................................................. 2 . REVIEW OF LITERATURE ............................................................... 10 Curriculum Reform .................................................................. 10 Biographies ofMathematicians and Their Contributions ........ 16 Teaching and Learning Mathematics ....................................... 19 Pedagogical Devices Used in Designing the Lessons .............. 24 3 . DE.SIGN AND PROCEDURES ........................................................... 27 The Questions ofthe Study ...................................................... 27 The Pilot Study ........................................................................ 28 Instructional Materials ............................................................. 29 Lewis Carroll LessonsExercises ............................................. 29 Archimedes' LessonsExercises ............................................... 30 Triangular Numbers ................................................................ 31 Oblong Numbers ..................................................................... 32 Sophie Germain LessonsExercises ........................................ 33 Instruments ............................................................................... 34 Content Validity of the Tests ................................................... 34 Internal Consistency of the Tests ............................................. 37 V Chauter P&€s Follow-Up Interviews ............................................................... 37 Experimental Procedures ......................................................... 40 Data Analysis ............................................................................ 41 Hypotheses ................................................................................ 41 summary ................................................................................... 42 4 . RESULTS................................................................................................ 43 Preliminary Analysis ................................................................... 43 Hypotheses .................................................................................. 48 Item Analysis .............................................................................. 50 Interviews ................................................................................... 53 5. CONCLUSIONS AND RECOMMENDATIONS .................. 58 Conclusions and Discussions ..................................................... 59 Educational Implications ........................................................... 61 Suggestions for Future Research ............................................... 62 Mathematics Curriculum ........................................................... 65 Mathematics Teaching .............................................................. 66 Concluding Remarks ................................................................. 67 APPENDICES ....................................................................................... 69 A . Instructional Materials for the Experimental Group .......... 71 B . Instructional Materials for the Control GTOUP.................... 132 C . The Instruments (Posttests and Solutions) .......................... 192 D . Human Subject Committee (Approval Letter) .................. 201 REFERENCES ...................................................................................... 202 BIOGRAPHICAL SKETCH ................................................................. 206 vi LIST OF TABLES Table Eazs 1 . Experiment Group: FCAT (Math) Test Scores Pretest ..................... 44 2 . Control Group: FCAT (Math) Test Scores Pretest ............................ 45 3 . Posttest: Experimental Group ........................................................... 46 4 . Posttest: Control Group ..................................................................... 47 5 . Posttest Means and Standard Deviations .......................................... 48 6 . Confidence Interval ............................................ :.............................. 49 7. Tests of Within-Subjects Effects ...................................................... 50 vii ABSTRACT The results reported here are the product of the research titled: Using History the Teaching of Mathematics. The subjects are students in two classes of Algebra D course at Florida State University High School-36 students-males and females whose ages are mostly 18 and a few 17 and 16 years old. Algebra Il is a course that is usually taken by high school seniors in 12' grade and a few 11' or 10' grade students which explains why the ages of the students are mostly 18 and a few 17 and 16 years old. In this investigation, both quantitative study and qualitative study were employed. The quantitative study was the main study-a teaching experiment using quasi- experimental methodology that involves two groupsgroup 1 and group 2. Group 1 is the control group, where various algebraichathematical concepts, or topics were taught or explained to students with the necessary formulas. Group 2 was the experimental group in which the accounts of the historical origin of algebraiclmathematicalconcepts and the mathematicians (Lewis Carroll, Archimedes, F'ythagoras, and Sophie Germain) who brought forward or created the concepts were used to augment pedagogical lessons and exercises used for this study as the main feature of pedagogy. The qualitative study augmented the main quantitative study; it was a follow-up interview for students to probe further an in-depth rationale for the research theme-using history in the teaching of mathematics. viii The statistical analysis result indicated that there is a significant difference in the mean of score for the control group students and the mean of scores of the experimental group students. The mean of the scores of students' performance in the experimental group is greater than the mean of scores of students' performance in he control group; and the interview questions' responses indeed corroborate the fact that the use offistoy in teaching mathematics does improve learning and understanding of algebraid mathematical concepts. ix CHAPER 1 THE PROBLEM Jneoduction There are various or many approaches devised to aid better understanding for students learning mathematics. One of such strategies is the use of history in the teaching and learning of mathematics. Teachers of mathematics are continually looking for ways to improve instruction. Several writers have suggested that using history in the teaching of mathematics will have a variety of educational benefits. Although it is difficult